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Q: I can't get the filename being executed by Python 3.6m I have tried to follow the instructions on this node:
However, if the file is using the exec command, all I get is this:
/project/cntrl_des_scripts/lior/temp/<string>
<string>
/project/cntrl_des_scripts/lior/temp/<string>
The main script code ran is:
#!/bin/python3.6m
exec( open( "foo/bar.py" ).read() )
The code in foo/bar.py is:
import inspect
from inspect import getsourcefile
from os.path import abspath
print( abspath(getsourcefile(lambda:0)) + "\n" )
print( inspect.getframeinfo(inspect.currentframe()).filename + "\n" )
print( abspath(getsourcefile(lambda:_)) + "\n" )
What I would expect the output to be is:
/project/cntrl_des_scripts/lior/temp/foo/bar.py
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,145
|
Produced by Chris Curnow, Carol Brown, and the Online
Distributed Proofreading Team at http://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)
NATURAL & ARTIFICIAL
SEWAGE TREATMENT
BY
LIEUT.-COL. ALFRED S. JONES, V.C.
ASSOC. M. INST. C.E., FELLOW AND MEMBER OF COUNCIL
OF THE SANITARY INSTITUTE, ETC.
AND
H. ALFRED ROECHLING
M. INST. C.E., F.G.S., FELLOW OF THE SANITARY INSTITUTE, ETC.
[Illustration: Printer's Logo]
London
E. & F. N. SPON, LTD., 125 STRAND
New York
SPON & CHAMBERLAIN, 123 LIBERTY STREET
1902
PREFACE.
The Authors, some time ago, read before different Societies of
professional men, Papers[1] dealing with the Natural and Artificial
Purification of Sewage, and as these were favourably received, the
thought occurred to them that the time might be opportune for making
the information there given available for a wider public.
As, however, a mere republication of the Papers would have been
against the rules of the Societies concerned, the Authors decided to
re-write entirely the subject matter, and to bring it up to date, so
that the present publication is not a mere repetition of their old
Papers clothed in a new garb, but an entirely fresh publication, right
up to date.
The Authors hope that they have given the information in such a form
as to be readily available for District Councillors, Sanitarians, and
all interested in this complicated subject.
When considering natural and artificial sewage treatment, it ought to
be borne in mind that in the natural treatment we have to deal with
one treatment only, and that, in order to bring the results obtained
from artificial processes up to the same standard, the artificial
treatment ought to be supplemented by a treatment for the removal of
nitrates from the effluent, and another for the removal of pathogenic
micro-organisms, which means one treatment in natural, as against
three separate treatments in artificial purification.
In addition to this it must be understood that, owing to the great
losses by evaporation and by growing plants, which are continually at
work on sewage farms, especially during the summer months, when, as a
rule, the flow of water in the brook that takes the effluent is
smallest, the quantity of the effluent from the natural treatment is
probably only from one-half to one-third that resulting from the
artificial treatment, which is a point of very great importance.
If it can be proved to them that Nature is not sure and true enough in
its methods, the Authors are prepared to assist it with methods and
means produced by the inventive brain of man. But if such proof is not
forthcoming, they adhere—in preference to groping in the dark—to
Nature's own methods, knowing from experience, that when allowed full
scope and fair treatment, it is most sure in all its ways. That will
not prevent them, however, from giving in the future, as they have
done in the past, the question of sewage treatment in all its aspects
their most careful consideration.
ALFRED S. JONES.
H. ALFRED ROECHLING.
LONDON: _September 15, 1902_.
[1] 'Sewage Treatment: Science with Practice.' By Colonel A.
S. Jones, V.C., C.E. Read at the International Engineering
Congress at Glasgow, 1901. And 'The Sewage Question during
the Last Century.' Read by H. Alfred Roechling, M. Inst.
C.E., F.G.S., F.S.I., etc., on December 2, 1901, before the
Society of Engineers, and awarded the Gold Medal of the
Society.
CONTENTS.
PART I. BY LIEUT.-COLONEL ALFRED S. JONES, V.C.
PAGE
INTRODUCTORY 1
THE CHEMIST DIBDIN DISCARDS CHEMICAL PRECIPITATION
IN FAVOUR OF M. PASTEUR'S AEROBIC ORGANISMS 3
THE CLEANLY AND THE DIRTY (SEPTIC) PROCESSES FOR
SLUDGE REMOVAL 5
THE BEST POSSIBLE MEDIUM FOR AEROBIC ORGANISMS TO
WORK IN 5
TABULAR STATEMENT DERIVED FROM THE LEEDS OFFICIAL
REPORT OF EXPERIMENTS 7
THE WREXHAM SEWAGE FARM 8
THE CAMP FARM, ALDERSHOT, TO WHICH SIX OTHER AREAS
OF SEWAGE WORKS HAVE BEEN ADDED FROM JULY 28, 1902 9
EVIDENCE AND REPORTS OF LORD IDDESLEIGH'S ROYAL
COMMISSION, 1898-1902 15
AUTOMATIC APPLIANCES FOR SEWAGE AND EFFLUENT DISCHARGE 17
SLUDGE TREATMENT 19
CROPPING A SEWAGE FARM 21
IMPORTANCE OF HAVING TIDY CONTOUR CARRIERS ACCURATELY
LEVELLED 23
SUMMARY OF THE EXPERIENCE OF A LIFETIME 23
ANTICIPATION OF A COMING REACTION AGAINST OVER-RIDDEN
"FADS" AND TOO MUCH PRESSURE IN SANITATION 25
PART II. BY H. ALFRED ROECHLING.
I. INTRODUCTORY REMARKS 28
II. THE SEWAGE QUESTION DURING THE LAST CENTURY:
A SHORT RETROSPECT 29
III. THE SUBSOIL:
1. Mechanical structure of soil 41
2. Permeability of soil 42
3. Water capacity of soil 42
4. Water-retentive power of soil 43
5. Capillary movements of water in soil 44
6. Temperature of soil 45
7. Subsoil air 47
8. Movements of water in soil 47
9. Micro-organic life in soil 50
10. Absorbing powers of soil 51
IV. SELF-PURIFYING POWERS OF SOIL. NATURAL SELF-PURIFICATION
OF SEWAGE 52
V. Artificial Self-Purification of Sewage:
1. General observations 68
2. Artificial self-purification of sewage in intermittent
contact beds:
_a._ Name of process 70
_b._ Explanation of process 71
_c._ Water capacity of bed, and silting up 73
_d._ Absorbing powers of filling material 78
_e._ Consumption of oxygen by the filling material 79
_f._ Formation of carbonic acid 80
_g._ Nitrogen 80
_h._ Formation of nitric acid 80
3. Artificial self-purification of sewage in septic
tanks:
_a._ Name of septic tank 81
_b._ Covered or open septic tank 81
_c._ Explanation of process 83
_d._ Velocity of flow through tank 85
_e._ Destruction and liquefaction of sludge in
septic tanks 87
_f._ Formation of gas in septic tank 88
_g._ Mixing action of septic tank 89
_h._ Micro-organisms in effluent from septic tank 89
4. Continuous contact beds 89
VI. MANAGEMENT OF PLANTS FOR THE ARTIFICIAL
SELF-PURIFICATIONOF SEWAGE 90
VII. SOME OBSERVATIONS ON THE DEPOSITION OF SUSPENDED
MATTERS IN TANKS 91
VIII. CONCLUDING REMARKS 93
POSTSCRIPT 95
NATURAL AND ARTIFICIAL
SEWAGE TREATMENT.
BY LIEUT.-COL. ALFRED S. JONES, V.C.
ASSOC. M. INST. C.E., ETC.
[Sidenote: Introductory remarks.]
"How extremely simple it all is!" was the remark of a recent visitor
at a sewage farm—which encourages me to venture on publication of the
most recent discussions on a "problem" complicated by engineers,
chemists, bacteriologists and inventors of systems, who have raised
clouds of dust through which it is difficult for ratepayers and
district councillors to find their way to "the best practical and
available means of sewage disposal."
I have a belief that publication of all attempts to purify _the whole_
of a town's sewage, rather than small scale experiments with equations
founded on such data, is the desideratum.
[Sidenote: 1872.]
Having begun in the year 1872, with a pamphlet, "Will a Sewage Farm
Pay?"[2] I desire to proceed with the present one thirty years later,
as my humble contribution to a right understanding of the intelligent
Scavenger's business.
At the earlier date agriculture was prosperous, and ratepayers of
Exeter were just as confident that sewage farming would bring large
dividends as some of the same city's councillors are at present not in
the least sceptical that their engineer's septic system is the true
specific for sewage disposal.
In adhering to land as the natural and best agent, I have had the
support of the Local Government Board with that of many Royal
Commissions, notably the one now sitting, and I have naturally chosen
cases where suitable land was accessible when I desired to demonstrate
the efficiency and simplicity with which the powers of Nature can be
applied for the use and convenience of man.
Nor have I failed to study all "artificial" substitutes for the best
means, wherever difficulties of obtaining suitable land presented
themselves, e.g. my Canvey Island scheme for dealing with the sewage
of London on a relatively small area, and other cases.
Of late years I have welcomed the light thrown on this subject by
bacteriologists, but lamented extravagant statements put forward by
those who fail to see that the previously unrecognised microbes can do
their work, as they have always done it, to most advantage in the
upper layers of any porous land.
[Sidenote: 1902.]
An interim report by Lord Iddesleigh's Royal Commission has, however,
awakened such theorists to the fact that land is not to be discarded
because it may not bring in a profit or because patentees of systems
find it to their interest to contrast neglected or badly managed
sewage farms with carefully nursed little experimental installations
for artificial treatment of selected samples of sewage.
Recognising the marvellous improvements in arts and manufactures of
all kinds due to steam, chemistry and electricity, the public has
naturally expected similar results from applied science in artificial
sewage treatment, and there has been no lack of study of every
imaginable process during the last thirty years.
[Sidenote: 1884. Lord Bramwell's Royal Commission establishes
principles.]
But the late Lord Bramwell's Royal Commission on Metropolitan Sewage
Discharge established two very important points of general
application, namely:—
1. The principle of separation in works of sewerage and drainage; and
2. The fact that the suspended matters in town sewage can be very
effectually removed from its liquid by _simple deposition_ without the
aid of any chemical reagent.
[Sidenote: 1887. The chemist Dibdin discards chemical reagents in
favour of M. Pasteur's aerobic organisms.]
And Mr. Dibdin three years later began to demonstrate the mistaken
policy of adding lime or any other precipitating agent in any quantity
likely to arrest the natural agency of abundant bacterial life, which
ultimately disposes of all dead and effete organic matter by forming
gases or natural compounds, with more or less offence to human senses,
according to the supply of oxygen and rate at which these bacteria can
carry out their work.
[Sidenote: Leeds and Exeter.]
It was soon found that the bacteria of two classes, aerobe and
anaerobe, abound in sewage, and the latest Leeds experiment with the
continuous or trickling filter show the marvellous rapidity with which
the _aerobic_ microbes at any rate, can accomplish their task where
air and liquid sewage are sufficiently diffused in the pores of a
filter; while Mr. Cameron, C.E., at Exeter has shown rapid evolution
of gases and considerable solution of organic solids by _anaerobic_
microbes in a septic tank.
But the enthusiasm of inventors and their converts has made too much
of the benefit to the human race supposed to be conferred by the
bacterial discovery of M. Pasteur as applied by them to sewage
treatment.
Without detracting from the credit due to the great French savant and
other bacteriologists who have followed up his interesting studies of
ferments for the last fifteen years, the practical man may well ask
how much forwarder have we got in the main and pressing business of
purifying our rivers—as a consequence of clearer knowledge of minute
forms of life?
[Sidenote: Intermittent filtration.]
The late civil engineer Bailey-Denton demonstrated, thirty years ago
at Merthyr Tydvil, the best conditions of intermittent downward
filtration, and his filters there and at Kendal, Abingdon, etc., are
still doing their work efficiently to this day, while the coke, coal,
clinker, burnt ballast, etc., beds, so popular of late, are clogging
up after a few years of more careful treatment than was ever accorded
to an acre of land under sewage.
Anaerobic action has also been proceeding in the old sewers of most
towns and, as it has now been proved that there is no advantage in the
exclusion of air, upon which Mr. Cameron laid so much stress when he
brought his Exeter tank to public notice in 1897, there can be no
novelty except its name attaching to the anaerobic or _septic_ system,
which has thrown many sanitary authorities off their balance of late
years.
The whole modern system of self-cleansing sewers having been only
rendered possible by public recognition of the horrible nuisance
arising from middens, cesspools, and irregularly built sewers of
deposit, it is hard for those concerned in the cleanly disposal of
sewage to be told that because sewage works are usually remote from
populous districts they must there put up with the cesspool nuisance
and fancy its old smell changed by the new name, because a preliminary
stage in the transmutation of sewage has not taken place, as was
formerly the case in the sewerage system of some modern towns, before
arrival at the works.
But in this as in other affairs there is force in the old maxim,
_Medio tutissimus ibis_, and a properly constructed open tank, for
simple deposition of the solids (frequently washed out), arrests most
of the solids and allows fresh liquid sewage, after slight anaerobic
action, to pass on to land or filter bed in a perfectly inoffensive
condition.
[Sidenote: The cleanly and dirty processes for sludge removal.]
As an example of this I have, at Aldershot, a pair of tanks close to a
public high road, one of which fills with sludge and is emptied every
fortnight or so, and as a contrast there is another pair of larger
tanks in a remote quarter of the same farm in use for years as septic
tanks, from which some sludge is drawn off at long intervals,
anaerobic action being allowed its full course as in the Exeter
experiments.
It is interesting to compare the results of these preliminary clean,
and dirty, processes respectively on similar _very fresh_ domestic
sewage which enters the clean depositing, and the septic tanks alike,
and my observations are as follows:—
1. The manurial result in growth of crop _slightly_ greater with the
septic liquid.
2. Labour increased by the greater deposit carried on to the land
under septic liquid.
3. The removal of sludge and washing out the clean tank gives an
hour's work with very little smell ten yards to leeward of the site,
but drawing off sludge from the septic tank is a very unpleasant
operation, and, at all times, the vicinity of tank and carriers is
malodorous for a radius of at least fifty yards from the septic tanks.
[Sidenote: Loam on sand and gravel the best medium for aerobic
organisms to work in.]
Passing now to the aerobic stage of sewage purification we find it
universally admitted, that a good loam resting on very porous sand or
gravel, affords the best medium for work by the oxygen-loving
nitrifying organisms when they are supplied with constantly moving
liquid sewage, and given intermittent periods for the aeration of the
pores of the soil.
The proportion of sewage to land is of course as variable as the
quality of the land itself, and the best sort of land is rarely
available, while the improvement of natural land is not understood by
the engineer or chemist, who are usually appealed to by sanitary
authorities in their sewage difficulties.
Hence the variety of artificial substitutes of contact beds, costing
from 5000_l._ to 12,000_l._ per acre, which have been proposed of late
years, with the object of purifying a large volume of sewage on a
small area.
[Sidenote: Leeds experiments.]
Mr. Dibdin first startled the world with the formula 1,000,000 gallons
per acre, but that has long been cut down to 200,000 gallons, and the
life of the contact bed has become the subject of serious concern, as
shown in the annexed table of experiment at Leeds.
Others have sought to increase the proportion of sewage to area by
arranging for _continuous_ instead of _intermittent_ application; but
the difficulty of sprinkling so that every part of a bed may be kept
just moist, in order that aeration may be continuous as well as the
dropping sewage, is very great, and increases with every gallon and
foot from the scale of a laboratory experiment to that of a practical
working for a town's sewage.
There was an article published a few years ago in the Journal Royal
Agricultural Society (England) on "The Making of the Land," showing
how nearly all the value of agricultural land in England has been
stored up in it by the exertions of our forefathers, through a process
of successive improvements from, in many cases, worthless sand and
clay, to a condition of the greatest fertility; and I often think that
the 12,000_l._ spent at Birmingham or elsewhere on an acre of contact
bed could be expended to better purpose in preparing 100 acres of the
worst land to deal, for any number of years, with as much sewage as
the contact bed may do for a few years. In the one case we know no
limit to the life of the purifier, and that it must be a very short
one in the other case.
TABLE SHOWING THE VARIATIONS IN CAPACITY OF CONTACT BEDS.
-------------------------+--------------------+-------------------+
| No. 1 Rough | No. 3 Rough |
| Contact Bed. | Contact Bed. |
-------------------------+---------+----------+--------+----------+
| Dates. | Gallons. | Dates. | Gallons. |
-------------------------+---------+----------+--------+----------+
Original water capacity }| 1897. | | 1898. | |
after putting }|October 1| 83,300 |Nov. 21 | 51,800 |
in the coke }| | | | |
| 1899. | | 1900. | |
After experiment | May 6 | 22,700 |March 10| 14,700 |
| | | | |
-------------------------+---------+----------+--------+----------+
Duration of each of } | | | | |
above experiments } |19 months| 60,600 | 25½ | 37,100 |
and loss in gallons } | | | mths. | |
| | | | |
Loss in percentage of } | | |
original capacity } | 73 per cent. | 71 per cent. |
-------------------------+--------------------+-------------------+
------------------------+----------------+----------------+-----------------+
| No. 5 Rough | No. 7 Single | No. 8 Single |
| Contact Bed. | Contact Bed. | Contact Bed. |
------------------------+-------+--------+-------+--------+--------+--------+
|Dates. |Gallons.| Dates.|Gallons.| Dates. |Gallons.|
------------------------+-------+--------+-------+--------+--------+--------+
Original water capacity}| 1899. | | 1899. | | 1899. | |
after putting }|Feb. 28| 53,100 | March | 75,000 |March 23| 29,500 |
in the coke }| | | 24 | | | |
| 1900. | | 1900. | | 1900. | |
After experiment |June 1 | 13,200 |October| 21,600 | June 1 | 9,800 |
| | | 20 | | | |
------------------------+-------+--------+-------+--------+--------+--------+
Duration of each of } | | | | | | |
above experiments } | 15 | 39,900 | 7 | 34,100 | 14 | 19,700 |
and loss in gallons } |months | | months| | months | |
| | | | | | |
Loss in percentage of } | | | |
original capacity } | 75 per cent. | 61 per cent. | 67 per cent. |
------------------------+----------------+----------------+-----------------+
_N.B._—The average duration of the above experiments was 14 months,
and average loss of capacity about 70 per cent. original water
capacity in that period.—A. S. J.
[Sidenote: Wrexham sewage farm.]
At Wrexham, in North Wales, I had nineteen years' management of about
150 acres of good land, with a mixed residential and manufacturing
sewage of some 15,000 population, with large breweries and leather
works. The owner of this land at the termination of lease asked so
exorbitant a price for the improved freehold, that the corporation
decided to sacrifice the sewage works on his land, and to carry out a
scheme of mine for carrying the outfall sewer two miles further to a
site of 200 acres, which they could acquire on reasonable terms in the
year 1889.
During my management there was no trouble about the effluent, although
it was carefully watched by the authorities of the city of Chester,
which takes its water supply from the river Dee, some twelve miles
below my late farm; and the fact that the scheme which took the
Wrexham sewage two miles nearer to the Chester waterworks intake was
carried out _unopposed_ is, I think, strong evidence of well-founded
confidence in the efficiency of land treatment where the public have
the opportunity of observing such results. It is easy to get up a case
with expert evidence against any sewage scheme where the land-owners,
clergy and others have no means of properly informing themselves, and
have a prejudice against sewage which it is very difficult to overcome
except by giving the utmost possible publicity to the truth.
[Sidenote: The Camp Farm, Aldershot.]
Of late years, while working for the War Department, I have found it
expedient to be more reticent, but the Camp Farm restoration has in
one way or another become known to the public, and there can be no
great harm in my now referring to the circumstances as neither martial
law nor a censorship has yet been proclaimed in Hampshire.
When Aldershot Camp was first hutted, soon after the Crimean War, a
certain Colonel Ewart, R.E., had imbibed true ideas of the separate
system through his association with the work of the late Mr. Menzies,
the Deputy Ranger of Windsor Forest, who preached and practised that
system in the drainage of Windsor Castle and the town of Eton at a
time when every other civil engineer scouted the possibility of
keeping rain or subsoil water out of foul sewers—they said it was
essential for flushing their big sewers.
Colonel Ewart, at any rate, impressed his corps, and after about 1866
one began to see the word FOUL painted up over gratings into which the
soldiers were to pour their slops. A civilian, James Blackburn, also a
friend of Menzies, was employed by the War Office to deal with the
camp sewage on about 100 acres of rough heather-covered land close by,
and he, knowing his business, watched what came down the sewers in wet
weather and kept the Royal Engineers up to the Menzies standard.
[Sidenote: Mr. Blackburn's successful management.]
Together with this initial advantage of having a regular volume of
sewage not much affected by storm water to deal with, Mr. Blackburn
had many drawbacks in the "pan," as it is usually called, of iron
conglomerate underlying the very irregular surface which was pitted
all over with holes from which gravel or sand had been dug many years
ago; but he persevered until he had got nearly all the area to bear
good crops, when he entered the Camp Farm in competition for the Royal
Agricultural Society's 100_l._ prize in 1879 for the best managed
sewage farm in the United Kingdom. The Report of the Judges at that
competition is recorded in the Society's Proceedings 1880, giving full
statistics except financial accounts, which Mr. Blackburn withheld
because he was then in treaty with the War Office for new terms after
fourteen years' work on the War Department Farm. My impression after
reading the judges' reports and having seen the farm a year or two
previously to its date, is that, if the condition as to the production
of the financial accounts could have been fulfilled, the first prize
would have been awarded to the Camp Farm instead of jointly to those
of Bedford and to Wrexham.
Mr. Blackburn had built a big wooden shed and sublet it to a man who
bought his ryegrass for some fifty cows (for whose milk there was a
great demand in the camp), so this subtenant made a tempting offer to
the War Office and got a fourteen years' lease of the whole farm,
while Blackburn retired in disgust.
I wish to write only from knowledge of facts, and will therefore take
up my narrative again in 1895, after an interval of some fifteen
years.
[Sidenote: Neglected state of, in 1895.]
In the month of May 1895, I was called upon to visit the Camp Farm and
report to Mr. Henry Campbell-Bannerman, the Secretary of State for War
at that date.
I found the whole farm in a deplorable condition of neglected
nuisance, stagnant lakes of sewage retained here and there by banks of
earth, buildings and fences in decay, and the greater part of the camp
sewage passing, by pipes laid by its tenant, under a road which forms
the lower boundary of War Department land, to some rough meadows held
by their tenant from civilian owners for the purpose of saving him the
trouble of spreading the sewage over the sloping surface of the War
Department Farm—work which required the use of a land surveyor's level
and staff.
In the ditches of these flat meadows the sewage could go through the
septic process to its fullest extent as the level of the river
Blackwater kept them nearly full at all times, and the supernatant
liquid could spread over the coarse herbage of these meadows only in
winter floods, with the result of heavy crops of hay, and sewage
disposal conveniently out of sight and outside War Office jurisdiction
when a Royal Engineer officer might come to inspect the Camp Farm from
time to time.
[Sidenote: _British Medical Journal's_ report.]
But before my visit an active Medical Officer of Health (Dr. Seaton),
taking an interest in the state of the river bounding his county of
Surrey, detected the camp origin of the stagnant sewage, and,
concluding that the meadows must form part of the Camp Farm over the
road, made a serious report about "Government Sewage Marshes," which
the _British Medical Journal_ took as a text for an article, and the
Thames Conservancy attacked the War Department as soon as their 1894
Act gave them jurisdiction in the matter.
[Sidenote: Temporary abatement of nuisance.]
I was told that the Camp Farm milk and grass had been condemned, and
that the tenant had consequently sold his cows and was to give up the
farm on June 20, 1895; therefore my report was wanted _forthwith_,
but it was only to take account of anything which could be done
_temporarily_ to abate nuisance, as an agreement was pending with the
Aldershot District Council for the removal of the camp sewage outfall
to some site, at least two miles distant from the camp, at which the
District Council was to become solely responsible for its future
disposal, together with their own Aldershot town sewage, and the War
Department to be rated for the purpose like any other householder.
I found the Commanding Royal Engineer then in office fully alive to
the existing nuisance and prepared to support any efforts I might make
to abate it. Accordingly I agreed to become manager in control of such
labour and material as was necessary for immediate temporary
improvement, and being supplied with army horses, and any necessary
buildings, tanks, etc. to be constructed by the Royal Engineers.
[Sidenote: 1897. The War Office resolve on permanent improvement.]
After about two years it became understood that the nuisance could be
permanently remedied on the Camp Farm, as I had said from the first,
and accordingly the draft agreement, which had then been in discussion
for five years, was abandoned. I was asked to prepare a scheme and
estimate for such permanent works as would enable the sewage to be
effectually disposed of on the Camp Farm.
Recollecting that the sewage had to be at once cut off from Dr.
Seaton's "Sewage Marsh," and its disposal provided for throughout on
War Department land, it will be observed that the improvement work had
to proceed piecemeal with some extra care and arrangement; but on the
whole I am satisfied that the work has been completed with greater
efficiency and economy than would have been the case if the sewage had
been turned into the river and the whole site handed over to a
contractor for two years in the usual course.
About the same date (end of 1897) about 13 acres of land was handed
over to my management with sewage from the Royal Military and Staff
Colleges at Sandhurst, about 8 miles distant from the Camp Farm, and,
being somewhat better land to begin with, this part now presents a
very pretty example of what a small installation for about 1000
population may accomplish.
But it is worked as part and parcel of the Camp Farm, horses being
sent out to Sandhurst from Monday to Saturday when required.
It is, perhaps, worthy of note that the reform of the Camp Farm was
initiated in 1895 by the Secretary of State for War in a Liberal
Ministry, and that it has weathered for seven years all the storms of
Jingoism and the fashionable crazes for artificial sewage treatment.
[Sidenote: Sir Redvers Buller's period of command at Aldershot.]
But whatever may be the rights or wrongs of General Sir Redvers
Buller's quarrel with the Press and the Government, his reputation as
a practical agriculturist is undeniable, and while in command at
Aldershot it was his custom to stroll over the Camp Farm on a Sunday
afternoon, occasionally leaving a message with cowman or bailiff to
warn me of anything he found amiss, for which I was very grateful,
living as I do ten miles away. I am proud, therefore, to be able to
publish the following letter from one who has shown that he is not to
be influenced by complaisance to superior or inferior in expressing or
modifying his opinions, and he writes as follows:—
17 LOWNDES SQUARE, S.W.
_July 14, 1902._
MY DEAR JONES,
I am delighted to hear that you are publishing a book about
sewage treatment.
The sewage farms at Aldershot and the Royal Military College
afford ample proof of what a sensible practical man can do.
But it is not every one who knows what those farms were
before you took charge of them, nor do I think that any one
seeing them now could conceive their previous condition. It
is to that I can testify; you have turned putrid sewage bogs
into fertile fields. You will confer an immense benefit on
the country if, by your book, you can only teach sanitary
authorities generally that the crux of the whole question is
the necessity for practical commonsense measures against
sewage stagnation, and if those measures are taken nature
will do the work of purification without the assistance of
expensive patents or artificial devices.
Yours very truly,
(_Signed_) REDVERS BULLER.
_To_ COL. A. S. JONES, V.C., C.E.
It must not be gathered from the foregoing account that the War Office
authorities are prejudiced in favour of the _natural_ treatment of
sewage, for, like many other sanitary authorities, they have been
bewildered of late years by the numerous forms of "_artificial_"
treatment in vogue, and I know of more than one experimental
installation for barracks where good available land has been
neglected, for I read last summer of ghastly failures among the
bacterial arrangements in some of those.
[Sidenote: Success mainly due to activity of farm bailiff, foremen and
other workers.]
I cannot quit the above account of the vicissitudes of the Camp Farm
in fourteen years' growth from a sandy waste to a condition which
tempted a tenant to pay a rent of 3_l._ odd per acre in 1880—its
retrogression to its primitive waste during the following fifteen
years—and restoration to its present measure of fertility, without
expressing the belief that Mr. Blackburn's success and my own have
been mainly due to our good fortune in obtaining the willing services
of excellent intelligent foremen and workers who, one and all, have
taken a real interest in their several tasks.
Mr. Cameron and other engineers may boast of their labour saving (?)
automatic appliances for opening and shutting valves on sewage works,
but practical workers, responsible for dealing with a million gallons
a day and upwards average, in hourly varying flow of town sewage, will
agree with me in hesitation as to placing entire confidence in the
substitution of automatic machines for any large proportion of their
manual labour.
[Sidenote: Education and encouragement of sewage employees advocated.]
I have for many years advocated education of sewage farm managers and
watermen, to be selected from the rapidly decreasing class of
agricultural labourers by the tender of high wages, houses and good
gardens, with other profit-sharing allowances which it will well pay
sanitary authorities to hold out to their sewage employees.
In this sense I am glad to note the recent formation of "_The
Association of Managers of Sewage Disposal Works_," Secretary, Charles
H. Ball, 5 Fetter Lane, London, E.C., as a Trades Union move from
within well calculated to raise the status of the class of men upon
whose exertions the community must mainly rely if there is to be any
hope of improving the condition of our streams and rivers.
[Sidenote: Evidence and Reports of Lord Iddesleigh's Royal
Commission.]
Two large Blue Books containing the evidence taken by Lord
Iddesleigh's Royal Commission have been published since the Interim
Report, and their contents more than warrant the opinion expressed in
the latter; indeed it must surely be admitted that the case for each
of the artificial systems was very fully gone into before that
Commission expressed the guarded conclusion, "We doubt if any land is
entirely useless."
I do not believe that the surface purification obtained by
distribution over even the densest of clay lands was _effectively_ put
in evidence, and too much weight was given to the difficulty of
increasing the effective top soil on such land; but on the whole I
think that the Interim Report is very satisfactory to the reasonable
advocates of a preference being given to the adoption of a large area
of land, where available, over any artificial treatment on a small
area, other things being equal.
At the time when the Interim Report was issued, however, a very full
and careful examination of a select number of sewage farms was still
in progress, and Appendix 22, with a casual mention by Dr. M'Gowan,
affords the only glimpse to be had in the bulky Blue Books, of any
results of that examination having been as yet adduced in evidence.
The Commission's officers, to my knowledge, were engaged for many
months in examining, surveying and taking numerous samples of sewage
and effluent at the Camp Farm, and, as they doubtless had equal
opportunities of independent observations on the other selected sewage
farms, the further reports of Lord Iddesleigh's Royal Commission
cannot fail to be interesting and instructive.
On one point Appendix 22 to the Blue Book abundantly supports an
opinion I have so often expressed, namely, that a good strong loamy
surface is a more efficient purifier of sewage than many feet of
barren sand.
I refer to the curves in Appendix 22, showing the greatly superior
purification effected at Nottingham with the best soil as compared to
that of the sandy one at Aldershot, which, in its natural character,
is about the worst for purification and for producing crops to be
found in England.
My experience, however, all points to the extreme importance of
studying local conditions from the first inception of plans in each
particular case, to their completion with the best available
materials.
But when the engineer has done his best, the sanitary authorities,
having borrowed the funds to pay for the work, will take no further
trouble about its sewage, and will often engage careless ignorant
workpeople at inadequate wages to carry on the hourly varying labour,
on efficient performance of which success depends.
[Sidenote: Automatic appliances for sewage and effluent discharge.]
It may seem idle to complain of boards and their employees showing
little interest in the work of sewage disposal, but it is worse to
pander to their failings by selling them automatic machines under the
pretence that all the thought, and fertility of resource, required for
efficient sanitary sewage disposal can be supplied by ingenious
applications of hydraulics on the principle that sewage is a fluid,
and, as such, will behave like clean water.
Of course, when the aerobic treatment is carried out on a bare level
surface of cinders or coke growing only weeds, the lack of interest is
very excusable, but in the natural system the growth of crops and
contouring a sloping surface with carriers so that every part shall
have its trickling water alternating with dry periods for cutting the
crops or hoeing out weeds, should be a matter of constant interest to
an agricultural worker, and, if he knows his business, good crops and
purity of effluent must go together.
[Sidenote: Managers should have a free hand.]
In order to attain this happy result, a manager must know his business
and be given a free hand, not pestered by members of a committee
(farmers, butchers, gardeners or town tradesmen) coming to give their
advice or orders. The river authority should take samples as often as
they like and send the manager as soon as possible the analyses with
day and hour of sampling as a guide for future working.
He will then have to explain any defect from average purity of
effluent, due to one of the hundred contingencies which may arise in
practice, after he and the river authorities have agreed about what
that average analysis should be for his particular farm or works; and
it will be for the advantage of all parties not to try and enforce a
fixed standard for a whole district, as some river authorities usually
attempt to do, because it is easier to lead than to drive a good
manager, and nothing at all can be done with a bad one.
It must not be supposed that I think river authorities should be easy
going, quite the contrary, but they should trust their inspectors'
reports, and "run in" those sanitary authorities who are careless
about the management of their sewage farms and trying to cut down
working expenses and capital.
In precipitation or other artificial sewage works it is easy to judge
this, but more difficult for any one except the good farm manager to
know whether the land is being made the most of for profit or for
purification; still the rivers authority ought to get to know if they
and their officers take pains.
[Sidenote: Purification and profit.]
It is a common idea that working a sewage farm for profit, and for
purification of the sewage, are two incompatible things, whereas, the
good manager with sufficient working capital (double or more what
would be enough for the same acreage in ordinary agriculture) and a
good market for produce will attain the two together in due proportion
in all ordinary seasons, when a fair allowance has been made him for
the necessary sanitary work.
It is easy to see how the popular idea of incompatibility has arisen
in a case like that above stated of the Camp Farm tenant, eating up
year by year all the fertility stored up in the land during the
previous period, and letting nearly all the sewage run to waste,
because its scientific application would cost much in thought and
labour. In much the same way district councils have been, all over the
country, stinting their labour bills and interfering with their
managers' purchases and sales in order to make as small a demand on
the rates as they can—each year bringing some change of system—to the
end that nobody is responsible or has any confidence in master or man.
With such a state of things up and down the country the way was
prepared for preachers of microbe agency to say, why should you buy
all that land when a septic tank, a few acres of coke or burnt
ballast, and a patent automatic opener and shutter of valves (which
you see working so nicely with tap water and model at some exhibition)
will give you "no more troublesome sludge," and a first class effluent
with hardly any labour bill? if you only agitate against that
arbitrary Local Government Board, which insists upon land!
But those gentlemen neglected the fact, that in a few years' time
their filters would have to be pulled to pieces, washed and put back,
while the land remains as efficient as ever, and a valuable asset, in
some cases saleable at building value, if it becomes desirable to move
the outfall further at some future time.
[Sidenote: Sludge treatment.]
In the above comparison between natural and artificial treatment
reference has been had chiefly to the aerobic branch of the business,
but the anaerobic, breaking down _some_ of the solid organic matter
and the sanitary disposal of the remainder in the state of sewage
sludge (containing fully 90 per cent. of moisture) must not be
overlooked or shirked as beneath the attention of the scientific
bacteriologists and chemists whose analyses of effluents, and often of
what they call crude sewage, are made from the liquid which has passed
through a filter paper in their laboratory before their "oxygen
absorbed" or "ammonia processes" are proceeded with.
On the contrary, I have always maintained that sludge, being the
foulest part of town sewage, ought to receive primary and earnest
attention if we desire to improve the condition of our watercourses.
When town sewage is pumped through a long rising main, it can often be
spread on the land in its really crude state, and if the soil is clay
ploughed up to receive it the sludge is most beneficial to its
texture.
But in every other case we must face the nuisance of extracting the
sludge, and its desiccation in one of the following ways.
1. On a farm at some distance from roads and houses, the cheapest plan
is to form a bank of earth about 18 inches high, enclosing a
rectangular area into which the wet sludge can be run or pumped out of
depositing tanks, and left alone until dry enough for cartage, when it
can be used on the farm or sold to neighbouring farmers for a shilling
or two a load.
2. A wall of farmyard _long_ manure may be used instead of earth, and
trench 5 feet wide dug on each side of the longer sides of the
rectangle, leaving 3 feet of ground between the wall and trench, on
which men can stand to scoop the sludge over the wall when it has
consolidated a little in the trench; the latter is then ready to
receive the sludge from another tank emptying, which is again scooped
over the wall on to a thin coating of farmyard manure, which has been
scattered over the last layer of sludge in the rectangle; and thus in
a year's time a solid mass of the mixture is raised four or five feet
high, and is in capital order for putting in drills for a crop of
mangold wurtzel.
This is the plan in use at the Camp Farm; it occupies little ground
and smells only like rotten dung does during the few days carting to
the mangold field.
3. Pressing by compressed air forcing a liquid mixture of sludge and
lime into the interstices between cloths supported by vertical iron
plates on a horizontal frame; and such pressing is a very expensive
process, only resorted to when the sewage works are in a confined
populated district where no accumulation of sludge can be tolerated.
[Sidenote: Expert examination of neighbourhood a very necessary
preliminary to any sewage scheme.]
Before any sewage scheme is conceived a very careful survey of the
neighbourhood ought to be made by a person who knows the requisites of
a site for sewage disposal, especially if land irrigation is intended,
because natural advantages of site both for tanks, main carriers,
roads, etc., may make all the difference in the world in expense and
efficiency not only in first cost of works but also in their use
afterwards.
And if land is to be acquired for sewage farming it will be very
desirable to include in the purchase some neighbouring high lying
area, not required for sewage disposal but for growing straw crops to
be used on the farm.
CROPPING A SEWAGE FARM.
[Sidenote: Vegetation of some kind, useful or weeds, _will_ grow from
sewage, and must be frequently removed from land or contact bed.]
This is a matter of vital importance, because when sewage is
_intermittently_ applied to land of any kind or to coke beds,
vegetation of some kind or other must result and must be removed in
order to leave a clear course for the next dose of sewage; the cost of
removal and destruction of weeds will be found very great when contact
beds are tried on any working scale and would be quite prohibitive if
allowed to grow on irrigated land.
Hence we must crowd out the weeds as much as possible by useful plants
which will bring something towards the cost of their removal; and as
that return from perishable greenstuff is dependent upon its immediate
sale or consumption on the farm, the manager must cast about for
demands for his abundant supply; but as both the sunshine (in this
climate) and markets are very capricious factors in the problem, he
has no easy task always to make both ends meet.
Theoretically the town which yields the sewage ought to provide an
abundant demand, but in practice it can rarely be depended upon,
Edinburgh being the only exception, where the Craigentinny sewage
meadows are rented at a very high figure by the cow-keepers of a city
situated in the heart of an arable district.
[Sidenote: Alternative destinations for vegetation thus removed. Milk
(everywhere in demand) or a destructor furnace.]
Fortunately, however, there is always an unlimited demand for milk,
and if he has the means of keeping a herd of cows on the farm, or can
arrange with a neighbouring cow-keeper to take all the grass and roots
he can supply at a low rate, it is about the best course a manager can
adopt.
If he maintains a herd of cows, tied up in good, well ventilated
stables, and has them daily brushed and groomed like horses, they
require no exercise and produce milk in perfection for an average
period of fifteen months from date of purchase after their third or
fourth calving.
Such a herd will consume rye-grass carted from the field from April to
November, and mangolds, kohl-rabi, and rye-grass hay during the
winter, thus securing a uniform demand for produce of the sewage land
throughout the year, and such cows will only require a little cotton
cake and oat straw bedding (of which latter they eat a good deal) to
fit them for sale to the butcher as soon as they become dry.
The advantage of such a steady demand is so great when rye-grass and
mangolds, etc., are indicated as the main crops of the farm, owing to
the large volume of sewage per acre, that the system of cow-keeping is
forced upon managers, however reluctant their sanitary authorities may
be to provide the necessary working capital, unless they can find a
reliable contractor to receive at a fixed price any quantity of grass
and roots the authority may grow and deliver.
[Sidenote: Permanent pasture grazed and for hay available in certain
cases.]
When a town has more land in proportion to its sewage, permanent
pasture may take the place of Italian rye-grass, and, with proper
precautions, a part of the permanent pasture may be grazed; but the
saving of labour, thus supposed to result from letting animals bite
and carry their food, is expended in making up, in a necessarily
imperfect manner, the carriers trodden in by the cattle.
[Sidenote: Importance of neat tidy contour carriers, correctly
levelled.]
And here I would observe that most of the bad odour into which sewage
farming has fallen of late years is distinctly traceable to the common
absence of sufficient regularly contoured and neatly cut distribution
carriers resulting from parsimony about wages bills natural to the
ratepayers' representatives in Council, and often to the manager's
dependence on a borough surveyor's coming to the farm with his level
and staff for great measures, or on his own guesses for smaller works,
instead of using an instrument to peg out every distribution carrier
at the right moment.
[Sidenote: Attract good labour.]
There is another important outlay of capital to be provided for in
every complete sewage scheme, which should embrace sufficient good
labourers' houses and gardens in order to attract and retain on the
spot the best class of workers.
[Sidenote: Summary of the experience of a lifetime.]
To sum up the general conclusions to which my experience points, and
which I trust may prove useful to district councillors, they are as
follows:—
1. In works of sewerage, limit and regulate, as far as
possible, the volume of sewage by excluding subsoil
water and clean surface water.
2. Where the outfall sewage enters the disposal works
provide a pair of open catch-pits (or grit-chambers), each
twice as wide as, and 2 feet deeper than the sewer, with
sluices allowing the sewage to pass through one pit at a
time in its free course, while the other pit is being dried
and the deposited detritus dug out. The depth below sewer
invert may be more than 2 feet, and length of catch-pit is
immaterial, but I confine its width to twice that of the
sewer in order to conserve sufficient velocity in the
current to carry forward organic matter, paper, etc., and
leave only clean sand and gravel in these catch-pits.
Continuing the course by open channel (of same width as
outfall sewer), it should expand to five or six times its
width, forming the screening chamber, and thence discharge
into the
3. Depositing tanks. These are best formed in concrete with
smooth surface, with a semicircular level weir from which
the liquid overflows into a semicircular collecting open
carrier leading to the aerobic process on land or contact
bed.
The semicircles above referred to are struck from centre of
the inlet to depositing tank with a radius of 50 feet or
more.
The weir level should be at least 1 inch below that of
invert of inlet, and the depth of tank immediately under
this point should be governed by consideration of the
facility of drawing off the sludge by valve at that depth to
the sludge drying beds by gravitation if possible, or pump
if necessary, and from this sludge emptying valve the smooth
concrete bottom of tank <DW72>s up to the semicircular weir
above described.
The bottom and sides of such a tank should be made with the
best Portland cement and finest granite chippings wrought to
a smooth surface, so that the sludge may be easily swept
clean away with a squeegee to its outlet valve, as it is
very necessary to have the tank thoroughly washed after each
emptying if my view of the _clean_ mode of sewage disposal
is to be carried out.
But with the dirty mode, on the contrary, some of the sludge
only should be drawn off and the septic anaerobic action
preserved continuously in the tank itself, whereas I prefer
that action to have its early and less offensive course in
the tank and its completion in a drying bed mixed if
possible with farm-yard manure.
4. The aerobic process. The one essential point in this
final process, whether in land or "contact beds," is
_sufficient_ aeration (excess as by blowing has no result
commensurate with cost of its introduction), and it can be
attained by intermittence of sewage and rest, or by
continuous passage of sewage through a bed of coarse medium
_kept always just moist in all its atoms_ by a rain-like
dropping on the surface so carefully adjusted as to moisten
all parts and not to form a water-seal in any part of the
bed. Intermittence is easily arranged on any scale of
working, and continuous filtration, on the contrary, is
difficult even for a few thousand gallons a day.
[Sidenote: Anticipation of a coming reaction against "fads" and
overpressure in sanitation.]
Since the above was written our grand old philosopher Herbert Spencer
has published a volume of "Facts and Comments"[3] containing a chapter
on "Sanitation in Theory and Practice," which points to a coming
reaction against the movement begun, some fifty years ago, by the late
Sir Edwin Chadwick and followed up by many enthusiastic exploiters of
the popular dread of "germs," which he associated with bad smells.
Of course the professor's practical acquaintance with Chadwick's hobby
is, as he says, very limited, and his argument, that because sewage
and manure smells are harmless in the open air of the country, they
should be equally innocuous in a town, falls to the ground when
brought to the test of experience, and I trust that Mr. Spencer will
forgive me for pointing out that sewer-gas, drawn into a dwelling
room, in town or country, through scullery waste pipe or other
connection with a sewer in which the air is of lower temperature than
that of the dwelling room, is really prejudicial to health whether
accompanied or not by disease germs.
And although, as one of the experts to whom Chadwick appealed and
whose moderate testimony was cast aside because it did not come up to
the standard desired by his enthusiasm, I fully endorse Mr. Spencer's
caution with regard to the mass of Blue Book evidence on sanitation, I
venture to express my regret that the dear old man has had an
unfortunate experience of sewage treatment, and my surprise that so
deep a reasoner should have published his judgment in this chapter
without having taken the pains to extend his acquaintance with sewage
treatment in other places than the single instance of Burton-on-Trent.
In thus despising an unsavoury subject Mr. Spencer is not alone, and I
am sorry to have to say that general indifference is answerable for
the waste of much public health and money, because it need not be
surprising if those following a _despised_ trade are sometimes ready
to take advantage of the prejudice and ignorance of their employers.
In this sense I beg to quote Professor Spencer as follows in
justification of the reflection with which I began the above essay:—
"New sanitary appliances are continually being devised,
sanctioned by authority, and required by surveyors; and
surveyors may have and certainly sometimes do have, personal
interests in pushing the use of them; either as being
shareholders in the companies they are manufactured by or as
receiving percentages on the numbers sold through their
recommendation."
[2]: Published by Longmans, London, 1874. Third edition
published by R. Potter, Wrexham, 1885.
[3]: 'Facts and Comments,' by Herbert Spencer. Williams and
Norgate, London, 1902.
NATURAL AND ARTIFICIAL
SEWAGE TREATMENT.
BY H. ALFRED ROECHLING,
M. INST. C.E., ETC.
I. INTRODUCTORY REMARKS.
At the request of Lieut.-Colonel A. S. Jones, V.C., Assoc. M. Inst.
C.E., who has done yeoman service in this matter, I have great
pleasure in putting down some observations on this old but ever
controversial question of sewage treatment.
Colonel Jones has done more than anyone else living to establish
correct views on sewage farming, and he has lately changed the
Government sewage marshes at Aldershot into a veritable "Garden of
Eden," watered by the waters from Aldershot Camp, growing healthy
crops, and causing not the slightest nuisance. After many struggles,
even the milk from the dairy cows is now recognised as good and
supplied to the military hospitals. This is an achievement of which
anyone might be proud; and all those who have been over the farm
during the time of the "deluge," and can now study the order and
system evolved out of chaos by Colonel Jones will testify to this! It
is pleasant to record that the War Office have recognised Colonel
Jones' work for them by having appointed him quite recently to manage
all the sewage disposal works in the Aldershot district. This will
involve the laying out of irrigation works in eight separate places,
in some of which artificial methods of sewage purification have been
tried and found wanting.
Before commencing with my task proper it may not be out of place to
describe here very shortly the various stages through which the sewage
question has passed during the century just closed. Such a retrospect
is of general interest and may throw some further light upon our
subject; it must of necessity be short, otherwise it would absorb more
time and space than is at my disposal, and any shortcomings in this
respect that the reader may discover, I trust he will kindly put down
to this cause.
"The man in the street" seems year after year more called upon to form
an important element in settling questions even of a scientific
nature, and if what I am going to say should prove of some service to
him my labours will be well repaid.
II. THE SEWAGE QUESTION DURING THE LAST CENTURY.
A SHORT RETROSPECT.
In dealing with the sewage question during the last century, it will
be an advantage to distinguish between the theory and practice of
sewage purification, as such a division of the subject will render it
less complicated and will tend to avoid misconceptions.
Dealing first with the theoretical side of the question, it is very
doubtful whether at the dawn of the century even a working hypothesis
existed to explain the process of sewage irrigation which was then
adopted in one or two instances, notably at Edinburgh, where the town
sewage was very successfully purified on the Craigentinny meadows. It
is more than likely, that at this time instinct took the place of
theory, and that sewage irrigation was an instinctive imitation of
irrigation with river water employed for many centuries in some
eastern countries.
Later on it is on record, that Cagniard de la Tour in France, about
the year 1825, and Schwann in Germany, about the year 1836, expressed
the view, that organised substances—micro-organisms—played some role
in fermentative and putrefactive changes. Almost diametrically opposed
to this were the views authoritatively laid down by the then star in
the chemical horizon, Justus von Liebig, who, about the year 1845,
maintained that these changes were brought about by the dead inert
matter itself—by molecular movements in the same—and not by organised
substances, the presence of which in fermenting or putrefying
substances was purely accidental. So great was Liebig's authority
then, that many almost blindly adopted his views, and the strife that
commenced around these opposing views was fought with the greatest
bitterness. But the stronghold of old ideas, which were gradually but
surely being supplanted by new ones, could not hold out for ever
against combined attacks, however stoutly it was defended by its
designer, and its final downfall came about the year 1860, when a
young Frenchman, Pasteur, established beyond doubt by his ever
classical researches, that fermentation and putrefaction were, in the
first instance, due to living organisms and not to dead matter.
Pasteur further demonstrated that living organisms were also the cause
of some and probably of all zymotic diseases.
So far, so good! But unfortunately the methods of biological research
employed by M. Pasteur were very cumbersome and left otherwise much to
be desired, so that his discoveries could not be fully utilised and
extended, until in 1882 Robert Koch of Berlin published his new
methods of investigation. This was the signal of raising the
floodgates of biological (bacteriological) research throughout the
world with this result, that the flood waters pent up until then
inundated practically other branches of scientific investigation and
drowned their individual life for some time to come.
During this interval, 1860 to 1882, investigators who wished to study
the organised impurities in sewage had to proceed by indirect methods.
They had no means of ascertaining by direct biological experiment the
number and character of the micro-organisms contained in sewage: all
they could do, was to determine chemically the dangerous nature of the
sewage by the amount and origin of organic matter it contained, which
would probably act as food to the germs; and the greater this amount
was, so it was inferred, the greater would be the number of germs it
harboured and the more dangerous its character.
This was the condition of things at the time the second Rivers
Pollution Commission carried out its investigations, which in many
respects, and rightly too, are still considered standard
investigations. It cannot be surprising, therefore, that, being
without proper means of biological examination, and having to rely
chiefly on chemical methods only, the Commissioners came to the
conclusion that the changes brought about in sewage purification were
due to mechanical and chemical agencies!
It is frequently a matter of the utmost difficulty to ascribe, after
the lapse of half-a-century, a new theory to one special author, as
several investigators may have been trending the same way quite
independently of each other, but may not have been equally successful
in the matter of their publications becoming generally known.
Theories, as a rule, do not drop out of the clouds like meteorites,
they force themselves gradually upon men's minds and are elaborated by
them until ripe.
Bearing this in mind, and subject to further research, it would appear
as if Alexander Müller had been the first to apply Pasteur's general
theories as to decomposition, fermentation and putrefaction to the
problem of the self-purification of sewage. He made his experiments in
1869 and published them in 1873. Since that date a very large number
of investigators have been at work on similar lines, and whilst it
would lead too far to deal with them minutely, it ought to be stated
that the results of their labour confirmed the view of living
organisms playing a very important part in the decomposition of
sewage. Among the many names prominent in this respect are those of
Schloesing, Müntz, Hatton, Warrington, Sorby, Winogradsky, Percy
Frankland, Dupré, Emich and Dibdin. That set of researches, however,
which has done more than any other to consolidate the theory of
bio-chemical changes taking place in the self-purification of sewage
are the investigations of the Massachusetts State Board of Health,
which were commenced in November 1887, and are still being continued.
Since 1895 a large number of additional experiments have been made,
which will be dealt with more in detail later on, but speaking
generally they have not materially increased our knowledge of the
processes taking place in sewage purification.
Summarising the remarks on the theoretical aspect of this question,
it may be said that, as to the agencies at work, we know now they are
of a mechanical, chemical and biological nature; but as to the
processes and products brought about by these agencies we know very
little beyond the initial and terminal stages, as will be pointed out
in some of the subsequent observations.
Directing now attention to the practical side of the question, it has
already been stated that the only known sewage treatment at the
commencement of last century was land irrigation. Then about the
middle of the century chemistry seems to have taken the matter in hand
and tried to make a lucrative business out of it. It is on record,
however, that it did not succeed in this attempt, and the financial
loss which this endeavour has caused is a dismal subject to
investigate.
There is before my mind's eye the case of a gallant officer of His
Majesty's land forces who, after having reached very near the summit
of his career, retired and employed his time in trying to make a
fortune out of sewage. So enamoured was he of the subject, that—so the
story goes—he commuted his pension to have all the more ready money;
but fortune did not smile on him, and his last days were spent under
the lengthening shadows of the sorrow of financial difficulties,
having practically lost all he possessed.
The emphatic verdict of the first Sewage Commission of 1857, the first
and second Rivers Pollution Commission, and, indeed, of all other
authoritative investigations, was in favour of land treatment; and it
cannot, therefore, be surprising to find that the Local Government
Board insisted, save in exceptional cases, that "any scheme of sewage
disposal, for which money is to be borrowed with their sanction,
should provide for the application of the sewage or effluent to an
adequate area of suitable land before it is discharged into a stream."
Indeed, had this body taken any different view and neglected the
findings of practically all authoritative inquiries, it would have
been singularly deficient in the discharge of its duties to the
ratepayers of this country.
But the best of land cannot go on for ever doing its duty if by
systematic neglect and ignorance the essential conditions for
successful purification are year after year violated; and the great
pity is that the Local Government Board, after deciding in favour of
land treatment, did not systematically superintend this operation. It
may not have had the power, but it is quite evident that had it done
so, things would not have drifted from bad to worse, until local
authorities, driven to despair by the apparent failure of land and not
discerning the right cause, refused altogether to be ruled by what
seemed to them a very unfair and absurd restriction.
It was at this time that Mr. Dibdin, who, on behalf of the London
County Council, had been carrying out a set of valuable experiments,
came forward with his application of well known theories to sewage
operations on a large scale. As I pointed out at the time, Mr.
Dibdin's experiments proved beyond a doubt that the application of
sewage to suitable land was right in principle and that the failures
were brought about by the non-observance of the rules laid down by
this gentleman—that, in fact, sewage irrigation was the only natural
method of sewage purification and that all the other methods were
artificial. I described land treatment as the natural self-purification
of sewage and the oxidation or contact bed system as the artificial
self-purification of sewage.
But the swift current of public opinion had set very strongly against
sewage farms, and nothing but the contact bed treatment would do. A
large number of experimental plants on this system grew up like
mushrooms all over the country, and the waves of enthusiasm seemed at
one time to engulf even the Local Government Board itself with its
"antiquated notions," until Parliament came to the rescue and
appointed on May 7, 1898, a new Royal Commission to study the question
of sewage purification.
This Commission consists of nine members,[4] i.e. six professional men
and three laymen. Of the professional men, one is a biologist, one a
chemist, two are medical men in administrative positions, and two are
engineers likewise in administrative positions. Of the laymen two are
members of special boards for the prevention of the pollution of
rivers.
So far the Commissioners have issued an Interim Report dated July 12,
1901, a volume of evidence and a volume of appendices. Quite lately,
it is stated, they have issued a further Interim Report, to which are
attached separate reports on some special subjects by their officers,
but this report has not yet come to hand.[5]
At the time of their first Interim Report, July 12, 1901, the
Commissioners had held altogether thirty-five sittings, the first of
which was on June 22, 1898, and the last on May 22, 1901. The period
thus covered is nearly two years, and out of the thirty-five sittings
thirty took place in London, and five in the provinces, viz. at Leeds,
Ripon, Manchester, Accrington and Reigate.
On these occasions, all in all, fifty-eight witnesses were examined,
who may be grouped as follows:
1 Zoologist
1 Botanist
2 Laymen
3 Bacteriologists
5 Lawyers
7 Medical men
11 Patentees
14 Chemists
14 Engineers
58 witnesses in all.
Out of this number twenty-five were officials, viz. five lawyers, six
medical men, six chemists and eight engineers. Four officials were
further managers of artificial sewage purification works, but not one
single manager of natural purification works, i.e. a sewage farm
manager, was called, the term "sewage farm manager" being used here to
indicate an official whose sole duty it is to manage a sewage farm.
The entire absence of this latter class of official is so striking
that it cannot be due to accident, but must be the outcome of a
settled policy not to reopen questions conclusively settled by
previous inquiries.
Another point that strikes the observer is that the Commission only
called one zoologist and one botanist, as it is to these scientists
that belongs in the first instance the question of studying the fauna
and flora of sewage before the subject is taken up by other branches
of natural science.
Speaking on the whole, the evidence taken by the Commissioners forms
very interesting reading, and ought to be carefully studied by those
who have to deal with the subject. When now and again opinions are
expressed, which seem directly opposed to each other, it must be borne
in mind that here, as in other things human, unanimity of opinion,
though much desired, is apparently unobtainable.
To understand the conclusions fully, at which the Commissioners in
their Interim Report have arrived, it ought to be pointed out that
they had either to accept the recommendations in favour of land passed
by all previous Royal Commissions and authoritative inquiries, or they
had to show by incontestable evidence that their predecessors had made
grievous mistakes, and where!
Of these two courses, the present Commissioners have adopted, no doubt
for very good reasons of their own, the first, and they have started
therefore, in the conclusions to which they have come, at the point
where previous inquiries had left off, viz. that land treatment is a
very proper method of sewage purification.
But before referring more in particular to their observations on land
treatment, it will be necessary to point out that the Commissioners
evidently divide all methods of sewage purification into two main
classes, viz. natural and artificial methods. Into the former they
only place land treatment, whilst they call all other methods
artificial.
This division seems to have given a great deal of offence to all those
who have expressed decided and frequently very one-sided views in
favour of the "bacterial" treatment of sewage; but on closer
examination it cannot be denied that the Commissioners were quite
right in forming this view, as the following remarks will show.
For main divisions of all methods of sewage treatment two factors seem
to be of primary importance, viz. the agencies which bring about this
purification, and the way in which these agencies are employed. Now,
it will not be denied that all agencies are natural ones, whether the
process employed is a purely chemical one, a purely "bacterial" one,
land treatment pure and simple, or a combination of these, and, at the
present time no such thing as an artificial agency is known; indeed,
it is perhaps not too much to say that there cannot be such a thing
as an artificial agency. Hence it is impossible to divide sewage
purification methods in this respect by the agencies employed, and one
is bound to fall back upon the way in which these agencies are
employed. Here it is no longer open to argument whether a chemical
process or the contact bed system—oxidation bed system—is artificial,
or whether the land treatment is natural! For who would deny that
masonry or concrete tanks and the materials contained in the same are
artificial products—i.e. products formed by man—and that land is a
natural product—i.e. formed by nature—and that further the soil is the
natural home of bacteria. Hence it must be perfectly clear, even to a
casual observer, that the line of demarcation drawn by the
Commissioners between all known systems of sewage purification is a
correct and legitimate one, and that all objections to such a division
are based on misconceptions.
Concerning land treatment, the Commissioners observe, "We doubt if any
land is entirely useless," but further on they observe that peat and
stiff clay lands are generally unsuitable for the purification of
sewage. Concerning peat, nobody acquainted with the subject would
probably differ from their conclusions owing to the great amount of
moisture contained in this material; but as to clay soils, the
Commissioners when making this statement must have known that there
are several successful sewage farms on this kind of land in existence,
such as the sewage farms at South Norwood, Wimbledon, Warwick and
Leicester, not to mention others. In the case of Leicester, although
the land is a very dense boulder clay, the Corporation of this town
have just purchased the freehold of the farm for about 160,000_l._
Dealing with the artificial processes from a chemical point of view,
the Commissioners are of opinion that it is practicable to produce by
these processes alone, either from sewage or from certain mixtures of
sewage and trade refuse, effluents which might be discharged without
fear of creating a nuisance, and that in consequence the Local
Government Board would be justified in modifying, under proper
safeguards, the present rule as regards the application of sewage to
land.
The artificial processes referred to in the observations appear to be
the following:—
Closed septic tanks and contact beds.
Open septic tanks and contact beds.
Chemical treatment, subsidence[6] tanks and contact beds.
Subsidence tanks and contact beds.
Contact beds alone.
Closed septic tank followed by continuous filtration.
Open septic tank followed by continuous filtration.
Chemical treatment, subsidence tanks, and continuous filtration.
Subsidence tanks followed by continuous filtration.
Continuous filtration alone.
The Commissioners do not say what these safeguards are, in fact they
state that no general rules concerning them can be laid down, and that
in the case of these artificial processes it is necessary to consider
every case on its own merits.
The next point dealt with is the bacteriological quality of effluents,
and here the Commissioners observe: "We find that, while in the case
of effluents from land of a kind suitable for the purification of
sewage there are fewer micro-organisms than in the effluents from most
artificial processes, yet both classes of effluents usually contain
large numbers of organisms, many of which appear to be of intestinal
derivation, and some of which are of a kind liable under certain
circumstances at least to give rise to disease."
No particulars of effluents from sewage farms are given, and later on
it will be shown that this conclusion of the Commissioners is not in
accord with the results published up to now and available concerning
the bacterial purity of effluents from land treatment.
The report concludes with some remarks on rivers pollution. The
Commissioners state that it is of the utmost importance to provide the
simplest possible means for adequately protecting all rivers, and they
think that this subject is of such grave importance "as to demand the
creation of a separate Commission or a new department of the Local
Government Board, which shall be a supreme Rivers Authority, dealing
with matters relating to rivers and their purification, and which,
when appeal is made to them, shall have power to take action in cases
where the local authorities have failed to do so."
Summing up the observations on the practice of sewage treatment, it
may be said that as a result of their extended inquiries, the present
Royal Commissioners have at the end of the century re-established land
in its position as the first and only natural method of sewage
purification, beside which they have recognised artificial
(biological) treatments as being under proper safeguards admissible
for the purification of sewage.
Before concluding this portion of the observations, it is necessary to
mention the valuable work done by Mr. Scott-Moncrieff and Mr. Cameron,
who, contemporaneous with Mr. Dibdin, but quite independently, had
experimented with sewage and evolved their own artificial methods of
sewage treatment.
These remarks must suffice for the more historic portion of the
subject, viz. the progress of sewage purification during the last
century, and it is time now to direct attention first to natural and
afterwards to artificial sewage treatments.
[4] Two of these have since retired.
[5] This report has just been issued (August 18, 1902), and
although the special reports it contains are of the greatest
interest, it is not necessary to refer to it again in these
observations.
[6] The expression "subsidence tanks" is intended to denote
tanks which are used in such way that little or no septic
action is produced.
III. THE SUBSOIL.
[Sidenote: General remarks on subsoil and its properties.]
Before dealing more in detail with the processes taking place in the
pores of the subsoil of sewage farms, it may not be out of place to
make here a few general observations on the mechanical structure of
soil, its permeability, water capacity, retentive power, the capillary
movements in the same, its temperature, the subsoil air, the movement
of water in and through the same, the micro-organic life in soil, and
its absorbing powers.
1. MECHANICAL STRUCTURE OF SOIL.
[Sidenote: Size of grain and pores.]
Here is of interest the size of the grains or particles composing the
soil, the size of the pores and their collective capacity.
According to the character of the soil, its grains or particles will
vary from very large in coarse gravel to very fine in fine sand and
clay.
[Sidenote: Variable size of pores.]
[Sidenote: Surface attraction.]
The size of the pores will vary as the size of its grains from large
to small, but frequently a certain kind of soil will contain a mixture
of large and small pores. The finer the pores the more energetic will,
as a rule, be the surface attraction of the grains composing the soil.
[Sidenote: Pore-volume.]
[Sidenote: With particles of equal size pore-volume amounts to about
38 per cent. of the total space, and sinks down to 10 or 15 per cent.
with particles of unequal size.]
[Sidenote: With equally sized particles the pore-volume is the same
whether the particles are small or large.]
The collective capacity of the pores or the pore-volume mainly depends
on the equal or unequal sizes of the particles. When the same are of
equal size the pore-volume amounts to about 38 per cent. of the total
space occupied by the soil, but when this is not the case it may sink
to as low as from 10 to 15 per cent. of this space. With equally sized
particles the pore-volume is the same whether the individual particles
are large or small. In nature it will be the exception to find all the
particles of equal size, such a condition of things prevails only when
careful sorting by sifting or riddling has taken place, and in the
majority of cases the larger pores will be partly filled up by the
smaller particles of the soil.
2. PERMEABILITY OF SOIL.
[Sidenote: Permeability depends first on the size of the pores, and
secondly on the pore-volume.]
The permeability of a soil for the passage of air and water depends,
in the first instance, on the size of the pores, and is further to
some extent influenced by the pore-volume.
[Sidenote: Effect of large and small pores.]
Soil with large pores will offer but little resistance to the passage
of air and water, but when the pores are small these movements will be
greatly impeded.
[Sidenote: Permeability is proportional to the fourth power of the
pore-diameter.]
It has been ascertained that the permeability of soils is proportional
to the fourth power of the diameter of the pores, so that it decreases
very rapidly with the diminishing size of the pores.
[Sidenote: In frozen soil permeability decreases rapidly.]
In subsoil with small pores all movements of air practically cease
when it is half full of water, and in frozen soil the decrease of the
permeability is still more marked.
3. WATER CAPACITY OF SOIL.
[Sidenote: Water capacity is equal to the pore-volume.]
[Sidenote: Air can never be wholly driven out of the pores.]
The water capacity of a soil is that quantity of water which can be
stored in its pores; it is therefore equal to the pore-volume. For
very accurate measurements allowance must be made for a small amount
of air, which even after filling remains in the pores and cannot be
dislodged, but for practical purposes this can be overlooked.
[Sidenote: 1 cubic yard of soil with particles of equal size will hold
about 85 gallons of water.]
As has already been stated, the pore-volume of a soil consisting of
equal particles throughout, amounts to about 38 per cent. of the space
occupied by it, and 1 cubic yard of such a soil—whether we have to
deal with coarse gravel or fine sand—will hold about 85 gallons of
water.
4. WATER-RETENTIVE POWER OF SOIL.
[Sidenote: The water-retentive power of soil is a percentage of its
water capacity.]
The water-retentive power of a soil is expressed by that quantity of
water which can be retained by it; it will always be a percentage or
portion of the water capacity of this soil.
[Sidenote: Soil with a large pore-volume and a large percentage of
fine pores retains more water than soil with a small pore-volume and
large pores.]
[Sidenote: Clean gravel retains about 10 gal. and clean sand about 70
gal.]
Soil with a large pore-volume and with a large percentage of fine
pores will retain more water than soil with a small pore-volume and
few fine pores. Clean gravel will retain about 12 per cent. of its
water capacity, i.e. 10 gallons per cubic yard, whereas fine sand may
retain as much as 84 per cent. of its water capacity, i.e. about 70
gallons per cubic yard.
[Sidenote: Organically polluted soil retains more water than clean
soil.]
This will explain why a polluted subsoil containing a large amount of
organic substances will retain more water than the same soil in a
clean condition.
[Sidenote: The retentive power of a soil is due to its surface
attractions.]
The retentive power of a soil is due to the surface attraction of its
particles, and when the space between them is small, or when, in other
words, the pores are small, this attractive power will be all the
greater.
[Sidenote: When, after the limit of the retentive power has been
reached, of water are poured upon the soil, a portion of the
previously stored water is driven out, and its place in the pores
taken up by the fresh supply.]
It is further of interest to observe here, that if after the limit of
the retentive power has been reached further quantities of water are
poured upon the soil, the water retained in the lower layers will
commence to drain away. This means that the water freshly poured upon
the soil will drive out a portion of the water previously stored in
the pores. It is important to bear this in mind when dealing with
polluted water, as owing to this action the water penetrating into
deeper layers will to some extent at least have become purified in the
upper layers.
5. CAPILLARY MOVEMENTS OF WATER IN SOIL.
[Sidenote: Capillary attraction causes an upward movement of the
water.]
Through capillary attraction an ascending movement of the water is
caused in direct opposition to the laws of gravity, and the height to
which water will thus ascend depends mainly on the smallness of the
pores; large pores do not assist in this movement. As the same,
however, extends over the whole pore-volume the quantity of water thus
raised may exceed the water-retentive power of soil.
[Sidenote: Capillary attraction also causes lateral and downward
movements.]
In addition to the upward movement brought about by capillary
attraction, this power is also continually at work in a lateral and
downward direction; but for the present purposes only the upward
movement will be noticed.
[Sidenote: Time occupied by upward movement. Height reached by upward
movement.]
In observing the upward movement, it is interesting to notice the time
occupied by it and the total height reached. As to the time occupied,
it has been established that the upward movement in gravel and coarse
sand is much quicker than in fine and loamy sand, but the heights
attained are reversed. For whereas the height in a material consisting
of coarse or large pores amounts to from 2 inches to 4 inches; a
height of about 4 feet after thirty to thirty-five days has been
recorded in fine or loamy sand; in peaty soil one observer states that
the upward movement of the water may reach a height of 20 feet.
6. TEMPERATURE OF SOIL.
[Sidenote: Three principal sources of heat.]
The earth's crust receives its supply of heat from three principal
sources, viz.:
1. From the sun through its rays;
2. From the interior of the earth through conduction; and
3. From various physical and chemical processes which take place in it
and create heat.
[Sidenote: Heat through sun's rays.]
[Sidenote: Dark soils absorb more heat than light- soils.]
[Sidenote: Capacity for heat is greater in damp and fine-grained
soils.]
[Sidenote: Evaporation and condensation of aqueous vapour produce the
greatest effect in fine-grained soils.]
Dealing with the upper layers of the crust, it may be said that,
besides the intensity of the sun's rays, the temperature also depends
on a variety of properties possessed by various kinds of soil, amongst
which latter may be mentioned the absorption of heat, which is much
greater in dark than in light- soils; the heat conductivity
and the capacity for heat, which lead to higher temperatures in damp
and fine-grained soils; and finally the evaporation and condensation
of aqueous vapour, which tend to prevent extremes of heat and cold and
which likewise produce the greatest effects in fine-grained soils.
[Sidenote: A fine-grained damp soil does not get so hot, but retains
the heat better.]
It follows from these observations that a coarse-grained, dark
and dry soil will show the highest and lowest temperatures,
whereas a fine-grained damp soil does not get so hot but retains the
heat better.
[Sidenote: The temperature of the surface of the soil may exceed that
of the air.]
It ought to be pointed out in this place that a variety of
circumstances may bring about very high temperatures on the surface of
the ground which considerably exceed the average temperatures of the
air at the same time.
[Sidenote: Laws regulating the subsoil temperatures.]
Concerning the laws that have been deduced from careful and long
continued observations of subsoil temperatures, it will not be
necessary at this point to deal minutely with them; it must on the
contrary suffice to summarise only the more important ones.
With the distance from the surface of the ground,
1. The differences of temperature become less,
2. The temperatures are retarded, and
3. The variations of short durations gradually disappear.
[Sidenote: Subsoil temperatures 18 in. below surface.]
[Sidenote: Subsoil temperatures at depths of 4 ft. 6 in. and 9 ft.]
At a depth of 18 inches below the surface the daily fluctuations are
hardly observable, the temperature differences of various days become
obscured, the differences between the monthly mean temperatures are
less by several degrees, and the yearly fluctuation amounts only to
about 10° C. At a depth of 4 feet 6 inches the latter is only 4° C.,
and at a depth of 9 feet it is only 1°C.
[Sidenote: Subsoil temperatures at depths from 9 ft. to 33 ft.]
Between 9 and 33 feet, according to the yearly mean of the surface,
the yearly fluctuation ceases and the temperature remains the same
throughout the year.
Below this point an increase of temperature is observable towards the
earth's centre, which amounts to about 1° C. for every 40 feet.
[Sidenote: Retardation of temperatures with increase in depth.]
Concerning the retardation of the temperatures with an increase in
depth below the surface, it is interesting to point out that this,
according to Fodor, amounts to about three weeks for every yard, so
that the yearly maximum at a depth of 1 yard will take place in
August, at a depth of 2 yards in the beginning of September, and at a
depth of 4 yards in October. This is on the assumption that the
maximum temperature of the atmospheric air is reached in July.
[Sidenote: Frost depth about 3 ft.]
The depth to which frost under ordinary conditions penetrates is about
3 feet, but there are cases on record where water pipes at depths of
from 4 to 5 feet have been frozen up during long continued severe
frost.
7. SUBSOIL AIR.
[Sidenote: Subsoil air is saturated with aqueous vapour and contains
large quantities of carbonic acid.]
The pores of soil are either partly or wholly filled with air, which
as a rule is saturated with aqueous vapour. This air consists very
largely of carbonic acid (from 0·2 to 14 per cent., on an average from
2 to 3 per cent.) and to a small extent of oxygen, which has been used
up for the formation of carbonic acid. It also contains traces of
ammonia and gases of decomposition.
The movements of subsoil air need not be considered here, and beyond
these few general observations it will not be necessary to deal with
the subject.
8. MOVEMENTS OF WATER IN SOIL.
[Sidenote: Strata above level of subsoil water.]
Two main strata may here be distinguished in subsoil, one above the
level of the subsoil water and one below this level. The latter strata
do not interest us, and those above the level of the subsoil[7] water
may again be subdivided into three zones, which in descending order
are as follows:—
The evaporation zone;
The passage zone; and
The capillary zone.
[Sidenote: One-third of the rain-water evaporates. One-third flows off
the surface. One-third percolates.]
All these three zones must be passed by the water in its descent from
the surface of the ground to the subsoil water level, and the quantity
of water retained by them will depend on their state of dryness.
Speaking quite generally and within wide limits, one-third of the
rain-water flows off the surface, one-third evaporates, and one-third
percolates into the subsoil.
[Sidenote: Evaporation zone.]
The evaporation zone reaches from the surface of the soil to that
point below, which marks the extent of the drying influence of the
atmospheric air. In the same the quantity of water stored in the pores
may at times sink below the retentive power of the soil, i.e. below
that quantity which can be retained in the pores owing to the
mechanical powers of adhesion, etc. When it has become very dry
through evaporation and other causes the zone, especially when it
extends some way down, may retain large quantities of water. In a
depth of 10 inches, 1 square yard of soil, with fine pores, may retain
about 10 gallons of water, and as a rainfall of ½ inch produces only
2·3 gallons per square yard, it is clear that subsoil of this nature
may retain a number of successive showers. During the height of summer
fine porous soil may become so dry that practically no water finds its
way into deeper zones; in this state the evaporation zone can be
compared to a large sponge.
[Sidenote: Passage zone.]
The next zone traversed by the water in its downward movement is the
passage zone, which lies beyond the drying influence of atmospheric
air. When too far removed from the level of the subsoil water, its
pores will not be completely filled with water, but will only contain
that amount which is due to the retentive powers of the soil. By
direct measurement it has been found that on an average a cubic yard
of fine porous soil will retain from 30 to 80 gallons of water, and it
can easily be calculated that in a layer from 1 to 2 yards in
thickness the rainfall of a whole year may be retained. The passage
zone, especially if it is of considerable thickness, represents a very
large storage reservoir.
[Sidenote: Capillary zone.]
The last zone before the level of the subsoil water is reached is the
capillary zone, in which the pores are partially or wholly filled by
the upward movement—due to capillary attraction—from the subsoil
water. The extent of this filling will depend on the size of the pores.
[Sidenote: Springs.]
When the descending water has finally reached the subsoil water it
either comes to a standstill altogether on the impervious layer or
moves along the same, if the latter is not horizontal, until it may
eventually leave the subsoil again by issuing therefrom in the form of
visible or invisible springs.
[Sidenote: Rate of downward movement governed by pores.]
The rate of movement of any liquid—rain-water, sewage or other
polluting liquid—is largely governed by the size of the pores. Where
these are large, as for instance in coarse gravel, the descent of the
water will be comparatively rapid, but when they are small it may take
a very long time before the water reaches the level of the subsoil
water, and in that case it will have undergone material changes as
regards its chemical or bacterial composition.
[Sidenote: With a high level of subsoil water zones become
indistinguishable.]
With a high level of subsoil water the zones may become
indistinguishable, one zone reaching into the other, with the result
that the whole of the soil becomes very wet.
When subsoil has been artificially drained the amount of water
reaching the subsoil water below the general level of the drains will
depend on the size of the latter and the distance between them. In
such a case the downward movement of the water through undrained soil,
previously described, may be further interfered with through the
ventilation of the subsoil by drains, and the drying up action caused
thereby.
[7] The term subsoil water is here used to denote that
portion of the water in the pores of the soil, which is
either at rest on or moves along the inclined plane of an
impervious layer.
9. THE MICRO-ORGANIC LIFE IN SOIL.
[Sidenote: Soil probably original home of micro-organisms.]
[Sidenote: Distribution of micro-organisms in soil.]
The soil is probably the original home of all micro-organisms, from
which they have emigrated into other media. It contains vast numbers,
and, according to some observers, 1 ccm. may hold 100,000 germs. By
far the greater number is found on or near the surface, and in lower
layers the numbers gradually diminish, until at last a depth is
reached, which depends on local conditions, where the soil is
perfectly sterile. The aerobes live near the surface and carry on
their work in this region, whereas the anaerobes are at work lower
down in the soil.
[Sidenote: Cycle of micro-organic activity during the year.]
The picture of the cycle of micro-organic activity in the upper layers
of the soil during the various seasons of the year is probably the
following. In winter, especially during that period when frost and ice
bind the earth, micro-organic life is apparently at its lowest ebb,
and may in some very cold climates come to a standstill altogether,
when micro-organisms may be said to hold their vegetative winter
sleep. With the return of life and the awakening of nature in
spring—especially with the approach of higher temperatures and the
formation of moisture—micro-organic activity once more makes itself
felt all round. During the summer months it is exposed to some
injurious influences such as the heating and drying up of the upper
layers of the soil, but, still gradually increasing, micro-organisms
reach the climax of their activity during the autumnal rains, to
remain in this state until with the advent of the cold season their
activity gradually declines again.
[Sidenote: Micro-organic life in layers from 3 ft. to 6 ft. in depth.]
In the lower layers of the soil, down to 3 feet and 6 feet,
micro-organisms are more protected against the injurious influences of
the atmosphere, sunlight and drying up, but the want of oxygen,
together with the greater difficulty of removing such products as
carbonic acid, has an injurious influence. As the temperature in these
layers is considerably more uniform, it may be inferred that the
micro-organic activity is there of a more uniform kind, less
influenced by sudden changes, probably also less intense, but without
pronounced periods of rest.
[Sidenote: Micro-organisms probably quickly perish in depths greater
than 6 ft.]
In depths greater than 6 feet micro-organisms probably perish very
quickly owing to unfavourable conditions, and if found their presence
must be explained by emigration from higher layers, not by actual
growth at these depths.
On sewage farms the micro-organic activity is without doubt greatly
modified, and proceeds all the year round at a more uniform rate than
on ordinary land, as the sewage always contains the necessary warmth
and moisture so beneficial for it.
10. THE ABSORBING POWERS OF SOIL.
[Sidenote: Absorbing powers due to surface attraction of the particles
of the soil.]
[Sidenote: The finer the pores the greater the absorption.]
The absorbing powers of soil are due to the surface attraction of its
particles or grains, and these, as has already been pointed out, will
be all the greater the finer the pores are; they extend on the one
hand to aqueous and other vapours and gases, and on the other to
matters in solution.
[Sidenote: 1 cub. yd. of coarse gravel may contain 50 sq. yds. of
surface and 1 cub. yd. of fine sand 9200 sq. yds.]
That the attractive force of the surface of the particles is pretty
considerable will be at once apparent when it is stated that 1 cubic
yard of coarse gravel may contain about 140,000 grains with a combined
surface of 50 square yards, and 1 cubic yard of fine sand 40 million
grains with a combined surface of 9200 square yards, which is a little
under 2 acres.
[Sidenote: Deodorising action of soil absorption of gases.]
Concerning the absorption by soil of aqueous vapour and gases (apart
from condensation through a fall in temperature), dry soil with fine
pores acts most energetically. The almost instantaneous deodorisation
of foul-smelling gases, such as are formed by decomposing fæcal
matters (earth closet) or coal gas, through a thin layer of fine dry
soil is well known, and is to be explained in this way.
[Sidenote: Absorption of dissolved substances by soil.]
More interesting still, and also more important, is the absorption of
dissolved substances by soil. In this way is to be explained the
decolorising effect and the retention of dissolved polluting
substances such as are contained in sewage. In the same way soil has
the power of destroying such poisons as strychnine, nicotine, coniine,
etc., and the experiments of Falk and others go to show that ptomaines
and toxines are likewise retained and rendered harmless by it. This
absorbing power of soil is of the utmost importance in agriculture,
and without it soil could not possess purifying powers for polluting
liquids. It is quite true that in this process of purification other
factors play an important part, but they could not come into play if
this absorption did not exist.
The absorbing powers of soil are in some way dependent on the presence
of micro-organisms and air, and in the absence of these they will soon
come to a standstill.
IV. SELF-PURIFYING POWERS OF SOIL. NATURAL SELF-PURIFICATION OF
SEWAGE.
[Sidenote: Self-purifying powers of soil.]
After these preliminary remarks it becomes necessary now to examine
into the self-purifying powers of soil with special reference to
sewage farms. Generally speaking, the term "self-purifying powers
powers of soil" comprises all those processes which go on on the
surface and in the pores of the soil of sewage farms, and by which
polluting liquids such as sewage become purified as these take place
under natural conditions and in a natural medium, the process of land
treatment of sewage is called—see previous observations—"the natural
self-purification of sewage."
[Sidenote: Self-purifying powers vary with local conditions.]
[Sidenote: Soil best suited for sewage farms.]
It should be stated at the outset that the self-purifying powers of
soil will depend largely on the soil itself and the local conditions
under which they come into play, so that observations made in one
locality will not be immediately applicable to others without making
full allowance for the differences; this will be clear from the
preliminary remarks as to the character and properties of soils made
in the previous pages. As will be pointed out more in detail later on,
a subsoil that combines great permeability for air with high retaining
and absorbing powers, is best suited for sewage farms.
Let us now consider what becomes of water, sewage or any other
polluting liquid containing organic substances after it has been
poured out upon the surface of the ground, and for this purpose we
will assume a subsoil of a suitable character and in fair condition
for work with proper under-drainage.
[Sidenote: Retention of liquid by pores of soil.]
The liquid thus poured out upon the surface will sooner or later
disappear in the soil, and will at first be retained in the pores of
the zone of evaporation, which may be said to extend to the level of
the under-drains. This retention is due to the retentive powers of
soil.
[Sidenote: Suspended matters retained on the surface, soil acts like a
sieve.]
[Sidenote: Coating of surface of the land.]
[Sidenote: Removal of suspended matters generally an advantage.]
Portion of the suspended matters will be retained on the surface and
the rest will be strained out in a mechanical manner in the pores, the
soil acting as a sieve more or less fine according to its character. If
the suspended matters are present in very large quantities it may
happen that they will gradually form a coat on the surface of the land
and choke the pores to the exclusion of air, and as this is a thing to
be avoided in sewage farming it is in most cases advisable to remove
them out of the liquid before it is poured upon the land.
[Sidenote: The more finely divided the suspended matters are, the
lighter the work of the land.]
Even where such a removal has taken place there will still be left a
certain portion of the suspended matters, and if these are in a finely
divided state, such as is probably the result of their passage through
fine strainers or pump valves, the work of the land will be
considerably lightened.
[Sidenote: Micro-organisms screened out in a mechanical way.]
The micro-organisms contained in the liquid will be to a large extent
screened out in a mechanical way with the suspended matters and
deposited on the surface and in the upper layers of the soil.
[Sidenote: Retention of matters in solution after removal out of the
liquid is due to physical and chemical agencies.]
The matters in solution will partly, after removal out of the liquid,
be retained by the absorbing powers of the soil in the pores, a
process that is due to physical and chemical agencies.
[Sidenote: Absorbing powers gradually ripen.]
It is well known that land which is being treated with sewage for the
first time does not purify sewage so well as land that has been under
systematic treatment for some time, and this is probably due to the
absorbing powers, which gradually ripen until they have reached their
maximum of efficiency. This process of gradual improvement seems to be
due to the formation of a slimy coating round each particle of soil,
which growth does not only assist mechanical filtration, but also
possesses high powers of absorbing oxygen.
[Sidenote: Depths to which polluting substances may penetrate into
soil.]
The depth to which polluting substances may penetrate into soil will
probably differ in each case, but the following factors may be said to
influence it, viz. the velocity of the downward flow, the nature and
degree of the polluting liquid, and the character of the soil. Where,
therefore, the powers of the soil are over-taxed the polluting
substances may reach the level of the underdrains and pass out through
them, in which case the effluent will be but little better than the
raw liquid. It must be the aim of careful management to avoid this.
[Sidenote: Process of decomposition of organic matters stored in soil
during periods of rest.]
The polluting substances of an organic nature thus stored in the pores
undergo here—and that probably chiefly during periods of rest—a
process of decomposition or disintegration, which goes on until the
whole of the organic matter has been converted into stable mineral
forms.
[Sidenote: Explanation of the term "self-purifying power of soil."]
This process of retention, absorption and decomposition of organic
impurities is called "the self-purifying power of soil."
[Sidenote: After conversion substances are removed out of the soil by
the plants, by the subsoil air and subsoil water.]
The substances thus converted do not remain in the pores, but they are
removed either by the plants, for which they act as food, or by the
currents of subsoil air, or by the subsoil water, and as the removal
of fertilising substances by the subsoil water indicates a waste it
must be the aim of a careful management to utilise them as much as
ever possible for the benefit of the plants.
[Sidenote: Process of digestion. "Sewage sick."]
The whole of these intricate and very complicated changes may be
likened to the process of digestion in animals, and when these
digestive powers are overtaxed signs of sickness may be noticed as the
inevitable result, which increase until, in sewage phraseology, the
land becomes "sewage sick." In this condition it remains until the
flow of the polluting liquid is stopped, when after a period of
rest—recreative period—the digestive powers gradually return and begin
to do their work afresh.
[Sidenote: Action of lime.]
When the soil of a sewage farm has got into this state, owing to
having received heavy doses of sewage, the application of lime has
proved very beneficial by accelerating the process of nitrification,
and in this respect interesting experiments have been made on the
Berlin sewage farms. The action of lime is said to be a twofold one.
1. It quickly attacks and splits up the organic matters and
accelerates afterwards their decomposition and their utilisation by
plants; and
2. It neutralises the excess of acid in the soil, and causes the
latter to part with its carbonic acid.
[Sidenote: Decomposition proceeds quickest at or near the surface.]
The process of decomposition proceeds as a rule at a much quicker rate
on the surface and in the upper layers of the soil, where, as already
mentioned, the number of micro-organisms is greatest.
[Sidenote: When carefully worked there is no time limit to the
purifying powers of the soil.]
It has been maintained that the soil of sewage farms will after a
while silt up and cease to purify sewage, but the results obtained
with carefully managed farms clearly disprove this, and under these
conditions there appears to be no limit as to time to the purifying
power of soil.
[Sidenote: Depth of soil necessary for purification.]
Concerning the depth of soil—evaporation zone—that is necessary for
the successful retention, absorption and decomposition of sewage, no
generally applicable rule can be laid down, as this will depend on a
variety of factors, amongst which may be mentioned: the character and
thickness of the top soil (humus), the nature and cultivation of the
top soil; the character of the subsoil—its permeability for air and
its retaining and absorbing powers; the surface <DW72>s of the land and
the level of the subsoil water.
[Sidenote: Greater depths than 4 ft. will be rarely necessary.]
On some farms a depth of 3 feet on an average has proved sufficient,
and on others the drains have been laid at depths ranging between 3
and 6 feet, but very special reasons ought to be shown for all depths
over 4 feet.
[Sidenote: Soil best suited for sewage farms.]
Whilst practically no soil is entirely useless for sewage farming,
with the exception perhaps of peat, owing to the quantity of moisture
it contains, a soil that combines great permeability for air with high
retaining and absorbing powers—such as a loamy sand with fairly large
grains—is probably the best.
[Sidenote: Clay soil not unsuitable for sewage farms, but it
necessitates a greater area of land.]
It has been maintained that clay, owing to its impervious character,
is totally unsuitable for sewage farming, but the experience of such
farms as South Norwood, Wimbledon, Warwick and Leicester disproves
this. It is true, however, that as the purifying powers of the soil
are restricted in a vertical sense to the upper layers, it may become
necessary in places to extend the area of the farm beyond what would
be necessary with a more pervious soil.
[Sidenote: Changes observed in the heavy clay land at Leicester since
sewage treatment was commenced.]
It may not be without interest to draw attention here to some of the
changes that have taken place on the Leicester sewage farm since the
land has received regular dressings of sewage. When I was engaged in
laying it out in 1888 my powers of locomotion over the land were
greatly impeded during wet seasons by the inordinate amount of clay
that adhered to the boots; but when engaged again for some
considerable time on the land during the winter 1900 to 1901 this
unpleasant peculiarity had completely disappeared even on land that
had recently been sewaged. Through the action of the sewage the very
dense clay had been disintegrated and become so pliable that, when
trod upon, it crumbled to pieces. The colour of the soil had been
changed from a yellowish-brown to a greyish-black, and altogether the
land had been greatly improved by the application of the sewage.
[Sidenote: Movement of liquid through the passage and capillary zones
to the impervious layer.]
If more sewage is poured upon the land than the effluent drains can
deal with—and here it may be well to bear in mind that on sewage farms
in our climate on a broad average throughout the year about one-third
of the total quantity is lost by evaporation—the excess will pass down
between the drains from the evaporation to the passage zone, and if
the flow of the sewage is not discontinued the downward movement in
the passage zone may be continued until, after having traversed the
capillary zone, the level of the subsoil water is reached.
[Sidenote: Length of downward movement of water may be very great.]
What length of time may elapse before this level is reached will
entirely depend on local circumstances, but it will be clear from the
preliminary remarks that the completion of this downward movement may
in places and under certain conditions take a very long time.
[Sidenote: Displacement of sewage held by the pores of the land by the
fresh discharge of sewage upon the surface of the land.]
In connection with this it is of importance to point out that not the
fresh sewage which is poured on the surface of the land will at once
pass into the lower layers, but a portion of the old sewage, which up
to then was stored in the pores and is now displaced by the fresh
discharge, so that the fresh raw sewage is retained and only purified
sewage allowed to escape into deeper layers, which means that in its
downward movement all sewage undergoes purification. Were this not the
case the raw sewage might reach the effluent drains.
It appears time now to examine somewhat more closely the processes of
decomposition and the products elaborated therein.
[Sidenote: Factors that influence the process of decomposition.]
Concerning the factors which have a favourable influence upon this
process, some of them, such as permeability for air, high retentive
and absorbing powers, have already been mentioned, and to these can be
added moisture and warmth, the latter of which are always present in
sewage.
[Sidenote: Advantages of a systematic underdrainage.]
One word here concerning the systematic under-drainage of the subsoil.
Its chief function is, of course, the carrying away of the effluent
water and by doing so to prevent the formation of a swamp, but after
the land has done its work, and during so-called periods of rest, the
under-drains act as ventilators of the subsoil and thus make it
artificially more permeable for air, with the result that a drying-up
action is set up and oxygen supplied for micro-organic life. For the
purpose of improving the ventilation of the soil it may become
advisable in places to connect the upper ends of the drains with a
short upcast shaft. The mouths of the drains should always discharge
above water so as to allow of a free circulation of air.
[Sidenote: Micro-organisms that carry on the work of splitting up and
converting organic compounds.]
The work of splitting up and converting the organic compounds is
primarily carried out by micro-organisms such as yeast fungi, mould
fungi, algæ, protozoa and even by higher forms of life such as
earthworms and insects.
To what extent in addition to these other agencies take part in this
bio-chemical process is not yet fully elucidated.
[Sidenote: Decomposition and putrefaction most complicated processes.]
Fischer in his interesting book, 'The Structure and Functions of
Bacteria,' observes (page 99): "The decomposition of dead animal
bodies, of vegetable tissues, or of substances like stable manure, is
far from being a simple putrefactive process. Side by side with the
disintegration of nitrogenous bodies there are going on a number of
fermentative changes by which non-nitrogenous compounds are being
broken up, besides nitrification and other bio-chemical processes. For
this reason it is always difficult and often impossible to determine
the respective parts played by the different species of bacteria.…
"The phenomena of putrefaction are so complicated that we do not know
all of the compounds that arise during the process.… Very careful
chemical investigations on pure cultures will be necessary before the
chaos of phenomena presented by putrefactive bacteria can be arranged
in something like order.
[Sidenote: In the decomposition of proteids five or rather six stages
may be distinguished.]
"Proteids are split up by putrefaction into a large number of simpler
compounds both nitrogenous and non-nitrogenous. The substances thus
produced are precisely similar to those resulting from the artificial
decomposition of proteids by fusion with caustic potash or boiling
with hydrochloric acid or barium hydrate. Five groups may be
distinguished:
[Sidenote: Albumoses and peptones.]
"1. Albumoses and peptones: soluble diffusible bodies closely
resembling albumen. They are produced by the action on albumen of
bacterial enzymes, similar to the enzymes (pepsin and pancreatin)
which give rise to peptones in the digestive tract of man.
[Sidenote: Aromatic compounds.]
"2. Aromatic compounds; among others indol and skatol, which give the
characteristic odour to human excrement; also some non-nitrogenous
substances such as phenol, phenylacetic acid, and phenylpropionic
acid.
[Sidenote: Amido compounds.]
"3. Amido compounds, all nitrogenous: leucin, tyrosin, aspartic acid,
glycocol.
[Sidenote: Fatty and aromatic acids.]
"4. Fatty and aromatic acids, all non-nitrogenous and therefore having
no part in the circulation of nitrogen; acetic, butyric, succinic and
valerianic acids.
[Sidenote: Inorganic end-products of putrefaction.]
"5. Inorganic end-products of putrefaction: free nitrogen, ammonia,
free hydrogen, methane, carbonic acid, methylmercaptan, sulphuretted
hydrogen. It is probable also, but not certain, that phosphuretted
hydrogen is formed and is oxidised at once by the free oxygen of the
atmosphere.
[Sidenote: Ptomaines.]
"Most of these substances are formed also by the chemical decomposition
of proteids, but there is a sixth group which may be termed specific
putrefactive products. These are the so-called ptomaines or
putrefactive alkaloids."
Some of these bodies are either not poisonous or only poisonous in
large doses, whilst others, derived from putrid foods of various kinds
(sausages, cheese), are highly toxic (ptomatropine, tyrotoxine).
[Sidenote: Definition of some terms.]
Concerning the work done by micro-organisms, it may not be out of
place here to define the meaning of certain terms, and to direct
attention at the same time to the modifications in the results brought
about by the presence or absence of air during the various stages of
the process.
The terms mineralisation, disintegration, oxidation, hydrolysis,
bacteriolysis, nitrification, decomposition, eremacausis,
putrefaction, fermentation, etc., have by many been used somewhat
promiscuously, and this has led to a good deal of confusion,
bewilderment and misconception. The cause of this has been undoubtedly
our small amount of knowledge concerning this process and the changes
brought about therein, but this would appear to be no reason why
complication should be made worse. For the purposes of these remarks
the undermentioned terms shall have the following meaning.
[Sidenote: Mineralisation.]
The term "mineralisation" is used for describing the whole process of
the disintegration and conversion of organic into mineral matter, and
no distinction shall be made between organic matter containing
nitrogenous and organic matter containing carbonaceous substances.
[Sidenote: Aerobic fermentation or decomposition.]
When this process of mineralisation is carried on in the presence of
sufficient quantities of air it is called "aerobic fermentation," or
"decomposition," which is generally characterised by the absence of
strong smells. The process may then be called one of complete
oxidation.
[Sidenote: Anaerobic fermentation or putrefaction.]
Where, however, the mineralisation proceeds in the absence of air the
process is called "anaerobic fermentation," or "putrefaction," and it
is then that very pronounced foul smells are emitted. The process may
then be called one of incomplete oxidation.
[Sidenote: Obligatory aerobes and anaerobes.]
[Sidenote: Facultative anaerobes.]
That class of micro-organisms which can only live in the presence of
oxygen is called "obligatory aerobes," and that which can only exist
in the absence of this gas "obligatory anaerobes." Between these two
is the group of "facultative anaerobes," which, while growing best
with a plentiful supply of oxygen, are nevertheless able to exist with
a very small amount, and even with none at all, although in this case
their vitality is often much impaired.
[Sidenote: Organic matters are first split up and then converted into
mineral substances.]
In the process of mineralisation two stages may be distinguished, viz.
the first or disintegration stage, and the second or oxidation stage,
i.e. the organic substances are first split up and afterwards
converted into inorganic ones; and frequently these processes are
taking place side by side and not after each other.
[Sidenote: The splitting up of organic substances is frequently
carried out in the presence of air.]
It has been maintained—probably with a view to justifying the
necessity of a septic tank—that the preliminary process of splitting
up is best carried out in the absence of oxygen, but sufficient proof
does not appear to have been advanced in support of this statement,
and in some cases at any rate it is evidently carried out quite
satisfactorily in the presence of air.
Concerning the presence or absence of oxygen, Fischer observes as
follows:—
"The effects of the presence of oxygen are somewhat better
understood. If air have free access, putrefaction
(decomposition) may go on without any odour at all, the
evil-smelling gases (NH{3} and SH{2}, for example)
being oxidised at once to form nitrates and sulphates.
Aerobic bacteria, too, such as the nitre and sulphur
bacteria, bring about this mineralisation of organic
nitrogen. Moreover, when air is circulating freely, there is
no accumulation of intermediate products such as skatol or
indol. It occurs on the surface of manure heaps, on the
outer surfaces of carcases, and in well ventilated soil.
"In anaerobic decomposition (putrefaction proper), as in
anaerobic fermentation, the organic molecules are at first
only partly disintegrated, intermediate products such as
leucine, tyrosine, skatol and indol being formed. In the
absence of air these accumulate, and hence it is that
putrefaction going on in the mud of ponds and ditches, or
inside carcases, is accompanied by such evil odours.
"Although the details of the process vary considerably,
according to the presence or absence of air, the ultimate
products of decomposition and putrefaction are in both cases
the same: namely, free nitrogen, free hydrogen, ammonia,
methane, carbonic acid and sulphuretted hydrogen. These are
also the end-results of the disintegration of the human
body.
"After the organic nitrogen of decomposing substances has
been converted into ammonia, and to a small extent into free
nitrogen, the latter can at once be utilised by the
root-nodule organisms and other bacteria in the soil, but
the ammonia must undergo two further changes and combine
with a base to form a nitric salt before it is available for
plant life. These two changes are brought about by bacteria,
which convert the ammonia first into nitrous and then into
nitric acid; this process has been called 'nitrification.'"
It will be clear from the foregoing remarks that the process of
mineralisation is a very complicated one, which under favourable
conditions, for instance in the pores of an open soil, may come to an
end fairly quickly, but which under very unfavourable conditions—such
as the interior of large heaps of refuse—may last many years.
[Sidenote: Chemical purification on sewage farms.]
Concerning the chemical purification effected on sewage farms, i.e.
the purification of the sewage as revealed by chemical analysis, it
has been put on record over and over again, and is now fully and
universally understood, that suitable land well managed is capable of
changing even the foulest sewage to a perfectly clear water devoid of
smell and danger, so that this point need not be laboured here. For
instance, on the Berlin sewage farms the degree of purification
attained has averaged for a period of 20 years 97 per cent., and on
the farm at Gennevilliers—one of the Paris sewage farms—the effluent
is so sparkling, bright and clear that the inhabitants drink it in
preference to other available water.
[Sidenote: Micro-organic purity of effluent from sewage farms.]
But in reference to the purity of the effluent as to the products of
micro-organic activity and pathogenic micro-organisms, it will be
necessary to make a few observations with a view to remove
misconceptions that have from time to time been put forward.
[Sidenote: Ptomaines have not been found in effluents from well
managed sewage farms.]
The question whether the specific products of putrefaction, i.e. the
putrefactive alkaloids "ptomaines and toxines," are capable of doing
further mischief by escaping with the effluent into the stream, may be
answered as follows. These substances are fortunately very unstable,
and the experiments conducted by Falk and others seem further to
indicate that soil is capable of retaining them and of rendering them
harmless. At any rate there is no well authenticated case on record
of these bodies having wrought mischief on sewage farms. (See here
also the remarks made on pages 51 and 52 under the heading "The
Absorbing Powers of Soil.")
[Sidenote: Pathogenic germs on sewage farms.]
It has further been maintained that the presence of pathogenic
organisms on sewage farms might in two ways lead to mischief, viz.
either by transmission through air or by transmission through water.
The pathogenic organisms after spreading over the land might rise into
the air through the movements of the atmosphere and then be carried
about by it, or they might escape through the land and be conveyed
with the effluent into the stream or river that takes the latter.
[Sidenote: Pasteur's fears as to mischief likely to be brought about
by pathogenic micro-organisms on sewage farms not borne out by facts.]
In connection with this point it may not be without interest to
mention here that even the late M. Pasteur at one time of his career
considered the wholesale spreading of disease germs on sewage farms
might prove highly injurious to the public health of the
neighbourhood. As he himself admitted, he based his fears on purely
theoretical considerations and opposed, for this reason, the extension
of the sewage farms in the neighbourhood of Paris. But when, later on,
he was made acquainted with the results observed on the Berlin farms,
he tacitly modified his views and ceased to oppose the extension of
the Paris farms.
[Sidenote: No well-authenticated case is on record where a sewage farm
has acted as the focus of a local outbreak of typhoid fever.]
Indeed, search as I might, I have not been able to discover one single
instance where a sewage farm has acted as the focus of a local
outbreak. On the contrary, during one or two small epidemics of
typhoid fever in Berlin, no case of this complaint has been observed
on the sewage farms of that city.
[Sidenote: Experience on the Berlin farms.]
Concerning the escape of pathogenic micro-organisms into streams and
rivers, no case is on record where such a thing has actually occurred:
indeed, the very painstaking investigations on the Berlin farms have
led to negative results.
[Sidenote: Observations made at the Freiburg sewage farm.]
Another sewage farm, that of Freiburg in Baden, has likewise been made
the subject of careful and long-continued investigation by Dr. Korn,
who, for the twelve months ending August 1897, made no less than 165
elaborate chemical and bacteriological examinations. Summing up his
observations on the presence of bacteria in the effluents from subsoil
drains, he remarks:
"Apart from the few exceptional cases of high numbers, generally
speaking my experiments show that the number of germs in the
subsoil drain effluents is relatively small, and even omitting
these experiments, in which a dilution with subsoil water must
have taken place, the number of micro-organisms is still so small
that the effects of filtration through soil are clearly
perceptible. In addition to this—and this is of considerable
importance in forming a judgment—it must be borne in mind that
the bacteria in sewage are principally derived from the
intestines, whereas in the subsoil drain effluents the
inhabitants of the intestines are either not present at all or
only in very small numbers compared with the number of soil and
water bacteria, which are always present. Out of 165 examinations
I only succeeded in 18 cases in proving the presence of bacterium
coli."
[Sidenote: Bacterium coli no longer a true criterion of sewage
pollution.]
[Sidenote: Dr. Weissenfels' conclusions.]
It may be convenient to point out in this place that bacterium coli
can no longer be looked upon as a typical inhabitant of the human
intestines after the very elaborate investigations carried out by Dr.
Weissenfels, who arrived at the following conclusions:
1. The so-called bacterium coli can be cultivated from almost every
kind of water, and its presence can be demonstrated in nearly every
case, provided a sufficient volume of water is utilised.
2. It is not possible by the result of the experiments upon animals to
decide whether the bacterium coli was cultivated from a pure or
infected water, and the discovery of a virulent bacterium coli in any
sample of water cannot, therefore, be regarded as a criterion that
such water has been polluted with fæcal bacteria.
After these remarks, it would seem quite possible that the bacterium
coli discovered in eighteen cases by Dr. Korn in the Freiburg
effluents was not derived from sewage at all but from the ordinary
subsoil water of the land.
[Sidenote: The possibility of further mischief by pathogenic
micro-organisms on sewage farms is exceedingly remote, if it exists at
all.]
Bearing these observations in mind, it is quite clear, therefore, that
neither theoretical investigations, as available up to now, nor
practical results, support the theory that pathogenic micro-organisms
may do mischief on sewage farms, and one is forced to conclude that
this possibility—if it exists at all—after systematic treatment on
land is an exceedingly remote one.
[Sidenote: Sewage farms reduce the quantity of final effluent.]
Before concluding these remarks on the natural purification of sewage
it is necessary to draw attention to another considerable advantage
which it possesses over artificial sewage treatments, and that is the
reduction in quantity of the effluent, which at times is very
considerable, whereas in the artificial methods such a reduction is
comparatively small.
[Sidenote: Loss of liquid by evaporation and by plant life.]
Spread over a large area of land, well cropped, evaporation is very
active—especially during the summer months, when the flow of water in
the brook that takes the effluent is as a rule at its lowest; and, in
addition to this, the growing plants further abstract a considerable
amount of the liquid that finds its way into the soil, so that the
quantity of the effluent may not be more than from 30 to 50 per cent.
of the total quantity that was poured over the land. In the artificial
treatment the evaporation is considerably smaller, and as plants are
altogether absent the quantity of the effluent is probably about 90
per cent. and more of the total quantity of the raw sewage. This is a
point of very considerable importance so far as the influence of the
effluent upon the water in the stream that takes the same is
concerned.
Although the subject of natural purification is by no means exhausted,
it is now time to direct attention to artificial methods.
V. ARTIFICIAL SELF-PURIFICATION OF SEWAGE.
1. GENERAL OBSERVATIONS.
[Sidenote: Enumeration of more important experiments.]
A great many experiments have been made during the last ten years with
artificial processes for the self-purification of sewage, and amongst
the more important the following may be mentioned:
London experiments.
Sutton "
Exeter "
Manchester "
Leeds "
Sheffield "
Leicester "
York "
Hamburg "
[Sidenote: Experiments have not been conducted on uniform lines.]
A casual observer might, therefore, consider himself justified in
thinking that all these experiments had added a great deal to our
knowledge of the intricate changes taking place in these processes,
but such a conclusion would not be justified in reality. For beyond
settling questions of local importance by chemical analysis, the
experiments, owing to a variety of causes, have not materially
enhanced the stores of our information, indeed not unfrequently the
results obtained are apparently contradictory and bewildering.
An experiment must be looked upon as a question addressed to nature,
and the answer will depend on the way the question has been put. If
this way differs in every case it must be clear that the answer, too,
will differ in every case, and it is this absence of uniformity which
greatly reduces the general value of these experiments.
These remarks must not be misunderstood to convey the impression as if
the experiments had not been conducted with care and skill! Far from
it! Some of them have been made with the greatest skill and care and
with the very evident desire to arrive at correct conclusions, and it
is only when they are placed side by side with other experiments, with
a view to deducing from them general conclusions concerning the
processes at work, that great difficulties are experienced. The result
of each experiment is governed by a large number of factors, which by
slightly different manipulations may attain in this ever-fluctuating
process different weights, so that the results may be contradictory,
and it is only by arranging these factors on a common basis, as it
were, and by addressing the questions to nature in the same systematic
and uniform way, that good general results may be expected.
It is well known, for instance, that in some cases septic tanks have
not given good results, whilst in others they have worked very well;
again, continuous filtration has failed in some experiments, whilst in
others, notably in the York experiments, it has given good results.
If, therefore, in future the mistake of the past is to be avoided, it
will be necessary to settle on a common line of action in all
experiments.
[Sidenote: Attempt to evolve general theory.]
In spite of all the difficulties which beset such a task, an attempt
will be made in the following observations to evolve some general
theory concerning the processes at work in the artificial
self-purification of sewage. Such a theory, it is quite clear, cannot
be complete in the present state of our knowledge, and it is sincerely
hoped that the many and serious gaps will be filled up by later
investigations.
For convenience of reference the different forms of the process, such
as are now employed, shall be dealt with separately, commencing with
contact or oxidation beds.
2. ARTIFICIAL SELF-PURIFICATION OF SEWAGE IN INTERMITTENT CONTACT
BEDS.
At the outset it may not be out of place to make a few remarks
concerning the various names given to this form of application. The
term "intermittent contact bed" is here used to distinguish this kind
of bed from the "continuous contact bed," frequently called
"continuous filtration."
[Sidenote: Names of process misleading.]
(_a_) _Name of Process._—This process has frequently been called
"biological process," "bacteriological process," "contact bed system"
or "oxidation bed system," but all these terms do not appear to define
it sufficiently, as they do not cover the whole, but only phases or
stages in the same; hence, they do not seem appropriate.
[Sidenote: Biological process.]
The name "biological process" is decidedly misleading, for besides
biological agencies there are also at work physical (mechanical) and
chemical ones.
[Sidenote: Bacteriological process.]
The term "bacteriological or bacterial process" is likewise erroneous,
for besides bacteria a number of other micro-organisms participate in
it—such as yeast fungi, mould fungi, algæ, protozoa, and even higher
forms of life, such as earthworms and insects.
[Sidenote: Contact bed system.]
[Sidenote: Oxidation bed system.]
The expressions "contact bed system" or "oxidation bed system" are in
so far inappropriate as they describe only portions of the process but
not the whole. The term "contact bed" describes the first stage, and
the term "oxidation bed" portion of the second stage only.
[Sidenote: Term most suitable.]
The term which seems most suitable of all is "artificial
self-purification in contact beds," as it includes every phase of this
lengthy process applied in an artificial form; the term "natural
self-purification" being applied to land treatment of sewage, as it is
the only method in which the self-purifying powers are employed under
natural conditions.
[Sidenote: Working operations.]
(_b_) _Explanation of Process._—The cycle of operations commences with
the filling of the bed, and during the same the sewage comes gradually
in contact with the filling material. When the bed is full, the inflow
is stopped and the sewage allowed to remain in contact with the
material for some time. The bed is then emptied, and a period of rest
is given it before the filling is commenced again.
[Sidenote: Purification of sewage in full bed due to absorbing powers
of filling material and only to a small extent due to activity of
micro-organisms.]
It has been held, that while the sewage is in the contact bed it
undergoes a very rapid process of decomposition by bacteria, but it
must be evident, that as the sewage—including filling—remains only for
about two hours in the bed, the micro-organisms would have to work at
an express rate. This fact alone is apt to make this theory very
doubtful, but apart from it, it has been proved by experiments that
the by far greater amount of purification—whilst the sewage is in the
beds—is due to the absorbing powers of the filling material, which are
derived from the surface attraction of its component particles.
[Sidenote: Retention of suspended matters by bed.]
[Sidenote: Absorbing powers of filling material.]
The filling material retains in its upper layers the suspended
matters, which it strains out of the sewage in a purely mechanical
manner, much after the fashion of a screen, and when the bed is filled
its absorbing powers come into play, which cause the removal of the
dissolved matters out of the liquid and their retention on the surface
of the particles. This latter process is probably a chemico-physical
one assisted by the micro-organic life in the sewage.
[Sidenote: Decomposition of organic substances by micro-organisms when
bed is empty.]
It is only after the bed has been emptied that the real activity of
the vast number of micro-organisms commences, which is directed
towards converting the organic substances into mineral ones. This
process of splitting up, decomposing, disintegrating and mineralising
organic waste products is an exceedingly complex one, which ever
fluctuates according to the prevailing conditions, and which does not
come to an end until finally stable mineral forms are reached. In the
presence of a plentiful supply of oxygen, the process proceeds as a
rule at a more rapid rate, and the intermediate forms produced are
less complex than in the comparative or total absence of this gas;
hence the progress of the process is largely determined by it. The
amount of oxygen necessary for bacterial activity is partly
abstracted, and with extraordinary energy, from the atmospheric air in
the pores of the filling material, and a portion of the substances
formed, such as carbonic acid and nitrogen—in gas form—escape into the
atmosphere, whilst the remaining portions are washed out of the bed
with other products, such as nitric acid, by the effluent.
Further remarks upon this process of mineralisation have been made in
connection with the subject of natural self-purification of sewage,
and these may be referred to here.
[Sidenote: Effluent from bed practically raw sewage as far as its
bacterial contents are concerned.]
The effect of the bed upon the bacterial flora of sewage is, as was to
be expected, but very slight, and it is on record now that, as far as
the micro-organic life is concerned, the effluent is to all intents
and purposes raw sewage.
[Sidenote: Silting up of bed.]
Some of the substances contained in raw sewage remain in the bed, no
matter how carefully the sewage has been previously strained, and
these, in combination with the slimy surface coating of the component
particles, the accumulation of mineralised substances in the pores,
the consolidation of the bed, the disintegration of the filling
material, and the liquid retained, lead gradually but surely to the
silting or sludging up of the bed.
[Sidenote: Theoretical original water capacity of bed.]
(_c_) _Water Capacity of Bed and Silting up._—The theoretical water
capacity of the bed, previous to commencing operations, is the
aggregate of the cubical space occupied by the pores or small passages
between the particles forming the filling material, and the pores of
the filling material itself; but in practice a certain amount of this
space is occupied by air, which it is impossible to dislodge
altogether in filling. The aggregate of the cubical space of the pores
may be called the pore-volume.
It is difficult to lay down general rules as to what the original
water capacity of a bed should be expressed in per cent. of the space
occupied by the filling material, but speaking within fairly wide
limits the following is somewhat near the truth.
[Sidenote: Original water capacity with spherical particles of uniform
size.]
When the particles forming the filling material are fairly spherical
and of equal size, the original water capacity of a bed amounts to
about 38 per cent. of the space occupied by the filling material; but
as in practice it is difficult to obtain spherical particles of
uniform size, the original water capacity is found to range from 35 to
45 per cent. of this space.
[Sidenote: Original water capacity with particles of different sizes.]
When, however, the particles are of materially different sizes, and
when the smaller ones fill up the spaces between the larger ones, the
original water capacity may sink down to as low as from 5 to 10 per
cent. of the space occupied by the filling material.
[Sidenote: Size of particles of filling material does, under certain
conditions, not affect original water capacity of bed.]
It has been further demonstrated that the water capacity of a bed is
not affected by the size of the particles, provided the latter are
spherical and of uniform size. In other words, the water capacity of
two beds filled with material of different sizes is the same, provided
the particles are spherical and of uniform size throughout each bed.
[Sidenote: Silting up of bed during regular work.]
[Sidenote: Rapid initial decrease of capacity.]
[Sidenote: Consolidation of bed.]
This original water capacity is, however, not maintained in regular
work, as has been pointed out already. Basing the observations on
regular work only, the original capacity decreases at first, after a
new bed has been started or after an old reconstructed bed has been
taken in hand, rapidly for some time and afterwards more slowly.
Graphically expressed, this decrease is not represented by a straight
line but approaches more nearly a parabolic curve. This initial rapid
decrease is chiefly due to the consolidation of the bed.
[Sidenote: Disintegration of filling material.]
In connection with the movements in the bed tending towards its
consolidation, it is also clear that the continual filling and
emptying operations cause the smaller particles to be washed out of
their original position and to be placed in the larger passages
between the filling material, and if this process is assisted by the
gradual disintegration of the particles composing the filling
material, it is clear that the pores must become smaller and smaller
in time, i.e. choked.
From these observations it follows that the filling material should be
a hard substance, which will only to a limited extent be subject to
this crumbling away process.
But besides these there are, as has already been pointed out, other
silting up agencies at work.
[Sidenote: Water-retentive power of filling material.]
Of the total quantity of sewage which has entered the bed a small
portion will always remain in it owing to the water retaining power of
the material. This power has sometimes been called "minimum water
capacity," but as this name is liable to be misunderstood, it is
better to adopt here the term "water-retentive power" of material.
The quantity of the sewage retained by the bed varies with the
material and pore-volume, and is due to adhesion and capillary
attraction. The greater the pore-volume, and the greater the
percentage of fine pores, the greater is the quantity thus retained.
Clean gravel retains about 12 per cent. and fine sand about 84 per
cent. of its water capacity—i.e. expressed per cubic yard of filling
material, one cubic yard of clean gravel will retain about 10 gallons
and one cubic yard of fine sand about 70 gallons of water.
Through draining a bed for several hours through evaporation and other
atmospheric influence, a portion of the sewage retained is lost, but
the quantity so lost will vary continually with the circumstances
under which the bed is worked.
The water-retentive power of the filling material does not decrease
with the working of the bed, but increases, which in a large measure
is probably due to the slimy coat which forms round the surface of the
component particles, and to which reference is made in the following
paragraph.
[Sidenote: Slimy surface coating of component particles.]
A further silting-up agency is the slimy surface coating of the
particles of the filling material. This accumulation is well known to
all who have had to do with intermittent contact beds, and has been
described as spongy bacterial growth. The Manchester report for the
year ending March 27, 1901, contains on page 62 the following passage:
"This (spongy bacterial growth) is at once the cause of increased
efficiency in the bed and loss of capacity. On examining the material
of a contact bed in active condition, every piece is seen to be coated
over with a slimy growth. If this is removed it soon dries to a stiff
jelly, which can be cut with a knife. Under the microscope masses of
bacteria and zoogloea will be found to be present."
[Sidenote: Accumulations of decomposed substances in the pores.]
In addition to this slimy surface-coating of the particles, there are
also found in the pores, especially in the upper layers of the filling
material—and in fine beds more so than in a coarse bed—accumulations
which are "akin to humus or garden soil." They contain to a limited
extent only putrescible substances, and appear to be the remains of
organic matter decomposed by the activity of micro-organisms.
[Sidenote: Periods of rest will not permanently restore portion of the
original water capacity of the bed.]
It was formerly maintained with considerable persistency that periods
of rest would permanently restore to a systematically worked bed a
portion of its lost water capacity, but such a contention has been
proved to be wrong. It is quite true that immediately after periods of
rest an increase of the water capacity is very noticeable, which is
probably due to drying up processes within the bed during the rest,
but such an increase is not permanent and is lost again more or less
quickly; it is therefore only temporary and not permanent.
Where, however, a bed has not been systematically worked, i.e. where
it has been worked at a greater rate than is suitable, and where in
consequence of this a large quantity of undecomposed substances is
stored in it, a period of rest may permanently restore a portion of
the lost capacity; but this is due to the mineralisation of these
undecomposed organic substances during the rest.
It follows from these remarks, as has been stated above, that when the
organic substances are regularly decomposed during systematic work a
period of rest cannot materially affect the water capacity, and that
where a considerable permanent restoration of the water capacity takes
place the bed has not been properly worked.
[Sidenote: Decrease of capacity is accompanied to some extent by
increase of efficiency and _vice versa_.]
It would, however, be incorrect to assume that the silting up of the
bed affects its efficiency besides reducing the capacity. On the
contrary! To some extent decrease of capacity is accompanied by
increase of efficiency and _vice versa_!
[Sidenote: Higher capacity of beds in summer than in winter.]
At this point it ought to be stated that in the Manchester experiments
(see page 61 of the report for the year ending 27th March, 1901) a
higher average capacity is maintained during the summer than during
the winter, which is no doubt due to the greater activity of the
micro-organisms during the warm weather of the year.
[Sidenote: Raking of beds not advantageous.]
The raking of the surface does not materially affect the capacity of
the bed, and it is better to scrape off the matters retained on the
surface than to rake them into the body of the bed.
[Sidenote: Renovation of filling material either partially or wholly.]
It will be clear from these observations that, no matter how carefully
the bed has been worked, sooner or later a time will come when the
decrease of capacity becomes so pronounced as to render it impossible
any longer to treat the daily flow of sewage with the available plant;
and when this point has been reached a renovation, either partially or
wholly, of the filling material becomes an inevitable necessity.
[Sidenote: Minimum capacity of beds to be provided for.]
To provide for this at the outset, and thus avoid the difficulties of
reduced capacity, it seems advisable to lay down, when designing the
works, a minimum capacity, which will just allow the daily volume of
sewage to be treated by the plant, and which when reached will
necessitate the cleansing of the bed.
The idea, formerly frequently expressed, that the filling material
when rationally worked need not be renewed or renovated, can no longer
be maintained and is outside the reach of practical possibilities.
[Sidenote: Underdrainage of intermittent contact beds.]
At this place a word or two about the under drainage of intermittent
contact beds may not be out of place. It is of the greatest importance
that all drains should work well, and that the entrance of the sewage
into them should not lead to disturbance in the filling material,
especially should the tearing of portions of the filling material into
the drain pipes be avoided.
By carefully arranging the position, number, size and fall of the
master drains and branch drains, it is possible to reduce the
resistance so as to allow of a fairly even flow of sewage through all
the drains, and to prevent a great rush of water through the drains
near the outlet end.
[Sidenote: The presence of lime is of no consequence.]
In passing it may not be out of place to point out that the view,
formerly expressed, that an admixture of lime in some form would prove
advantageous to the purification of sewage, is not supported by the
experience gained.
[Sidenote: Absorbing effect increases with the time of contact.]
(_d_) _Absorbing Powers of Filling Material._—The absorbing effect of
any filling material seems to increase with the time of contact.
[Sidenote: Absorbing powers increase until bed has become ripe.]
It ought further to be pointed out that the absorbing powers of the
filling material gradually increase until the bed has become ripe.
This fact was formerly stated to be due to the development of the
proper micro-organisms within the bed, but it would seem to be
chiefly due to the slimy surface coating of the particles of the
filling material, or spongy bacterial growth, as it has frequently
been called, which does not only assist mechanical filtration but also
possesses high powers of absorbing oxygen.
[Sidenote: Absorbing powers soon cease in the absence of
micro-organisms and air.]
But it cannot be open to doubt that the absorbing powers of the
filling material are dependent in some way or other on the presence of
micro-organisms, for Dunbar has shown that in the absence of
micro-organisms and without periods of aeration these powers soon
cease.
[Sidenote: Oxygen is absorbed from air in the pores with great
energy.]
(_e_) _Consumption of Oxygen by the Filling Material._—The oxygen
necessary for the proper work of an intermittent contact bed is
abstracted with great energy from the atmospheric air, with which the
pores become filled during periods of rest. Through diffusion, and
through the vacuum created by the processes of absorption, further
quantities of oxygen are taken from the atmospheric air, even under
difficult conditions, and, as pointed out in the Manchester report for
the year ending 27th March, 1901, "there is, therefore, little need to
force air into a bed."
[Sidenote: The oxygen taken up during aeration is not imparted to the
sewage at the next filling and does not escape in the effluent.]
The oxygen thus taken up is not imparted in gas form to the sewage
during the next filling, and the effluents from intermittent contact
beds are not saturated with oxygen. Dunbar states that the effluents
of a satisfactorily worked bed frequently only contain one cubic
centimetre of free oxygen per litre. Clowes reports a similar result
in his third report on the London experiments.
[Sidenote: The greatest quantity of oxygen is consumed during the
oxidation of the products formed by micro-organisms.]
There can be no doubt that by far the greatest quantity of oxygen is
consumed during the process of oxidation of the products formed by
micro-organisms from putrescible organic substances.
[Sidenote: Consumption of oxygen and formation of carbonic acid not
solely due to biological agencies.]
(_f_) _Formation of Carbonic Acid._—Dunbar has shown by his
experiments that the consumption of oxygen and the formation of
carbonic acid is not solely due to biological agencies, but is to some
extent the result of physico-chemical processes.
[Sidenote: More free carbonic acid contained in the effluent than in
the raw sewage.]
[Sidenote: By far the greatest portion of carbonic acid escapes into
the air.]
He further reports that in his experiments the effluents contained on
an average 100 milligram per litre more free carbonic acid than the
raw sewage, and that the quantity contained in the effluents
represents only a small portion of the total amount of carbonic acid
formed during the whole process. The by far greatest portion of
carbonic acid escapes into the air. Concerning the air in the pores of
the filling material during periods of aeration, Dunbar states that it
contains sometimes not less than from 6 to 10 per cent. carbonic acid.
[Sidenote: Nitrogen escapes in gas form into the air.]
(_g_) _Nitrogen._—It is quite clear from all experiments that a
considerable amount of the total nitrogen contained in raw sewage is
abstracted by the filling material of intermittent contact beds, and
it is interesting to ascertain what becomes of it! Does it accumulate
in the bed? In that case, one has a right to assume that the
satisfactory work of the bed would gradually cease! As this is,
however, not the case, and as, further, the sludge formed in the bed,
whether it be fairly fresh or very stale, only contains a very small
amount of total nitrogen, we must surmise that the nitrogen after its
retention by the bed escapes in gas form—like the carbonic acid—into
the atmosphere.
[Sidenote: The presence of nitric acid is not an unfailing guide for
determining the satisfactory character of the effluent.]
(_h_) _The Formation of Nitric Acid._—Concerning the presence of
nitric acid in the effluents from intermittent contact beds, Dunbar is
of opinion that it offers certain means for forming an opinion of the
processes taking place in the same, but that it is only in a
subordinate sense an indication of the degree of purification attained
and must not be taken as an unfailing guide for determining the
satisfactory character of the effluent.
[Sidenote: Nitrifying bacteria always present in town's sewage.]
[Sidenote: Nitric acid is formed very rapidly, but only during periods
of rest.]
Nitrifying bacteria are always present in ordinary town's sewage, but
it would appear that other micro-organisms besides Winogradsky's
bacteria assist in the process of nitrification. Nitric acid is formed
very rapidly, but only during periods of rest, and besides aeration
other less powerful influences are at work.
[Sidenote: Reduction of nitric acid when bed is filled from bottom
with an upward flow.]
It is further interesting to note that, according to Dunbar, the
greater portion of nitric acid which has been formed during periods of
aeration becomes completely reduced in a very short time, when the bed
is filled with an upward flow from the bottom, and that only a small
portion remains in the form of nitrous acid.
3. ARTIFICIAL SELF-PURIFICATION OF SEWAGE IN SEPTIC TANKS.
[Sidenote: Septic tanks only used in combination with contact beds.]
Although it has never been claimed, and is further not open to doubt,
that a septic tank alone and unaided by subsequent treatment in
intermittent or continuous contact beds does not sufficiently purify
the sewage, in these remarks the work of the septic tank only will be
considered, as the treatment in contact beds will be dealt with
separately.
[Sidenote: Septic tank a suitable name.]
(_a_) _Name of Septic Tank._—A good many names have been suggested by
different observers—such as "anaerobic fermentation tank," "putrefying
tank," "liquefying tank," "cess-pit," etc.—but there appears to be no
reason why the name "septic tank" should not be adhered to, as it
describes sufficiently correctly the work done by the tank, which is
chiefly of a septic nature.
(_b_) _Covered or Open Septic Tank._—Before dealing with the processes
taking place in a septic tank, it will not be out of place to consider
here, shortly, whether a closed septic tank confers advantages over an
open septic tank sufficiently great to justify the considerably
greater expenditure necessitated by its construction.
It is well known, that at Exeter in the first experimental
installation of this process, the septic tank was covered in by an
arched roof; but subsequent experiments made elsewhere do not seem to
support the theory then advanced, that such a tank should be a closed
one. This is chiefly due to the thick skin which, after a few months'
work, forms on the surface of closed or open tanks, and which
according to locality and season may reach a thickness of from 1 to 2
feet; it is maintained then that this cheap natural cover does away
with the expensive artificial cover.
In the report on the treatment of the Manchester sewage, by Messrs.
Baldwin Latham, Percy F. Frankland and W. H. Perkin, it is stated on
page 54, amongst the conclusions and recommendations, as follows:—"The
anaerobic or septic process is found to take place as effectively in
an open tank as in a closed one." This conclusion does not appear to
have been modified by the experiments made subsequent to the issue of
this report.
In the Leeds experiment a similar result was obtained.
[Sidenote: Closed septic tanks possess generally speaking no
advantages over open ones.]
Whilst it would, therefore, appear to be correct to say, generally,
that closed septic tanks afford no material advantages over open ones,
so far as the purification of the sewage is concerned, they may become
necessary in special cases, when the smells emanating from open ones
might create nuisances in crowded neighbourhoods.
The following remarks refer, therefore, equally to open as well as to
closed septic tanks, and no distinction will be made between them.
[Sidenote: The work in the septic tank is chiefly done by obligatory
anaerobes.]
(_c_) _Explanation of Process._—Although the processes taking place in
septic tanks are at present but imperfectly understood, they may be
said to be in the main due to anaerobic micro-organisms, i.e. due to
such micro-organisms which carry on their life's work in the absence
of oxygen. They split up or peptonise the organic compounds in the
absence of air, and the group of changes brought about by them has
been termed "anaerobic fermentation" or "putrefaction." During the
same, it is claimed that a considerable amount of the sludge retained
in the tank is liquefied or destroyed, and that the rest becomes so
changed as to be denser than ordinary sludge, and to contain less
moisture.
[Sidenote: Dissolved matters entering and leaving the septic tank.]
Concerning the amount and nature of the dissolved matters entering and
leaving an open septic tank, the following is taken from the
Manchester report for the year ending March 27, 1901:—
[Sidenote: Manchester observations.]
"A series of determinations have been made of the amount of
dissolved matter entering and leaving the tank, by evaporating
known volumes of the sewage and effluent after filtration through
paper and weighing the solid residue.
"An average of six determinations (confirmed by similar
observations in connection with the closed septic tank) gave the
following results:—
----------------------------------+--------------------------------
Raw Sewage. | Open Septic Tank Effluent.
Dissolved matter, grains | Dissolved matter, grains
per gallon. | per gallon.
------------+--------------+-------+----------+-------------+-------
| Organic and | | | Organic and |
Mineral. | Volatile. | Total.| Mineral. | Volatile. | Total.
-----------+--------------+-------+----------+-------------+-------
33·0 | 33·0 | 66·0 | 30·8 | 25·0 | 55·8
| | | | |
| | | Reduction, in per cent.
| | | 6·67 | 24·24 | 15·45
-----------+--------------+-------+----------+-------------+-------
"A certain amount of loss of ammonia, as ammonium carbonate, will
take place on evaporation in both cases, and this will probably
be greater with septic tank effluent.
"An examination of the residue obtained by evaporating large
quantities of open septic tank effluent (filtered through paper),
shows that the mineral matters largely consist of iron oxide,
from the decomposition of organic compounds of iron, and calcium
sulphate. Among the volatile constituents have been detected
ammonium carbonate, mercaptan-like compounds of very offensive
smell, acetic and butyric acids. No evidence of the presence of
amines could be found in the residue on evaporation, but by
distilling large volumes of the liquid and carefully analysing
the platinum salts obtained from the distillate, the presence of
amines is indicated.
"Research in this direction is being continued; careful
comparison especially will be made of the products obtained by
evaporation and distillation of crude sewage and septic tank
effluent respectively.
"The evidence, however, points to a breaking down of albuminoid
and cellulose matter in the septic tank into simpler and to some
extent volatile compounds. The reactions are probably hydrolytic
in character, ammonia, amines, carbonic acid, water, and possibly
alcohol, being produced.
"A further quantity of organic matter also disappears as methane,
nitrogen and hydrogen."
[Sidenote: Must aerobic fermentation in all cases be preceded by
anaerobic fermentation?]
It will be clear from the foregoing, that the changes going on in a
septic tank are entirely different from those brought about in contact
beds, and the question whether a septic tank is a necessity for the
subsequent contact bed treatment, or whether it is a distinct
disadvantage, can only be definitely settled when we know whether
aerobic fermentation, i.e. decomposition, must in all cases be
preceded by anaerobic fermentation, i.e. putrefaction, and to what
extent, or whether such a succession of changes is not necessary.
[Sidenote: At Manchester contact beds accustomed to septic tank
effluent did not at once purify raw sewage.]
It is interesting to note in connection with this point, that during
the Manchester experiments it was established that contact beds, which
have become accustomed to septic tank effluent, will not at once
purify comparatively fresh sewage.
(_d_) _Velocity of Flow through Tank._—The velocity of flow through
the septic tank is of great importance, as on it depends the size of
the installation.
It seems to have become a habit to express this velocity by the length
of the sojourn of the sewage in the septic tank—for instance, "the
flow of sewage through the tank was such that it would fill it in
twenty-four hours"; but as all tanks vary in size, and as in
consequence the distance which has to be traversed by the sewage from
the entrance to the exit in twenty-four hours is different in nearly
every case, such a habit is, to say the very least, very misleading.
It will not be disputed that the deposition of the suspended solids in
sewage is dependent on the rate of movement of the liquid, and that in
a quickly moving liquid there will be less deposition than in a very
slowly travelling liquid.
-----------------+----------+---------+-----------+-------------
Town. | Length. | Width. | Depth. | Contents.
-----------------+----------+---------+-----------+-------------
| | | |
| feet. | feet. | ft. in. | gallons.
Manchester tanks | 300 | 100 | 6 0 | 1,125,000
| | | |
Leeds " | 100 | 60 | 7 7 | 250,000
-----------------+----------+---------+-----------+-------------
Bearing this in mind it will not be without interest to examine the
velocities employed during the Manchester and Leeds experiments. The
tanks employed in these have the dimensions given in the table on the
preceding page.
Now assuming that each tank is to be filled once in twenty-four hours
we obtain the following velocities:
Manchester (300′ 0″ × 12″)/1440 = 2″·5 per minute.
Leeds (100′ 0″ × 12″)/1440 = 0″·84 per minute.
Which means that in the Manchester experiments the velocity would have
been three times as large as in Leeds; and it is clear that if the
sewage of both towns was identical the results, so far as the
retention of the suspended matters in the tanks are concerned, could
not have been identical. As a matter of fact, considerably greater
velocities have been used in the Manchester experiments, as will be
shown later on.
[Sidenote: Rate of flow through septic tanks should not be expressed
by the length of sojourn in tank but by some linear measurement in a
stated time.]
It will be clear from this, that it is most misleading and erroneous
to express the rate of flow by the length of the sojourn of the sewage
in the tank, and that the velocity should in each case be expressed by
some linear measurement in a stated time—probably inches per minute.
The next point to consider is the velocity to be employed in septic
tanks; and here it is not without interest to refer to the various
experiments enumerated with their results in the next table.
The difference in the results obtained, so far as the suspended
matters are concerned, is probably due to the different character of
the various sewages experimented with; but so low a velocity as 0·52
inch, as used in the Exeter experiments, does not appear to be
necessary.
In the Leeds experiments, it was found that the filling of the tank
once in twenty-four hours gave the best results; and as the velocity
then was 0·84 inch per second it will be somewhat near the mark to
recommend generally a velocity of 1 inch per minute. On the assumption
that the sewage shall remain twenty-four hours in the tank, this gives
a length of tank of 120 feet, which is a very suitable one.
SEPTIC TANK EXPERIMENTS.
_Rate of Flow and Deposition of Suspended Matters._
-----+------------+-----------------------+
| | Rate of Flow. |
| +-----------------------+
| | | |
No. | Name of | Length of | Velocity |
| Town. | Sojourn | of Flow |
| | of Sewage | per |
| | in Tank. | minute. |
| | | |
-----+------------+-----------+-----------+
| | | |
| | days. | inches. |
1 | Exeter | 1·0 | 0·52 |
| | | |
2 | Manchester | 0·44 | 5·58 |
| | | |
3 | " | 0·56 | 4·44 |
| | | |
4 | Leeds | 0·5 | 1·68 } |
| | | |
5 | " | 1·0 | 0·84 } |
| | | |
6 | " | 2·0 | 0·42 } |
-----+------------+-----------+-----------+
-----+-----------------------------------------------
| Suspended Matters in Sewage.
|-----------+-----------+------------+----------
| | | |
No. | Remaining | Destroyed | Leaving |
| in | and | Tank | Total.
| Tank. | Liquefied | in |
| | in Tank. | Effluents. |
| | | |
-----+-----------+-----------+------------+----------
| | | |
| per cent. | per cent. | per cent. |
1 | 17 | 39 | 44 | 100
| | | |
2 | 41 | 22 | 37 | 100
| | | |
3 | 23 | 33 | 44 | 100
| | | |
4 | .. | .. | .. | ..
| | | |
5 | average | 28 | .. | ..
| say | | |
6 | | .. | .. | ..
-----+-----------+-----------+------------+----------
[Sidenote: Septic tanks reduce the sludge difficulty to some extent,
but do not altogether remove it.]
(_e_) _Destruction and Liquefaction of Sludge in Septic Tanks._—It was
formerly maintained that the employment of a septic tank did away with
all sludge difficulties, and one sees even now advertisements to that
effect, that there is "no sludge" with a septic tank; but experience
everywhere does not bear out this contention. On the contrary, there
must be sludge with a septic tank, and the only question one has to
consider is, to what extent does a septic tank reduce the quantity of
sludge?
The table above contains the results obtained in the various
experiments, and from these it would appear as if on an average, with
a velocity of 1 inch per minute, 25 per cent. of the total sludge
would be destroyed or liquefied in a septic tank. Generally speaking,
therefore, the following figures will be somewhat near the mark, where
the plant is worked systematically and carefully supervised.
Per cent.
Suspended matters remaining in tank 35
" " destroyed or liquefied in tank 25
" " escaping in effluent 40
---
Total 100
These figures mean that 35 per cent. of the total suspended matters
will have to be dealt with as sludge, 25 per cent. will be destroyed
or liquefied in the septic tank, and the remaining 40 per cent. will
be deposited on and in the contact beds.
It has already been pointed out that it is claimed that the septic
tank sludge is denser and contains less moisture than ordinary sludge,
and that about half of it is mineral matter.
As previously stated, at Manchester a reduction of about 16 per cent.
in the dissolved matter has been observed in the open septic tank.
(_f_) _Formation of Gas in Septic Tank._—It was at one time suggested
that the gases formed in septic tanks during anaerobic fermentation
might be utilised for lighting or heating purposes, but anyone well
acquainted with the subject will admit that such a use is outside the
range of practical possibilities.
At Manchester, 100 gallons of sewage evolved in twenty-four hours
about a cubic foot of gas, which on an average contained:
Per cent.
Marsh gas, CH{4} 73
Carbon dioxide, CO{2} 6
Hydrogen, H 5
Nitrogen, N (by difference) 16
---
Total 100
At this rate 1 million gallons of sewage will evolve 10,000 cubic feet
of gas, or 0·2 tons of gas, in twenty-four hours.
[Sidenote: Septic tank effluent more suitable for nitrification.]
(_g_) _Mixing Action of Septic Tank._—There is one advantage possessed
by a septic tank which cannot be disputed, and that is the mixing
action going on within it. The fresh sewage on its arrival becomes
mixed with stale sewage, and, owing to the rising of lumps of sludge
from the bottom, and other causes, the contents of the tank become of
a more uniform composition, which must entail a corresponding
advantage for the subsequent contact bed treatment.
[Sidenote: The septic tank effluent is so far as bacterial purity is
concerned practically raw sewage.]
(_h_) _Micro-organisms in Effluent from Septic Tank._—Although the
available number of experiments on the micro-organisms contained in
the effluent from a septic tank is not large, yet they support the
conclusion which one would form by analogous reasoning, that so far as
the bacterial flora is concerned the effluent is practically raw
sewage.
4. CONTINUOUS CONTACT BEDS.
[Sidenote: Continuous contact beds still in an experimental stage.]
It is necessary to make at this point a few short observations on the
artificial self-purification in continuous contact beds.
This method of artificial purification has frequently been called
"continuous filtration," but it will be much better to reserve the
term "filtration" for the percolation of water through fine material,
such as sand, and to call the continuous flow of sewage through
coarser material continuous contact bed treatment, as the processes
going on during the same are more analogous to those going on in an
intermittent contact bed than to those taking place in a waterworks
filter.
Formerly it was attempted to use the same kind of contact bed for
continuous treatment as is used for intermittent treatment, but, as
was to be expected, the results obtained were so unsatisfactory that
the experiments had to be discontinued. Now somewhat different forms
are utilised, which are mostly protected by patent rights, and the
mode of distribution has also been altered by the introduction of
patent distributors or sprinklers, which cause the sewage to fall in
very thin streams upon the filling material.
In the Manchester experiments, the proprietary continuous contact bed
does not appear to have given satisfactory results. Better effluents
were obtained at Leeds, and at York the results obtained are said to
have been very good.
On the whole, however, it is but right to say that the experience
gained so far is not sufficient to entitle us to form definite
opinions, and for this reason it will be better to await further
results.
VI. MANAGEMENT OF PLANTS FOR THE ARTIFICIAL SELF-PURIFICATION OF
SEWAGE.
[Sidenote: Plants for the artificial self-purification of sewage
require very careful handling.]
It was formerly frequently concluded that neither septic tank nor
contact beds required careful superintendence, but that they could be
worked by automatic machinery and left to themselves. It was therefore
maintained that the working expenses of plants of this nature would be
next to nil. This was, however, not Mr. Dibdin's view, who, after
years of careful study, came to the conclusion that they were delicate
pieces of mechanism which required careful watching.
Since, Mr. Dibdin's conclusions have been amply confirmed by all
careful experimenters.
For instance, Mr. Fowler, the chemist in charge of the Manchester
experiments, observed before the Royal Commission on Sewage Disposal
as follows: "It is a delicate operation (the management of septic tank
and contact beds), which requires careful watching! There is no doubt
whatever about that!" (Question 5651.)
Again, the conditions of successful working of contact beds, laid down
by the same gentleman on page 64 of the Manchester report for the year
ending March 27, 1901, are ample proof of this, and they show very
clearly how extremely careful the supervision of such a plant ought to
be, and that in the hands of inexperienced men it will soon come to
grief.
Professor Percy Frankland stated in his evidence before the Royal
Commission, that in his opinion land required less skilled supervision
than contact beds. (See Questions 9937, 10071-74.)
A similar view was expressed by Mr. H. M. Wilson, the chief inspector
of the West Riding of Yorkshire Rivers Board. (Question 6380.)
VII. SOME OBSERVATIONS ON THE DEPOSITION OF SUSPENDED MATTERS IN
TANKS.
[Sidenote: Definition of the term "deposition."]
The term "deposition" shall here be held to mean the precipitation of
the suspended matters without chemicals or other artificial means,
i.e. the unaided subsidence of these matters at such a rate of flow
that septic action is not set up within the tanks.
The question that is of interest here, is: Which is the most
favourable rate of flow of the sewage through the tank, so far as
the deposition of the suspended matters is concerned? To some extent
the answer to this question will depend on the special characteristics
of the particular sewage under consideration, but for general purposes
the following observations will not be without interest.
Although of very great importance, this question does not appear to
have received very general consideration, as the available number of
careful experiments is but small.
[Sidenote: Tank velocity at Barking.]
It appears that the calculated velocity in the channels of the
precipitation tanks at Barking is about 4 feet per minute, and that
with this velocity about 77 per cent. of the suspended matters were
deposited in the year 1894.
[Sidenote: Tank velocity at Manchester.]
At the Manchester tanks it is stated that a velocity of 3 feet 4
inches per minute is employed.
[Sidenote: Velocity frequently adopted.]
A rate of velocity now frequently adopted in this country for new
works is 6 inches per minute.
[Sidenote: Frankfort experiments.]
In the settling tanks at Frankfort on the Main there are deposited
about 84 per cent. of the suspended matters, with velocities ranging
from 9½ inches to 16½ inches per minute.
[Sidenote: Cassel experiments.]
With a velocity of 7 inches per minute, it is stated that at the
Cassel sewage works 97 per cent. of the suspended matters are retained
in the tanks.
[Sidenote: Hanover experiments.]
At Hanover a set of interesting observations has lately been made, on
tanks 246 feet long, with a view to ascertaining the most advantageous
rate of flow.
With a velocity of 9·44 inches per minute, 62·7 per cent. of the
suspended organic matters were precipitated, with a velocity of 14·17
inches per minute 61·7 per cent. were deposited, and with a velocity
of 35·43 inches per minute 57·3 per cent.; from which figures it will
be clear that there is not much difference in the result on the
suspended matters between these velocities.
Against these results must be placed the results obtained with septic
tanks, where, as has frequently been stated, a velocity of 1 inch per
minute and a sojourn of twenty-four hours in the tank may be expected
to lead to a deposition of about 60 per cent. of the suspended
matters.
[Sidenote: Reduction of cost.]
Where, therefore, a previous septic treatment of the sewage by
anaerobes is not necessary, it is clear that the substitution of
ordinary settling tanks for septic tanks will be accompanied by a very
considerable reduction of cost.
VIII. CONCLUDING REMARKS.
Since the foregoing observations were penned, the Chairman of the
Royal Commission on Sewage Disposal has delivered a very interesting
inaugural address, in August last, at the Congress in Exeter of the
Institute of Public Health, to which attention ought to be drawn at
this point.
According to _The Times_ he is reported to have stated as follows: "He
regretted that he could not give some idea of the probable date at
which the Commission would issue its final report and recommendations.
They would soon, he hoped, be able to publish the results of a
prolonged investigation into the treatment of sewage on land; and
their experts were now making elaborate parallel examinations of some
of the processes of filtration by artificial means. But he feared that
they would ultimately be obliged to bring their proceedings to an
arbitrary close; for, however much they could learn, he was quite
certain they could never come to a point at which they could say there
was nothing more to be learned. The subject was inexhaustible."
These very guarded observations are almost in direct contrast with the
very positive assurance of some enthusiastic supporters of artificial
treatments, who a year or two ago did not hesitate in proclaiming
throughout this country that the panacea for all sewage difficulties
had been discovered, and that the investigations of the Royal
Commission were a mere matter of form and a foregone conclusion.
To all those who did not share these very sanguine expressions of
faith, and who were painfully aware of the great gaps in our knowledge
of the processes taking place in sewage purification, these words of
Lord Iddesleigh will prove an assurance that the commissioners are not
swayed by popular likes and dislikes, however fascinating they may be,
but that they are earnestly endeavouring, in an impartial manner, to
throw such light upon this abstruse question as will enable them to
arrive at correct conclusions.
For a like purpose the foregoing remarks have been written; and if the
facts recorded in the previous pages, and the opinions expressed
therein, should prove of assistance to anyone in forming correct
views, the labour spent on them will be amply repaid.
POSTSCRIPT.
Since the foregoing remarks were written, I have been somewhat struck
with the views expressed at one or two meetings by some of those who
ought to have the full facts of the case at their fingers' ends. There
seems to be a considerable vagueness as to the sanitary results to be
obtained by either the natural or one of the artificial methods of
sewage treatment, and with a view to making this point quite clear I
have prepared the following comparative statement (see next page),
which, I trust, will show at a glance what one may expect from either
system.
This statement has not been prepared from experimental installations,
where, as a rule, better results are obtained than in actual every-day
work; but it refers to fairly large works dealing from day to day with
the whole town's sewage. It has further been assumed, that the plant
both for the natural as well as for the artificial treatment is
suitable, and managed carefully and on intelligent lines.
As in all sewage treatments the sanitary results have first to be
considered, I have only dealt with them in the statement, but even if
I had extended it to economic considerations the result would have
been practically the same.
From a careful examination of the facts recorded in the statement it
follows that with natural treatment we get five distinct advantageous
results, against which we have to place only two on the side of the
artificial treatments; but this means, that if we wish to bring up the
results of these treatments to those obtained by the natural
treatment, we have to supplement them by three further treatments for
the extraction of pathogenic germs, and of the manurial elements, and
for the reduction of the liquid.
It is these facts which ought to be carefully considered by all those
who wish to study the comparative advantages of these two systems, or
who have to decide on a definite method to be employed in a particular
case, and no step ought to be taken before every one of these five
points has been very carefully weighed. Generally speaking, that
system will be preferred which confers the greatest number of
advantages.
STATEMENT.
_Results to be obtained from_
(A) _Natural Treatment._ (B) _Artificial Treatment._
1. Removal of suspended 1. Removal of suspended
matters. matters.
2. Removal of from 75 to 95 2. Removal of from 50 to 75
per cent. of the dissolved per cent. of the dissolved
organic matters. organic matters.
3. Removal of pathogenic 3. Nil. Effluent bacterially
germs. practically raw sewage.
4. Utilisation of large portion 4. Nil. All manurial elements
of manurial elements. escape into the rivers.
5. Great reduction of quantity 5. No appreciable reduction
of liquid. of quantity of liquid.
LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,
GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
Transcriber's Note:
Words and phrases in italics are surrounded by underscores, _like
this_. Chemicals are displayed with the numbers surrounded by braces,
e.g. CO{2}.
Footnotes were numbered sequentially and moved to the end of the
section in which the related anchors appear.
Wide tables were split for easier viewing on small screens.
An unprinted letter "S" was added to sidenote, "Springs."
Obsolete and alternate spellings were not changed.
End of the Project Gutenberg EBook of Natural & Artificial Sewage Treatment, by
Alfred S. Jones and H. Alfred Roechling
***
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Carmel-By-The-Sea, CA(WorkersCompensation.com) – It's imperative that business owners stay on top of their workers' compensation policies; failure to do so could cause it to lapse, resulting in potentially severe consequences when or if they are caught. A business owner in Monterey County learned that the hard way.
Back in September of 2018, an investigator with the state Labor Commissioner's office arrived at the Lafayette Bakery and told the owner that they had to immediately shut their doors because they had failed to carry workers' compensation insurance for their employees. They were not to open until they obtained a new policy.
A spokesperson for the Department of Industrial Relations (DIR) said the inspection had been initiated after the DIR requested proof of workers' compensation insurance last June.
The owner was given 10 days to fulfill the request but never did; as a result, in September the matter was passed along to the Labor Commissioner's Office Bureau of Field Enforcement (BOFE) which conducted the inspection and issued the citation to Lafayette Bakery.
Four days later the bakery did open after securing workers' compensation for their workers; however, the company lost thousands of dollars in lost product. Under the stop order, the owner also had to pay all employees that were affected by the work stoppage. The owners scrambled to reopen as quickly as possible; but in the process, lost the money they spent three years saving to buy a new oven for the bakery.
Little did the bakery owner know, he worst was yet to come. Since the bakery had not paid the monetary amount that was due from the citation issued in September, a judgment was filed last month in Monterey County Superior Court.
On March 5 the court ordered Lafayette Bakery to pay a penalty of $166,080 to the Labor Commissioner's Uninsured Employers Fund, which was more than what the bakery would have paid in workers' compensation insurance premiums during the time in which it was uninsured.
In the judgment paperwork, Lafayette went without workers' comp insurance from April 2, 2017, to Sept. 11, 2018. Marion Vial, baker and owner Jean Bernard Vial's daughter, says the insurance lapsed after the bakery's accountant failed to update a debit card that made automatic payments, and the situation went unnoticed until the Labor Commissioner's inspector showed up.
"California labor law requires that all employers provide workers' compensation benefits if they employ one or more employees. As seen in this case, complying with the law is less costly than violating it," noted a DIR spokesperson in a statement to WorkersCompensation.com.
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\section{Introduction}
There are several approaches to representing and solving constraint satisfaction problems: constraint programming (CP; \citeay{dechter03}, \citeay{robewa06a}), answer set programming (ASP; \citeay{baral03}), propositional satisfiability checking (SAT; \citeay{bihemawa09a}), its extension to satisfiability modulo theories (SMT; \citeay{niolti06a}), and many more. Each has its particular strengths: for example, CP systems support global constraints, ASP systems permit recursive definitions and offer default negation, whilst SAT solvers often exploit very efficient implementations. In many applications it would often be helpful to exploit the strengths of multiple approaches. Consider the problem of timetabling at a university~\cite{jaoijani09a}. To model the problem, we need to express the mutual exclusion of events (for instance,
we cannot place two events in the same room at the same time). A
straightforward representation of such constraint with clauses and rules uses
quadratic space. In contrast, global constraints such as \emph{all-different} typically supported by CP systems can give a much more concise encoding. On the other hand, there are features which are hard to describe in traditional constraint programming, like the temporary unavailability of a particular room. However, this is easy to represent with non-monotonic rules such as those used in ASP. Such rules also provide a flexible mechanism for defining new relations on the basis of existing ones.
Answer set programming has been put forward as a powerful paradigm to solve constraint satisfaction problems. \citeap{niemela99a} shows that ASP embeds SAT but provides a more expressive framework from a knowledge representation point of view. Moreover, modern ASP solvers compete\footnote{\texttt{http://www.satcompetition.org}} with the best SAT solvers.
An empirical comparison of the performance of ASP and constraint logic programming (CLP; \citeay{jama94a}) systems on solving combinatorial problems conducted by \citeauthor{dofopo05a} shows ASP encodings to be more compact, more declarative, and highly competitive.
However, as some problems are more naturally modelled by using non-pro\-po\-si\-tional constructs, like resources or functions over finite domains, and by using global
constraints in particular, there is an increasing desire to handle constraints beyond pure ASP.
One approach to combining ASP and CP is to integrate theory-specific predicates into propositional formulas (motivated by SMT), and to extend the ASP solver's decision engine with a higher level proof procedure \cite{baboge05a,melgel08a,geossc09a}. However, the resulting systems have a number of limitations. First, they are tied to particular ASP and CP solvers. Second, the support for global constraints is limited. Third, communication between the ASP and CP solver is restricted.
Alternative techniques, such as reformulating constraints into ASP have received little attention.
The key contribution of our work is an investigation of reformulation in the context of answer set programming, illustrated by reformulations of the popular \emph{all-different} constraint. The resulting approach has been implemented in the new preprocessor \systemname{inca}. Empirical evaluation demonstrates its computational potential.
\section{Background}
\paragraph{Answer Set Programming}
A \emph{(normal) logic program} $\Pi$ over a set of primitive propositions $\mathcal{A}$ is a finite set of rules of the form
$
a_0 \leftarrow a_1 , \dots , a_m, not\ a_{m+1} , \dots , not\ a_n
$
where $0 \leq m \leq n$ and $a_i \in \mathcal{A}$ are \emph{atoms} for $0 \leq i \leq n$. A \emph{literal} $\hat{a}$ is an atom $a$ or its default negation $not\ a$.
For a rule~$r$, let $\head{r} = a_0$ be the \emph{head} of $r$ and $\body{r} = \{a_1 , \dots , a_m, not\ a_{m+1} , \dots , not\ a_n \}$ the \emph{body} of $r$. The set of atoms occurring in a logic program $\Pi$ is denoted by $\atom{\Pi}$, and the set of bodies in $\Pi$ is $\body{\Pi} = \{ \body{r} \mid r \in \Pi \}$. For regrouping bodies sharing the same head~$a$, define $\body{a} = \{ \body{r} \mid r \in \Pi,\ \head{r} = a \}$.
The semantics of a logic program is given by its answer sets, being total well-founded models of $\Pi$. For a formal introduction to ASP, we refer the reader to \citeap{baral03}.
The semantics of important extensions to logic programs, such as choice rules, integrity, and cardinality constraints, is given through program transformations that introduce additional propositions (cf. \citeay{siniso02a}).
A \emph{choice rule} allows for the non-deterministic choice over atoms in $\{a_1, \dots, a_k\}$ and has the form
$
\{a_0, \dots, a_k\} \leftarrow a_{k+1} , \dots , a_m, not\ a_{m+1} , \dots , not\ a_n.
$
An \emph{integrity constraint} of the form
$
\leftarrow a_1 , \dots , a_m, not\ a_{m+1} , \dots , not\ a_n
$
is a short hand for a rule with an unsatisfiable head, and thus forbids its body to be satisfied in any answer set.
A~\emph{cardinality constraint} of the form
$
\leftarrow k \{\hat{a}_1 , \dots, \hat{a}_n\}
$
is interpreted as no $k$ literals of the set $\{\hat{a}_1 , \dots, \hat{a}_n\}$ are included in an answer set.
\citeauthor{siniso02a} provide a transformation that needs just $\mathcal{O}(nk)$ rules, introducing atoms $l(\hat{a}_i,j)$ to represent the fact that at least $j$ of the literals with index $\geq i$, i.e. the literals in $\{ \hat{a}_i, \dots, \hat{a}_n \}$,
are in a particular answer set candidate. Then, the cardinality constraint can be encoded by an integrity constraint $\leftarrow l(\hat{a}_1,k)$ and the three following rules, where $1 \leq i \leq n$ and $1 \leq j \leq k$:
\[
\begin{array}{l@{\qquad\quad}r}
l(\hat{a}_i,j) \leftarrow l(\hat{a}_{i+1},j) & l(\hat{a}_i,j+1) \leftarrow \hat{a}_i, l(\hat{a}_{i+1},j)\\
l(\hat{a}_i,1) \leftarrow \hat{a}_i &
\end{array}
\]
\paragraph{Nogoods of Logic Programs}
We want to view inferences in ASP as unit-propagation on nogoods.
Following \citeap{gekanesc07a}, inferences in ASP rely on atoms and program rules, which can be expressed by using atoms and bodies. Thus, for a program~$\Pi$, the \emph{domain} of Boolean assignments~$\mathbf{A}$ is fixed to $\domain{\mathbf{A}} = \atom{\Pi} \cup \body{\Pi}$.
Formally, a Boolean \emph{assignment} $\mathbf{A}$ is a set $\{ \sigma_1, \dots, \sigma_n \}$ of \emph{signed literals}~$\sigma_i$ for $1 \leq i \leq n$ of the form $\tass{a}$ or $\fass{a}$ where $a \in \domain{\mathbf{A}}$. $\tass{a}$ expresses that $a$ is assigned \emph{true} and $\fass{a}$ that it is \emph{false} in $\mathbf{A}$. (We omit the attribute \emph{Boolean} for assignments whenever clear from the context.) The complement of a signed literal~$\sigma$ is denoted by $\overline{\sigma}$, that is $\overline{\tass{a}} = \fass{a}$ and $\overline{\fass{a}} = \tass{a}$.
In the context of ASP, a \emph{nogood} is a set $\delta = \{ \sigma_1, \dots, \sigma_n \}$ of signed literals, expressing a constraint violated by any assignment~$\mathbf{A}$ such that $\delta \subseteq \mathbf{A}$.
For a nogood $\delta$, a signed literal $\sigma \in \delta$, and an assignment $\mathbf{A}$, we say that $\delta$ is \emph{unit} and $\overline{\sigma}$ is \emph{unit-resulting} if $\delta \setminus \mathbf{A} = \{\sigma\}$.
Let $\assignment^\mathbf{T} = \{ a \in \domain{\mathbf{A}} \mid \tass{a} \in A \}$ the set of true propositions and $\assignment^\mathbf{F} = \{ a \in \domain{\mathbf{A}} \mid \fass{a} \in A \}$ the set of false propositions. A \emph{total} assignment, that is $\assignment^\mathbf{T} \cup \assignment^\mathbf{F} = \domain{\mathbf{A}}$ and $\assignment^\mathbf{F} \cup \assignment^\mathbf{T} = \emptyset$, is a \emph{solution} for a set $\Delta$ of nogoods if $\delta \not\subseteq \mathbf{A}$ for all $\delta \in \Delta$.
As shown in \citeap{lee05a}, the answer sets of a logic program $\Pi$ correspond to the models of the completion of $\Pi$ that satisfy the loop formulas of all non-empty subsets of $\atom{\Pi}$. For $\beta = \{ a_1 , \dots , a_m, not\ a_{m+1} , \dots , not\ a_n \} \in \body{\Pi}$, define
\[
\Delta_\beta = \left\{ \begin{array}{l}
\{\tass{a_1}, \dots, \tass{a_m}, \fass{a_{m+1}}, \dots \fass{a_n}, \fass{\beta} \}, \\
\{\fass{a_1}, \tass{\beta}\}, \dots, \{\fass{a_m}, \tass{\beta}\}, \\
\{\tass{a_{m+1}}, \tass{\beta}\}, \dots, \{\tass{a_n}, \tass{\beta}\} \\
\end{array} \right\}.
\]
Intuitively, the nogoods in $\Delta_\beta$ enforce the truth of body~$\beta$ iff all its literals are satisfied.
For an atom $a \in \atom{\Pi}$ with $\body{a} = \{\beta_1, \dots, \beta_k\}$, let
\[
\Delta_a = \left\{ \begin{array}{l}
\{\fass{\beta_1}, \dots, \fass{\beta_k}, \tass{a} \}, \\
\{\tass{\beta_1}, \fass{a}\}, \dots, \{\tass{\beta_k}, \fass{a}\}
\end{array} \right\}.
\]
Then, the solutions for $\Delta_\Pi = \bigcup_{\beta \in \body{\Pi}} \Delta_\beta \cup \bigcup_{a \in \atom{\Pi}} \Delta_a$ correspond to the models of the completion of $\Pi$. Loop formulas, expressed in the set of nogoods~$\Lambda_\Pi$, have to be added to establish full correspondence to the answer sets of $\Pi$.
Typically, solutions for $\Delta_\Pi \cup \Lambda_\Pi$ are computed by applying \emph{conflict-driven nogood learning} (CDNL; \citeap{gekanesc07a}). This combines search and propagation by recursively assigning the value of a proposition and using \emph{unit-propagation} to determine logical consequences of an assignment \cite{mitchell05a}.
\paragraph{Constraint Satisfaction Problem}
The classic definition of a constraint satisfaction problem is as follows (cf. \citeay{robewa06a}). A \emph{constraint satisfaction problem} is a triple $(V,D,C)$ where $V$ is a set of \emph{variables} $V = \{v_1, \dots , v_n\}$, $D$ is a set of finite \emph{domains} $D=\{D_1, \dots , D_n\}$ such that each variable~$v_i$ has an associated domain $\domain{v_i} = D_i$, and $C$ is a set of \emph{constraints}. A constraint~$c$ is a pair~$(R_S,S)$ where $R_S$ is a $k$-ary \emph{relation} on the variables in $S \subseteq V^k$, called the \emph{scope} of $c$. In other words, $R_S$ is a subset of the Cartesian product of the domains of the variables in $S$. To access the relation and the scope of $c$ define $\range{c} = R_S$ and $\scope{c} = S$. For a \emph{(constraint variable) assignment} $A : V \to \bigcup_{v \in V} dom(v)$ and a constraint $c = (R_S, S)$ with $S = (v_1, \dots, v_k)$, define $A(S) = (A(v_1), \dots, A(v_k))$, and call $c$ \emph{satisfied} if $A(S) \in \range{c}$. Given this, define the set of constraints satisfied by $A$ as
$
sat_C(A) = \{ c \mid A(\scope{c}) \in \range{c},\ c \in C\}.
$
A binary constraint~$c$ has $|scope(c)|=2$. For example,
$v_1 \neq v_2$ ensures that $v_1$ and $v_2$ take different
values. A global (or $n$-ary) constraint~$c$ has parametrized
scope. For example,
the \emph{all-different} constraint ensures that
a set of variables, $\{v_1,\ldots,v_n\}$ take all different values.
This can be decomposed into $O(n^2)$ binary
constraints, $v_i \neq v_j$ for $i<j$. However, as
we shall see, such reformulation can hinder inference.
An assignment~$A$ is a \emph{solution} iff it satisfies all constraints in $C$.
Constraint solvers typically use backtracking search to explore the space of partial assignments. Various heuristics affecting, for instance, the variable selection criteria and the ordering of the attempted values, can be used to guide the search. Each time a variable is assigned a value, a deterministic propagation stage is executed, pruning the set of values to be attempted for the other variables, i.e., enforcing a certain type of local consistency.
A binary constraint~$c$ is called \emph{arc consistent} iff when a variable~$v_1 \in \scope{c}$ is assigned any value~$d_1 \in \domain{v_1}$, there exists a consistent value~$d_2 \in \domain{v_2}$ for the other variable~$v_2$.
An $n$-ary constraint~$c$ is \emph{hyper-arc consistent} or \emph{domain consistent} iff when a variable~$v_i \in \scope{c}$ is assigned any value~$d_i \in \domain{v_i}$, there exist compatible values in the domains of all the other variables~$d_j \in \domain{v_j}$ for all $1 \leq j \leq n,\ j \neq i$ such that $(d_1, \dots, d_n) \in \range{c}$.
Relational consistency \cite{debe97a} extends the concept of local consistency. I.e. a constraint~$c$ is \emph{relationally $k$-arc consistent} if any consistent assignment of a $k$-elementary subset of variables from $\scope{c}$ extends to a consistent assignment of all variables in $\scope{c}$.
The concepts of bound and range consistency are defined for constraints on ordered intervals.
Let $min(D_i)$ and $max(D_i)$ be the minimum value and maximum value of the domain~$D_i$. A constraint~$c$ is \emph{bound consistent} iff when a variable~$v_i$ is assigned $d_i \in \{min(\domain{v_i}), max(\domain{v_i})\}$ (i.e. the minimum or maximum value in its domain), there exist compatible values between the minimum and maximum domain value for all the other variables in the scope of the constraint. Such an assignment is called a \emph{bound support}. A constraint is \emph{range consistent} iff when a variable is assigned any value in its domain, there exists a bound support. Notice that range consistency is in between domain and bound consistency, where domain consistency is the strongest of the three formalisms.
\section{Encoding Global Constraints in ASP}
In this section we explain how to reformulate multi-valued variables and constraints on finite domains into a logic program under answer set semantics. In what follows, we assume $\domain{v} = \lbrack 1, d\rbrack$ for all $v \in V$ to save the reader from multiple superscripts.
\paragraph{Direct Encoding}
A popular choice is called the \emph{direct encoding} \cite{wa00}. In the direct encoding, a propositional variable $e(v, i)$, representing $v = i$, is introduced for each value~$i$ that can be assigned to the constraint variable~$v$. Intuitively, the proposition $e(v, i)$ is true if $v$ takes the value $i$, and false if $v$ takes a value different from $i$. For each $v$, the truth-assignments of atoms $e(v, i)$ are encoded by a choice rule (1). Furthermore, there is an integrity constraint (2) to ensure that $v$ takes at least one value, and a cardinality constraint (3) that ensures that $v$ takes at most one value.
\begin{align}
\{ e(v, 1), \dots, e(v, d) \} &\leftarrow \\
&\leftarrow not\ e(v, 1), \dots, not\ e(v, d) \\
&\leftarrow 2\ \{ e(v, 1), \dots, e(v, d) \}
\end{align}
In the direct encoding, each forbidden combination of values in a constraint is expressed by an integrity constraint. On the other hand, when a relation is represented by allowed combinations of values, all forbidden combinations have to be deduced and translated to integrity constraints. Unfortunately, the direct encoding of constraints hinders propagation:
\begin{theorem}
Enforcing arc consistency on the binary decomposition of the original constraint prunes more values from the variables domain than unit-propagation on its direct encoding.
\end{theorem}
\paragraph{Support Encoding}
The \emph{support encoding} has been proposed to
tackle this weakness \cite{gent02}. A \emph{support} for a constraint variable~$v$ to take the value~$i$ across a constraint~$c$ is the set of values $\{i_1, \dots, i_m\} \subseteq \domain{v'}$ of another variable in~$v' \in \scope{c}\setminus \{v\}$ which allow $v = i$, and can be encoded as follows, extending (1--3):
\[
\leftarrow e(v, i), not\ e(v', i_1), \dots, not\ e(v', i_m)
\]
This integrity constraint can be read as whenever $v = i$, then at least one of its supports must hold.
In the support encoding, for each constraint~$c$ there is one support for each pair of distinct variables $v, v' \in \scope{c}$, and for each value~$i$.
\begin{theorem}
Unit-propagation on the support encoding enforces arc consistency on the binary decomposition of the original constraint.
\end{theorem}
We illustrate this approach on an encoding of the global \emph{all-different} constraint. For variables $v, v'$ and value $i$ it can be reduced from the definition by using the equivalence covered by (2--3) to
\[
\leftarrow e(v, i), e(v', i).
\]
Observe, that this is also
the direct encoding of the binary decomposition of the global \emph{all-different} constraint. However, this observation does not hold in general for all constraints.
As discussed in the Background section of this paper, we can express above condition as $\mathcal{O}(d)$ cardinality constraints:
\begin{align}
&\leftarrow 2\ \{ e(v_1, i), \dots, e(v_n, i) \}
\end{align}
\begin{corollary}
Unit-propagation on (1--4) enforces arc consistency on the binary decomposition of the global \emph{all-different} constraint in $\mathcal{O}(nd^2)$ down any branch of the search tree.
\end{corollary}
\paragraph{k-support Encoding}
The support encoding can be generalized to the \emph{$k$-support encoding} \cite{behewa03a} representing supports on subsets of $\scope{c}$ for an assignment of another $k$-elementary subset of variables in $\scope{c}$. More formal, a $k$-support~$S$ for an assignment $A$ of $k$~variables from $\scope{c}$, say $v_1 = i_1, \dots, v_k = i_k$, is an assignment $v'_1 = i'_1, \dots, v'_l = i'_l$ such that $\{v'_1, \dots, v'_l\} \subseteq \scope{c} \setminus \{v_1, \dots, v_k\}$ which allows $A$. We introduce a \emph{support-variable}~$s$, that evaluates to true iff $S$ holds:
\[
s \leftarrow e(v'_1, i_1), \dots, e(v'_l, i'_l)
\]
Furthermore, let $\{S_1, \dots, S_m\}$ be the set of all $k$-supports of $A$. A $k$-support rule for $A$ is defined as
\[
\leftarrow e(v_1, d_1), \dots, e(v_k, d_k), not\ s_1, \dots, not\ s_m
\]
meaning that as long as $A$ holds then at least one of its $k$-supports $S_1, \dots S_m$ must hold.
In the $k$-support encoding, for each constraint~$c$ there is one $k$-support rule for each assignment~$A$ of $k$~variables from $\scope{c}$.
\begin{theorem}
Unit-propagation on the $k$-support encoding enforces relational $k$-arc consistency on the original constraint.
\end{theorem}
\paragraph{Range Encoding}
In the \emph{range encoding}, a propositional variable~$r(v, l, u)$ is introduced for all $\lbrack l, u \rbrack \subseteq \lbrack 1, d \rbrack$ to represent whether the value of~$v$ is between $l$ and $u$. For each range~$\lbrack l, u \rbrack$, the following $\mathcal{O}(nd^2)$ rules encode $v \in \lbrack l , u \rbrack$ whenever it is safe to assume that $v \not\in \lbrack 1, l-1 \rbrack$ and $v \not\in \lbrack u+1, d\rbrack$, and enforce a consistent set of ranges such that $v \in \lbrack l, u\rbrack \Rightarrow v \in \lbrack l-1, u\rbrack \land v \in \lbrack l, u+1\rbrack$:
\begin{align}
r(v, l, u) &\leftarrow not\ r(v, 1, l-1), not\ r(v, u+1, d) \\
&\leftarrow r(v, l-1, u), not\ r(v, l, u) \\
&\leftarrow r(v, l, u+1), not\ r(v, l, u)
\end{align}
Constraints are encoded into integrity constraints representing conflict regions. When the combination $v_1 \in \lbrack l_1, u_1\rbrack, \dots, v_n \in \lbrack l_n, u_n\rbrack$ violates the constraint, the following rule is added:
\[
\leftarrow r(v_1, l_1, u_1), \dots, r(v_n, l_n, u_n)
\]
\begin{theorem}
Unit-propagation on the range encoding enforces range consistency on the original constraint.
\end{theorem}
A propagator for the global \emph{all-different} constraint that enforces range consistency pruning Hall intervals has been proposed by \citeap{le96a} and encoded to SAT by \citeap{bekanaquwa09a}.
An interval~$\lbrack l, u \rbrack$ is a \emph{Hall interval} iff $|\{ v \mid dom(v) \subseteq \lbrack l, u \rbrack \}| = u - l + 1$. In other words, a Hall interval of size~$k$ completely contains the domains of $k$~variables. Observe that in any bound support, the variables whose domains are contained in the Hall interval consume all values within the Hall interval, whilst any other variable must find their support outside the Hall interval.
The following reformulation of the global \emph{all-different} constraint will permit us to achieve range consistency via unit propagation. It ensures that no interval $\lbrack l, u\rbrack$ can contain more variables than its size.
\begin{align}
&\leftarrow u-l+2\ \{ r(v_1, l, u), \dots, r(v_n, l, u) \}
\end{align}
This simple reformulation can simulate a complex propagation algorithm like \citeauthor{le96a}'s with a similar overall complexity of reasoning.
\begin{corollary}
Unit-propagation on (5--8) enforces range consistency on the global \emph{all-different} constraint in $\mathcal{O}(nd^3)$ down any branch of the search tree.
\end{corollary}
A hybrid that links the range encoding of $v$ to its direct representation extends the range encoding as follows, for each $i \in \domain{v}$:
\[
\begin{array}{r@{\ \leftarrow\ }l}
e(v, i) & r(v, i, i)\\
& e(v, i), not\ r(v, i, i)\\
\end{array}
\]
These rules encode the equivalence $v=i \Leftrightarrow v \in \lbrack i, i \rbrack$.
\paragraph{Bound Encoding}
A last encoding is called the \emph{bound encoding} \cite{crba94a}. In the bound encoding, a propositional variable~$b(v, i)$ is introduced for each value $i$ to represent that the value of~$v$ is bounded by~$i$. That is, $v \leq i$ if $b(v,i)$ is assigned \emph{true}, and $v > i$ if $b(v,i)$ is assigned \emph{false}. Similar to the direct encoding, for each $v$, the truth-assignments of atoms~$b(v, i)$ are encoded by a choice rule (9). In order to ensure that assignments represent a consistent set of bounds, the condition $v \leq i \Rightarrow v \leq i+1$ is posted as integrity constraints (10) $\forall i \in \lbrack 1, d-1 \rbrack$. Another integrity constraint (11) encodes $v \leq d$, that at least one value must be assigned to $v$:
\begin{align}
\{ b(v, 1), \dots, b(v, d) \} &\leftarrow \\
&\leftarrow b(v, i), not\ b(v, i+1) \\
&\leftarrow not\ b(v, d)
\end{align}
Constraints are encoded into integrity constraints representing conflict regions similar to the range encoding. When all combinations in the region
\[
l_1 < v_1 \leq u_1, \dots, l_n < v_n \leq u_n
\]
violate a constraint, the following rule is added:
\[
\leftarrow b(v_1, u_1), \dots, b(v_n, u_n), not\ b(v_1, l_1), \dots, not\ b(v_n, l_n)
\]
\begin{theorem}
Unit-propagation on the bound encoding enforces bound consistency on the original constraint.
\end{theorem}
In order to get a representation of the global \emph{all-different} constraint that can only prune bounds, the bound encoding for variables is linked to (8) as follows:
\begin{align}
r(v, l, u) &\leftarrow not\ b(v, l-1), b(v, u) \\
&\leftarrow r(v, l, u), b(v, l-1) \\
&\leftarrow r(v, l, u), not\ b(v, u)
\end{align}
\begin{corollary}
Unit-propagation on (8--14) enforces bound consistency on the global \emph{all-different} constraint in $\mathcal{O}(nd^2)$ down any branch of the search tree.
\end{corollary}
Note that an upper bound $h$ can be posted on the size of Hall intervals. The resulting encoding with only those cardinality constraints (5) for which $u - l + 1 \leq h$ detects Hall intervals of size at most $h$, and therefore enforces a weaker level of consistency.
To access the value of $v$, the bound encoding can be extended to a hybrid by adding the following rules to the bound encoding for each $i \in \lbrack 1, d \rbrack$:
\[
\begin{array}{r@{\ \leftarrow\ }l}
e(v, i) & b(v, i), not\ b(v, i-1) \\
& e(v, i), not\ b(v, i)\\
& e(v, i), b(v, i-1)
\end{array}
\]
The first rule enforces $e(v, i)$ to be true if possible values for $v$ are bound to the singleton $i$, i.e. $v \leq i$ and $v \not\leq i-1$ are in the assignment. On the other hand, the condition $v = i \Rightarrow v \leq i \land v \not\leq i-1$ is represented as integrity constraints.
\paragraph{Non-ground Logic Programs}
Although our semantics is propositional, atoms in $\mathcal{A}$ and can be constructed from a first-order signature $\Sigma = (\mathcal{F}, \mathcal{V}, \mathcal{P})$, where
$\mathcal{F}$ is a set of function symbols (including constant symbols),
$\mathcal{V}$ is a denumerable collection of first-order variables, and
$\mathcal{P}$ is a set of predicate symbols.
The logic program over $\mathcal{A}$ is then obtained by a grounding process, systematically substituting all occurrences of variables $\mathcal{V}$ by terms in $\mathcal{T}(\mathcal{F})$, where $\mathcal{T}(\mathcal{F})$ denotes the set of all ground terms over $\mathcal{F}$. Atoms in $\mathcal{A}$ are formed from predicate symbols $\mathcal{P}$ and terms in $\mathcal{T}(\mathcal{F})$.
\section{Experiments}
To evaluate these reformulations, we conducted experiments on encodings containing \emph{all-different} and \emph{permutation} constraints.
The global \emph{permutation} constraint is a special case of \emph{all-different} when the number of variables is equal to the number of all their possible values. A reformulation of \emph{permutation} extends (4) by
\[
\leftarrow not\ e(v_1, i), \dots, not\ e(v_n, i)
\]
or (8) by the following rule where $1 \leq l \leq u \leq k$:
\[
\leftarrow d-u+l\ \{ not\ r(v_1, l, u), \dots, not\ r(v_n, l, u) \}
\]
This can increase propagation.
Our reformulations have been implemented within the prototypical preprocessor \systemname{inca}\footnote{\texttt{http://potassco.sourceforge.net/} provides the systems \systemname{clasp}, \systemname{clingo}, \systemname{gringo}, \systemname{inca}, and the benchmark set} which compiles an (extended) logic programs with high-level statements for global constraints, constraint variables, first-order variables, function symbols, and aggregates, etc. in linear time and space, such that the logic program can be obtained by a \emph{grounding} process.
Experiments consider \systemname{inca} in different settings using different reformulations. We denote the support encoding of the global constraints by $S$, the bound encoding of the global constraints by $B$, and the range encoding of the global constraints by $R$. To explore the impact of small Hall intervals, we also tried \encbouh{k} and \encranh{k}, an encoding of the global constraints with only those cardinality constraints (8) for which $u-l+1 \leq k$. The consistency achieved by \encbouh{k} and \encranh{k} is therefore weaker than full bound and range consistency, respectively.
We also include the pure CP system \systemname{gecode}\footnote{\texttt{http://www.gecode.org/}} (3.2.0), and the integrated system \systemname{ezcsp}\footnote{\texttt{http://krlab.cs.ttu.edu/\~{}marcy/ezcsp/}} (1.6.9; \citeay{ba09a}) in our empirical analysis. The latter combines the grounder \systemname{gringo} (2.0.3) and ASP solver \systemname{clasp} (1.3.0) with \systemname{sicstus}\footnote{\texttt{http://www.sics.se/sicstus/}} (4.0.8) as a constraint solver.
Since \systemname{inca} is a pure preprocessor, we select the ASP system \systemname{clingo} (2.0.3) as its backend to provide a representative comparison with \systemname{ezcsp}. Note that \systemname{clingo} stands for \systemname{clasp} on \systemname{gringo} and combines both systems in a monolithic way.
All experiments were run on a 2.00~GHz PC under Linux. We report results in seconds, where each run was limited to 600 s time and 1 GB RAM.
\paragraph{Pigeon Hole Problem}
The \emph{pigeon hole problem} (PHP) is to show that it is impossible to put $n$ pigeons into $n-1$ holes if each pigeon must be put into a distinct hole.
Clearly, our bound and range reformulations are faster compared to weaker encodings (see Table \ref{tab:php}). It appears that \systemname{sicstus}' and \systemname{gecode}'s default configuration uses filtering algorithms for the global \emph{all-different} constraint achieve arc consistency on its binary decomposition. However, on such problems, detecting large Hall intervals is essential.
\begin{table}
\centering
\begin{tabular}{cccccccc} \hline\hline
$n$ & $S$ & \encbouh{3} & $B$ & \encranh{3} & $R$ & \systemname{ezcsp} & \systemname{gecode} \\ \hline
10 & 5 & \textbf{$<$1} & \textbf{$<$1} & $<$1 & \textbf{$<$1} & 2 & \textbf{$<$1} \\
11 & 46 & 1 & \textbf{$<$1} & 2 & \textbf{$<$1} & 17 & 9 \\
12 & 105 & 4 & \textbf{$<$1} & 3 & \textbf{$<$1} & 184 & 104 \\
13 & --- & 25 & \textbf{$<$1} & 30 & \textbf{$<$1} & --- & --- \\
14 & --- & 125 & \textbf{$<$1} & 197 & \textbf{$<$1} & --- & --- \\
15 & --- & --- & \textbf{$<$1} & --- & \textbf{$<$1} & --- & --- \\
16 & --- & --- & \textbf{$<$1} & --- & \textbf{$<$1} & --- & --- \\ \hline\hline
\end{tabular}
\caption{Runtime results in seconds for PHP. \label{tab:php}}
\end{table}
\paragraph{Latin Squares}
A \emph{Latin square} is an $n \times n$-table filled with $n$ different elements such that each element occurs exactly once in each row and each column of the table. The \emph{Latin square puzzle}~(LSP) is to determine whether a partially filled table can be completed in such a way that a Latin square is obtained.
Randomly generated LSP has been proposed as a benchmark domain for CP systems by \citeauthor{gose97a} since it combines the features of purely random problems and highly structured problems.
\begin{table}
\centering
\begin{tabular}{cccccccc} \hline\hline
\% & $S$ & \encbouh{3} & $B$ & $R$ & \systemname{ezcsp} & \systemname{gecode} & \systemname{gecode}$_{B}$ \\ \hline
10 & \textbf{3} & 5 & 8 & 7 &30 (7) & 2 (4) & $<$1 (1) \\
20 & \textbf{2} & 5 & 8 & 7 &21 (20) & 5 (4) & $<$1 (3) \\
30 & \textbf{2} & 5 & 8 & 7 &10 (30) & 3 (13) & 1 (5) \\
35 & \textbf{2} & 5 & 8 & 7 &22 (24) &14 (13) & 6 (7) \\
40 & \textbf{2} & 5 & 8 & 7 &52 (29) &12 (20) & 6 (9) \\
45 & \textbf{2} & 5 & 8 & 7 &36 (35) &18 (25) & 6 (13) \\
50 & \textbf{2} & 5 & 8 & 7 &36 (50) &25 (32) & 6 (18) \\
55 & \textbf{2} & 4 & 8 & 7 &61 (51) &20 (41) &31 (29) \\
60 & \textbf{2} & 4 & 8 & 7 &60 (63) &36 (51) &27 (35) \\
70 & \textbf{2} & 4 & 7 & 6 &70 (66) &28 (45) &17 (27) \\
80 & \textbf{2} & 4 & 7 & 5 &16 (18) &17 (13) & 7 (7) \\
90 & 2 & 4 & 7 & 5 & \textbf{1} & $<$1 (1) & 3 \\ \hline\hline
\end{tabular}
\caption{Average times over 100 runs on LSP. Timeouts are given in parenthesis, if any.\label{tab:qcp}}
\vspace{-1\baselineskip}
\end{table}
Table \ref{tab:qcp} compares the runtime for solving LSP problems of size $20 \times 20$ where the first column gives the percentage of preassigned values. We included \systemname{gecode} with algorithms that enforce bound and domain consistency, denoted as \systemname{gecode}$_{B}$ and \systemname{gecode}$_{D}$ (not shown due to space constraints), in the experiments. Our analysis exhibits phase transition behaviour of the systems \systemname{ezcsp}, \systemname{gecode}, and \systemname{gecode}$_{B}$, while our Boolean encodings and \systemname{gecode}$_{D}$ solve all problems within seconds. Interestingly, learning constraint interdependencies as in our approach is sufficient to tackle LSP. In fact, most of the time for $S$, $B_k$, $R_k$ is spent on grounding, but not for solving the actual problem.
\paragraph{Graceful Graphs}
A labelling $f$ of the nodes of a graph $(V,E)$ is \emph{graceful} if $f$ assigns a unique label~$f(v)$ from $\{0,1,\dots,|E|\}$ to each node $v \in V$ such that, when each edge $(v,w) \in E$ is assigned the label $|f(v)-f(w)|$, the resulting edge labels are distinct. The problem of determining the existence of a graceful labelling of a graph (GGP) has been modelled in CP \citeap{pesm03a}, using auxillary variables $d(v,w)$ for edge labels. We represent the equivalence $d(v,w) = |f(v)-f(w)|$ in the direct encoding which weakens the overall consistency. Our experiments consider double-wheel graphs $DW_n$ composed by two copies of a cycle with $n$ vertices, each connected to a central hub.
\begin{table}
\centering
\begin{tabular}{cccccccc} \hline\hline
$n$ & $S$ & \encbouh{1} & \encbouh{3} & $B$ & $R$ & \systemname{ezcsp} & \systemname{gecode} \\ \hline
$3$ & 11 & 4 & 6 & 9 & 6 & 6 & \textbf{2} \\
$4$ & 1 & 2 & 1 & 3 & 3 & \textbf{$<$1} & \textbf{$<$1} \\
$5$ & 4 & 5 & 4 & 13 & 12 & 1 & \textbf{$<$1} \\
$6$ & 7 & 11 & 18 & 48 & 21 & \textbf{1} & 7 \\
$7$ & 24 & 28 & 68 &228 & 60 & \textbf{18} & --- \\
$8$ & 48 & 68 & --- &208 & 58 & \textbf{4} & --- \\
$9$ & \textbf{83} &106 &200 &487 & --- & 390 & --- \\ \hline\hline
\end{tabular}
\caption{Runtime results in seconds for GGP. \label{tab:ggp}}
\vspace{-1\baselineskip}
\end{table}
Table \ref{tab:ggp} shows that our encodings compete with \systemname{ezcsp} and outperform \systemname{gecode}, where the support encoding performs better than bound and range encodings. In most cases, the branching heuristic used in our approach appears to be misled by the extra variables introduced in $B_k$ and $R_k$. That explains some of the variability in the runtimes.
\section{Conclusions}
We have reformulated global and other constraints into answer set programs. In particular, we have investigated various generic ASP encodings for constraints on finite domains and proved which level of consistency unit-pro\-pa\-ga\-tion achieves on them.
Our techniques were formulated as preprocessing and can be applied to any ASP system without changing its source code, which allows for programmers to select the ASP solver that best fit their needs. We have empirically evaluated the performance of
such an approach on benchmarks from CP and found that such reformulations outperform integrated ASP(CP) systems as well as pure CP solvers.
Our future works includes the reformulation of other useful
global constraints into answer set programming like the
\emph{regular} constraint, as well as global constraints
like \emph{lex} which are very useful for symmetry breaking .
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,562
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import org.geotools.styling.*;
import org.locationtech.jts.geom.*;
import org.locationtech.jts.geom.Polygon;
import org.opengis.feature.simple.SimpleFeature;
import org.opengis.feature.simple.SimpleFeatureType;
import org.opengis.filter.FilterFactory2;
import org.opengis.filter.expression.Expression;
import org.w3c.dom.Document;
import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.DocumentBuilderFactory;
import javax.xml.parsers.ParserConfigurationException;
import javax.xml.transform.TransformerException;
import java.awt.*;
import java.awt.Dimension;
import java.io.*;
import java.net.URISyntaxException;
import java.net.URL;
public class SvgRendering {
static StyleFactory styleFactory = CommonFactoryFinder.getStyleFactory();
static FilterFactory2 filterFactory = CommonFactoryFinder.getFilterFactory2();
public static void main(String[] args) throws Exception {
Coordinate[] listOfPoints = new Coordinate[5];
listOfPoints[0] = new Coordinate(-73.82, 41.24);
setupSVG(listOfPoints);
}
public static DefaultFeatureCollection createBoundingBox(Coordinate[] listofP){
SimpleFeatureTypeBuilder b = new SimpleFeatureTypeBuilder();
b.setName("MyFeatureType");
b.add("location", Polygon.class);
final SimpleFeatureType TYPE = b.buildFeatureType();
SimpleFeatureBuilder featureBuilder = new SimpleFeatureBuilder(TYPE);
GeometryFactory geometryFactory = JTSFactoryFinder.getGeometryFactory();
Polygon polygon = geometryFactory.createPolygon(listofP);
featureBuilder.add(polygon);
SimpleFeature feature = featureBuilder.buildFeature("polygon");
DefaultFeatureCollection featureCollection = new DefaultFeatureCollection("internal", TYPE);
featureCollection.add(feature); //Add feature 1
return featureCollection;
}
private static void setupSVG(Coordinate[] listofP)
throws IOException, ParserConfigurationException, URISyntaxException, TransformerException {
//URL url = new URL("http://localhost:8080/");
URL url = new URL("file:///C:/poc/mapreport/Map_marker.svg");
//File file = new File(baseFilePath + "mapreport\\Map_marker.svg");
//URL url = file.toURI().toURL();
PointSymbolizer symb = styleFactory.createPointSymbolizer();
ExternalGraphic eg = styleFactory.createExternalGraphic(url, "image/svg+xml");
symb.getGraphic().graphicalSymbols().add(eg);
Expression size = filterFactory.literal(54);
symb.getGraphic().setSize(size);
Rule rule = styleFactory.createRule();
rule.symbolizers().add(symb);
FeatureTypeStyle fts = styleFactory.createFeatureTypeStyle(rule);
Style style = styleFactory.createStyle();
style.featureTypeStyles().add(fts);
MapContent mc = new MapContent();
DefaultFeatureCollection boundingbox = createBoundingBox(listofP);
Layer layer = new FeatureLayer(boundingbox, style);
mc.addLayer(layer);
DocumentBuilderFactory dbf = DocumentBuilderFactory.newInstance();
DocumentBuilder db = dbf.newDocumentBuilder();
// Create an instance of org.w3c.dom.Document
Document document = db.getDOMImplementation().createDocument(null, "svg", null);
// Set up the map
SVGGeneratorContext ctx1 = SVGGeneratorContext.createDefault(document);
SVGGeneratorContext ctx = ctx1;
ctx.setComment("Generated by GeoTools2 with Batik SVG Generator");
SVGGraphics2D g2d = new SVGGraphics2D(ctx, true);
Dimension canvasSize = new Dimension(1024, 1024);
g2d.setSVGCanvasSize(canvasSize);
StreamingRenderer renderer = new StreamingRenderer();
renderer.setMapContent(mc);
Rectangle outputArea = new Rectangle(g2d.getSVGCanvasSize());
ReferencedEnvelope dataArea = mc.getMaxBounds();
dataArea.expandBy(5); // some of these have 0 size
renderer.paint(g2d, outputArea, dataArea);
File fileToSave = new File("C:\\poc\\markers.svg");
OutputStreamWriter osw = null;
try {
OutputStream out = new FileOutputStream(fileToSave);
osw = null;
osw = new OutputStreamWriter(out, "UTF-8");
g2d.stream(osw);
} catch (FileNotFoundException e) {
// TODO Auto-generated catch block
e.printStackTrace();
} finally {
if (osw != null)
try {
osw.close();
} catch (IOException e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
}
mc.dispose();
}
}
Expected Output:-
Final Output:-
So, in the final output SVG marker is getting cut from the right-hand side.
Help would be appreciated.
Thanks in advance
This is different from the previous question.
A: This happens near the bounds of the layer. You can enlarge the layer's bounds manually in the layer config page.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,392
|
The position is within the team 'Model Validation' which is part of the division 'Group Risk Controlling'. The core competences of the validation team are the initial and regular validation of (credit) risk models for the purpose of Pillar I as well as for the purpose of IFRS 9.
In order to strengthen our team, we are looking for a person with a strong quantitative background in credit risk or IFRS 9.
Extracting, transforming and processing of data from relevant sources (Oracle DB, SAS tables, Excels, CSVs).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,889
|
{"url":"https:\/\/www.vietlod.com\/trac-nghiem-kinh-te-vi-mo-en","text":"# Tr\u1eafc nghi\u1ec7m kinh t\u1ebf Vi m\u00f4\n\n## Ti\u1ebfng Anh\n\n1. The \u201claw of demand\u201d states that, other things remaining the same, the quantity demanded of any good is\nA. directly related to its price.\nB. directly related to the supply of the good.\nC. positively related to its price.\nD. inversely related to its price.\n\nCorrect: D\n\n2. Suppose that the price of cereal rises. As a result, people have cereal for breakfast on fewer days and eat eggs instead. This behavior is an example of\nA. a decrease in quantity supplied of cereal because of the substitution effect.\nB. an increase in quantity demanded of eggs because of the income effect.\nC. a decrease in the quantity demanded of cereal because of the substitution effect.\nD. an increase in quantity supplied of eggs because of the income effect.\n\nCorrect: C\n\n3. Pizza is a normal good. When the price of a pizza decreases from $12 to$10,\nA. the quantity demanded of pizza will not change.\nB. the income effect means people buy less pizza.\nC. the income effect means people buy more pizza.\nD. None of the above answers is correct.\n\nCorrect: C\n\n4. If the price of chocolate chip cookies rises, then\nA. there would be a movement downward along the demand curve.\nB. the demand curve would shift rightward.\nC. there would be a movement upward along the demand curve.\nD. the demand curve would shift leftward.\n\nCorrect: C\n\n5. What happens to the demand for CDs if the price of a CD player falls?\nA. The demand for CDs increases because the price of a complement falls.\nB. The demand for CDs decreases because the price of a complement falls.\nC. The demand for CDs decreases because the price of a substitute falls.\nD. The demand for CDs remains unchanged.\n\nCorrect: A\n\n6. Cupcakes and granola bars are substitutes in consumption. The price of a granola bar increases. As a result, the demand for\nA. granola bars will increase, that is, the demand curve will shift rightward.\nB. cupcakes will decrease, that is, the demand curve will shift leftward.\nC. granola bars will decrease, that is, the demand curve will shift leftward.\nD. cupcakes will increase, that is, the demand curve will shift rightward.\n\nCorrect: D\n\n7. If consumers expect that the price of soda will rise in November, the\nA. supply of soda in October will increase.\nB. supply of soda in October will decrease.\nC. demand for soda in October will increase.\nD. demand for soda in October will decrease.\n\nCorrect: C\n\n8) Georgine buys more sweaters when her income increases. For Georgine, sweaters are a(n)\nA. complement.\nB. normal good.\nC. substitute.\nD. inferior good.\n\nCorrect: B\n\n9) Coke and Pepsi are substitutes. When Pepsi Cola advertises on television it is trying to cause\nA. an increase in the demand for Pepsi.\nB. a decrease in the supply of Coke.\nC. an increase in the supply of Pepsi.\nD. None of the above answers is correct.\n\nCorrect: A\n\n10) Consider the market for soft drinks shown in the figure above. A movement from point a to point b represents\nA. an increase in quantity demanded.\nB. an increase in demand.\nC. a decrease in quantity demanded.\nD. a decrease in demand.\n\nCorrect: B\n\n11) The \u201claw of supply\u201d states that, other things remaining the same,\nA. firms will produce less of a good as the required resources become scarcer.\nB. firms will produce more of a good the less it costs to produce it.\nC. firms will produce more of a good the higher its price.\nD. firms will produce less of a good the more it costs to produce it.\n\nCorrect: C\n\n12) Which of the following will decrease the supply of restaurant meals?\nA. The demand for restaurant meals decreases.\nB. Consumers\u2019 income increases and restaurant meals are a normal good.\nC. The price of movies, a complement to restaurant meals, falls.\nD. Waiters get a pay raise.\n\nCorrect: D\n\n13) If there is an increase in demand for lumber, then, in the market for sawdust,\nA. the supply curve of sawdust shifts leftward.\nB. the supply curve of sawdust shifts rightward.\nC. there would be a movement upward along the supply curve for sawdust.\nD. there would be a movement downward along the supply curve for sawdust.\n\nCorrect: B\n\n14. A shift of the supply curve for pick-up trucks might be the result of all of the following EXCEPT\nA. an increase in the price of a resource used to produce pick-up trucks.\nB. a change in production technology.\nC. a change in the number of suppliers of pick-up trucks.\nD. a change in the price of pick-up trucks.\n\nCorrect: D\n\n15. When a market is in equilibrium,\nA. there is no shortage and no surplus at the equilibrium price.\nB. everyone has all they want of the commodity in question.\nC. the supply curve has the same slope as the demand curve.\nD. the number of buyers is exactly equal to the number of sellers.\n\nCorrect: A\n\n16. When demand increases, the equilibrium price ________ and the equilibrium quantity ________.\nA. falls; increases\nB. rises; increases\nC. rises; decreases\nD. falls; decreases\n\nCorrect: B\n\n17. Suppose that coffee and sugar are complements. If the supply curve of coffee shifts leftward because of poor weather, then there will be\nA. a decrease in the price of sugar.\nB. a leftward shift of the supply curve for sugar.\nC. an increase in the price of sugar.\nD. a rightward shift of the demand curve for coffee.\n\nCorrect: A\n\n18. If technological advances lower the cost of computer chips, in the market for computers the equilibrium price will ________ and the equilibrium quantity will ________.\nA. fall; increase\nB. rise; increase\nC. fall; decrease\nD. rise; decrease\n\nCorrect: A\n\n19. What will happen to the equilibrium price and quantity of coffee if it\u2019s discovered to help prevent colds and, at the same time, Brazil and Vietnam emerge in the global market as massive producers of coffee?\nA. The quantity will increase while the price will remain unchanged.\nB. The quantity will increase while the effect on the price is uncertain.\nC. The price will fall while the effect on the quantity is uncertain.\nD. The quantity will decrease and the price will rise.\n\nCorrect: B\n\n20. The price elasticity of demand equals the magnitude of\nA. the percentage change in the quantity demanded of a good divided by the percentage change in its price.\nB. the slope of the demand curve.\nC. the inverse of the slope of the demand curve.\nD. the percentage change in the price of a good divided by the percentage change in the quantity demanded.\n\nCorrect: A\n\n21. If a 20 percent increase in the price of a used car results in a 10 percent decrease in the quantity of used cars demanded, then the price elasticity of demand equals\nA. 0.5.\nB. 10.0.\nC. 2.0.\nD. 1.0.\n\nCorrect: A\n\n22. Suppose the quantity demanded is 5 units when the price is $1.00. If the price rises to$2.00, the quantity demanded falls to 3 units. The price elasticity of demand is\nA. 2.00.\nB. 0.5.\nC. 0.75.\nD. 1.33.\n\nCorrect: C\n\n23. If the demand for a good is elastic, that means that when price increases\nA. the demand will decrease.\nB. the quantity demanded will decrease by a greater percentage than the price increased.\nC. the quantity demanded will increase.\nD. the quantity demanded will decrease by a smaller percentage than the price increased.\n\nCorrect: B\n\n24. If demand is inelastic, an increase in the price will\nA. not change total revenue.\nB. increase the quantity demanded.\nC. increase total revenue.\nD. decrease total revenue.\n\nCorrect: C\n\n25. At a local ice cream parlor, when the price of half-gallons of chocolate ice cream was lowered by fifty cents per half-gallon, total revenue from the sale of chocolate decreased. This result indicates that\nA. there are more people who like vanilla ice cream than there are people who like chocolate ice cream.\nB. the demand for chocolate ice cream is elastic.\nC. the demand for chocolate ice cream is inelastic.\nD. None of the above answers is correct.\n\nCorrect: C\n\n26. If students\u2019 expenditures on airline travel increase as a consequence of more heavily discounted fares, students\u2019 demand for airline travel must be\nA. income elastic.\nB. price elastic.\nC. income inelastic.\nD. price inelastic.\n\nCorrect: B\n\n27. For many goods, the price elasticity of demand increases over time because\nA. inflation causes all prices and incomes to increase over time.\nB. the ability to find substitutes for a good whose price has risen increases over time.\nC. people\u2019s incomes tend to increase over time.\nD. None of the above answers is correct.\n\nCorrect: B\n\n28. The ________ the portion of your income spent on a good, the ________ is your demand for the good.\nA. smaller; less price elastic\nB. smaller; more income elastic\nC. larger; more income elastic\nD. larger; more price elastic\n\nCorrect: A\n\n29. If the cross elasticity of demand between coffee and tea is positive, an increase in the price of tea will shift the demand curve for\nA. tea leftward.\nB. tea rightward.\nC. coffee leftward.\nD. coffee rightward.\n\nCorrect: D\n\n30. The income elasticity of demand is\nA. always negative.\nB. always positive.\nC. negative for a normal good and positive for an inferior good.\nD. positive for a normal good and negative for an inferior good.\n\nCorrect: D\n\n31. If the income elasticity of demand for spaghetti is -1.3, then spaghetti\nA. is income elastic.\nB. is a normal good.\nC. has an elastic demand.\nD. is an inferior good.\n\nCorrect: D\n\n32. Over time, the supply of a good or service\nA. initially becomes more elastic and then becomes less elastic.\nB. becomes less elastic.\nC. initially becomes less elastic and then becomes more elastic.\nD. becomes more elastic.\n\nCorrect: D\n\n33. Which of the following is a typical effect of a price ceiling set below the equilibrium price?\nA. People can buy more than they can at the equilibrium price because the ceiling price is lower.\nB. The price ceiling has no effect on the market equilibrium.\nC. Less of the good is produced with the ceiling than would be produced without the ceiling.\nD. None of the above answers is correct.\n\nCorrect: C\n\n34. A minimum wage is a government-imposed price ________ that is designed to be ________ the equilibrium wage rate.\nA. floor; below\nB. floor; above\nC. ceiling; above\nD. ceiling; below\n\nCorrect: B\n\n35. As long as the supply curve for a good is upward sloping and the demand curve is downward sloping, a sales tax imposed on sellers shifts the supply curve\nA. leftward and definitely increase the equilibrium price.\nB. rightward and possibly increase the equilibrium quantity.\nC. leftward and possibly increase the equilibrium price.\nD. rightward and definitely decrease the equilibrium quantity.\n\nCorrect: A\n\n36. A sales tax imposed on sellers shifts the supply curve leftward for the taxed good because\nA. the tax causes the demand curve to shift leftward.\nB. it is paid by the seller to the government and is, therefore, like a cost of production.\nC. the higher price causes entry into the market.\nD. it is actually shifted entirely onto the buyer who can afford only a smaller supply.\n\nCorrect: B\n\n37. The seller pays the entire sales tax levied on a good when\nA. demand is perfectly inelastic or supply is perfectly inelastic.\nB. demand is perfectly elastic or supply is perfectly inelastic.\nC. demand is perfectly inelastic or supply is perfectly elastic.\nD. demand is perfectly elastic or supply is perfectly elastic.\n\nCorrect: B\n\n38. When the supply curve of corn shifts leftward, farmers\u2019 revenue ________ because ________.\nA. increases; demand is inelastic\nB. increases; supply is inelastic\nC. decreases; supply is elastic\nD. decreases; demand is elastic\n\nCorrect: A\n\n39. A period of time in which the quantity of at least one resource used by a firm is fixed is called\nA. the market period.\nB. the intermediate run.\nC. the long run.\nD. the short run.\n\nCorrect: D\n\n40. Which of the following is characteristic of the long run?\nA. The firm\u2019s plant is fixed.\nB. It must exceed 12 months in length.\nC. All resources can be varied.\nD. All of the above answers are correct.\n\nCorrect: C\n\n41. A firm\u2019s total product curve shows\nA. that inefficiency is not possible.\nB. that in the long run the firm must adjust the quantity of all the resources it employs.\nC. how the quantity of output changes when the quantity of labor changes.\nD. how the cost of the fixed resources change when output changes.\n\nCorrect: C\n\n42. At that amount of output where diminishing marginal returns first sets in,\nA. total product will begin to decline.\nB. marginal product will begin to decline.\nC. average product will begin to decline.\nD. all of the above\n\nCorrect: B\n\n43. Total cost is\nA. the difference between the average variable cost and the average fixed cost.\nB. the sum of the total fixed cost and the total variable cost.\nC. the sum of the average fixed cost and the average variable cost.\nD. the product of the marginal cost times the average total cost.\n\nCorrect: B\n\n44. Total fixed cost\nA. does not change as output changes.\nB. increases as output increases.\nC. decreases as output increases.\nD. initially decreases and then increases as output increases.\n\nCorrect: A\n\n45. Total variable cost\nA. decreases as output increases.\nB. does not change as output changes.\nC. initially decreases and then increases as output increases.\nD. increases as output increases.\n\nCorrect: D\n\n46. Average variable cost is equal to\nA. total cost divided by quantity.\nB. average total cost times quantity.\nC. average total cost minus average fixed cost.\nD. the change in total cost divided by the change in quantity.\n\nCorrect: C\n\n47. The average total cost curve eventually slopes upwards because of the\nA. increase in capital costs.\nB. reductions in average fixed costs.\nC. decrease in labor costs.\nD. law of diminishing returns.\n\nCorrect: D\n\n48. A firm\u2019s long-run average cost curve\nA. tells the firm which plant size to use and which quantity of labor to use to minimize the cost of producing any level of output.\nB. shows the lowest attainable average total cost of producing any level of output when capital and labor are fixed.\nC. is the sum of all of its short-run average cost curves.\nD. all of the above\n\nCorrect: A\n\n49. Economies of scale occur when the percentage increase in output\nA. is less than the percentage increase in all inputs.\nB. exceeds the percentage increase in all inputs.\nC. is less than the percentage decrease in all inputs.\nD. exceeds the percentage decrease in all inputs.\n\nCorrect: B\n\n50. Which of the following is a defining characteristic of a perfectly competitive industry?\nA. no restrictions on entry into the industry\nB. persistent economic profits in the long run\nD. higher prices being charged for certain name brands\n\nCorrect: A\n\n51. Which of the following is NOT an assumption of perfect competition?\nA. restricted entry into the industry\nB. many firms\nC. each firm sells an identical product\n\nCorrect: A\n\n52. In perfect competition\nA. the size of demand for the good or service relative to the minimum efficient scale of a single producer does not affect competition.\nB. demand for the good or service can be small relative to the minimum efficient scale of a single producer as long as the goods or services are not identical.\nC. demand for the good or service is small relative to the minimum efficient scale of a single producer.\nD. demand for the good or service is large relative to the minimum efficient scale of a single producer.\n\nCorrect: D\n\n53. Individual firms in perfectly competitive industries are price takers because\nA. each individual firm is too small to affect the market price.\nB. the government sets all prices.\nC. firms decide together on the best prices to charge.\n\nCorrect: A\n\n54. The firm\u2019s goal is to\nA. maximize its total revenue.\nB. maximize its normal profit.\nC. maximize its economic profit.\nD. maximize its industry\u2019s revenue.\n\nCorrect: C\n\n55. Which of the following is always true for a perfectly competitive firm?\nA. MR = ATC\nB. P = AVC\nC. P = MR\nD. P = ATC\n\nCorrect: C\n\n56. A perfectly competitive firm\u2019s economic profit is maximized at the output level such that\nA. total revenue equals total variable cost.\nB. total revenue equals total cost and marginal cost.\nC. marginal revenue is equal to total revenue.\nD. marginal revenue equals marginal cost.\n\nCorrect: D\n\n57. If marginal revenue exceeds marginal cost, to increase its profit the firm will\nA. shut down.\nB. keep its output the same.\nC. increase its output.\nD. decrease its output.\n\nCorrect: C\n\n58. In the short run, a perfectly competitive firm\nA. must earn a normal profit.\nB. can earn an economic profit, incur an economic loss, or earn a normal profit.\nC. cannot shut down.\nD. will not incur an economic loss if it shuts down.\n\nCorrect: B\n\n59. For a perfectly competitive firm, the shutdown point is\nA. the level of output at which price equals minimum average total cost.\nB. the price at which total opportunity cost is zero.\nC. the price at which economic profit is zero.\nD. the level of output at which price equals minimum average variable cost.\n\nCorrect: D\n\n60. The short-run market supply curve for a perfectly competitive industry is obtained by summing\nA. each firm\u2019s AVC curve that lies below the MC curve.\nB. the part of each firm\u2019s AVC curve that lies above its MC curve.\nC. each firm\u2019s MC curve that lies below the AVC curve.\nD. the part of each firm\u2019s MC curve that lies above its AVC curve.\n\nCorrect: D\n\n61. If firms in a perfectly competitive industry are presently earning zero economic profit, then\nA. some of those firms will leave the industry, because firms cannot persistently go without making economic profit.\nB. some of the firms will temporarily shut down.\nC. there will be no incentive for either entry or exit.\nD. new firms will enter the industry, because the new entrants would be ensured of doing as well as in their best foregone alternative.\n\nCorrect: C\n\n62. In the long run, perfectly competitive firms earn zero economic profit. This result is due mainly to the assumption of\nA. price taking by the firms.\nB. unrestricted entry and exit.\nC. a perfectly elastic market demand.\n\nCorrect: B\n\n63. Suppose a perfectly competitive industry is in a long-run equilibrium when a permanent decrease in the market demand occurs. In the long run, which of the following definitely occurs?\nA. marginal revenue increases.\nB. the number of firms decreases.\nC. the price decreases.\nD. the firms\u2019 marginal cost increases.\n\nCorrect: B\n\n64. In perfectly competitive industries, the long-run supply curve\nA. must slope upwards.\nB. must slope downwards.\nC. may slope upwards, downwards, or be horizontal.\nD. must be horizontal.\n\nCorrect: C\n\n65. An example of an external cost is\nA. getting a discount for buying in bulk.\nB. doctors referring patients to a specialist.\nC. contributions from a corporation to a charitable organization.\nD. a firm polluting the ocean.\n\nCorrect: D\n\n66. A monopolist\nA. is a price setter.\nB. is a price taker.\nC. produces a product that has close substitutes.\nD. must constantly worry about other firms entering the industry.\n\nCorrect: A\n\n67. A barrier to entry is\nA. a brick wall that a firm places around its corporate headquarters.\nB. the result of highly elastic demand.\nC. a natural or legal impediment that makes it difficult for new firms to enter a market.\nD. a necessary condition for perfect competition.\n\nCorrect: C\n\n68. A natural monopoly\nA. is an industry in which economies of scale exist at the level of output where the market demand curve intersects the long-run average cost curve.\nB. is an industry where two or more smaller firms can supply the market at a lower cost than one big firm could.\nC. exists because of legal barriers to entry.\nD. is not protected by any barrier to entry.\n\nCorrect: A\n\n69. Which of the following is true for a single-price monopolist?\nA. P > MR\nB. P = elasticity of demand\nC. P = MR\nD. P < MR\n\nCorrect: A\n\n70. Which of the following is ALWAYS true for a single-price monopolist in equilibrium?\nA. P = MR\nB. P = MC\nC. MR = MC\nD. MC = ATC\n\nCorrect: C\n\n71. Why can a monopoly earn an economic profit in the long run?\nA. because there is only a single firm in the market\nB. because the firm is protected by barriers to entry\nC. because there are close substitutes for the firm\u2019s product\nD. ALL of the above are reasons why a monopoly can earn an economic profit in the long run.\n\nCorrect: B\n\n72. Relative to a perfectly competitive industry with the same cost and demand, a single-price monopolist produces\nA. less output and has a lower price.\nB. more output and has a higher price.\nC. less output and has a higher price.\nD. more output and has a lower price.\n\nCorrect: C\n\n73. Price discrimination is the practice of charging different prices to\nA. different countries because of tariffs and transportation costs.\nB. different customers because the costs of selling are different.\nC. different customers even though cost of selling to each is the same.\nD. the same customers because of changes in cost.\n\nCorrect: C\n\n74. What condition must exist for a monopolist to effectively price discriminate?\nA. The monopolist must produce a good that cannot be resold.\nB. The monopolist must produce a good or service that can be resold.\nC. The monopolist must charge the highest price possible.\nD. The monopolist must face consumers with identical willingness to pay.\n\nCorrect: A\n\n75. As a result of using the marginal cost pricing rule to regulate a natural monopoly, the\nA. natural monopoly will incur an economic loss.\nB. monopolist is allowed to cover all its costs and earn a normal profit.\nC. monopolist produces an inefficient amount of product.\nD. natural monopoly earns a normal profit.\n\nCorrect: A\n\n76. In monopolistic competition, there are\nA. many firms making a differentiated product.\nB. few firms making a differentiated product.\nC. few firms making an identical product.\nD. many firms making an identical product.\n\nCorrect: A\n\n77. Monopolistic competition is a market structure in which\nA. there are barriers to entry.\nB. a small number of firms compete.\nC. firms only compete on product price.\nD. each firm produces a differentiated product.\n\nCorrect: D\n\n78. Which of the following is NOT a characteristic of the market structure for monopolistic competition?\nA. Firms are free to enter and exit.\nB. Firms are price takers.\nC. There are a large number of firms.\nD. Firms compete on product quality, price, and marketing.\n\nCorrect: B\n\n79. A product that is a close substitute but not a perfect substitute for the products of the other firms is called a\nA. an efficient product.\nB. a differentiated product.\nC. homogeneous product.\nD. an inelastic product.\n\nCorrect: B\n\n80. In monopolistic competition, a firm can determine what price to set for its product because\nB. there are many sellers.\nC. the demand for its product is not perfectly elastic.\nD. the demand for its product is perfectly elastic.\n\nCorrect: C\n\n81. In the short run, a firm in monopolistic competition produces where\nA. MR = MC.\nB. MR = MC and economic profit is equal to zero.\nC. the given market price is equal to MC and economic profit is equal to zero.\nD. the given market price is equal to MC.\n\nCorrect: A\n\n82. The above figure shows the demand and cost curves for a firm in ________ in the ________.\nA. perfect competition; long run\nB. monopolistic competition; long run\nC. perfect competition; short run\nD. monopolistic competition; short run\n\nCorrect: D\n\n83. The above figure shows the demand and cost curves for a firm in monopolistic competition. The firm maximizes its profit by\nA. producing 4 units at a price of $20 each. B. producing 8 units at a price of$15 each.\nC. producing 8 units at a price of $5 each. D. producing 12 units at a price of$10 each.\n\nCorrect: B\n\n84. The above figure shows the demand and cost curves for a firm in monopolistic competition. The firm earns total revenue of\nA. $0. B.$160.\nC. $40. D.$120.\n\nCorrect: D\n\n85. The above figure shows the demand and cost curves for a firm in monopolistic competition. The firm earns the maximum profit when the marginal cost of last item produced equals\nA. $15. B.$5.\nC. $10. D.$20.\n\nCorrect: B\n\n86. In the long run, a firm in monopolistic competition produces an output at which\nA. price equals average total cost but exceeds marginal cost.\nB. price equals average total cost but is less than marginal cost.\nC. price equals marginal cost but exceeds average total cost.\nD. price equals both marginal cost and average total cost.\n\nCorrect: A\n\n87. In the long run, in monopolistic competition\nA. firms earn an economic profit.\nB. firms earn zero economic profit.\nC. price equals marginal cost.\nD. Both answers A and C are correct.\n\nCorrect: B\n\n88. A firm has excess capacity if its output is\nA. less than the quantity at which economic profit is maximized.\nB. less than the quantity at which average total cost is minimized.\nC. less than the quantity at which marginal cost is minimized.\nD. more than the quantity at which average total cost is minimized.\n\nCorrect: B\n\n89. An oligopoly is a market structure in which there are\nA. many sellers selling a differentiated product.\nB. only a few buyers but many sellers.\nC. a few products sold by many sellers.\nD. only a few sellers selling either an identical or differentiated product.\n\nCorrect: D\n\n90. The kinked demand curve model assumes that a firm\u2019s rivals will\nA. follow the firm\u2019s price decreases but not its price increases.\nB. not follow any of the firm\u2019s price changes.\nC. follow any price change the firm makes.\nD. follow the firm\u2019s price increases but not its price decreases.\n\nCorrect: A\n\n91. In the dominant firm model of oligopoly,\nA. the dominant firm sets market price, and all other firms are price takers.\nB. all firms have the same costs.\nC. all firms are price setters.\nD. all firms are roughly of equal size.\n\nCorrect: A\n\n92. Game theory can be used for studying which of the following types of market structure?\nA. perfect competition\nB. monopoly\nC. monopolistic competition\nD. oligopoly\n\nCorrect: D\n\n93. Which group of features is shared by all games?\nA. rules, profit, payoffs, outcome\nB. profit, strategies, payoffs, cheating\nC. rules, cheating, payoffs, outcome\nD. rules, strategies, payoffs, outcome\n\nCorrect: D\n\n94) The table above shows the payoff matrix for a prisoners\u2019 dilemma game. The Nash equilibrium is that\nA. prisoner A confesses while prisoner B does not confess.\nB. prisoner A does not confess while prisoner B confesses.\nC. both prisoners confess.\nD. both prisoners do not confess.\n\nCorrect: C\n\n95) The table above shows the payoff matrix for a prisoners\u2019 dilemma. In the Nash equilibrium,\nA. both prisoners get 3 years in jail.\nB. both prisoners get 1 year in jail.\nC. both prisoners get 10 years in jail.\nD. both prisoners get 2 years in jail.\n\nCorrect: A\n\n96) Cartels are typically subject to cheating by their members because\nA. product differentiation allows the cartel firms to cheat.\nB. barriers to entry do not exist for these firms so that new entrants will join.\nC. the U.S. Justice Department will punish any cartel agreement before the cartel has had a chance to operate.\nD. a firm can increase its profits by cutting its price if other firms stick to the agreement.\n\nCorrect: D\n\n97) A group of firms that has entered into a collusive agreement to increase profits is known as\nA. game theory.\nB. a dominant firm.\nC. cartel.\nD. monopolistic competition.\n\nCorrect: C\n\n98. There are two can companies, American and National, which have entered into a collusive agreement. The payoff matrix of economic profits is above. If both firms cheat on the collusive agreement, what amount of economic profit is earned by American?\nA. $0 B.$3,000\nC. -$2,000 D.$4,000\n\nCorrect: A\n\n99. A market in which firms can enter and leave so easily that firms in the market face competition from potential entrants is called a\nA. monopolistic competition market.\nB. cartel.\nC. contestable market.\nD. limit pricing market.\n\nCorrect: C\n\n100. The practice of charging a price below the monopoly profit-maximizing price and producing a quantity greater than that at which marginal revenue equals marginal cost in order to deter entry is called\nA. undercutting.\nB. collusion.\nC. limit pricing.\nD. dominant pricing.\n\nCorrect: C\n\n### Thuy\u1ebft Nguy\u1ec5n\n\n- Gi\u1ea3ng d\u1ea1y Kinh t\u1ebf l\u01b0\u1ee3ng \u1ee9ng d\u1ee5ng, PPNCKH - Chuy\u00ean gia ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u1edbi Stata - D\u00e0nh h\u01a1n 15000 gi\u1edd nghi\u00ean c\u1ee9u Kinh t\u1ebf l\u01b0\u1ee3ng \u1ee9ng d\u1ee5ng - \u0110am m\u00ea nghi\u00ean c\u1ee9u, h\u1ecdc h\u1ecfi c\u00e1i m\u1edbi; - L\u00e0m vi\u1ec7c \u0111\u1ed9c l\u1eadp & t\u1ef1 h\u1ecdc cao.","date":"2021-03-07 21:09:05","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\": 0.4956098198890686, \"perplexity\": 4446.046775812498}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"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-2021-10\/segments\/1614178378872.82\/warc\/CC-MAIN-20210307200746-20210307230746-00291.warc.gz\"}"}
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{"url":"https:\/\/www.physicskey.com\/27\/damped-oscillation-and-resonance","text":"# Damped Oscillation and Resonance\n\n## Damped Oscillation\n\nWhen a body is left to oscillate itself after displacing, the body oscillates in its own natural frequency. Let that natural frequency be denoted by $\\omega _n$. But the amplitude of the oscillation decreases continuously and the oscillation stops after some time.\n\nThe decrease in amplitude is caused by the non-conservative forces such as friction in the system of the oscillation. The non-conservative forces are also called dissipative forces.\n\nIn real life situations the dissipative forces do work on the oscillating systems and the oscillations die out after some time and such oscillations are called damped oscillations.\n\nIn Figure 1 from simple harmonic motion you can see a mass-spring system in which a box oscillates about its equilibrium position.\n\nIf the friction between the surface of the box and the floor is not neglected, the oscillations die out after some time. The force that causes damping of the oscillation is called damping force. The restoring force provided by the spring is\n\n$F_\\text{spring} = - kx$\n\nHere we consider the simpler case of velocity dependent damping force. The expression for the damping force is,\n\n${F_{dx}} = -b{v_x} \\tag{1} \\label{1}$\n\nThe negative sign in the above equation shows that the damping force opposes the oscillation and $b$ is the proportionality constant called damping constant. We consider that such a damping force is along x-axis as indicated by the subscript $x$.\n\nTherefore, the net force on the harmonic oscillator including the damping force is,\n\n\\begin{align*} {F_{{\\rm{net}}}} &= - kx - b{v_x}\\\\ {\\rm{or,}}\\quad m{a_x} &= - kx - b{v_x}\\\\ {\\rm{or,}}\\quad m\\frac{{{d^2}x}}{{d{t^2}}} &= - kx - b\\frac{{dx}}{{dt}} \\tag{2} \\label{2} \\end{align*}\n\nWe do not go into solving Eq. \\eqref{2} (but you can go ahead and solve it), the solution is,\n\n$x = A{e^{ - bt\/2m}}\\cos (\\omega t + \\phi ) \\tag{3} \\label{3}$\n\nIn Eq. \\eqref{3} the amplitude of the damped oscillation is $A' = A{e^{ - bt\/2m}}$ which decreases exponentially with time (see Figure 1).\n\nIn Eq. \\eqref{3} the angular frequency of the damped oscillation is $\\omega = \\sqrt {\\frac{k}{m} - \\frac{{{b^2}}}{{4{m^2}}}}$. We apply a condition that when $\\omega = 0$, you'll get,\n\n\\begin{align*} \\frac{k}{m} - \\frac{{{b^2}}}{{4{m^2}}} &= 0\\\\ {\\rm{or,}}{\\kern 1pt} \\quad b &= 2\\sqrt {km} \\tag{4} \\label{4} \\end{align*}\n\nWhen the value of the damping constant is equal to $2\\sqrt {km}$ that is, $b = 2\\sqrt {km}$, the damping is called critical damping and the system is said to be critically damped. In critical damping an oscillator comes to its equilibrium position without oscillation.\n\nAnd when $b < 2\\sqrt {km}$ the system is said to be under-damped and the damping is called under-damping. In under-damped oscillating system the oscillator oscillates but the amplitude of the oscillation decreases continuously and finally the oscillations stop.\n\nIn another case when $b > 2\\sqrt {km}$ the oscillating system is over-damped and the damping is called over-damping. In over-damped case the oscillator comes more slowly to its equilibrium position without oscillating.\n\n## Resonance\n\nEvery object can oscillate about its equilibrium position when displaced by an external force. When a particular body is displaced from its equilibrium position, the body starts oscillating with its own natural frequency $\\omega _\\text{n}$.\n\nIf you apply an external periodically varying driving force on the oscillator, you can change the frequency of the oscillating body in your need called driving frequency $\\omega_d$. And the corresponding periodically varying force is called driving force.\n\nWhen the natural frequency of the oscillator is equal to the driving frequency of the external force, the amplitude of the resultant oscillation increases dramatically.\n\nThe effect of the largest amplitude peak obtained when $\\omega_d$ equals $\\omega_n$ is a phenomenon called resonance.\n\nIn Figure 2 you can see how the amplitude of a forced oscillation increases when the frequency of an external force nears the natural frequency of the oscillator.\n\nIn Figure 2 you can also see different curves for the same oscillator for different damping forces - greater the damping force, lower the amplitude at resonance. In curve $a$ the damping force is lesser than the damping force in curve $b$. And in curve $b$ the damping force is lesser than the damping force in curve $c$.\n\nThat's the reason why solders are said to stop marching while crossing a bridge to avoid destructive effect. The reason is that when the solders march over a bridge, the driving frequency of their marching may nearly equal to the natural frequency of the bridge and the bridge can oscillate with the greatest amplitude possible due to the phenomenon of resonane which can destroy the bridge.\n\nMechanics","date":"2019-04-26 03:41:59","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\": 2, \"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\": 0.9679049253463745, \"perplexity\": 492.8421689496903}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-18\/segments\/1555578759182.92\/warc\/CC-MAIN-20190426033614-20190426055614-00405.warc.gz\"}"}
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Author : Timothy Coleman Date : 4th April 2016
Victim & Perpetrator Reconciliation
A Miracle of Forgiveness
Almost all of Renata's family had been killed in the genocide. On top of this she had been raped many times and now is HIV positive. She was very traumatised and could trust no-one. Then in 2005 someone invited her to a healing seminar. When she arrived she saw that there were released prisoners there, also, and this was too painful for her so she almost left. But then the teachings began to heal her and she felt the seminar had been designed solely for her. Hearing that Jesus was her Pain Bearer was astounding to her. (She already was a believer.) She cried a lot and gave Him all her sufferings and felt a great release. The next day a prisoner stood and confessed he had killed
her family. She was shocked and felt great sorrow. But then she told him he had been very courageous to confess and she walked up to him and hugged him, telling him she forgave him. Since then she has also been able to forgive those who raped her, and says her health is much better since then.
Francois' story was very different. With head bowed, he related that he had killed many people but had come under a heavy weight of guilt in prison and had confessed. After his release, awaiting trial, he was invited to a seminar. Here he heard what he described as wonderful teachings, especially about the cross. This was new to him, and during the cross workshop he took everything to the cross. For the first time he felt clean and pure. "But the amazing thing," he said, "was that that the survivor of the family I killed was present and was able to forgive me." Renata was that survivor. They are now working together in the community visiting both victims and perpetrators to share their testimonies.
A Unique Association
A seminar was held in Ruhengeri (northern Rwanda), with survivors and released prisoners. At the beginning, the survivors were quite bitter and resisted mixing with those from the prison. One of the survivors said that though he wouldn't harm anyone from prison, in his heart he wished them dead. After the Cross Workshop, Daniel–one of the survivors–forgave and started to be friendly toward the prisoners, but they feared and avoided him. Eventually, however, Daniel was able to bring both groups together and they started helping each other. They came together and cultivated a field for either a survivor or one of the released prisoners. They started contributing money so they could help any of them with a need. This Association has grown to the point that they are putting their money together now to buy livestock for their members! They are now living in peace with one another. Daniel says, "We are alive now. We want to be a river of life flowing out to bless Rwanda."
Reconciliation Village to Village on a Bicycle
Gaston's parents were killed, his father being brutally hacked to pieces, and he was hunted during the genocide. When the Interahamwe caught him they beat him over the head with a club and threw him into a pit, along with his sister and her son. Somehow, Gaston got out of the pit, but his sister and her son were buried alive. Only Gaston and 1 sister survived from the whole family. Once "peace" returned, Gaston found himself in emotional turmoil. He still lived in the same village and was paralyzed every time he saw any of those who had thrown him into the pit. His heart was troubled and full of fear. Every night he had nightmares about being hunted again. He couldn't go back to church, because those who had hunted him were also in the church. He was sick with headaches every day and had to go the hospital nearly every week. But the doctor told Gaston, "Your problem is not physical. Go to the church and pray and try to get help there." When Gaston finally did go back to the church, God started to work in his heart. He joined the choir and the pain started to go away, so he became bolder to face the people in the church. Then he was invited to a healing and reconciliation seminar.
But when he arrived at the seminar he saw Elijah–one of the men who had killed his father-in-law and his sons–immediately Gaston's headaches and trauma returned. Still, he stuck it out and began to feel blessed and began to open up and on the last day his heart was changed. He hesitated to testify to his healing, because Elijah and the others knew what they had done to his
family, so why should he have to tell them? But then Elijah stood and confessed! He didn't just stand in the gap in a general way for other Hutu, but he confessed that he, himself, had killed. Gaston felt a light shine in his heart. In tears, he went to Elijah to extend forgiveness. Since then Gaston has not needed to return to the hospital because of headaches.
Elijah's experience in the seminar was quite different. "People were talking about their pain and wounds from being hunted, but I was different – I am one of those who hunted and killed. I didn't know what to do with that identity. During the seminar I started to offload my burden. I felt accepted by the victims in the seminar – the people I had hunted."
When Gaston went home and told his wife that Elijah had confessed to killing her father and brothers, his wife struggled, thinking Gaston had forgiven too much. Gaston realized he had taken a large step down the road of forgiveness and had left her behind, so he taught her the principles in the seminar. Still, she struggled, especially with the idea of Elijah visiting their home. Gaston told her, "He has completely changed and is not the man you saw leading the mob that came to kill you and your family." When Elijah came to their home, she hid in the bedroom, in fear of her life. Then she attended a full seminar. When she returned she excitedly told Gaston, "I got more than what you received in the seminar!" She had completely changed and desired to live in the spirit of reconciliation.
Later, Gaston was appointed the head Gacaca judge at his area's sector level. He found himself having to judge some of the people who had thrown him into the pit and others who had killed his relatives. Gaston says, "I felt God was sending me there as a test to my healing. Those being tried thought for sure that I would ignore all the rules and just sentence them to the maximum sentence. I even presided as judge over the man who chopped off my father's legs and arms. Until he confessed to me, I didn't know who had done it. I asked him how he could have done it and he told me he was horrible. I was still committed to forgive him. He wanted my forgiveness, but still he recognized that I had to carry out justice. The man killed many, many people. He was sentenced, but it was a fair sentence."
Elijah reports, "It was hard for the community to understand the unity that took place between me and the people I hunted during the genocide. I discovered the power of this message. Gaston and I agreed to come together for a new beginning. When people see us together on a bicycle – one carrying the other, this is enough – it speaks so much.
"We enjoy this unity and want to share it with others. We went to many places in the country together and shared our testimony. Many people were healed. God has called us to this ministry, and we continue to work together. My message is not the seminar, but the fruit that I have experienced from the seminar – I talk about my own story, how I grew up, what I did, how the message has changed me. God has done miracles wherever I have gone."
Elijah and Gaston have been interviewed together on BBC radio, and have also spoken at a government reconciliation conference where they shared their story with all the top government leaders, including parliament and the president. These days they continue to work together, carrying the message of reconciliation through their testimonies and the principles they learned in the seminar village to village by bicycle. They have also started an Association of ex-killers and neighborhood victims. They build houses for Tutsi victims. Soon Elijah will also start to teach carpentry to the group (a skill he learned in prison).
Child-Headed Household
Gaudence in her own words. . .
"I want to thank God because I got healed from my wounds. In 1994 we fled to Congo and faced many difficulties in the refugee camps. When we came back to Rwanda my father was put in prison. I loved my father, so when he was imprisoned, I was very sad and grieved. I began to hate the Tutsi because they had deprived me of my father. I lived with the hatred and resentment for many years. When I would think of my father in prison I would cry and be filled with anger. But my mom didn't seem to care. I said "You, woman, are silly. You are stupid. You don't care at all." I was trying to contaminate my mother, because I thought we needed to join together in hatred. Since I couldn't see the hatred in her I began to hate her, too! I was very judgmental. I was even angry with my Tutsi pastor and thought, "Even though they say they are saved, they will perish, and go to hell. All of them!"
"In 1998 I went to a reconciliation workshop with Anastase & Joseph facilitating. In the teaching about roots, I started to realize where I was – I was bitter about my own ethnicity. I also had denominational pride. When it was time for the cross workshop, I realized I had something heavy to give to Jesus. We were told to think about the pain we have experienced and to write the pain down and to give to Jesus. For me the only thing I wrote on the paper was, "I hate Tutsi." The reason why I hated them is because they took my father to prison. I wrote "I don't fellowship with other people. I don't believe in their denomination." Every time I came back to the memory of my father, I would stop and cry. I gave that to Jesus.
"Then I remembered my mother. I tried to poison her every day so now what could I do about that? When I told her my testimony she was very happy because she didn't have the same hatred that I had. Now she could expose her own hurt and the pain she had tried to bury. I also encouraged her to express her pain because suppressing it wasn't helpful. So my mom came to salvation and healing through my witness. She died a few years later, but she was saved and healed when she died!
"After my mother died we were orphans – my father was still in prison. I had to take care of my 6 younger siblings. It was very hard to be a parent to all these children. I didn't know how to cultivate the land. I would pray and ask Jesus "What am I going to do with these children?" One day we were invited to a reconciliation team retreat in Byumba. I wasn't on the list of attendees, but I replaced someone. God had already told me I must go and there was something great waiting for me there. Before going to Byumba, I prophesied about an orphan child that God was about to give parents. Because there were so many of us, I didn't receive that as a personal prophesy.
"In our small group I shared my pain, and said to the other two men, I want to be in the ministry, but if I do it, there will be no one to help with my siblings. So the pastor from Kibungo (a Tutsi) prayed for me. I heard God telling me, "I bought you here because I want to give you a father. This man from Kibungo (Mugasa) is your father now!" I didn't dare speak it out because I was too young and these men were older pastors. Later in the big group, Phineas prayed "Someone here has a message but is hiding it." Then Phineas came to me and said "You! You are hiding a message God has given you." So I said "God said Mugasa is to be my father!" Mugasa came over and hugged me. I went to Kibungo to visit, and it was a surprise for him. My mother loved me a lot before she died. When I went to Kibungo, Mugasa's wife received me like a mom. They welcomed me so well into their Tutsi family, and really wanted me to feel like their child. Since then, they are family to me and display so much kindness. They love me like their own child. When ever Mugasa comes to Gikongoro he visits me and gives me so much advice
"My family – my siblings – have been blessed through my experience. As a wounded person I could have poured all my bitterness into the children, if I hadn't been healed. I always tell my siblings "you should praise the Lord that I have been healed, because I can hear you, value you, and give you love. Please thank the Lord for this because otherwise I could be very bad parent for you!"
"World Vision has a sponsorship program to help children who are raising children. I am now the head of 79 households headed by children. I give the seminar teaching there, and help these other children raise their siblings. I am so grateful to God that I've been through this experience. My desire is to see every Rwandan to go through the same experience. I want to say thank you for this ministry. God bless you!
"Recently, my father has been sentenced by the Gacaca court to 30 years. I wanted to help my father, teaching him the things I have learned, help him acknowledge his sin and confess, but he refused. The evidence is against him. He did what he is accused of. If he would have confessed it, the sentence would have been reduced, but he wouldn't be honest. I still love him but my friends are helping me see that his confession isn't my responsibility."
Widowed Survivor
Odette in her own words. . .
"I was living in sorrow and pain for many years. Looking at the killing and genocide in this area, my pain became even worse. After the genocide I was
isolated. I became menally dysfunctional. I had lost my husband and children. My parents were killed in a very cruel way, also my husband and children. My first born was buried alive. I couldn't function anymore.
"When Rhiannon first came after the genocide, the church sent me to the seminar. When she talked about letting ourselves cry, it was something new. I couldn't cry then, because my head and heart were so heavy with many terrible memories. At a second seminar, I went into a small group, but I couldn't talk. I attended many different seminars, for 4 years, but, still, I couldn't talk. Because most of the people in the seminar were Hutu from Gisenyi and Ruhengeri, I couldn't speak.
"But one day, God really blessed me with a lot of tears. At the next seminar, I exploded into tears during the teaching about the Holy Nation, and at the King's Table. A pastor from Ruhengeri gave me the bread and wine. I was crying. Then Joseph (a Hutu) crowned me. That opened my heart to the Hutu from these areas and I wept and wept. I started to walk into my healing. Since then I could start sharing my story and receive love in my heart.
"I started to share with other people. I could have a new love for those regions that I had hated so much. (People from these regions killed my husband and children). I could sleep for the first time in many years. I became genuine in my evangelism and ministry for the Lord.
"I was invited to the training for a reconciliation team. When the team formed, I became good friends with Aimable, and he is a good friend of my church. Before, our different churches would be a barrier to our friendship, but now we work together, bringing genocide survivors and released prisoners together. People thought we were such a strange combination. But after each seminar we ran there was unity between the participants. Seeing a genocide survivor hugging a killer gives me strength. The cross workshop has given me strength. I preach about it wherever I go. I was changed through the seminars. We have run 12 seminars with 30-40 people at each one.
"Then I started feeling strongly about widows. We brought together 60 women, most of whom had been raped and infected with aids. Most had lost all their children. Their stories were very difficult to hear. Rape is not something you share with other people. You don't talk about it. After the seminar, we decided to keep meeting, and have now formed an association. We meet twice a month, praying together and exchanging stories and testimonies and needs. There is trust among us. There were some who couldn't talk, but this has given them a platform to share. Some were not interested in life anymore, not taking care of themselves, not even washing themselves. But today you see them clean and with a desire to live. Other raped women are now coming to us to be able to share their stories here. Every time we meet we are building hope.
"This year our focus is on improving our welfare. Some have adopted orphans to help. Some are stuck in their houses, unable to leave. We are doing advocacy work with the government and another NGO. Our dream is to become a "medication"– an answer to many widows who are hurting. We were given a study Bible with focus on widows and this is a very good tool. Now we are looking at teaching how to make baskets. We need prayers for the Lord's provision to break out of our poverty and dependency."
Category : Uncategorised
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\section{Introduction}
As a preface to the themes of this paper, it is difficult to improve on the introduction
by \citet{geisler_etal1996}, which we quote directly:
\smallskip
\parbox{8.0cm}{\emph{``One of the major goals of modern astronomy is an understanding of galaxy formation.
An ideal tool for this study would be a witness which was both present at the long-since-vanished
first epoch when most galaxies formed, and yet still survives today to tell us its story.
In addition, we would like many such witnesses, to corroborate their stories, and we would like them to
be easy to find. Enter the globular clusters. They are among our most powerful cosmological probes for
investigating this key topic.''}}
\smallskip
In this paper we continue an exploration of the globular cluster systems (GCSs) around Brightest
Cluster Galaxies (BCGs), the central dominant objects in rich clusters of galaxies.
This BCG program extends our earlier work on central giant galaxies at distances within 100 Mpc
\citep{harris_etal2006,harris2009a} outward to richer galaxy-cluster environments and higher BCG luminosities.
Paper I of the current series \citep{harris_etal2014} presents new deep photometry obtained with the Hubble Space Telescope
(HST) cameras around seven BCGs at distances from 100 to 250 Mpc,
along with an analysis of the luminosity functions (LFs) of their GCs.
We found the GCLFs to be strikingly similar in all systems, with trends that extend previous
analyses for smaller galaxies \citep{jordan2007,villegas2010} smoothly upward to the largest galaxy sizes known.
Paper II \citep{harris_etal2016} presents a more comprehensive analysis of the GCS around one of these
BCGs, NGC 6166 in Abell 2199, with the focus on its GCS metallicity distribution, spatial distribution, and total GC
population.
In this paper, we present similar data for two of the other BCGs in our program,
UGC 9799 (Abell 2052) and UGC 10143 (Abell 2147), as well as new data reductions for the two supergiant
galaxies NGC 4874 and 4889 in the Coma cluster (Abell 1656), constructed from HST Archive data.
In all cases, the photometry reaches
very similar depths in absolute magnitude and employs the same color indices,
enabling homogeneous comparisons among all the systems. As in Paper II, our focus in this paper is on
the metallicity and spatial distributions.
In Section 2 a review of the
literature for GC metallicity distributions is presented.
In Section 3 and 4 the target galaxies and the photometric
reductions are described. The color-magnitude diagrams for the GC systems are presented
in Section 5, and an analysis of the color (metallicity) distributions is presented in
Section 6 along with their notable galaxy-to-galaxy
differences. The spatial distributions are discussed in Section 7.
In Sections 8 and 9 we discuss some implications of our findings and a brief summary.
Our complete photometric data for the 5 BCGs discussed here and in Paper II can be obtained from
the webpage address http://physwww.mcmaster.ca/~harris/BCGdata.html
or by request to the first author.
\section{Metallicity and Color Distributions}
A particularly informative feature of globular cluster (GC) populations in galaxies
is their \emph{metallicity distribution function} (MDF). In many
galaxies, a long-standing empirical feature of the MDF is its \emph{bimodal} nature, with
a canonical metal-poor (MP) ``blue'' sequence centered
near $\langle$[Fe/H]$\rangle \simeq -1.5$
and a metal-rich (MR) ``red'' sequence near $\langle$[Fe/H]$\rangle \simeq -0.5$.
Many authors have adopted the view that this two-part structure of the MDF
is evidence for two major and perhaps distinct
star-forming epochs in the formation histories of large galaxies,
a view that has persisted for many years
\citep[e.g.][among many others]{zepf_ashman93,forbes_etal97,forbes_etal2011,brodie_strader06,arnold_etal2011,blom_etal2012a,cantiello_etal2014,brodie_etal2014,kartha_etal2016}.
However, bimodal MDFs are not characteristic of the field-halo stars in their parent
galaxies, in the few cases where it has been possible to compare the both GCs and halo stars
directly in the same galaxy
\cite[e.g.][]{harris_etal2007,durrell_etal2010,rejkuba_etal2011,rejkuba_etal2014,monachesi_etal2016}.
Reconciling this apparent mismatch between field stars and GCs presents an intriguing challenge for quantitative formation modelling.
As is the case for all GC work, the origins of the topic start with the Milky Way.
\citet{zinn85} clearly established the bimodal nature of the Milky Way GC
population, finding that the cluster metallicities coupled closely with systematically
different kinematics and spatial distributions for the MP and MR subcomponents. Gradually growing evidence for
these two Milky Way subsystems had accumulated in earlier papers
\citep[including among others][]{mayall1946,morgan1956,baade1958,kinman1959,marsakov_suchkov1976,searle_zinn1978,harris_canterna1979},
but culminated in Zinn's definitive analysis.
For distant galaxies, spectroscopically measured GC metallicities
are observationally far more time-consuming to build up, and probing the full three-dimensional kinematics
of the halo is out of reach. Instead, GC integrated colors
are commonly used as proxies for metallicity, since large samples of GCs can be efficiently
measured this way. For very old and relatively simple stellar systems such as GCs,
integrated color is sensitive only to metallicity while
other factors such as mean age or CNO abundances have only second- or third-order effects.
The key empirical question is then how to convert the \emph{color distribution function}
(CDF) of a sample of GCs to its MDF and whether or not these different forms
are measuring the same thing.
The literature on this topic is extensive and continually developing, so
a full synthesis is probably still premature. However, the issue seems to boil down
to two central and only partially related questions:
\begin{enumerate}
\item For GC systems, is the MDF intrinsically bimodal?
\item Does the CDF correctly represent the MDF shape after the appropriate transformation?
\end{enumerate}
The answer to the first question, based strictly on spectroscopic evidence,
now appears to be that bimodality is common but that there is no truly universal pattern.
As has been emphasized elsewhere \citep{strader_etal2011,usher_etal2012,brodie_etal2014},
spectroscopy of significant samples of GCs,
in many galaxies, is needed to go beyond the default assumption of bimodality confidently.
The Milky Way GC system is clearly bimodal (see the Appendix of Paper II for
a recent version of its MDF based on high-dispersion spectroscopy measures of [Fe/H]).
But several other galaxies now have GC metallicity data constructed from spectrum line
strengths and for these, differing results emerge.
In M31, the nearest large galaxy, the GC MDF
displays a broad and more uniformly populated distribution that is less easily matched
by a bimodal-Gaussian form
\citep{caldwell_romanowsky2016,caldwell_etal2011,cezario_etal2013,perrett_etal2002,barmby_etal2000},
which may reflect
the complex and extended growth history of the galaxy \citep{mcconnachie_etal09}.
Other large galaxies with well populated GC systems are rather well described
by bimodal, spectroscopic MDFs: these include NGC 5128 \citep{woodley_etal2010},
M81 \citep{ma_etal2013}, NGC 4472 \citep{strader_etal2007}, NGC 4594 \citep{alves-brito_etal2011},
NGC 3115 \citep{arnold_etal2011,brodie_etal2012}, and 8 other large normal ellipticals
\citep{foster_etal2010,usher_etal2012}. However, notable
galaxy-to-galaxy differences appear in the degree of overlap between the MP and
MR `modes' and their internal dispersions.
Spectroscopically based evidence for trimodality or simply a more uniform [Fe/H] distribution
is indicated for M87 \citep{strader_etal2011}, NGC 4494 \citep{usher_etal2012}, and perhaps
NGC 4365 \citep{chies-santos_etal2012a,blom_etal2012b} as well as M31.
The answer to the second question -- how well the CDF represents the MDF --
depends strongly on which color index is being used.
Many indices from near-UV through to near-IR have now been tested and compared.
Several discussions have claimed that a unimodal MDF is
capable of being converted to a bimodal
CDF if the transformation is sufficiently nonlinear
\citep[e.g.][]{yoon_etal2006,yoon_etal2011a,yoon_etal2011b,cantiello_blakeslee2007,chies-santos_etal2012b,kim_etal2013,chung_etal2016}.
As a numerical exercise this claim is certainly true, though
the continuing issue with these discussions is that they rely very heavily on
single-stellar-population (SSP) theoretical modelling to develop translation
curves from [Fe/H] to a given color index. These model curves usually have quite complex
shapes, and the various available SSP libraries show notable disagreements
\citep[e.g.][]{peacock_etal2011,alves-brito_etal2011,brodie_etal2012,chung_etal2016}.
By contrast, empirically based transformations from metallicity to color
that do not rely heavily on modelling tend to be much more nearly linear and thus
to yield CDFs that resemble the intrinsic MDFs rather well
\citep[e.g.][]{barmby_etal2000,caldwell_etal2016,usher_etal2012,usher_etal2015,peng_etal2006,spitler_etal2008,foster_etal2010,sinnott_etal2010,fan_etal2010,peacock_etal2011,vanderbeke_etal2014,brodie_etal2012,brodie_etal2014,cantiello_etal2014,sakari_wallerstein2016}.
SSP theoretical models, however, are useful for comparing the relative metallicity sensitivity and linearity of
different color indices. The most effective ones include $(V-K), (B-I), (g'-i'), (g'-I), (g'-K)$, or $(C-T_1)$
\citep{barmby_etal2000,harris_etal2006,cantiello_blakeslee2007,spitler_etal2008,blakeslee_etal2012,forte_etal2013,kundu_zepf2007,sinnott_etal2010,fan_etal2010,foster_etal2010}.
These indices combine high metallicity sensitivity with modest degrees of nonlinearity.
However, a large fraction of the CDFs available in the literature have been measured in $(V-I)$
(which is less sensitive to metallicity) or $(g'-z')$ (which is more nonlinear than others listed above)
\citep[e.g.][]{gebhardt_kissler-patig99,larsen_etal01,peng_etal2006,villegas2010}.
A diagnostic index that has gained more frequent use recently is the Ca triplet
line strength, which correlates near-linearly with [Fe/H] in the
range [Fe/H] $\lesssim -0.5$ \citep{sakari_wallerstein2016,brodie_etal2012}.
At the highest metallicities, CaT may become less sensitive, but any change in slope
above [Fe/H] $\simeq -0.5$ will not be able to generate the intermediate-metallicity
``valley'' at [Fe/H] $\simeq -1$ between the normal MP and MR modes.
Interestingly, \citet{usher_etal2015} discuss evidence that different galaxies may have
different color-to-metallicity conversions. \citet{cantiello_blakeslee2007} and
\citet{forte_etal2013} note that for a given galaxy,
every color index should yield the same MDF if the
transformations are correct. So far, applying this self-consistency test in practice
has rarely been possible.
A useful conclusion for the present seems to be that CDFs reflect the intrinsic shapes of
the MDFs, if the color indices being used are chosen well. The extensive literature
that reveals clearly bimodal CDFs for many galaxies therefore continues to be important
\citep[e.g.][among many others]{geisler_etal1996,neilsen_tsvetanov1999,larsen_etal01,kundu_whitmore01,rhode_zepf2004,bassino2006,peng_etal2006,harris2009a,harris2009b,faifer_etal2011,jennings_etal2014,cantiello_etal2014,kartha_etal2014}.
At the same time, some galaxies are better described as trimodal, unimodal, or simply
broad without matching a simple Gaussian-type model
\citep[for specific examples, see][]{larsen_etal01,peng_etal2006,blom_etal2012a,larsen_etal2005,kundu_zepf2007,usher_etal2012}.
A valid theoretical model for GC formation in the larger context of galaxy formation must be
able to deal with this diversity of outcomes.
Starting with either the CDF or MDF,
the first empirical question is simply to establish how many
components or ``modes'' are present
regardless of shape, and how similar these might be to the Milky Way;
or (alternately) whether or not a bimodal deconstruction is justified in the first place.
The first mention of a \emph{specifically Gaussian
shape} for these modes that we are aware of is in \citet{zinn85}.
\citet{zepf_ashman93} introduced a mixture-modelling numerical code (the
since-popular KMM package) to make objective tests of unimodality (the null hypothesis) versus
multimodality, using the CDFs for the two giant ellipticals NGC 4472 and 5128 as testbed cases.
They concluded strongly that their CDFs are bimodal.
A Gaussian model was implicitly used for fitting the components,
and, more or less by default, this quickly became the norm for later studies.
Just a few years later, the ``bimodal Gaussian''
model was already rather firmly established in the literature of the subject
\citep[e.g.][]{geisler_etal1996}.
\begin{figure}[t]
\vspace{-3.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{gIcal.pdf}
\end{center}
\vspace{-0.2cm}
\caption{\emph{Left panel:} $(g-I)_0$ versus $(g-i)_0$ for clusters in NGC 5128.
\emph{Middle panel:} $(g-I)_0$ versus $(g-Z)_0$ for the same clusters.
\emph{Right panel:} $(g-I)_0$ versus [Fe/H] for the same clusters.
The equations for the interpolation lines are given in the text: in the right
panel, the solid line
is for [Fe/H] as the independent variable, and the dashed line for $(g-I)_0$
as the independent variable. Equation (1) in the text lies in between the two.}
\vspace{0.0cm}
\label{fig:gIcal}
\end{figure}
\citet{gebhardt_kissler-patig99} used various nonparametric tests to establish
the Gaussian bimodal form more
strongly, though of necessity they
were forced to work with the rather metallicity-insensitive color index $(V-I)$ that
dominated the available data at the time. \citet{muratov_gnedin2010} discuss different
indicators of either Gaussianity or bimodality within the context of their GMM fitting
code, noting that a unimodal but asymmetric
MDF will often favor a bimodal-Gaussian fit.
The bimodal-Gaussian form continues to be widely used simply because it continues
to match the CDFs and MDFs rather accurately
in large numbers of galaxies of all types, sizes, and environments
as the quality and internal precision of the data have steadily increased.
Nevertheless, there is not yet any \emph{a priori} astrophysical reason to say that
the MP and MR components should be specifically Gaussian. GC formation models within the
context of their parent galaxies are not yet advanced enough to make predictions for
the shape of the MDF at that level of precision \citep[e.g.][]{li_gnedin2014}.
Thus the main purpose of these numerical model fits is to conveniently characterize
the first-order features of the MDF: the mean metallicities of the modes (however many
there are), their widths (intrinsic metallicity spread), and the metallicity
separation between modes.
In the present survey of globular cluster systems in BCGs, we use the color index
$(F475W-F814W) \simeq (g-I)$ (from here on we drop the accents on the SDSS indices).
In the following discussion it will be useful to have
a calibration of this index versus cluster metallicity [Fe/H]. To do this, we would
ideally need to
have GC photometry of the same clusters in both the Kron-Cousins and SDSS systems, in
addition to spectroscopically based metallicity measurements. At present, there are no
ideal solutions to that problem. Galaxies satisfying all three
of these criteria are rare; in principle the Milky Way GC databases could be used, but
cluster-to-cluster foreground reddenings differ strongly, the published SDSS indices
\citep{vanderbeke_etal2014} show considerable scatter versus metallicity,
and the variety of studies from which the $UBVRI$ indices
were derived are completely different from the SDSS survey, so aperture-size mismatches
are significant. Similar problems affect the M31 GC sample. The best
option at the present time for developing a $(g-I)$ transformation is likely to be
from the nearby early-type giant galaxy NGC 5128:
here, $UBVRI$ photometry is available from \citet{peng_etal2004}, $griz$ photometry
from \citet{sinnott_etal2010}, and [Fe/H] values derived through $(C-T_1)$ from
\citet{woodley_etal2010}; these [Fe/H] values are in turn well correlated with
the Sloan-system spectroscopic index [MgFe]' (see Woodley et al.). We have extracted the GCs in common
from these three catalogs, with the results shown in Figure \ref{fig:gIcal}. The great majority
of these GCs lie well outside the central few kiloparsecs of NGC 5128 and thus are
unaffected by the well known dust lane. We have therefore applied only the foreground
reddening of the galaxy, for which we adopt $E_{g-I} = 2.2 E_{B-V} = 0.25$
\citep{cardelli_etal1989} to obtain the intrinsic colors.
We note, however, that the $UBVRI$ measurements were done on $3''$ aperture diameters corrected
to $14''$ through median curves of growth \citep{peng_etal2004}, while the $griz$ measures
were done through $7.6''$ apertures \citep{sinnott_etal2010}, so a small aperture mismatch
may exist here as well affecting the zeropoint of $(g-I)$.
The first two panels of Fig.~\ref{fig:gIcal} show the correlations between $(g-i)_0$ and
$(g-z)_0$ versus $(g-I)_0$. These correlations rely purely on the
photometric data independently of [Fe/H] estimates. Simple linear relations
derived from direct least-squares fits are
\begin{eqnarray}
(g-i)_0 \, & = & \, (-0.268 \pm 0.024) + (0.856 \pm 0.018) (g-I)_0 \nonumber \\
(g-z)_0 \, & = & \, (-0.475 \pm 0.042) + (1.123 \pm 0.030) (g-I)_0 \, . \nonumber
\end{eqnarray}
The $(g-i)_0$ vs. $(g-I)_0$ relation is more tightly defined and valid over a wider range
of colors than $(g-z)_0$ vs. $(g-I)_0$.
Both $(g-i)$ and $(g-I)$ do well as metallicity indicators, but $(g-I)$ is a bit more sensitive
and takes good advantage of the broadband HST filter system.
The $(g-z)$ index is in turn slightly more sensitive than
$(g-I)$, but a noticeable nonlinearity remains between them.
It should be noted again (see above) that the $g$ and $I$ photometric data come from two different observational
programs and therefore do not have the internal homogeneity that would normally be desired,
so any error in the zeropoint of the $(g-I)$ scale is hard to assess at present. Fortunately, the slope and curvature
of the relations are more important for the purposes here rather than the absolute values of [Fe/H].
The third panel of Fig.~\ref{fig:gIcal} connects $(g-I)_0$ with [Fe/H].
A modestly nonlinear quadratic relation accounting for scatter in both axes is
\begin{equation}
(g-I)_0 \, = \, 1.770 + 0.428 {\rm [Fe/H]} + 0.045 {\rm [Fe/H]}^2 \,
\end{equation}
which is plotted in Fig.~\ref{fig:gIcal}c.
We recognize that this proposed calibration is only temporary; in particular,
the zeropoint depends on the accuracy of the separate zeropoints of $g$ and $I$ from
two different observational programs and thus has a higher degree of uncertainty than usual.
The conversion of $(g-I)$ to [Fe/H] can be
greatly solidified once larger numbers of high-quality spectroscopically based
[Fe/H] values become available for GC systems outside the Local Group particularly,
where aperture-size corrections on the photometry become unimportant.
\begin{table*}[t]
\begin{center}
\caption{\sc BCG Parameters}
\label{tab:basics}
\begin{tabular}{llcclcr}
\tableline\tableline\\
\multicolumn{1}{l}{Galaxy} &
\multicolumn{1}{l}{Cluster} &
\multicolumn{1}{c}{$(m-M)_I$} &
\multicolumn{1}{c}{$d$} &
\multicolumn{1}{l}{$M_K$} &
\multicolumn{1}{c}{$L_X$} &
\multicolumn{1}{r}{$R_c$ }
\\ & & & (Mpc) & & ($10^{44}$ erg s$^{-1}$) & (kpc) \\
\\[2mm] \tableline\\
NGC 4874 & A1656 & 35.02 & 100 & -26.1 & 3.98 & (0) \\
NGC 4889 & A1656 & 35.02 & 100 & -25.6 & 3.98 & 169 \\
NGC 6166 & A2199 & 35.60 & 130 & -25.7 & 1.90 & 7 \\
UGC 9799 & A2052 & 35.95 & 150 & -25.5 & 1.33 & 38 \\
UGC 10143& A2147 & 35.99 & 154 & -24.9 & 1.66 & 82 \\
\\[2mm] \tableline
\end{tabular}
\end{center}
\vspace{0.4cm}
\end{table*}
\section{Target Galaxies}
In this paper, we present new photometry for the GC populations around UGC 9799 and UGC 10143. For
comparison with these and the other BCGs in our program, we include as well NGC 4874 and NGC 4889
in the Coma cluster. In all cases, the main data are from the ACS Wide Field Camera on board HST,
with identical filters and similar exposure time. Here, we briefly summarize basic
features of these galaxies and the Abell clusters they dominate.
UGC 9799 is the central and brightest galaxy in Abell 2052 at a distance
$d = 150$ Mpc (for $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$). As in Paper I we
adopt an apparent distance modulus $(m-M)_I = 35.95$ and foreground
reddening \citep[from NED, following][]{schlafly_finkbeiner2011} $E_{B-V} = 0.037$.
Detection of the GC system around UGC 9799 was first done by \citet{harris_etal1995}
through deep CFHT imaging. A reproduction of our ACS/WFC field is shown in
Figure \ref{fig:ugc9799}.
\begin{figure}[t]
\vspace{-0.0cm}
\begin{center}
\includegraphics[width=0.20\textwidth]{ugc9799_im.pdf}
\end{center}
\vspace{-0.2cm}
\caption{The ACS/WFC field centered on UGC 9799. The field of
view is roughly 3.4 arcmin across.}
\vspace{0.0cm}
\label{fig:ugc9799}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.20\textwidth]{ugc10143_im.pdf}
\end{center}
\vspace{-0.2cm}
\caption{The ACS/WFC field centered on UGC 10143.} \vspace{0.0cm}
\label{fig:ugc10143}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.20\textwidth]{ngc4889_im.pdf}
\end{center}
\vspace{-0.2cm}
\caption{The ACS/WFC field containing NGC 4889.} \vspace{0.0cm}
\label{fig:ngc4889}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.40\textwidth]{ngc4874_im.pdf}
\end{center}
\vspace{-0.2cm}
\caption{The ACS/WFC field (F2) centered on NGC 4874.} \vspace{0.0cm}
\label{fig:ngc4874}
\end{figure}
The core of UGC 9799 shows clear evidence for gas and (modest) nuclear activity.
As a radio source it is 3C 317, and Chandra observations reveal a compact core
X-ray source \citep{donato_etal2004,balmaverde_etal2006}. At the center, GALEX
ultraviolet profiles and infrared excess lead to a deduced present-day star formation
rate of $\sim 1 M_{\odot}$ y$^{-1}$ \citep{hicks_etal2010,hoffer_etal2012}, while
nuclear optical emission lines and a small star-forming filament visible in the
near-UV further confirm star-forming activity \citep{buttiglione_etal2010,martel_etal2002};
the filament is also visible in our $F475W$ image.
There is presumably a central supermassive black hole (SMBH), but only an upper limit
of $4.6 \times 10^9 M_{\odot}$ exists for it \citep{dallabonta_etal2009}.
The larger-scale distribution of hot X-ray gas in A2052 is discussed recently by
\citet{blanton_etal2011} and \citet{machado_limaneto2015}; the hot gas shows much substructure
(bubbles, shocks) indicative of previous AGN activity and/or merging of galaxies.
UGC 10143 is the central giant in A2147, at $d = 154$ Mpc; and A2147 is part of the
Hercules Supercluster along with A2151 and A2152 \citep{barmby_huchra1998}. We adopt
$(m-M)_I = 35.99$ and $E_{B-V} = 0.031$. The BCG is radio-quiet and has a deduced
central star formation rate consistent with zero from its lack of UV or infrared signature
\citep{hoffer_etal2012}. Close inspection of our images shows a smooth, featureless optical
core with no indications of peculiarities.
Detection of the GC system around UGC 10143 was first done by
\citet{blakeslee1999} through ground-based imaging and surface brightness fluctuation (SBF) analysis.
A reproduction of our ACS/WFC field is shown in Figure \ref{fig:ugc10143}.
According to \citet{tovmassian_andernach2012}
A2147 is not a Bautz-Morgan class I cluster since the luminosity difference in $M_K$
between its first- and second-ranked galaxies is only 0.2 mag (the second-ranked member is
PGC056770, which lies 180 kpc to the south of UGC 10143). However, the overall
cluster richness, the velocity dispersion, and the moderately low peculiar motion
of the BCG are all typical of BM I clusters, so the classification remains a bit
ambiguous.
\begin{table*}[t]
\begin{center}
\caption{\sc Exposure Times and Completeness Parameters}
\label{tab:t}
\begin{tabular}{llllrll}
\tableline\tableline\\
\multicolumn{1}{l}{Galaxy} &
\multicolumn{1}{l}{GO Program} &
\multicolumn{1}{l}{Detector} &
\multicolumn{1}{l}{Filter} &
\multicolumn{1}{r}{$t$(sec)} &
\multicolumn{1}{l}{$m_0$} &
\multicolumn{1}{l}{$\alpha$}
\\[2mm] \tableline\\
UGC 9799 & 12238 & ACS/WFC & F475W & 7977 & 29.60 & 3.5 \\
& & & F814W & 5253 & 28.13 & 3.5 \\
& & WFC3 & F475W & 8041 & 29.30 & 3.0 \\
& & & F814W & 5343 & 27.85 & 2.7 \\
UGC 10143& 12238 & ACS/WFC & F475W & 10726 & 29.45 & 3.5 \\
& & & F814W & 5262 & 27.95 & 3.3 \\
& & WFC3 & F475W & 10856 & 29.20 & 3.0 \\
& & & F814W & 5352 & 27.30 & 3.3 \\
NGC 4889 & 11711 & ACS/WFC & F475W & 4770 & 29.20 & 2.6 \\
& & & F814W & 9960 & 28.00 & 3.2 \\
NGC 4874-F1 & 10861 & ACS/WFC & F475W & 2677 & 28.30 & 2.6 \\
& & & F814W & 1400 & 27.10 & 3.2 \\
NGC 4874-F2 & 11711 & ACS/WFC & F475W & 2394 & 28.60 & 2.6 \\
& & & F814W & 10425 & 28.00 & 3.2 \\
NGC 4874-F3 & 12918 & ACS/WFC & F475W & 2568 & 28.30 & 2.6 \\
& & & F814W & 1400 & 26.90 & 3.2 \\
\\[2mm] \tableline
\end{tabular}
\end{center}
\vspace{0.4cm}
\end{table*}
The giants NGC 4874 and NGC 4889 are the dominant galaxies in the rich and well known Coma cluster
(A1656), for which we adopt $d = 100$ Mpc, $(m-M)_I = 35.02$, and
$E_{B-V} = 0.01$.
Reproductions of the NGC 4889 and NGC4874-F2 fields from the ACS/WFC camera are shown
in Figures \ref{fig:ngc4889} and \ref{fig:ngc4874}.
NGC 4874 is surrounded by a handful of smaller satellite galaxies
\citep[see Fig.~1 of][for their identification numbers]{cho_etal2016}, though as will be seen
below these do not contribute noticeably to the overall GC population, with the exception
of a small excess around NGC 4873 (at left center in Fig.~\ref{fig:ngc4874}).
Though NGC 4874 and 4889 have similar $V-$band luminosities, NGC 4874 is clearly the one lying
at or near the center of the Coma potential well (as defined by the intracluster X-ray gas)
and has a cD-type envelope. By contrast NGC 4889 resembles a structurally more normal elliptical though
with a supergiant-level luminosity. On our images, both have smooth featureless isophotes all the way inward
to the galaxy center. The first detections of GC populations around these
galaxies were done 30 years ago by \citet{harris1987} and \citet{thompson_valdes1987}
through deep imaging with the CFHT.
Later ground-based imaging by \citet{blakeslee_tonry1995} and \citet{marin-franch_aparicio2002}
including SBF techniques verified that both galaxies had rich GC systems. \citet{harris_etal09}
presented homogeneous photometry of the GC systems in 5 Coma ellipticals including the two
supergiants, all with data from the HST WFPC2 camera. These reached deep enough to gauge the GC luminosity
function turnover point and to obtain useful values for the GC specific frequencies in the
galaxies, but color indices ($V-I$ in this case) were not precise enough to clearly resolve the CDF and determine whether
or not these systems fall within the conventional bimodal pattern.
More recently, \citet{peng_etal2011} discussed the distribution of GCs throughout the Coma cluster,
using the HST/ACS Coma Cluster Treasury Survey imaging.
Their analysis shows that NGC 4874 is
essentially at the center of the GC distribution in Coma and that its own GC spatial profile makes a clear transition to
a newly discovered Intra-Galactic cluster (IGC) population, which becomes dominant beyond
a projected radius of $\sim 300$ kpc.
In the CDF, two modes (MP and MR) are clearly present and the MP mode is much more dominant for
the IGC. Color-magnitude diagrams for
the GC populations around both NGC 4874 and 4889 from HST ACS imaging are presented
and discussed briefly
by \citet{lee_jang2016a}, while \citet{cho_etal2016} complete a more comprehensive discussion
specifically for the NGC 4874 system now including 3-color $(g,I,H)$ photometry.
A structural feature held in common by all four of the galaxy clusters discussed here
(Coma, A2052, A2147, and A2199 from Paper II) is a prominent X-ray halo gas component.
Of 60 nearby clusters listed by \citet{edwards_etal2007} selected
from the NOAO Fundamental Plane Survey, these four rank among the highest in X-ray
luminosity, though not all of them have strong cooling flows or central optical emission.
IGC populations have clearly been established to date only for Virgo and Coma
\citep{durrell_etal2014,peng_etal2011}, and more tentatively in Abell 1689
\citep{alamo-martinez_etal2013}, Abell 1185 \citep{west_etal2011},
and Abell 2744 \citep{lee_jang2016b}, and it is not yet known how well their presence correlates with
hot halo gas. However, the X-ray halos demonstrate that the BCGs studied here all reside in
very massive potential wells defined by their surrounding clusters.
The virial masses of these clusters as confirmed through galaxy velocity dispersions,
X-ray gas temperature, or weak lensing are typically $M_{200} \sim 10^{14} - 10^{15} M_{\odot}$
\citep[e.g.][]{falco_etal2014,wojtak_lokas2010,wen_etal2010,kubo_etal2007,lokas_etal2006,blanton_etal2003}.
In Table \ref{tab:basics}, we summarize
some of the fiducial properties of the BCGs discussed in this paper.
The last column gives the projected distance $R_c$ of each BCG from
the center of its Abell cluster (see the references cited above).
\section{Photometric Reductions}
Imaging for our program was done
with the $F475W$ and $F814W$ filters. The resulting color index in the
native filters, $(F475W-F814W)$, is close to standard $(g-I)$ and is both
metallicity-sensitive and nearly linearly correlated with metallicity (see Section 2).
The magnitude scale we adopt here, as in previous work \citep[][and Papers I and II]{harris2009a},
is on the VEGAMAG system.
The raw imaging data for UGC 9799 and 10143 are from HST program GO-12238 (PI Harris).
Design parameters for this program are summarized in Paper I; full details
of the photometric data reductions are laid out in Paper II, and we follow the
same procedures here. For these two galaxies, ACS/WFC exposures were taken roughly
centered on the BCG, while Parallel exposures with WFC3/UVIS (in the same filters)
were taken simultaneously to give an offset field located in the outskirts of the
galaxy cluster.
From the \emph{*.flc} raw image files provided in the $HST$ Archive we constructed
a single combined image in each filter with \emph{stsdas/multidrizzle}. We used
SourceExtractor \citep{bertin_arnouts1996} to detect candidate objects in
each field, and to do a preliminary rejection of nonstellar objects.
From there we used the normal sequence of steps in \emph{iraf/daophot/allstar}
\citep{stetson1987} to complete the photometry from PSF (point-spread function) fitting
and to do further rejection of nonstellar objects from the goodness-of-fit $\chi$
parameter and the internal measurement uncertainties in each filter.
In all cases, the candidate GCs we are searching for are expected to be starlike in
structure for galaxies more distant than $d \gtrsim 80$ Mpc
\citep[see Papers I and II as well as][]{harris2009a}. This is an important
advantage for our purposes, because it facilitates the removal
of the vast majority of the field contamination, which
is dominated by faint, very small but resolved background galaxies.
Lastly, artificial-star tests were run with \emph{daophot/addstar} to quantify the detection
completeness fraction as a function of magnitude, $f(m)$, separately for each
target field and filter. The $f(m)$ data were fit to a smooth curve of the form
\begin{equation}
f(m) \, = \, {1 \over {1 + e^{\alpha (m - m_0)} }}
\end{equation}
as defined in Paper II.
Here $m_0$ represents the 50\% completeness level and $\alpha$ the steepness
of falloff as the curve passes through $m_0$. Nominally, $f$
is also a function of the background light intensity and therefore the
projected galactocentric distance. However, for these distant and rather
diffuse BCGs, at
$R \gtrsim 15''$ the surface brightness has already fallen to a low enough level
that the radial dependence beyond that radius is negligible (see Paper I for discussion).
In our following analysis, we do not use any of the raw data within $15''$
of the galaxy centers.
More detailed descriptions of the procedures and examples can be found
in Paper II and \citet{harris2009a}.
In Table \ref{tab:t}, we list in successive columns the galaxy name, GO program
ID from the HST Archive, camera, filter name, total exposure time, and completeness
function parameters.
\section{Color-Magnitude Diagrams}
In Figure \ref{fig:ugc9799_xy}, we show the distribution of \emph{measured starlike objects}
brighter than $F814W = 27.0$
in the UGC 9799 ACS and WFC3 fields. In this magnitude range, as shown in Paper II
almost all of these objects are expected to
be GCs. In the ACS field, two smaller companion galaxies are visible as separate
compact groups of GCs of their own: these are PGC054528 (at upper left, marked out
by a circle of $15''$ radius), and PGC05421 (below UGC 9799 and marked out by a
$r=10''$ circle). In the WFC3 field, the galaxy at upper left with an obvious GC
population of its own is PGC054533, marked by a $r=25''$ circle. At upper right is a smaller elliptical
PGC054530.
In Figure \ref{fig:ugc10143_xy}, we show the distribution of measured starlike objects
with $F814W < 27.0$ in the UGC 10143 fields.
In the ACS field (left panel) one obvious clump of points at lower left marks PGC056777
($r=20''$ circle), a nearly face-on disk
galaxy with a complex and distorted array of spiral arms.
In the WFC3 field, only one relatively small galaxy appears at upper left ($r=15''$ circle), which is
2MASXJ16023373+1555259.
\begin{figure*}[t]
\vspace{-5.0cm}
\begin{center}
\includegraphics[width=0.9\textwidth]{ugc9799_xypair.pdf}
\end{center}
\vspace{-1.5cm}
\caption{Locations of the measured starlike objects brighter
than $F814W = 27.0$ in the ACS field centered near
UGC 9799 (left panel) and in the Parallel WFC3 field (right panel).
Fiducial directions on the sky (North, East) are marked in both panels.
Small red circles mark smaller companion galaxies with GC populations
of their own, as listed in the text. For WFC3, the red dashed line indicates
the border between contaminating small galaxies (above the line) and a
cleaner sample of IGC GCs (below the line).}
\vspace{0.0cm}
\label{fig:ugc9799_xy}
\end{figure*}
\begin{figure*}[t]
\vspace{-5.0cm}
\begin{center}
\includegraphics[width=0.9\textwidth]{ugc10143_xypair.pdf}
\end{center}
\vspace{-1.5cm}
\caption{Locations of the measured starlike objects brighter
than $F814W = 27.0$ in the ACS field centered near
UGC 10143 (left panel) and in the Parallel WFC3 field (right panel).
In the ACS field the companion galaxy PGC056777 is shown by the $20''$
circle at lower left, while in the WFC3 field one small galaxy is marked
by a $15''$ circle at upper left (see text).}
\vspace{0.0cm}
\label{fig:ugc10143_xy}
\end{figure*}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ngc4889_xy.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Locations of the measured starlike objects brighter
than $F814W = 26.5$ in the ACS field centered near
NGC 4889. A circle of $20''$ radius is marked around both the
center of NGC 4889 and the companion E0 galaxy NGC 4886 (at left).}
\vspace{0.0cm}
\label{fig:ngc4889_xy}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.6\textwidth]{ngc4874_xy.pdf}
\end{center}
\vspace{-1.0cm}
\caption{Locations of the measured starlike objects brighter
than $F814W = 26.0$ in the three overlapping ACS fields centered near
NGC 4874. Coordinates plotted are relative to the center of NGC 4874,
aligned following the cardinal axes
with East at left and North at top. Three small galaxies with noticeable GC populations of their
own are marked with red circles of $15''$ radius. The concentric
circles around the center of NGC 4874 have radii of $20''$, $50''$, and
$100''$.}
\vspace{0.0cm}
\label{fig:ngc4874_xy}
\end{figure}
The same photometric procedures were followed for NGC 4889, with the resulting
$xy$ plot as shown in Figure \ref{fig:ngc4889_xy}. The clump of points to the
left of the central giant galaxy indicates a GC population around the nearby
galaxy NGC 4886 (= NGC 4882), classified E0. In between
these is the lenticular galaxy PGC044708, but this does not contribute significantly
to the GC population.
As noted above, the GC population around NGC 4874 has been analyzed by
\citet{cho_etal2016} from the single field NGC4874-F2 as listed in Table
\ref{tab:t}. To add a bit more statistical weight to our measurements
of this rich GC system and especially to increase the radial coverage, we added data
from two other overlapping fields with ACS exposures in the same filters
(listed as NGC4874-F1 and NGC4874-F3 in Table \ref{tab:t}), though the exposures
in field F2 reach the deepest of the three (see below).\footnote{The
measurements by Cho et al.~are on the ABMAG system, whereas our independent reductions
are on the VEGAMAG system to make them strictly comparable with the other BCGs in our study.
Their photometry also uses SExtractor parameters for the photometry whereas our data are from \emph{daophot/allstar};
we used SE only for object detection and preliminary culling.}
To guarantee that all three fields
were on the same internal magnitude scale, we used the overlapping objects measured
in more than one field to define mean magnitude offsets in both filters and
normalize fields F1 and F3 to the magnitude scales of F2. These offsets were all less than
$\pm 0.03$ mag in either filter, which is within the internal uncertainties of the
large-aperture corrections to the \emph{allstar} PSF-fitting magnitudes (see Paper II).
To define a final photometric dataset, we used F2, plus the regions of F1 and F3
that fall outside the area covered by F2.
The $xy$ plot for the three fields combined is shown in Figure \ref{fig:ngc4874_xy}.
As is evident in the Figure, the camera orientation angles were
different for each field, leaving a somewhat irregularly shaped composite field.
The three smaller galaxies marked with $r=15''$ circles are NGC 4873 (at top),
NGC 4875 (lower left), and NGC 4869 (lower right), and these are excluded from
later analysis.
The color-magnitude diagrams for UGC 9799 are shown in Figure \ref{fig:ugc9799_cmd}.
The pattern seen in the CMD is reminiscent of what we found for NGC 6166
(Paper II), with a noticeable blue MP sequence centered near $(F475W-F814W) \simeq 1.6$
and a broader distribution of objects to the red, but with no clear `valley' at intermediate
colors. In the WFC3 field (unlike for NGC 6166), remarkably few objects are seen in the
expected GC color range, suggesting that the `intragalactic' GC population
within A2052 is small. Note, however, that the data plotted here comprise
only the objects with $y < 95''$ in Fig.~\ref{fig:ugc9799_xy}. We used only
the lower part of the WFC3 field to avoid the contamination
from the smaller galaxies in the top half of the field. For WFC3, the large
number of objects fainter than the 50\% completeness line is a result of a very conservatively
faint initial detection threshold, so most of these `objects' are likely not to be real.
None of our analysis uses data fainter than the
completeness limit.
\begin{figure*}[t]
\vspace{-2.0cm}
\begin{center}
\includegraphics[width=0.6\textwidth]{ugc9799_cmdpair.pdf}
\end{center}
\vspace{-1.0cm}
\caption{Color-magnitude diagrams for the measured starlike objects around
UGC 9799, for the ACS/WFC field (left panel) and the outlying WFC3/WFC field
(right panel).
Here the native filter magnitudes $F475W, F814W$ are plotted,
closely equivalent to $I$ versus $(g'-I)$ in the Vegamag system. These values are
not corrected for reddening. For the WFC3
field, objects with $y < 95''$ are plotted to avoid contamination from another
galaxy (see text). Detection completeness levels of $f=0.5$ are marked with
the red dashed lines, and the photometric measurement uncertainties are indicated
by the errorbars at left.
}
\vspace{0.0cm}
\label{fig:ugc9799_cmd}
\end{figure*}
\begin{figure*}[t]
\vspace{-2.0cm}
\begin{center}
\includegraphics[width=0.6\textwidth]{ugc10143_cmdpair.pdf}
\end{center}
\vspace{-1.0cm}
\caption{Color-magnitude diagrams for UGC 10143, for ACS (left) and
WFC3 (right).}
\vspace{0.0cm}
\label{fig:ugc10143_cmdpair}
\end{figure*}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.6\textwidth]{ngc4889_cmd.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Color-magnitude diagram for 7892 measured starlike objects around
NGC 4889. Objects within $R < 15''$ of either NGC 4889 or NGC 4886 are excluded.}
\vspace{0.0cm}
\label{fig:ngc4889_cmd}
\end{figure}
\begin{figure*}[t]
\vspace{-3.0cm}
\begin{center}
\includegraphics[width=0.8\textwidth]{ngc4874_cmd3.pdf}
\end{center}
\vspace{-1.5cm}
\caption{Color-magnitude diagrams for the measured starlike objects in the
three fields F1, F2, and F3 around NGC 4874. F1 and F3 each overlap partially with F2,
so the samples in these three diagrams are not fully independent. Note the differences
in limiting magnitude.}
\vspace{0.0cm}
\label{fig:ngc4874_cmd3}
\end{figure*}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.6\textwidth]{ngc4874_cmd.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Color-magnitude diagram for the measured starlike objects around
NGC 4874, for the combination of three fields as described in the text.}
\vspace{0.0cm}
\label{fig:ngc4874_cmd}
\end{figure}
For UGC 10143 the ACS and WFC3 CMDs are shown in Figure \ref{fig:ugc10143_cmdpair}.
The overall color distribution resembles UGC 9799, although a closer look shows relatively
few red (MR) clusters; this will be quantified in the discussion below.
Again, very few objects in the GC color range appear in the WFC3 field, where we have
excised only the datapoints within $15''$ of the small galaxy at upper left in
Fig.~\ref{fig:ugc10143_xy}.
For NGC 4889, the CMD is shown in Figure \ref{fig:ngc4889_cmd}. In this case a more
noticeable classic separation between the MP and MR subpopulations is visible, primarily
because the MP sequence is narrower than for the other BCGs discussed here. Still, significant overlap is present.
For NGC 4874, the CMDs of the three ACS fields (F1, F2, F3 in Table \ref{tab:t})
are shown individually in Figure \ref{fig:ngc4874_cmd3}. The F2 data are clearly the
deepest and a bit more internally precise than the shorter exposures of F1 and F3.
The CMD for the combined fields is shown in Figure \ref{fig:ngc4874_cmd}.
The net result leaves 16064 objects over all magnitudes, though in this combined graph
there is no single well defined limiting magnitude. All the data are, however, highly
complete ($f > 0.9$) for $F814W \lesssim 26.0$.
The GC populations in these BCGs consist of many thousands of objects
and are completely dominant over any field contamination. In Paper II we used photometry
from a local control field, similar data from the Hubble Ultra-Deep Field, and a standard model
for the expected population of Milky Way foreground stars to evaluate the field contamination
quantitatively. The numbers
of contaminating objects within the magnitude and color range of interest here ($I \simeq 22-27$,
$(g-I) \simeq 1.2-2.5$) amount to less than a dozen starlike objects per ACS field and thus
are negligible by comparison with the GC populations. In what follows, no corrections
are made for field contamination.
\section{The Color Distribution Functions}
\subsection{UGC 9799 and UGC 10143}
For UGC 9799, the CDF for 6630 objects brighter than $F814W = 27.0$, in the color range
$(F475W-F814W) = 1.2 - 2.5$, and $R > 10''$ from
galaxy center is shown in Figure \ref{fig:ugc9799_cdf}. Quite clearly, the raw histogram
has a unimodal, skewed shape. However, a bimodal-Gaussian model applied to the data
returns an excellent match to the entire histogram: two modes are required, but more than
two are unnecessary. As in Paper II, we use here the GMM
fitting code \citep{muratov_gnedin2010}. In NGC 6166 we found the same pattern -- two
broad and heavily overlapped CDF modes with no minimum or `valley' between them -- but UGC 9799 is even more extreme
(compare Fig.~11 from Paper II). Though the mode peaks $(\mu_1, \mu_2)$ are separated
by the same amount in color (0.32 mag, corresponding to $\simeq 0.8$ dex in metallicity),
the dispersions of each mode are distinctly larger.
The $D-$statistic, a useful measure of the separation between modes relative to their dispersions
(see Muratov \& Gnedin and Paper II), is $D \simeq 1.70$, below the $D \gtrsim 2$ range
where intrinsic bimodality can be strongly favored.
The fitting parameters for comparison are listed in Table \ref{tab:gmm}.
Here, the MP and MR modes have peak colors ($\mu_1, \mu_2$) and dispersions
($\sigma_1, \sigma_2$), $p_1$ is the fraction of objects belonging to the MP mode,
and $D$ measures the statistical significance of the mode separation.
For UGC 9799, the ACS field excludes the two satellite galaxies marked in
fig.~\ref{fig:ugc9799_xy}, while
the WFC3 field excludes the upper part of the frame containing the smaller
galaxies as described above.
For UGC 10143, the CDF for 3784 objects brighter than $F814W = 27.0$, in the color range
$(F475W-F814W) = 1.1 - 2.3$, and $R > 20''$ from
galaxy center is shown in Figure \ref{fig:ugc10143_cdf}. The satellite galaxy at lower left
in Fig.~\ref{fig:ugc10143_xy} is excluded. The CDF
has a unimodal, skewed shape as for UGC 9799, but again a bimodal-Gaussian model produces
an excellent fit with the results given in Table \ref{tab:gmm}. The main difference compared
with UGC 9799 is a noticeably lower proportion of the MR component (just 40\% of the total
GC population, compared with $\sim$60\% for NGC 6166 and UGC 9799).
\subsection{The Coma Giants}
For NGC 4889 the CDF for 2956 objects in the range $F814W = 23.5 - 26.0$ and
$(F475W-F814W) = 1.3 - 2.2$ is shown in Figure \ref{fig:ngc4889_cdf}. The innermost
circle $R < 20''$, most affected by background light and incompleteness, is not included.
The best-fit bimodal Gaussian shown in the figure does well at reproducing the wings of the
CDF and the blue peak, but less well in the intermediate color range $\sim 1.6-1.8$ where
noticeable discrepancies with the model occur. Attempts at adding a third or fourth mode do not improve the
fit (the GMM solution damps down these additional modes to negligible levels).
Lastly, for NGC 4874 we show the CDF for 5140 objects in the magnitude range $F814W = 24.0 - 26.0$ and
color range $(F475W-F814W) = 1.2 - 2.2$ in Figure \ref{fig:ngc4874_cdf}. We restrict the
magnitude range at the bright end ($F814W < 24$) to deliberately avoid the high-luminosity
end of the GC distribution where the CDF becomes unimodal
\citep[see][and the next section]{cho_etal2016}. We also exclude the range fainter than $\simeq 26$
where the Field 3 data start to
become incomplete. Fortunately, an adopted limit of $F814W \simeq 26.0-26.5$ for the Coma giants
corresponds to about the same luminosity ($M_I \simeq -9$) as in UGC 9799/10143, which are
about one magnitude more distant. For NGC 4874, a bimodal-Gaussian fit produces
a match to the CDF, but again not as cleanly as in
NGC 6166, UGC9799, or UGC10143: the color range near the blue
peak stands out as discrepant. Nevertheless, for both the Coma giants
a standard Kolmogorov test (i.e. a one-sample KS test) does not suggest a statistically significant
deviation from the bimodal model.
Just as for NGC 4889 above, adding more modes to the
solution does not improve the overall fit, nor does
the imposition of equal variances (homoscedasticity).
As we discussed extensively in Paper II, the internal precision of the color indices
in the magnitude range of interest ($F814W \lesssim 27$) is high enough to be
easily capable of resolving the widths ($\sigma_1, \sigma_2$) of the two modes
without adding significant spreading to either one. The evidence then suggests that
these high color dispersions seen in all of the BCGs, along with the near-linearity of the $(g-I)$ color
index, are due to the intrinsic metallicity spread of each mode.
\begin{table*}[t]
\begin{center}
\caption{\sc Bimodal Gaussian Fits}
\label{tab:gmm}
\begin{tabular}{llrllllcc}
\tableline\tableline\\
\multicolumn{1}{l}{Galaxy} &
\multicolumn{1}{l}{$F814W$ Range} &
\multicolumn{1}{r}{$n$} &
\multicolumn{1}{l}{$\mu_1 (\pm)$} &
\multicolumn{1}{l}{$\mu_2 (\pm)$} &
\multicolumn{1}{l}{$\sigma_1 (\pm)$} &
\multicolumn{1}{l}{$\sigma_2 (\pm)$} &
\multicolumn{1}{c}{$p_1$} &
\multicolumn{1}{c}{$D$}
\\[2mm] \tableline\\
NGC6166-ACS & 23.0-26.5 & 4712 & 1.401(0.009) & 1.719(0.015) & 0.122(0.005) & 0.178(0.006) & 0.42(0.04) & 2.08(0.12) \\
NGC6166-WFC3 & 23.0-26.5 & 147 & 1.324(0.021) & 1.674(0.074) & 0.136(0.033) & 0.244(0.013) & 0.71(0.12) & 1.77(0.95) \\
UGC9799-ACS & 20.0-27.0 & 6630 & 1.575(0.009) & 1.904(0.013) & 0.148(0.005) & 0.231(0.002) & 0.40(0.03) & 1.70(0.03) \\
UGC9799-WFC3 & 20.0-27.0 & 181 & 1.369(0.025) & 1.877(0.051) & 0.089(0.016) & 0.300(0.017) & 0.39(0.06) & 2.29(0.23) \\
UGC10143-ACS & 24.0-27.0 & 3784 & 1.516(0.011) & 1.818(0.033) & 0.138(0.006) & 0.193(0.012) & 0.60(0.07) & 1.80(0.19) \\
UGC10143-WFC3 & 24.0-27.0 & 119 & 1.473(0.093) & 1.921(0.092) & 0.205(0.048) & 0.083(0.048) & 0.77(0.20) & 2.87(0.31) \\
NGC 4889 & 23.5-26.0 & 2956 & 1.497(0.006) & 1.802(0.009) & 0.084(0.003) & 0.163(0.004) & 0.40(0.02) & 2.35(0.09) \\
NGC 4874 & 24.0-26.0 & 5140 & 1.436(0.006) & 1.725(0.009) & 0.107(0.003) & 0.184(0.003) & 0.43(0.03) & 1.92(0.05) \\
\\[2mm] \tableline
\end{tabular}
\end{center}
\vspace{0.4cm}
\end{table*}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ugc9799_histo_color.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Color distribution function (CDF) for objects around UGC 9799
with $F814W<27.0$ and $R > 10''$. A bimodal-Gaussian fit to the
data is shown by the superimposed curves; the numbers at upper right
give the means and standard deviations of the two modes.}
\vspace{0.0cm}
\label{fig:ugc9799_cdf}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ugc10143_histo_color.pdf}
\end{center}
\vspace{-0.5cm}
\caption{CDF for objects around UGC 10143
with $F814W<27.0$ and $R > 20''$. A bimodal-Gaussian fit and its parameters
are shown by the superimposed curves and the numbers at upper right
as in the previous figure.}
\vspace{0.0cm}
\label{fig:ugc10143_cdf}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ngc4889_cdf.pdf}
\end{center}
\vspace{-0.5cm}
\caption{CDF for objects around NGC 4889
with $F814W = 23.5 - 26.0$ and $R > 15''$. A bimodal-Gaussian fit and its parameters
are shown by the superimposed curves and the numbers at upper right
as in the previous figure.}
\vspace{0.0cm}
\label{fig:ngc4889_cdf}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ngc4874_cdf.pdf}
\end{center}
\vspace{-0.5cm}
\caption{CDF for objects around NGC 4874
with $F814W = 24.0-26.0$ and $R > 20''$, along with the best-fit bimodal Gaussian.}
\vspace{0.0cm}
\label{fig:ngc4874_cdf}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{fblue_rad.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Blue fraction $p_1 = N(blue)/N(tot)$ as a function of projected
galactocentric distance. The outermost point for NGC 4874 (magenta
arrow at upper right) refers to the GCs in the Intragalactic Medium
of the Coma cluster.
}
\vspace{0.0cm}
\label{fig:fblue}
\end{figure}
\begin{figure*}[t]
\vspace{-1.2cm}
\begin{center}
\includegraphics[width=0.7\textwidth]{3gal_meanpoints.pdf}
\end{center}
\vspace{-1.0cm}
\caption{Mean points along the blue (MP) and red (MR) sequences for
UGC 9799, UGC 10143, and NGC 4889, calculated in 0.5-mag intervals.
In these three galaxies, little or no evidence appears for a systematic
trend of GC color with luminosity.}
\vspace{0.0cm}
\label{fig:mmr}
\end{figure*}
\subsection{MP and MR Populations Versus Radius: Gradients?}
Previous evidence for many large galaxies (Paper II and references cited above)
shows the common existence of radial metallicity gradients in their GC systems,
which show up primarily as a changing ratio of blue to red clusters with galactocentric
radius. A convenient way to characterize these gradients is to plot the blue
fraction $p_1 \equiv N(blue)/N(total)$ versus $R_{gc}$.
For the four galaxies discussed here, the data for $p_1(R)$ are shown in Figure \ref{fig:fblue}.
In each case, GMM fits were done in radial zones, and the mean $\langle R \rangle$
for the clusters in each zone is
expressed as a ratio of the effective radius $R_{eff}$ of the galaxy light profile.
Although noticeable differences occur between galaxies in the overall mean level of
$p_1$, a repeated trend emerges for $p_1$ to rise fairly steeply from $R = 0$
out to $\simeq 1.5 R_{eff}$, then to plateau or rise more gradually until the blue fraction
reaches $p_1 \sim 0.5$, and finally
beyond $\sim 4 R_{eff}$ to increase more steeply again. For NGC 4874, we have
added an outermost data point from \citet{peng_etal2011}, who note that the
intragalactic GC population becomes progressively more dominant beyond $R \simeq 270''$
($7 R_{eff}$) and that the ICL has $p_1 \simeq 0.8$. The ICL value is shown as
in the Figure as an outward arrow.
\begin{figure*}[t]
\vspace{-0.1cm}
\begin{center}
\includegraphics[width=0.45\textwidth]{radsigma.pdf}
\end{center}
\vspace{-1.0cm}
\caption{\emph{Upper panel:} Gaussian width $\sigma_1$ of the blue (MP) sequence
for the five BCGs discussed in this paper, plotted as a function of radius, in kiloparsecs.
\emph{Lower panel:} Width of the red (MR) sequence $\sigma_2$ versus $R$.
NGC 6166 is in \emph{black}, NGC 4874 in \emph{blue}, NGC 4889 in \emph{red},
UGC 9799 in \emph{green}, and UGC 10143 in \emph{magenta}. }
\vspace{0.0cm}
\label{fig:radsigma}
\end{figure*}
As emphasized above, a major result of this study is that the MDFs summed over all radii are broad with
heavy overlap between the standard MP and MR sequences. Two straightforward ways this result
could be generated are that
(a) the intrinsic dispersions of the two modes are actually small at a given radius, but there is a
strong radial gradient in the mean colors $\mu_1, \mu_2$ so that the two modes are blurred together
when all radii are combined; or alternately that
(b) the intrinsic dispersions $\sigma_1, \sigma_2$ are
high at all galactocentric radii, so that any smaller radial zone would be fairly representative of the
whole.
In option (a), the MDF should actually appear more distinctly
bimodal the more restricted the range of radii.
Option (b) appears to be the correct one. To test option (a) directly, we performed
GMM bimodal-fit solutions in smaller
radial bins. These show that there is no significant variation of either $\mu_1$ or $\mu_2$ with radius (see
also Paper II for NGC 6166 in more detail). A direct test of option (b) is in
Figure \ref{fig:radsigma}, where we show the dispersions $\sigma_1, \sigma_2$ versus mean radius,
and where $R$ is renormalized to the same physical scale (kiloparsecs) for all five galaxies discussed
here. There are some differences in the mean $\sigma$'s from one galaxy to another, but the
clear signal from this plot is that the two modes are both quite broad at all radii, and
furthermore that within any one GCS they undergo very little change with $R$. In other words,
the MP and MR modes are heavily overlapped at all projected locations in their halos.
As expected, the most obviously bimodal system of the five (NGC 4889) has the lowest $\sigma-$values
in both modes. (We recognize here, again, that for cases such as UGC 9799 and UGC 10143,
where the MDFs are in fact quite smooth and continuous, discussing them in terms of two clearly
distinguishable `modes' begins to look like only a numerical exercise.)
The combined evidence points to a picture where the mean radial metallicity gradient in the
entire GCS is due entirely to a \emph{population gradient}, which shows up as a steadily increasing
ratio of MP to MR clusters with increasing radius.
Very similar results -- little change with radius in the mean colors and dispersions of both modes,
combined with a radial increase in $f(blue)$ -- have been found for other giant ellipticals including
M87, M49, and M60 \citep{geisler_etal1996,lee_etal2008,harris2009b},
NGC 1399 \citep{bassino2006}, NGC 6861 \citep{escudero_etal2015}, NGC 4278 \citep{usher_etal2013},
and other BCGs and giants \citep{bassino_etal2008,harris2009a,faifer_etal2011}. One notable exception is NGC 1407, which
shows distinct radial decreases in mean color \citep{forbes_etal2011}; small but nonzero gradients
appear in intermediate-luminosity Fornax members \citep{liu_etal2011}.
\subsection{Mass-Metallicity Trends}
In NGC 6166 we found clear evidence for a mass-metallicity relation (MMR) along the
blue sequence in the sense that mean GC color becomes redder at higher luminosity.
Quantitatively the effect corresponded to a simple power law where heavy-element
abundance scales with GC mass as $Z \sim M^{\gamma}$ where $\gamma = {0.27 \pm 0.06}$ over almost the entire
luminosity range brighter than the GCLF turnover point. A scaling similar to this
along the blue sequence has been found in several other giant and supergiant ellipticals at high statistical
significance \citep[e.g.][among others]{harris_etal2006,mieske_etal2006,strader_etal2006,wehner_etal2008,cockcroft_etal2009,peng_etal2009,faifer_etal2011,fensch_etal2014,cho_etal2016}.
No galaxy has revealed convincing nonzero color trends along the red MR sequence.
For UGC 9799 and UGC 10143 the results from a similar analysis
are shown in Figure \ref{fig:mmr}. For these two galaxies, the strong
overlap between the MP and MR components essentially continues upward to the brightest
magnitude ranges more or less unchanged, making clear conclusions about color slopes
quite difficult. For UGC 9799, quantitatively we find
for the blue sequences $\gamma = 0.07 \pm 0.12$ if we use only the points
in the range $24.5 < F814W < 27.0$, but if we use all points $F814W < 27.5$ then
$\gamma = 0.48 \pm 0.21$. For this galaxy, we cannot rule out any of $\gamma \sim 0$,
or a positive slope similar to other cases, or a nonlinear solution.
For UGC 10143, the mean points along the MP sequence give a much more consistent value
$\gamma = 0.01 \pm 0.05$, i.e. indistinguishable from zero.
In NGC 4889, which has more clearly separated blue and red modes,
a more well defined trend along the blue sequence is seen, giving for a
linear fit $\gamma = 0.25 \pm 0.06$. This is very similar to the
result we found for NGC 6166, $\gamma = 0.27 \pm 0.06$.
In NGC 4874, \citet{cho_etal2016} find strong evidence for a blue-sequence MMR,
and we will not repeat their extensive analysis here. They find
a nonlinear trend becoming steeper at brighter magnitudes, which is thus not well described
by a single slope $\gamma = const$. Nevertheless, from our data using field F2 alone (the deepest and
most internally precise part of the photometry) we find $\gamma = 0.26 \pm 0.05$
using only a simple linear fit for $F814W < 26$.
For $F814W \lesssim 24$, the CDF becomes much
more nearly unimodal and symmetric; in this high-luminosity range, blue GCs become very rare while
the red sequence continues upward.
A composite graph for the blue sequences in all five BCGs discussed here is shown in
Figure \ref{fig:mmr_composite}. Here, the sequences have been shifted to a mean color
$(g-I)_0 = 1.5$ for all of them, to enable better direct comparison. UGC 9799 is shown with
the solution from all the meanpoints, giving a positive but very uncertain slope.
NGC 4874, 4889, and 6166 are mutually very consistent at $\gamma \sim 0.25$, while UGC 10143
fairly clearly shows no color trend.
As more BCGs are added to the analysis, it is becoming clearer that the existence
of a MMR (or lack of one) is not universal, and even where one is present, no single
description (such as $\gamma = const$) may necessarily be valid.
UGC 9799 and UGC 10143 in Fig.~\ref{fig:mmr} can be added to NGC 4472 in Virgo, and NGC 1399 in Fornax,
as supergiant ellipticals that do not exhibit a definite MMR.
The model most often adopted to produce the blue-sequence trend is that of \citet{bailin_harris2009},
which is based on the approach that self-enrichment of the cluster stars
takes place while the GC is still in its formation
stages and thus while both gas and young stars are mixed together. Quantitative
examples of fits of this self-enrichment model to various data are in
\citet{mieske_etal2010,cockcroft_etal2009,forbes_etal2010,harris_etal2010,fensch_etal2014}.
It is worth emphasizing that the use of BCGs in particular for model tests
is crucial, because only the BCGs have large enough numbers of GCs to populate the
highest-luminosity range $L \gtrsim 10^6 L_{\odot}$ where the color trend becomes most obvious.
In Paper II we suggested that the Bailin/Harris model, at least in its basic form, has difficulty
matching the observed range of MMRs (essentially, the observed range of blue-sequence slopes $\gamma$).
If the MMR is due entirely to self-enrichment then it should be driven by
very local conditions for the structure of the proto-GC, primarily its mass and
central concentration (scale radius). The higher the mass and the smaller
the scale radius, the more efficiently gas is retained in the protocluster and
the more effect pre-enrichment can have. But this scenario then
suggests that the MMR should look similar from one galaxy to the next, with no immediately obvious role
for larger-scale environmental effects that could differ strongly between host galaxies.
In addition, self-enrichment in this model is highly nonlinear in cluster
mass and thus it would predict that the slope $\gamma$ should
increase with GC mass, which is not observed in all cases.
Another and more physically based obstacle faced by internal self-enrichment is simply that
it would require a fairly extended initial star formation period of $\gtrsim$10 My
for the first round of SNeII to appear and contaminate the remaining gas in the protocluster,
which could then go on to form more low-mass stars of higher metallicity \citep[see][]{bailin_harris2009}.
But direct modelling of GC formation within giant molecular clouds indicates that most
of the star formation happens within $\lesssim 4$ My \citep[e.g.][]{howard_etal2016,hartmann_etal2012}.
Observations of young clusters indicate small internal age ranges as well
\citep[e.g.][]{lada_lada2003,schneider_etal2014,melena_etal2008,andersen_etal2009}.
The high-mass regime suitable for GCs has, however, not yet been probed either in theory or
observation: ideally we would
like to determine the expected internal age range for young clusters
at masses well above $10^5 M_{\odot}$. It is potentially promising that in
the recent \citet{li_etal2016} models, cluster
formation proceeds over $\gtrsim 15$ My in some of the most massive cases.
An alternate approach, though at this point still simplistic, would be to introduce \emph{pre-}enrichment
of the proto-GCs \citep{forte_etal2007,vandalfsen_harris2004} and invoke higher pre-enrichment
for higher-mass clusters. Different amounts of pre-enrichment
among GCs, presumably drawn from their host giant molecular clouds,
would in principle allow for a wider range of environmental influences. It is not yet
clear, however, exactly how pre-enrichment should depend on GC mass.
BCGs are likely to be products of mergers, and the sheer number of mergers could also have
differed noticeably from one case to another. If we then assume that
their progenitors experienced different
levels of pre-enrichment before the formation of their MP clusters, then in general
the MP sequence in the final combined BCG should have a higher internal color dispersion
and a weaker net MMR slope in the cases where more mergers took place.
In observational terms, $\sigma_1$ should increase as $\gamma$ decreases.
Some hints that this is the case can be seen from the comparison of UGC 9799 and UGC 10143
with the Coma giants, from the numbers in Table \ref{tab:gmm}.
It also remains unclear whether or not the MMR phenomenon is connected with
the multiple stellar populations that have been detected within massive GCs in the Milky Way, an issue that
continues to be a serious challenge for modelling \citep[e.g.][]{renzini_etal2015}.
For additional discussion, see Paper II and \citet{fensch_etal2014}.
\section{Spatial Distributions}
\subsection{Radial Profiles}
At the distance of these target galaxies the ACS field of view is large enough to enclose
a significant radial range of their halos. In Figures \ref{fig:ugc9799_radprof},
\ref{fig:ugc10143_radprof}, and \ref{fig:ngc4889_radprof}
the projected radial distributions $\sigma_{cl}$ (number of GCs per
arcsec$^2$) of the GCs are shown for UGC 9799, UGC 10143, and NGC 4889,
along with fits to S\'ersic-type functions obtained by $\chi^2-$minimization,
\begin{equation}
\sigma_{cl} \, = \, \sigma_e {\rm exp}(-b_n [({R \over R_e})^{1/n} - 1] ) \,
\end{equation}
or else to simple power-law form where appropriate.
In the first two figures, the outermost datapoints are from the outlying WFC3 field, which allow us to
track $\sigma_{cl}$ out to nearly $R \simeq 300$ kpc.
We note that the radial distributions for the GCs in NGC 4874 are analyzed by \citet{peng_etal2011} and
\citet{cho_etal2016} and we do not repeat their discussion here.
They find clearly that the MP clusters follow a distinctly
shallower distribution than the MR clusters.
The fact that the blue/red GC fraction increases with radius also means the
radial profiles are a function of metallicity.
To minimize the effects of the strong overlap between the MP and MR modes,
we follow Paper II and define the \emph{extreme metal-poor} (EMP) clusters as those bluer than
the blue-mode peak, and \emph{extreme metal-rich} (EMR) clusters as those redder than the red-mode
peak. Although this step eliminates half the total GC sample, it gives a clearer view
of the structural differences versus metallicity.
In Figures \ref{fig:ugc9799_xy2} -- \ref{fig:ngc4874_xy2}
the $xy$ distributions for the EMP and EMR clusters in each galaxy
are shown in the form of smoothed isocontour maps. The differences in central concentration
are evident, with the EMP component distributed much more widely and often less symmetrically
than the EMR clusters.
\smallskip \noindent \emph{UGC 9799:} The profile fits use the data $F814W < 27.0, R > 10''$.
The solutions for the radial fits are summarized in Table \ref{tab:radial}.
The EMR component does not fit a
single S\'ersic profile as well, but it is certainly more centrally concentrated than the
EMP component: very roughly, in simple power-law terms for $R \gtrsim 30''$ the EMP clusters
follow $\sigma \sim R^{-1.4}$ and the EMR clusters $\sigma \sim R^{-2.1}$. For comparison,
in NGC 6166 we found $\sigma(EMP) \sim R^{-1.0}$, $\sigma(EMR) \sim R^{-1.8}$. Thus the overall
halo of UGC 9799 is a bit more centrally concentrated, but the difference between
EMP and EMR components is similar. Perhaps more importantly, the EMR distribution matches
the surface brightness of the halo light well, as shown by the dashed line in Fig.~\ref{fig:ugc9799_radprof}.
Surface-brightness profiles in the $R$ filter have been measured by
\citet{seigar_etal2007} with a double S\'ersic profile out to $R \simeq 150''$, whereas
\citet{donzelli_etal2011} measure it out to $R \simeq 100''$ and fit it to a single S\'ersic profile.
Here we adopt the Seigar et al.~data.
\smallskip \noindent \emph{UGC 10143:} Again we use all data $F814W < 27.0, R> 10''$ for profile fitting.
The EMR data more closely resemble
a power-law with $\sigma \sim R^{-1.2}$, only slightly steeper than the whole population.
Thus in this galaxy, both GC components appear to follow rather shallow distributions, though
at large radii the EMP component dominates strongly in total numbers.
For the halo light profile, \citet{donzelli_etal2011} fit a two-component model with an
inner S\'ersic and outer exponential profile; the exponential part contains almost 80\% of
the total luminosity. Just as for UGC 9799 and NGC 6166, there is a close match between
the EMR cluster distribution and the halo light.
\smallskip \noindent \emph{NGC 4889:} In this case we use data in the range $F814W < 26.5$,
$1.3 < (g-I) < 2.2$. Before carrying out radial fits to a S\'ersic function,
we attempted to assess the contribution to the GC population in the field from
the companion galaxy NGC 4886, which is a moderately large elliptical
around which a noticeable GC system is seen
(Fig.~\ref{fig:ngc4889_xy}). A numerical approach similar to that described in
\citet{wehner_etal2008} for the Hydra BCG NGC 3311 and its companion NGC 3309
was used here: the field is divided up into a grid of small
$10'' \times 10''$ squares, and the observed number
of GCs within each square is assumed to be the sum of the contributions from both
galaxies combined. With the assumption that their GC systems follow Hubble-type or S\'ersic profiles,
a $\chi^2-$minimization can then be used to solve for the profile parameters
(see Wehner et al.~for details). NGC 4886 was found to contribute negligibly to the
totals beyond a $15''$ circle centered on it, so we simply exclude that region of the
image and fit a single S\'ersic profile centered on NGC 4889 alone using the remaining
area.
The halo light profile in $\mu_V$ as given in \citet{pahre1999} is shown as the
dotted line in Fig.~\ref{fig:ngc4889_radprof};
its slope matches the outer part of the EMR clusters well, though all
parts of the GC distribution are very much shallower than the halo light for
$R < 30''$ (a radius which is very nearly equal to $R_{eff}$ for the $\mu_V$ profile).
Neither metallicity component follows a simple power law well, but in rough terms
the outer regions can be described as $\sigma(EMP) \sim R^{-0.7}$ and
$\sigma(EMR) \sim R^{-1.8}$, a difference at least as large as we found for
NGC 6166 and the other BCGs.
We note that in all cases above, the halo-light radial profiles shown in the figures have been corrected for
their ellipticity (see below) as $r_{circ} = a \sqrt{1-\epsilon}$, as described in Paper II.
\begin{figure}[t]
\vspace{-0.0cm}
\begin{center}
\includegraphics[width=0.4\textwidth]{mmr_composite.pdf}
\end{center}
\vspace{-0.0cm}
\caption{Mass-metallicity relations for the blue (metal-poor) sequences
in the five galaxies discussed here. For each galaxy the shaded region shows
the $\pm 1 \sigma$ uncertainty of the slope and intercept. NGC 6166 is in grey,
NGC 4874 in blue, NGC 4889 in red, UGC 9799 in green, UGC 10143 in magenta.
Note the result for UGC 9799
(light green region) is for a particular selection of the data points; see text.}
\vspace{0.0cm}
\label{fig:mmr_composite}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ugc9799_radprof.pdf}
\end{center}
\vspace{-0.5cm}
\caption{UGC 9799: Radial profile for the entire GC system (black points and solid curve),
the EMP clusters (blue points and curve), and the EMR clusters (red points
and curve). The dashed line fitted to the EMR datapoints shows the integrated
surface brightness profile of the galaxy's halo light in $\mu_R$ \citep{seigar_etal2007}
with scale shown along the right-hand axis (see text).
}
\vspace{0.0cm}
\label{fig:ugc9799_radprof}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ugc10143_radprof.pdf}
\end{center}
\vspace{-0.5cm}
\caption{UGC 10143: Radial profile for the entire GC system,
the EMP clusters, and the EMR clusters, with symbols as in the previous figure.
The S\'ersic function fit is shown for the entire system (black line) and
the EMP clusters (blue line).
The dashed line fitted to the EMR datapoints shows the integrated
surface brightness profile $\mu_R$ of the galaxy's halo light,
from \citet{donzelli_etal2011}.
}
\vspace{0.0cm}
\label{fig:ugc10143_radprof}
\end{figure}
\begin{figure}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.5\textwidth]{ngc4889_radprof.pdf}
\end{center}
\vspace{-0.5cm}
\caption{NGC 4889: Radial profile for the entire GC system,
the EMP clusters, and the EMR clusters, with symbols as in the previous figure.
The S\'ersic fits to each of the three components are shown as the solid line
(all GCs), dashed blue line (EMP), and red line (EMR). The dotted line
indicates the integrated $V-$band surface brightness profile $\mu_V$ of the halo light
from \citet{pahre1999}.
}
\vspace{0.0cm}
\label{fig:ngc4889_radprof}
\end{figure}
\begin{table*}[t]
\begin{center}
\caption{\sc Radial Profiles}
\label{tab:radial}
\begin{tabular}{lrcclccl}
\tableline\tableline\\
\multicolumn{1}{l}{Galaxy} &
\multicolumn{1}{r}{$R_e$(all)} &
\multicolumn{1}{c}{$R_e$(EMP)} &
\multicolumn{1}{c}{$R_e$(EMR)} &
\multicolumn{1}{l}{$n$(all)} &
\multicolumn{1}{c}{$n$(EMP)} &
\multicolumn{1}{c}{$n$(EMR)} &
\multicolumn{1}{l}{Note}
\\ & (kpc) & (kpc) & (kpc) \\
\\[2mm] \tableline\\
NGC 4874 & 122 & 203 & 47 & 1.5 & 1.9 & 1.2& Cho 2016 \\
NGC 4889 & 110 & 214 & 44 & 2.6 & 1.7 & 1.7 & this paper \\
UGC 9799 & 61 & 80 & -- & 1.4 & 1.0 & ($R^{-1.4}$) & this paper \\
UGC 10143& 114 & 120 & -- & 2.0 & 1.5 & ($R^{-1.2}$) & this paper \\
\\[1mm] \tableline
\end{tabular}
\end{center}
\vspace{0.4cm}
\end{table*}
\begin{figure*}[t]
\vspace{0.0cm}
\begin{center}
\includegraphics[width=0.7\textwidth]{u9799_xy2.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Spatial distributions in UGC 9799 for the extreme-MP clusters (left panel)
and the extreme-MR clusters (right panel), shown as smoothed isocontour maps.}
\vspace{0.0cm}
\label{fig:ugc9799_xy2}
\end{figure*}
\begin{figure*}[t]
\vspace{-0.0cm}
\begin{center}
\includegraphics[width=0.7\textwidth]{u10143_xy2.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Spatial distributions in UGC 10143 for the EMP clusters (left panel)
and the EMR clusters (right panel). }
\vspace{0.0cm}
\label{fig:ugc10143_xy2}
\end{figure*}
\begin{figure*}[t]
\vspace{-0.0cm}
\begin{center}
\includegraphics[width=0.7\textwidth]{n4889_xy2.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Spatial distributions in NGC 4889 for the EMP clusters (left panel)
and the EMR clusters (right panel). }
\vspace{0.0cm}
\label{fig:ngc4889_xy2}
\end{figure*}
\begin{figure*}[t]
\vspace{-0.0cm}
\begin{center}
\includegraphics[width=0.7\textwidth]{n4874_xy2.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Spatial distributions in NGC 4874 for the EMP clusters (left panel)
and the EMR clusters (right panel). }
\vspace{0.0cm}
\label{fig:ngc4874_xy2}
\end{figure*}
\subsection{Azimuthal Distributions}
Another way in which the MP and MR subcomponents may reveal structural differences is in the ellipticity
$\epsilon$ of their azimuthal distribution. In NGC 6166, we found that the mean $\epsilon$ for the EMR clusters
matched the halo light, but the EMP clusters were more nearly spherically distributed.
For the BCGs in this study, it can already be seen from the contour maps described in the previous section
that this feature appears to be a more general one. As in Paper II the method of moments
\citep{mclaughlin_etal1994} is used to quantify the mean ellipticities $\epsilon$ of the subsystems.
For UGC 9799, clusters in the radial range $10'' < R < 100''$ were used.
For the EMP component, $\epsilon = 0.13 \pm 0.08$ and $\theta = 25^o \pm 60^o$ E of N for the position
angle of the major axis; while for the EMR component $\epsilon = 0.39 \pm 0.08, \theta = 38^o \pm 5^o$.
For all GCs combined, $\epsilon = 0.37 \pm 16, \theta = 41^o \pm 4^o$. For the halo light,
\citet{donzelli_etal2011} give $\epsilon = 0.35, \theta = 35.5^o$ for the outer region (the more relevant
comparison here).
Clearly the EMR clusters fairly accurately follow the halo light in both azimuthal and radial terms, while
the EMP clusters follow a distribution that is scarcely distinguishable from spherical.
For UGC 10143, the results for GCs in the range $10'' < R < 70''$ are
$\epsilon = 0.19 \pm 0.15$ and $\theta = 21^o \pm 62^o$ for the EMP sample;
$\epsilon = 0.51 \pm 0.23, \theta = 11^o \pm 11^o$ for the EMR sample; and lastly
for all GCs combined, $\epsilon = 0.40 \pm 0.09, \theta = 22^o \pm 10^o$.
The ellipticity of the halo light increases rather markedly with $R$ \citep{donzelli_etal2011}, and
to trace this out we carried out our own isophotal mapping using \emph{stsdas/ellipse} on the $F475W$ image.
Over $10''-70'', \epsilon_{F475W}$ increases from 0.27 to 0.47, but the position angle stays nearly
constant at $\theta \simeq 14^o$. Again, the EMR component matches the halo light
within the uncertainties of the solution. An interesting additional feature of the EMP clusters is that
their distribution appears to be somewhat asymmetric, with more of them spread to the upper right
(northeast) in Fig.~\ref{fig:ugc10143_xy2}; without having wider-field data to draw on, it is difficult
to speculate what the cause might be.
Comparable studies for other galaxies of ther azimuthal distributions for the MP and MR populations separately with
comparable sample sizes are rare, but these other studies confirm a consistent pattern for the MP population
to be distributed roughly spherically while the MR population closely follows the halo light; see
\citet{geisler_etal1996,lee_etal2008,bassino2006,harris2009b,escudero_etal2015} among others.
\subsection{Total Populations and Specific Frequencies}
In UGC 9799, the total population of GCs out to $R = 150''$ (the limit of the ACS field of view,
as well as the limit of the halo-light photometry) is $n = 9650 \pm 190$
brighter than $I = 27.0$ from integration of the radial profile. This limit is 0.12 mag fainter than
the GCLF peak (Paper I) and thus should include 54\% of the total over all luminosities
assuming the GCLF is Gaussian in number per unit magnitude, and using the parameters from Paper I.
We therefore obtain $N_{tot} = 18000 \pm 400$ for $R < 150''$ (110 kpc).
Integrating the light profile \citep{seigar_etal2007} to the same radius gives a total integrated magnitude
$R_{tot} = 12.55$, which corresponds to $M_V^T \simeq -22.85$ assuming a mean color $(V-R) = 0.6$ for
giant early-type galaxies. The specific frequency of the GC system is then
$S_N = N_{tot} \cdot 10^{0.4(M_V^T + 15)} = 13.0 \pm 0.3$.
If we choose to integrate the entire GC system profile all the way to the WFC3 field at $R = 300$ kpc,
the result would be $N_{tot} \simeq 22000$ clusters, though this estimate is much more uncertain.
For UGC 10143, if again we restrict the calculation conservatively to the ACS field of view
($R < 155''$),
the total number of GCs with $I < 27.0$ is $n = 6450 \pm 100$, which translates to
$N_{tot} = 12500 \pm 200$ over all magnitudes.
Integration of the halo light \citep{donzelli_etal2011} to the same
radius gives $R_{tot} = 12.43$, $M_V^T \simeq -22.96$. Finally then, $S_N = 8.2 \pm 0.1$
to that radius. The more risky extrapolation of the GC profile out to the WFC3 field limit
at $R = 370''$ (270 kpc) would give $N_{tot} \simeq 20000$.
The UGC 9799 GC system is therefore relatively richer than for UGC 10143, but the specific frequencies of
both are in the range observed for other BCGs \citep[e.g.][]{harris_etal2013}.
For NGC 4889 the profile integration gives $n = 8080 \pm 120$ clusters brighter than
$F814W = 26.5$ ($M_I = -8.53$), a limiting magnitude which is very near the GCLF peak
point. We therefore double that number to $N_{tot} \simeq 16000 \pm 250$, which when
combined with $M_V^T = -23.65$ gives a specific frequency of $S_N = 5.5 \pm 0.1$.
This galaxy is very luminous, but relative to its size it does not have an exceptionally
populous cluster system in the more typical BCG range.
The story is somewhat different and more complex
for the central Coma cD NGC 4874: \citet{peng_etal2011} estimate
$N_{tot} = 23000 \pm 700$ GCs \emph{not} including the more extended IGC population.
If we use $M_V = -23.46$ as did \citet{harris_etal09}, we obtain $S_N = 9.5 \pm 0.3$.
If instead $N_{tot}$ is normalized to the entire luminosity profile out to a much
larger radius of 520 kpc then $S_N$ decreases markedly to $3.7 \pm 0.1$
\citep{peng_etal2011}; but since the IGC clusters outnumber the ``intrinsic'' GCs
more definitely associated with the galaxy itself, this lower specific frequency
is perhaps more of a statement about $S_N(IGC)$.
In this respect it is worth noting that \citet{durrell_etal2014} find $S_N = 2.8 \pm 0.7$
for the Virgo cluster GCs in their entirety, of which a large fraction are IGCs and
less than a quarter are from M87 itself.
\section{Discussion}
For extremely broad and nearly featureless MDFs such we find in NGC 6166 (Paper II), UGC 9799, and UGC 10143,
the imposition of a bimodal Gaussian numerical model, or any simplistic multimodal fitting
process, begins to look increasingly arbitrary. Transformation of their CDFs back into
the underlying metallicity distribution by way of
Eqn.~(1) yields a similarly broad unimodal MDF. We stress that this is a
different issue than
the one raised by \citet{yoon_etal2006}, who proposed that an \emph{intrinsically
unimodal MDF} could be translated into the \emph{bimodal CDF} seen in many galaxies because of the
nonlinearity of the transformation (in their case, specifically the $(g-z)$ index, which as noted
above is among the most nonlinear of the indices in common use). Here, we
are essentially discussing the reverse: a CDF that is already smooth and unimodal
cannot have come from an intrinsically bimodal MDF,
because $(g-I) \rightarrow$ [Fe/H] is (mildly) nonlinear in the sense that
it will produce a slightly more compressed MDF rather than one that is more spread out.
The same argument would apply to any of the other color indices used in other papers
such as $(g-z), (g-i), (V-I), (B-I), (C-T_1)$, and others.
The MDF we observe today is the visible
outcome of a rapid sequence of individual GC-forming events that took place within many
halos along a hierarchical merger tree. For a galaxy at the BCG scale, thousands of such
halos take part in this sequence at high redshift, each bringing in its own partially enriched gas.
For a complex enough chain and a large enough
number of halos, the end product might be expected to approach a continuous MDF,
stretching from the most metal-poor GCs at an epoch where significant enrichment had
not yet occurred, to the last major rounds of GC formation at roughly Solar metallicity.
In these supergiant cases, it is evident that the merging halos over their full range
of masses contained enough gas to form large numbers of GCs at every metallicity from
[Fe/H] $\sim -1.5$ up to above Solar abundance, filling in every part of the MDF.
At later times, individual accretions of small satellites continue that will add mostly
to the metal-poor GC population in the outer halo.
Rather than attempting to reverse-engineer the formation events from properties of the
color distributions and radial distributions, ultimately
it would be preferable to move forward from a physically based formation model
to generate true model MDFs and GC spatial distributions which can then be compared with the observed cases.
Early steps in this direction include
\citet{kravtsov_gnedin2005,griffen_etal2010,muratov_gnedin2010,tonini2013,li_gnedin2014,li_etal2016},
though each of these uses particular simplifying prescriptions for the formation
of GCs within the halos in the merger tree. Nevertheless, for galaxies at the highest masses
the outcome MDF in the models is broader and seen to approach a continuous distribution \citep{li_gnedin2014}.
An interesting result emerging from the BCGs, however, is that there are still notable differences
in their MDFs even at these very highest galaxy masses. For M87 and NGC 4889 the MDFs
still show a clearly bimodal form, while others (NGC 4874, NGC 6166) have MP and MR modes that
have begun to merge, and in others (UGC 9799, UGC 10143) the MDF from the raw observations
is smooth and unimodal, and the GMM-fitted $D-$values fall below the threshold $D \simeq 2$.
Nevertheless, in strict numerical terms a bimodal-Gaussian
deconstruction matches all these cases extremely well. We emphasize, however
(see again Section 2), that this model for the MDF is primarily a convenient description of its
first-order features, emerging from what is intrinsically a continuous process of cluster formation.
The overall appearance of the MDF is governed primarily by the internal dispersions $\sigma_1,\sigma_2$
of the MP and MR modes and thus the amount of overlap between the modes.
By contrast, a near-uniform result we find is that the MP and MR mode centers
$\mu_1, \mu_2$ in all the BCGs remain
separated by very similar amounts $\Delta$[Fe/H] $= (0.81 \pm 0.04)$ dex, even though their dispersions
may differ quite a lot.
Perhaps the most interesting feature is connected with the MP and MR relative numbers ($p_1, p_2$).
These supergiants contain roughly equal numbers of MP and MR clusters, but there are
still striking differences such as in UGC 10143, where there are relatively few MR clusters
at all radii, even in much of the inner region where the numbers of accreted MP clusters
should have been small. This is, perhaps, an indication that the numbers of
major gas-rich mergers from the big, metal-enriched halos
that would have produced the metal-richer GCs may differ strongly between different
BCGs \citep[see, e.g.,][]{burke_collins2013,lidman_etal2013}. Other possibilities are
that by the time such mergers occurred the gas was already either largely converted to
stars or heated to the point where less
metal-rich GC formation could occur.
Our material strongly supports the identification of the metal-richer GCs with the halo light
of their parent galaxies: their spatial distributions are similar in both radial and azimuthal
distributions, and their overall spatial structure is consistently smoother and more regular
than the MP clusters, like the galaxy light. Subdividing the sample into the EMP and EMR subgroups
helps to emphasize their distinctive spatial distributions. This material adds to
to the similar evidence in other large galaxies (see Paper II), pointing to the conclusion
that the MR clusters formed along with the main stellar population of the galaxy.
By contrast, the EMP clusters
consistently follow a distribution that in power-law terms $\sigma_{cl} \sim R^{-\alpha}$
is shallower by $0.8-1.0$ dex than the EMR clusters, very different from the structure
of the halo light and fairly close to an isothermal
form similar to the dark-matter halos.
The relation between gas metallicity and host galaxy mass \citep[see][]{muratov_gnedin2010,li_gnedin2014}
suggests strongly that the MP GCs formed within small, very metal-poor dwarfs.
These GCs could therefore have accumulated either extremely early in the hierarchical chain, before
the major body of the galaxy had fully assembled;
or from accreted dwarf satellites that may come in at any later time. By contrast, the MR
GCs should form within much bigger halos with more enriched gas. The importance
of accretion in the buildup of the MDF that is observed today was first pointed out by
\citet{cote_etal1998,cote_etal2000} and has frequently been discussed in the later literature
\citep[for comprehensive recent discussions of the relative importance of accretions, see][]{kartha_etal2016,ferrarese_etal2016}.
BCGs are in highly privileged locations at the dynamical centers of rich
galaxy clusters, and thus may gain the most from satellite accretions.
The importance of their growth by dissipationless (dry) merging especially for redshifts $z < 1$
has been emphasized in numerous recent discussions
\citep[e.g.][among many others]{liu_etal2013,laporte_etal2013,laporte_etal2015,oliva-altamirano_etal2015,oogi_etal2016}.
The individual satellites
may contribute both their own GCs and their stripped nuclei, which are structurally similar
to luminous GCs. For example, \citet{ferrarese_etal2016} calculate that almost 40\% of the GCs in the
core region of the Virgo cluster around M87 may come from former satellites.
A potentially related pattern that may be emerging from our BCG study is that the relative dominance
of the MP clusters increases markedly beyond $R \gtrsim 4 R_{eff}$. This rough transition
may mark the characteristic radius beyond which late accretions of metal-poor
satellites dominate the GC population.
\section{Summary}
Continuing our series of studies of the extraordinarily rich globular cluster
systems around Brightest Cluster Galaxies
(BCGs) with the HST ACS and WFC3 cameras, we present new comprehensive photometric analyses of the
GC systems around UGC 9799 and UGC 10143, along with comparison data for the
Coma supergiants NGC 4874 and NGC 4889.
Our principal findings are these:
\begin{enumerate}
\item{} The GC systems in all these galaxies are as expected extremely populous, yielding
total populations of anywhere from 12000 to 23000 clusters within
galactocentric radii $\lesssim 120$ kpc. Extrapolation to larger radii
might almost double those totals, though the presence of as-yet unknown numbers
of intragalactic GCs will come into play there.
\item{} The color distribution (CDF) of the GCs has been measured in the $(F475W-F814W) \simeq
(g-I)$ color index. In all the BCGs the CDF is broad, nominally unimodal, and
skewed (asymmetric). Nevertheless,
a simple bimodal-Gaussian deconstruction continues to match the CDF
very well, as it has for most smaller galaxies. The primary difference between
these BCGs and smaller galaxies is that the intrinsic dispersions of the MP and MR
modes become significantly higher, forcing the two modes to overlap heavily.
\item{} The broad, near-continuous form of the CDF implies that the intrinsic metallicity
distribution function (MDF) must also be broad and unimodal, because the transformation
from color to metallicity is only slightly nonlinear and acts in the direction
of making the MDF slightly more compressed than the CDF.
\item{} Of the four galaxies discussed here, the Coma giants NGC 4874 and NGC 4889 show a
mass-metallicity relation (MMR) along the MP sequence, in the conventional sense
that the blue sequence becomes systematically redder at higher luminosity.
The heavy-element abundance scaling with GC mass is $Z \sim M^{0.25}$,
which was also the case for NGC 6166 (Paper II).
For UGC 10143, no detectable trend shows up along either
the red or blue sequences. For UGC 9799, the results are uncertain, with
either a zero or positive slope along the blue sequence not ruled out.
These results do not appear to support a simple self-enrichment model during
GC formation, and instead may point to the need for some form of pre-enrichment
in the most massive GCs driven by environmental differences at the time of formation.
\item{} The relative numbers of MP and MR clusters within these supergiants
differ significantly in detail, with at least one case
(UGC 10143) where the MP clusters dominate at all radii. This result suggests that the relative
importance of gas-rich mergers with big, metal-enriched halos (which built the MR clusters)
could have differed between BCGs.
\item{} The ratio N(MP)/N(tot) increases with radius in all these galaxies, particularly
past $R \gtrsim 4 R_{eff}$. We suggest tentatively that this transition radius
may mark the region outside which the MP clusters that came from
late, discrete accretions of dwarf satellite galaxies are most important.
\item{} In all these BCGs, as in other large galaxies, the extremely metal-poor GCs follow a roughly spherical
spatial distribution not far from the form $\sigma \sim R^{-1}$ that would
characterize the dark-matter halo. By contrast, the most metal-rich GCs follow
a more concentrated, smooth, and regular distribution that matches the halo
light of the galaxy. The MR clusters are most likely to have formed along with the
main stellar body of the galaxy.
\end{enumerate}
\section*{Acknowledgements}
Based on observations made with the NASA/ESA Hubble Space Telescope, obtained
at the Space Telescope Science Institute,
which is operated by the Association of Universities for
Research in Astronomy, Inc., under NASA contract NAS 5-26555.
WEH and GME acknowledge financial support
from NSERC (Natural Sciences and Engineering Research Council of Canada).
JB acknowledges financial support from program HST-AR-13908.001-A
provided by NASA through a grant from the Space Telescope Science Institute.
OYG was supported in part by NASA through grant NNX12AG44G, and by NSF through grant 1412144.
DG gratefully acknowledges support from the Chilean BASAL Centro de
Excelencia en Astrof\'isica y Tecnolog\'ias Afines (CATA) grant PFB-06/2007.
{\it Facilities:} \facility{HST (ACS, WFC3)}
\makeatletter\@chicagotrue\makeatother
\bibliographystyle{apj}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 856
|
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E20 Kuppammal
E21 Suresh Chinnasamy
E22 Paulraj
Josh Talks - Tamil - Season 1
Food • Motivational • Inspirational | 18 mins | 5+
Suresh Chinnasamy used to wash the dishes full of leftovers to earn a living. It was one of his friends who helped him walk the right path and find the purpose of his life. He found his passion for cooking and was determined about doing something big with his talent. Today, Suresh is celebrity chef of a 5-star hotel.
E1 Perazhagi Gayathri
Gayathri is a renowned name in the Tamil TV industry. She is the lead actress of the Colors Tamil TV Show 'Perazhagi'. People around her never encouraged her to become an actress and ridiculed her for being dark-skinned. But she successfully broke through all the roadblocks that come onto her way.
E2 Rajendran Mani
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E3 Vinod Senthil
Vinod Sethil, an Ethical Hacker, is the founder of InfySEC, a cyber-security company providing services across the globe. He's a prime role model people should look up to if you want to understand what it is to convert all the discouragement you get from life into a lifetime of appraisals and massive success.
E4 IAS Gayathri
Gayathri IAS is the sub-collector of Pollachi, Tamil Nadu. Born and brought up in Kerala, she lived in an environment where children had to go further with either Medical studies or Engineering. She went further with engineering, got married after she graduated, and gave birth to a son. The society expected her to entangle herself within the duties of the household but she had other plans for herself. She realized her potential and started with her journey of becoming an IAS officer.
E5 Kuppulakshmi
Kuppulakshmi's journey began from a small village in Salem. She failing in Maths when she was in 12th grade made a lot of people to throw blasphemy on her and make her feel underconfident about herself. But she successfully grew above her failure and her success is something people love and envy her for.
E6 Kolapasi Santhosh
Success is sure to come if one is ready to face anything boldly. Santhosh was born and raised in a typical middle-class family in Chennai. He had a keen interest in the business at an early age. In this video, he talks about how he started the Kolapasi Take Away and how it has been successful. Santhosh is a great example of how one can achieve success if you face problems bravely.
E7 Kathik Subbaraj
Karthik Subbaraj's success story will inspire all the film direction aspirants to take that leap in life that scares you the most as his story proves that great things await you on the other side of your fears. He is a famous film director of the south today.
E8 RJ Settai Sethu
One incident and RJ Settai Sethu's life turned upside-down. His story is a lesson for all of us to not to give up even if life is up to throwing the darkest of its shades on you. He contracting to polio made him define himself as 'differently-abled'. He took inspiration from the life of Charlie Chaplin. Today, he has numerous awards to his credit as proof to how remarkable of an RJ he is.
E9 Shankar Subramanian
Shankar Subramanian hails from the Tirunelveli district of Tamil Nadu, having a humble family background. He lived his part of his struggles after moving to Chennai as everything was new for him. He also faces a lot of hardships when his business ideas failed initially. But he overcame everything he had to go through and is now a renowned name in the world of business.
E10 Shankar Shanmugam
Shanmugan has known the sorrows of slavery closely as he worked in a brick factory with his family and was subjected to brutal treatment. But every time life made him stumble and fall, he grew up stronger. He started a small business initially and helped people in need while dealing with the blocks of his own. His strength and determination made him a successful businessman. Now, he helps people overcome the pain he has been through in his past.
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E16 Sibidharan
Sibidharan was inclined towards technology since a very young age and began to learn to hack all by himself. After schooling, he went on for Engineering but soon realized it is not his cup of tea. Understanding his potential of becoming something greater than who he was then, he entered the world of entrepreneurship and now he is a well-known Cyber Security analyst.
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Kuppammal is one of those who didn't let feast on the sorrows of his past but learned from it. She was a victim of child-marriage and was forced to work in the rice mill. Her son died amid the activities happening in the mill. But she was courageous enough to step out of that place and develop herself. Today, she helps people who face similar problems in current times.
Before he could even learn to walk his parents left this world. Paulraj started working menial jobs at the age of 8 to earn a living. He spent many of his nights sleeping on the Avadi Railway station for he couldn't afford a room to stay at all. Today, his Banana business is running smoothly and has a Charitable Trust of his own.
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,562
|
Emmerson Mnangagwa (* 15. září 1942) je zimbabwský politik zastávající funkci současného zimbabwského prezidenta od 24. listopadu 2017. Byl dlouholetým spojencem svého předchůdce Roberta Mugabeho a významným členem vládnoucí strany ZANU-PF. Mnangagwa byl Prvním viceprezidentem Zimbabwe od roku 2014 do svého odvolání v listopadu 2017, které vyvolalo převrat. 21. listopadu 2017 Mugabe rezignoval na svou funkci.
Život
Mnangagwa byl partyzánským vůdcem během občanské války v Rhodesii. Po uznání nezávislosti roku 1980 Mnangagwa zastával několik vysokých vládních pozic včetně pozice ministra vnitřní bezpečnosti. Během výkonu této funkce došlo k masakrům příslušníků etnické skupiny Ndebele. Během prezidentských voleb v roce 2008 vedl Mugabeho volební kampaň, při které násilně zastrašoval opozici, což donutilo kandidáta Hnutí pro demokracii Morgana Tsvangiraie ukončit kampaň a vyjednat s Mugabem dohodu o sdílení moci. V letech 2009 až 2013 zastával funkci ministra obrany, když se později stal ministrem spravedlnosti. Mnangagwa byl jmenován viceprezidentem v prosinci 2014 a byl považován za pravděpodobného následníka Roberta Mugabeho.
Na začátku listopadu 2017 byl z postu viceprezidenta odvolán za údajné projevy neloajality a odjel ze země. Po převzetí kontroly v zemi armádou a Mugabeho rezignaci se Mnangagwa po dvou týdnech vrátil připraven převzít prezidentský úřad. Přísahu složil 24. listopadu a slíbil, že pozvedne rozvrácenou ekonomiku a odškodní bělošské farmáře. Dále projevil záměr bojovat proti chudobě a korupci, rovněž zmínil, že bude usilovat o ukončení mezinárodní izolace země a přilákání zahraničních investic. Připustil tak určité chyby Mugabeho vlády, ale vzdal bývalému prezidentovi hold a nazval jej otcem národa. Při nástupu do funkce se také vyslovil pro uspořádání demokratických voleb v nadcházejícím roce.
Tyto volby se konaly v červenci 2018 a Mnangagwa v nich obhájil své setrvání v úřadu, když obdržel téměř 51 % hlasů. Největším soupeřem mu byl opoziční politik Nelson Chamisa, který získal 44 %. Ten se ale prohlásil za vítěze a tento výsledek označil za fiktivní a klamný. Mnangagwa zvítězil i v souběžně konaných parlamentních volbách, které vyhrála jeho strana ZANU-PF, když získala dvoutřetinovou většinu potřebnou k prosazení ústavních změn. Mnangagwa se i přes protesty v srpnu nového mandátu ujal, jeho inauguraci navštívili například Cyril Ramaphosa a Paul Kagame. Při projevu staronový prezident zopakoval předvolební sliby a navrhl nezávislé vyšetření povolebnímu zásahu armády.
Odkazy
Reference
Externí odkazy
Ministři obrany
Prezidenti Zimbabwe
Absolventi Londýnské univerzity
Narození v roce 1942
Narození 15. září
Žijící lidé
Muži
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,618
|
{"url":"http:\/\/nrich.maths.org\/4879\/solution","text":"Pebbles\n\nPlace four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?\n\nIt Figures\n\nSuppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?\n\nBracelets\n\nInvestigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?\n\nStair Climb\n\nStage: 2 and 3 Short Challenge Level:\n\nBoris has to run up $99$ steps, and runs up $5$ in each unit of time, so it takes him $99 \\div 5 = 19\\frac{4}{5}$ units of time to reach the top.\n\nSpike has to run up $78$ steps, and runs up $4$ in each unit of time, so it takes him $78 \\div 4 = 19\\frac{1}{2}$ units of time.\n\nPercival has to run up $61$ steps, and runs up $3$ in each unit of time, so it takes him $61 \\div 3 = 20\\frac{1}{3}$ units of time.\n\nTherefore they finish in the order Spike, Boris Percival.\n\nThis problem is taken from the UKMT Mathematical Challenges.\nView the archive of all weekly problems grouped by curriculum topic\n\nView the previous week's solution\nView the current weekly problem","date":"2016-02-06 07:26:21","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\": 0.24265891313552856, \"perplexity\": 884.0043822797596}, \"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-2016-07\/segments\/1454701146196.88\/warc\/CC-MAIN-20160205193906-00154-ip-10-236-182-209.ec2.internal.warc.gz\"}"}
| null | null |
Kuwait estuvo representado en los Juegos Olímpicos de Moscú 1980 por un total de 56 deportistas masculinos que compitieron en 7 deportes.
El equipo olímpico kuwaití no obtuvo ninguna medalla en estos Juegos.
Referencias
Enlaces externos
Base de datos olímpica del Comité Olímpico Internacional .
Kuwait
V 1980
Kuwait en 1980
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,418
|
Q: GZIP compression did not work good for a data of 64K Hi I have created compressin and decompression technique using gZipinputstream in both c#.NET and java
If I compress upto 15000 bytes in c#.NET then i can decompress it in java
but if i compress 64000 bytes in c#.NET then i am not able to decompress it in java.
But I can decompress it using C#.NET.
So how to come out of this problem
Thanks
Bapi
A: At a guess you are probably using DEFLATE_64 in the .net code. This will compress in up to 64K blocks, DEFLATE, which is what Java supports only compresses up to 32K blocks. On the .net side, try setting your compressor to only use DEFLATE instead of allowing it to use DEFLATE_64 and you might have more luck.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,587
|
package org.hisp.dhis.analytics.event;
import org.hisp.dhis.common.Grid;
/**
* @author Markus Bekken
*/
public interface EnrollmentAnalyticsManager
{
/**
* Retrieves aggregated data based on enrollments.
*
* @param params the query to retrieve aggregated data for.
* @param grid the grid to insert data into.
* @param maxLimit the max number of records to retrieve.
* @return a grid with data.
*/
Grid getAggregatedEventData( EventQueryParams params, Grid grid, int maxLimit );
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 958
|
We constantly execute our spirit of ''Innovation bringing progress, Highly-quality making sure subsistence, Administration advertising advantage, Credit rating attracting consumers for 1100w Demolition Braker , 1100W Demolition Braker , 2100W Demolition Braker , Based on goods with high quality competitive price and our full range service we've accumulated experienced strength and experience and now we have built up a very good reputation in the field. Along with the continuous development we commit ourselves not only to the Chinese domestic business but also the international market. May you moved by our high quality products and solutions and passionate service. Let's open a new chapter of mutual benefit and double win.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 23
|
Android News / Special Features / Android Headliner: How Will YouTube Connect Change Livestreaming?
Android Headliner: How Will YouTube Connect Change Livestreaming?
By Justin Diaz
Livestreaming on mobile devices is in no way unpopular, but it isn't as big as it could be, and there's a chance that Google's rumored livestreaming app that's set to launch in the future, called YouTube Connect, could change the landscape. YouTube Connect is said to be in the same realm of Periscope and Meerkat, competing for territory and user numbers in a market that is still very new and growing. YouTube already has a tiny foothold in livestreaming capabilities with the help of the YouTube Creator Studio tool, and within YouTube Gaming if you're looking to livestream your game sessions for others to watch. This limited capability though locks out a large number of potential users when compared to the capabilities of competitor Periscope, which had around 10 million users as of the middle of last August, 2 million of which were active on a daily basis. How will YouTube Connect change the live stream landscape on mobile devices? It's tough to say at this point really, as the service is still just a rumor and is "currently under development." Along with the rumor about its existence though, is a statement that it will have a robust offering of features that bring it up to scale with the bigger services that are already available to users.
One of those features is said to be a chat capability, a function that is readily available on Periscope which allows users who are viewing content to interact with broadcasters as the stream is happening. This sort of interaction is a feature that will be a must if Google wants YouTube Connect to be able to compete in the space. While viewers will be able to chat with broadcasters, those who are livestreaming are rumored to have the ability to chat back, although it's a little tough to envision how that might work if someone is trying to type back a message in chat without causing any sort of interruption to their broadcast, then again, this is also something which already available through YouTube as streamers have a live chat option they can enable or disable for during broadcasts. These are of course speculative features for a still speculative app without any confirmation from Google on what will be available. When and if YouTube Connect launches however, YouTube not only has the opportunity to grab some of Periscope's user base, but they also have a large number of users of their own for YouTube who will likely be able to jump right into using YouTube Connect without having to put in much effort, other than logging in for the first time. With YouTube's 1 billion users and counting, that's a huge chunk of marketshare that is ripe for the taking.
As the service would be based on a Google account, users should immediately be ready to install a YouTube Connect application and sign in with the Google account they may already have for YouTube, Gmail, and other Google services. These users may already have a Periscope account and may not want to go through the hassle of switching services of course, but since YouTube Connect would be tied to Google and likely YouTube itself, any livestreams would have the potential to effortlessly upload to a user's channel on YouTube, and this kind of seamless interaction between the two services could make it really simple for anyone to livestream and post those livestreams for playback, making them available for people to watch on YouTube who may not have the time to watch a livestream as it's happening but may want to follow that particular content creator. There's also the fact that many YouTube users aren't active on Periscope. Having an application like YouTube Connect available would presumably be much easier to get into since it's already tied to a Google account. If this is the case, any YouTube users, however many hundreds of millions there likely are which don't already use a livestreaming service, just might join up with YouTube Connect as it would be part of Google's sort of all-inclusive package of one Google account for nearly all of their services, which would have the potential to really help push the livestreaming market even further. Periscope has at least 10 million users while YouTube has over a billion users. That's a huge untapped well of potential as Periscope only has about one percent of the users of YouTube, leaving a large number of people open that Google could snatch up with YouTube Connect.
Although YouTube Connect should have easy integration with Google's other services like YouTube and Google+, it's also likely to gain support for sharing livestreams on other social networks such as Twitter and Facebook, although it reportedly doesn't currently have integration with those outside social networks in its current stage of development. With YouTube Connect having integration with multiple social networks though, as it should if Google really wants to reach the largest number of users possible, YouTube Connect users would be able to share their content with virtually anyone including those who may not use YouTube Connect or YouTube themselves. Aside from the average user, YouTube Connect would pose as a pretty big benefit for the top content creators on YouTube as well as top brands. Periscope for example has about 15% of the top brands that are on Twitter which actually use the service to livestream. It's hard to quantify how many top brands that is without knowing how many top brands are actually on Twitter, but 15% doesn't seem like a whole lot. This opens up another potential area for YouTube Connect. YouTube is arguably much larger than Twitter with many brands having their own channel for videos and ad spots, and YouTube Connect would simply be one more outlet for top brands to reach their customer base. Brands like Angry Birds, Coca-Cola, PlayStation, Red Bull, GoPro, and LEGO are all brands in the top 10 of the most popular brands on YouTube according to socialbakers. These are brands which could benefit from having an app like YouTube Connect to livestream from. Red Bull in particular, could stream events like the Flugtag and get plenty of viewers as not everyone that may want to see the event in person is able to make it to the location where it's held.
Major global brands are of course not the only ones who could benefit from a YouTube livestreaming application. Having an app like YouTube Connect would make for a push of innovation from competitors like Periscope, Facebook Live, and Meerkat. With the amount of experience that Google and YouTube have in video, they stand to bring some real change with plenty of compelling features to livestreaming that may not already be available from other services, and that can only help the livestreaming market as a whole. More options means more choice for consumers, which is of course a good thing, but it also means that Periscope, the current leader in the livestreaming space, would have to push themselves to improve their app to keep their own momentum going. That's not to say that Periscope's plans are anything but improvement, but with an app like YouTube Connect nipping at its heels, it would certainly help to drive things along a lot faster and make for a much more interesting set of offerings from all of the companies who are looking to grab up pieces of the pie in this particular industry. Livestreaming is still relatively new and has lots of room to grow, and with YouTube aiming to help it grow, there's bound to be plenty of change in the landscape as well as a change to the already existing services that people are using.
Justin Diaz
Justin has written for Android Headlines since 2012 and currently adopts a Editor role with a specific focus on mobile gaming and game-streaming services. Prior to the move to Android Headlines Justin spent almost eight years working directly within the wireless industry. Contact him at [email protected]
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,900
|
Sufata – rodzaj sieciowej tkaniny, która jest luźno rozpięta na dwóch skrzyżowanych drewnianych trzonkach. Tkanina Sufata służy do wyjmowania ryb z wody.
Tkaniny
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,664
|
import {Injectable, OnDestroy} from '@angular/core';
import {Api} from "@catflow/Api";
import {ActivatedRoute, NavigationEnd, NavigationStart, Router, RoutesRecognized} from "@angular/router";
import {PublishSubject} from "@frontend/util/PublishSubject";
import {BehaviorSubject, Subject} from "rxjs";
import {operators} from "rxjs/internal/Rx";
import {untilDestroyed} from "ngx-take-until-destroy";
import {componentDestroyed} from "ng2-rx-componentdestroyed";
@Injectable()
export class AppState implements OnDestroy{
public settings:any = undefined;
public training: boolean = false;
public routedProjectId: number;
public routedModelId: number;
public onProjectChange = new PublishSubject<{projectId: number}>();
public onProjectOrModelChange = new PublishSubject<{projectId: number, modelId: number}>();
constructor(
private api: Api,
private router: Router,
activatedRoute: ActivatedRoute
)
{
this.onProjectOrModelChange.last;
/* update routed
*/
router.events.takeUntil(componentDestroyed(this))
.subscribe(event => {
if (!(event instanceof RoutesRecognized))
return;
if (event.state.root.children.length <= 0)
return;
let params = event.state.root.children[0].params;
console.log('changed params: ', params);
if (this.routedProjectId != params.projectID || this.routedModelId != params.modelID) {
console.log('route changed ', params);
let projectChanged = this.routedProjectId !== params.projectID;
this.routedProjectId = params.projectID;
this.routedModelId = params.modelID;
if (projectChanged && params.projectID !== undefined)
this.onProjectChange.next({projectId: this.routedProjectId});
if (params.projectID !== undefined && params.modelID !== undefined)
this.onProjectOrModelChange.next({projectId: this.routedProjectId, modelId: this.routedModelId});
}
});
/* subscribe to settings
*/
api.object('settings').object()
.takeUntil(componentDestroyed(this))
.subscribe((obj) => {
this.settings = obj;
});
api.object('settings').subscribe();
}
ngOnDestroy(): void {
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 799
|
Q: Что значат знаки ^,~ в зависимостях? Что значат знаки ^,~ в зависимостях?
A: Вероятно это поможет:
Семантическое Версионирование
В npm может использоваться (~) и (^) для указания версий зависимостей.
Если Вы видите ~1.0.2 это значит что подходит версия от 1.0.2 включительно до 1.1.0 не включая её, то есть максимально доступная патч версия после версии 1.0.2.
Если Вы видите ^1.0.2 это значит что подходит версия от 1.0.2 включительно до версии 2.0.0 не включая её, т.е. максимальная минорная+патч версия после версии 1.0.2.
Почерпнуто отсюда:
Семантическое Версионирование 2.0.0
Нумерация версий программного обеспечения
npm-semver
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,372
|
Q: Issue installing zip file created by setup.py for deploying custom prediction to AI platform Am following google doc on creating custom prediction(https://cloud.google.com/ai-platform/prediction/docs/custom-prediction-routines). While building a new version for a model AI-platform prediction API threw below error:
Error Create Version failed. Bad model detected with error: "Failed to load model: User-provided package <>-0.1.tar.gz failed to install: Command '['python-default', '-m', 'pip', 'install', '--target=/tmp/custom_lib', '--no-cache-dir', '-b', '/tmp/pip_builds', '/tmp/custom_code/<>.tar.gz']' returned non-zero exit status 1. (Error code: 0)"
Was testing my zip file locally
pip install --target=/tmp/custom_lib --no-cache-dir -b /tmp/pip_builds dist/<>
Throws below error:
Processing ./dist/<tar>
ERROR: Command errored out with exit status 1:
command: bin/python -c 'import sys, setuptools, tokenize; sys.argv[0] = '"'"'/private/var/folders/mj/b_g4b4yj26q278g9k58w92fck5d9wj/T/pip-req-build-9dmmje_z/setup.py'"'"'; __file__='"'"'/private/var/folders/mj/b_g4b4yj26q278g9k58w92fck5d9wj/T/pip-req-build-9dmmje_z/setup.py'"'"';f=getattr(tokenize, '"'"'open'"'"', open)(__file__);code=f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' egg_info --egg-base /private/var/folders/mj/b_g4b4yj26q278g9k58w92fck5d9wj/T/pip-pip-egg-info-ic3qhcpo
cwd: /private/var/folders/mj/b_g4b4yj26q278g9k58w92fck5d9wj/T/pip-req-build-9dmmje_z/
Complete output (6 lines):
Parent directory: /private/var/folders/mj/b_g4b4yj26q278g9k58w92fck5d9wj/T/pip-req-build-9dmmje_z
Traceback (most recent call last):
File "<string>", line 1, in <module>
File "/private/var/folders/mj/b_g4b4yj26q278g9k58w92fck5d9wj/T/pip-req-build-9dmmje_z/setup.py", line 22, in <module>
REQUIRED_PACKAGES = [line.strip() for line in open(base/"requirements.txt")] + \
FileNotFoundError: [Errno 2] No such file or directory: '/private/var/folders/mj/b_g4b4yj26q278g9k58w92fck5d9wj/T/pip-req-build-9dmmje_z/requirements.txt'
----------------------------------------
ERROR: Command errored out with exit status 1: python setup.py egg_info Check the logs for full command output.
Ran "python setup.py egg_info" on the mac terminal, nothing useful popped.
Parent directory: .
Packages: ['numpy==1.17.3', 'pandas==1.2.1', 'setuptools==53.0.0', 'Pillow==6.2.1', 'torchvision==0.5.0', 'torch @ https://download.pytorch.org/whl/cpu/torch-1.4.0%2Bcpu-cp37-cp37m-linux_x86_64.whl']
running egg_info
writing <>.egg-info/PKG-INFO
writing dependency_links to <>.egg-info/dependency_links.txt
writing requirements to <>.egg-info/requires.txt
writing top-level names to <>.egg-info/top_level.txt
reading manifest file '<>.egg-info/SOURCES.txt'
writing manifest file '<>.egg-info/SOURCES.txt'
Python packages:
Packages: ['numpy==1.17.3', 'pandas==1.2.1', 'setuptools==53.0.0', 'Pillow==6.2.1', 'torchvision==0.5.0', 'torch @ https://download.pytorch.org/whl/cpu/torch-1.4.0%2Bcpu-cp37-cp37m-linux_x86_64.whl']
Setup.py
from pathlib import Path
"""
Purpose: Package your Predictor and its dependencies by packaging Predictor as a .tar.gz.
For deploying any PyTorch model, the PyTorch package is needed to be provided in the below-mentioned command. In this case,
we have used the package:
torch-1.3.1+cpu-cp37-cp37m-linux_x86_64.whl
For getting pytorch packages according to your requirements,
Visit this link: Pytorch Packages(google search)
Download the package you require and store it in the GCS bucket.
The package we are using provides version resource with PyTorch 1.3.1 for Python 3.7, built to run on a CPU in Linux.
NOTE: We could have directly added 'torch' in the 'REQUIRED_PACKAGES' list in setup.py file in order to provide pytorch as a dependency to be installed while deployment.
This way, it uses the PyPI installation of pytorch.
But the issue with this approach is that it internally downloads PyPI package for pytorch which is of 720 MB Which causes the failure of our model deployment because the AI platform allows custom models of 500MB or below to be deployed on it.
So it is recommended to provide a pytorch package manually using gsutil command under — package-uris.
Try: pip install --target=/tmp/custom_lib --no-cache-dir -b /tmp/pip_builds <>.4.tar.gz for troubleshooting
"""
base = Path(__file__).parent
print(f"Parent directory: {base}")
REQUIRED_PACKAGES = [line.strip() for line in open(base/"requirements.txt")] + \
['torchvision==0.5.0', 'torch @ https://download.pytorch.org/whl/cpu/torch-1.4.0%2Bcpu-cp37-cp37m-linux_x86_64.whl']
print(f"\nPackages: {REQUIRED_PACKAGES}\n\n")
setup(description="Extract features of a image",
author=<>,
author_email=<>,
name=<>,
version=<>,
url='<>',
install_requires=REQUIRED_PACKAGES,
project_urls={
'Documentation': 'https://cloud.google.com/ai-platform/prediction/docs/custom-prediction-routines#tensorflow',
'Deploy': 'https://cloud.google.com/ai-platform/prediction/docs/deploying-models#gcloud_1',
'Ai_platform troubleshooting': 'https://cloud.google.com/ai-platform/training/docs/troubleshooting',
'Say Thanks!': ['https://medium.com/searce/deploy-your-own-custom-model-on-gcps-ai-platform-7e42a5721b43',
'https://stackoverflow.com/questions/61933879/unexpected-error-when-loading-the-model-problem-in-predictor-modulenotfounder',
'https://stackoverflow.com/questions/56428037/what-is-the-best-way-to-save-pil-image-in-json'],
'google Torch wheels': "http://storage.googleapis.com/cloud-ai-pytorch/readme.txt",
'Torch & torchvision wheels': "https://download.pytorch.org/whl/torch_stable.html ",
'Raised issue with google github branch': "https://github.com/GoogleCloudPlatform/python-docs-samples/issues/5257",
"Stackoverflow": "https://stackoverflow.com/questions/65795374/gcp-ai-platform-error-when-creating-a-custom-predictor-model-version-trained"
},
python_requires='~=3.7',
scripts=[<>])```
Have tried the usual upgrading python setuptools to 52.0.0, but can't seem to shake this error off.
A: I was able to make it work by removing the 'requirement.txt' and copy packages directly to setup.py. Don't know the real reason for this weird behaviour.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,423
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Raiffeisen Bank Polska ist eine polnische Geschäftsbank mit Sitz in Warschau.
Sie konzentriert sich auf die Betreuung mittlerer und kleinerer Unternehmen, verfügt jedoch auch über ein umfangreiches Angebot an Produkten und Dienstleistungen für große Unternehmen.
Geschichte
Auf dem polnischen Markt war er von 1991 bis 2000 als Raiffeisen Centrobank SA tätig. Alleinige Gesellschafterin war die Raiffeisen Bank International AG (RBI).
Am 30. April 2012 gab die Raiffeisen Bank International AG (RBI) die Übernahme der Polbank EFG bekannt. Am 4. Dezember 2012 genehmigte die polnische Finanzaufsichtsbehörde die Fusion der Raiffeisen Bank Polska SA und der Polbank EFG SA, die am 31. Dezember 2012 abgeschlossen wurde.
Von Januar 2013 bis Oktober 2018 firmierte die fusionierte Bank unter der Marke "Raiffeisen Polbank". 2014 war sie gemessen an den Vermögenswerten die achtgrößte polnische Bank.
Bis 2016 war sie (zusammen mit Raiffeisen-Leasing) Miteigentümerin der Leasinggesellschaft Raiffeisen-Leasing Polska S.A. In diesem Jahr wurde Raiffeisen-Leasing Polska S.A. an die PKO Bank Polski verkauft.
Im April 2018 kündigte die Bank BGŻ BNP Paribas an, das Kerngeschäft der Raiffeisen Bank Polska von der Raiffeisen Bank International AG für 3,25 Mrd. Złoty zu kaufen.
Die Übernahme wurde am 3. November 2018 vollzogen, nachdem am 14. September 2018 die polnische Finanzaufsichtsbehörde die Teilung der Raiffeisen Bank Polska S.A. und die Übernahme des getrennten Teils durch die Bank BGŻ BNP Paribas S.A. genehmigt hatte. Am 11. November 2019 fand die operative Verschmelzung der BNP Paribas mit der Raiffeisen Bank Polska statt.
Seit dieser Teilung wickelt die verbleibende Niederlassung ausschließlich Services ab, die mit dem Portfolio in Verbindung stehen, das im Zuge des Verkaufs übertragen wurde. Dieses Portfolio beträgt ca. € 3,3 Mrd. Gesamtkapital und besteht hauptsächlich aus Fremdwährungs-Hypothekarkrediten aus dem Privatkundengeschäft. Es werden weder neue Veranlagungen entgegengenommen, noch wird sonstiges Neukundengeschäft betrieben.
Einzelnachweise
Börsennotiertes Unternehmen
Unternehmen (Polen)
Unternehmen (Warschau)
Kreditinstitut (Polen)
Raiffeisengruppe Österreich
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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\section*{Appendix}\label{sec:App}
\subsection{Proof of theorem \ref{thm:Monotone}}\label{sec:AppendPfa}
\begin{proof}
The result is a direct consequence of the strong monotonicity of $F_{W}$ over $\mathcal{C}\br{W}$. By lemma \ref{lem:Jac}, the Jacobian of $F_{W}$ is given by
\[\Jac{F_{W}}{\beta}=\sum_{i=0}^n W\br{M_iV^x_i+N_iV^y_i}\]
where $\beta=\stc{V^x}{V^y}$.
$F_{W}$ is strongly montone with modulus $m$ if (theorem \ref{thm:VIcond})
\[\Sym{\Jac{F_{W}}{\beta}}=\sum_{i=0}^n \Sym{W\br{M_iV^x_i+N_iV^y_i}}\succeq mI\]
Thus, $F_{W}$ is strongly monotone over the domain $\beta\in\mathcal{C}\br{W}$. The remaining results follow from theorem \ref{thm:VI}
\end{proof}
\subsection{Proof of theorem \ref{thm:MonotoneC}}\label{sec:AppendPfb}
\begin{proof}Let $Q_0=\sum_{i=0}^{n} \Sym{W\br{M_iv^x_i+N_iv^y_i}}$. Then,
\begin{align}
&\sum_{i=0}^{n} \Sym{W\br{M_iV^x_i+N_iV^y_i}}=\nonumber\\
&Q_0+\sum_{i=0}^{n} \Sym{W\br{M_i\br{V^x_i-v^x_i}+N_i\br{V^y_i-v^y_i}}}\label{eq:Pfa}
\end{align}
\begin{align*}
&V^c\in \C_{op}\br{\delta}\equiv \sqrt{|V^x_i-v^x_i|^2+|V^y_i-v^y_i|^2}\leq \delta_{i}\\
&\implies \stc{V^x_i-v^x_i}{V^y_i-v^y_i}\in \delta_i\Conv{\left\{\stc{K_{1l}}{K_{2l}},\stc{-K_{1l}}{K_{2l}}\right\}_{1\leq l \leq 4}}
\end{align*}
This can be seen simply by plotting the points $\delta_i\br{K_{1l}+\mathbf{j} K_{l2}}$ on the complex plane and observing that their convex hull contains the disc of radius $\delta_{i}$ centered at the origin. Thus, for any $V^c\in \C_{op}\br{\delta}$,
\begin{align*}
&-\br{M_i\br{V^x_{i}-v^x_{i}}+N_i\br{V^y_{i}-v^y_{i}}}\in\\
&\delta_{i}\Conv{\left\{-K_{1l}M_i-K_{2l}N_i,K_{l1}M_i-K_{2l}N_i\right\}_{l=1,\ldots,4}}
\end{align*}
From \eqref{eq:Pfa}, we now have
\begin{align*}
& \sum_{i=0}^{n} \Sym{W\br{M_iV^x_i+N_iV^y_i}}\succeq Q_0-\sum_{k\in\mathcal{E}} X_k \forall \,V^c\in \C_{op}
\end{align*}
By \eqref{eq:CCa}, we have $V^c\in \C_{op}\br{\delta} \implies V^c\in\mathcal{C}\br{W}$, so that $\C_{op}\br{\delta}\subset\mathcal{C}\br{W}$.
\end{proof}
\begin{lemma}\label{lem:Jac}
The Jacobian of $F\br{V^x,V^y}$ is given by:
\begin{align}
\Jac{F}{V^x,V^y}=\sum_{i=0}^n M_i V^x_i+N_iV^y_i
\end{align}
\end{lemma}
\begin{proof}
The entries of the Jacobian are given by:
\begin{align*}
\Jac{F}{V^x,V^y}=\begin{pmatrix}
S & T \\
O & L
\end{pmatrix}
\end{align*}
with each block being $n \times n$.
\begin{align*}
S_{ii} &= 2G_{ii}V^x_i+\sum_{j\sim i} B_{ij}V^y_j -\sum_{j\sim i} G_{ij}V^x_j\\
S_{ij} &= -B_{ij}V^y_i-G_{ij}V^x_i\\
T_{ii} &= 2G_{ii}V^y_i-\sum_{j\sim i} B_{ij}V^x_j -\sum_{j\sim i} G_{ij}V^y_j\\
T_{ij} &= B_{ij}V^x_i-G_{ij}V^y_i
\end{align*}
The entries of $O,L$ depend on whether $i$ is a (P,Q)~bus or (P,V)~bus. For $i\in\mathrm{pq}$, we have
\begin{align*}
O_{ii} &= 2B_{ii}V^x_i+\sum_{j\sim i} B_{ij}V^x_j -\sum_{j\sim i} G_{ij}V^y_j\\
O_{ij} &= B_{ij}V^x_i+G_{ij}V^y_i\\
L_{ii} &= 2B_{ii}V^y_i+\sum_{j\sim i} B_{ij}V^y_j -\sum_{j\sim i} G_{ij}V^x_j\\
L_{ij} &= B_{ij}V^y_i+G_{ij}V^x_i
\end{align*}
For $i\in\mathrm{pv}$, we have
\begin{align*}
O_{ii} = 2V^x_i,O_{ij} = 0,L_{ii} = 2V^y_i,L_{ij} = 0
\end{align*}
Using these expressions, it is not hard to see that
\begin{align*}
\Jac{F}{V^x,V^y}=\sum_{i=0}^n M_iV^x_i+N_iV^y_i
\end{align*}
\end{proof}
\subsection{Proof of lemma \ref{lem:ConvFeas}}\label{App:ConvFeas}
\begin{proof}
Suppose $\exists \tilde{W},X_i \in\mathcal{S}^{2n}$ such that the constraints are feasible for some $\rho$. Then, clearly, with the same choice, they are also feasible for any smaller $\rho$. Then, the sub-level sets of the problem are convex, and hence the problem is a quasi-convex optimization problem. Suppose $\sum_{i=0}^n M_iv^x_i+N_iv^y_i$ is full-rank. When $\rho=0$, for any fixed $\tilde{W}$, we can choose $X_k=0$ and $T_k,S_k$ to satisfy the final equality constraints. Then, one needs to find $W$ such that
\begin{align*}
&\Sym{W\br{\sum_{i=0}^n M_iv^x_i+N_iv^y_i}}\succeq mI
\end{align*}
This can always be done if $\sum_{i=0}^n M_iv^x_i+N_iv^y_i$ is full rank, since one can simply choose
\[W=m\inv{\sum_{i=0}^n M_iv^x_i+N_iv^y_i}\]
Hence, this optimization problem is always feasible when $\sum_{i=0}^n M_iv^x_i+N_iv^y_i$ is full rank.
\end{proof}
\begin{comment}
\begin{lemma}
$F\br{\rho,\theta}$ is monotone over the domain given by
\begin{align*}
\begin{pmatrix}
0 & 4\diagb{\Rep{Y_{ii}}}\\
4\diagb{\Rep{Y_{ii}}} & 4\diagb{\Imp{Y_{ii}}}
\end{pmatrix}\\
+\sum_{\br{i,j}\in\mathcal{E}}2|Y_{ij}|\cos\br{\psi_{ij}}\Mat{\begin{pmatrix} s\br{\delta_i}\cos\br{\delta_i}\begin{pmatrix} \expb{\rho_j-\rho_i} & -1 \\ -1 & \expb{\rho_i-\rho_j} \end{pmatrix} & \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \\
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & -\frac{1}{\cos\br{\theta_{ij}}}\begin{pmatrix} \expb{\rho_j-\rho_i} & 1 \\ 1 & \expb{\rho_i-\rho_j}
\end{pmatrix}\end{pmatrix} }{i,j,n-1+i,n-1+j}{\mathcal{V}\setminus\{\mathcal{S}\}}\\
& \quad\qquad-2|Y_{ij}|\cos\br{\delta_i}\sin\br{\psi_{ij}}\Mat{D_{ij} \begin{pmatrix} \expb{\rho_j-\rho_i} & -1 \\ -1 & \expb{\rho_i-\rho_j} \end{pmatrix}\otimes \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}D_{ij}}{i,j,n-1+i,n-1+j}{\mathcal{V}\setminus\{\mathcal{S}\}}
\end{align*}
\end{lemma}
\begin{lemma}
Define the operator $F^{ij}\br{\rho,\theta}$ as
\begin{subequations}
\begin{align}
F_k^{ij}\br{\theta,\rho} & =|Y_{ij}|\expb{\rho_i+\rho_j}\sin\br{\theta_i-\theta_j-\psi_{ij}} \text{ if } k=i \text{ or } k=j,k\in\mathcal{V}\setminus\{\mathcal{S}\}\label{eq:Fija}\\
F_{n-1+k}^{ij}\br{\theta,\rho} &=-|Y_{ij}|\expb{\rho_i+\rho_j}\cos\br{\theta_i-\theta_j-\psi_{ij}}-Q_i \text{ if } k=i \text{ or } k=j,k\in\mathrm{pq}\label{eq:Fijb}
\end{align}\label{eq:Fij}
\end{subequations}
and all the other coordinates of $F^{ij}$ are $0$.
\begin{comment}
Then
\begin{align}
&\Jac{F^{ij}}{\rho,\theta}+\tranb{\Jac{F^{ij}}{\rho,\theta}}\\
&\succeq 2|Y_{ij}|\cos\br{\psi_{ij}}\Mat{D_{ij} \begin{pmatrix} s\br{\delta_i}\cos\br{\theta_{ij}}\begin{pmatrix} \expb{\rho_j-\rho_i} & -1 \\ -1 & \expb{\rho_i-\rho_j} \end{pmatrix} & \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \\
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & -\frac{1}{\cos\br{\theta_{ij}}}\begin{pmatrix} \expb{\rho_j-\rho_i} & 1 \\ 1 & \expb{\rho_i-\rho_j}
\end{pmatrix}\end{pmatrix} D_{ij}}{i,j,n-1+i,n-1+j}{\mathcal{V}\setminus\{\mathcal{S}\}}\\
& \quad\qquad-2|Y_{ij}|\cos\br{\delta_i}\sin\br{\psi_{ij}}\Mat{D_{ij} \begin{pmatrix} \expb{\rho_j-\rho_i} & -1 \\ -1 & \expb{\rho_i-\rho_j} \end{pmatrix}\otimes \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}D_{ij}}{i,j,n-1+i,n-1+j}{\mathcal{V}\setminus\{\mathcal{S}\}}
\end{align}
where
\[|\theta_{ij}|\leq\delta_i,D_{ij}=\mathrm{di}{\begin{pmatrix}\expb{\rho_i}\\ \expb{\rho_j}\\ \expb{\rho_i}\\ \expb{\rho_j}\end{pmatrix}}\]
\[s\br{\delta_i}=\min_{|t|\leq \tan\br{\delta_i}} \sigma_{\min}\br{\begin{pmatrix}
1 & 0 & 0\\
t & 1 & 0 \\
t & 0 & 1
\end{pmatrix}}\]
\end{lemma}
\begin{proof}
Suppose that $i,j\in\mathrm{pq}$. The analysis is similar for the other cases. Let $\phi=\theta_i-\theta_j,\psi=\psi_{ij}$. The non-zero elements of $\Jac{F^{ij}}{\theta,\rho}=|Y_{ij}|\expb{\rho_i+\rho_j}\Mat{H}{i,j,n-1+i,n-1+j}{\mathcal{V}\setminus\{\mathcal{S}\}}$, are
\begin{align*}
H_{11}= \cos\br{\theta_i-\theta_j-\psi_{ij}}=\cos\br{\phi-\psi} \\
H_{12}= -\cos\br{\theta_i-\theta_j-\psi_{ij}}=-\cos\br{\phi-\psi}\\
H_{13}= \sin\br{\theta_i-\theta_j-\psi_{ij}}=\sin\br{\phi-\psi}\\
H_{14}= \sin\br{\theta_i-\theta_j-\psi_{ij}}=\sin\br{\phi-\psi}\\
H_{21}= -\cos\br{\theta_j-\theta_i-\psi_{ij}}=-\cos\br{\phi+\psi} \\
H_{22}= \cos\br{\theta_j-\theta_j-\psi_{ij}}=\cos\br{\phi+\psi}\\
H_{23}= \sin\br{\theta_j-\theta_i-\psi_{ij}}=-\sin\br{\phi+\psi}\\
H_{24}= \sin\br{\theta_j-\theta_i-\psi_{ij}}=-\sin\br{\phi+\psi}\\
H_{31}= \sin\br{\theta_i-\theta_j-\psi_{ij}}=\sin\br{\phi-\psi}\\
H_{32}= -\sin\br{\theta_i-\theta_j-\psi_{ij}}=-\sin\br{\phi-\psi}\\
H_{33}= -\cos\br{\theta_i-\theta_j-\psi_{ij}}=-\cos\br{\phi-\psi}\\
H_{34}= -\cos\br{\theta_i-\theta_j-\psi_{ij}}=-\cos\br{\phi-\psi}\\
H_{41}= -\sin\br{\theta_j-\theta_i-\psi_{ij}}=\sin\br{\phi+\psi} \\
H_{42}= \sin\br{\theta_j-\theta_i-\psi_{ij}}=-\sin\br{\phi+\psi} \\
H_{43}= -\cos\br{\theta_j-\theta_i-\psi_{ij}}=-\cos\br{\phi+\psi}\\
H_{44}= -\cos\br{\theta_j-\theta_i-\psi_{ij}}=-\cos\br{\phi+\psi}\\
\end{align*}
Symmetrizing this matrix, we obtain
\[
\begin{pmatrix}
\cos\br{\phi-\psi} & - \cos\br{\phi}\cos\br{\psi} & \sin\br{\phi-\psi} & \sin\br{\phi}\cos\br{\psi}\\
- \cos\br{\phi}\cos\br{\psi} & \cos\br{\phi+\psi} & -\sin\br{\phi}\cos\br{\psi} & - \sin\br{\phi+\psi}\\
\sin\br{\phi-\psi} & -\sin\br{\phi}\cos\br{\psi} & -\cos\br{\phi-\psi} & -\cos\br{\phi}\cos\br{\psi}\\
\sin\br{\phi}\cos\br{\psi} & -\sin\br{\psi+\psi} & -\cos\br{\phi}\cos\br{\psi} & -\cos\br{\phi+\psi}
\end{pmatrix}\]
Taking Schur-complement's with respect to the $1-1$ entry, we get
\[
\begin{pmatrix}
- \frac{\sin^2\br{\phi}\sin^2\br{\psi}}{\cos\br{\phi-\psi}} & -\frac{\sin\br{\psi}\cos\br{\psi}}{\cos\br{\phi-\psi}} & -\frac{\sin\br{\psi}\cos\br{\psi}+\sin^2\br{\psi}\sin\br{\phi}\cos\br{\phi}}{\cos\br{\phi-\psi}}\\
-\frac{\sin\br{\psi}\cos\br{\psi}}{\cos\br{\phi-\psi}} & -\frac{1}{\cos\br{\phi-\psi}} & -\frac{\cos^2\br{\psi}}{\cos\br{\phi-\psi}}\\
- \frac{\sin\br{\psi}\cos\br{\psi}+\sin^2\br{\psi}\sin\br{\phi}\cos\br{\psi}}{\cos\br{\phi-\psi}} & -\frac{\cos^2\br{\psi}}{\cos\br{\phi-\psi}} & -\frac{\cos^2\br{\psi}-\sin^2\br{\psi}\sin^2\br{\phi}}{\cos\br{\phi-\psi}}
\end{pmatrix}\]
Further, we have
\[
\begin{pmatrix}
- \frac{\sin^2\br{\phi}\sin^2\br{\psi}}{\cos\br{\phi-\psi}} & 0 & -\frac{\sin^2\br{\psi}\sin\br{\phi}\cos\br{\phi}}{\cos\br{\phi-\psi}}\\
0 & 0 & 0\\
- \frac{\sin^2\br{\psi}\sin\br{\phi}\cos\br{\psi}}{\cos\br{\phi-\psi}} & 0 & \frac{\sin^2\br{\psi}\sin^2\br{\phi}}{\cos\br{\phi-\psi}}
\end{pmatrix}\succeq \frac{-\sin^2\br{\psi}}{\cos\br{\phi-\psi}}\begin{pmatrix}
1 & 0 & 0\\
0 & 0 & 0 \\
0 & 0 & 0\end{pmatrix}\]
This is easily verified by adding the negated RHS to the LHS and verifying that this is a positive semidefinite matrix. We are then left with
\[
\frac{-1}{\cos\br{\phi-\psi}}
\begin{pmatrix}
\sin^2\br{\psi} & \sin\br{\psi}\cos\br{\psi} & \sin\br{\psi}\cos\br{\psi}\\
\sin\br{\psi}\cos\br{\psi} & 1 & \cos^2\br{\psi}\\
\sin\br{\psi}\cos\br{\psi} & \cos^2\br{\psi} & \cos^2\br{\psi}
\end{pmatrix}
\]
This matrix can be broken into two pieces:
\begin{align*}
\cos\br{\psi_{ij}}\begin{pmatrix}
\cos\br{\theta_{ij}}\begin{pmatrix} 1 & -1 \\ -1 & 1\end{pmatrix}
& \sin\br{\theta_{ij}}\begin{pmatrix} 1 & 1 \\ -1 & -1\end{pmatrix}\\
\sin\br{\theta_{ij}}\begin{pmatrix} 1 & -1 \\ 1 & -1\end{pmatrix} &
\cos\br{\theta_{ij}}\begin{pmatrix} -1 & -1 \\ -1 & -1\end{pmatrix}
\end{pmatrix}+
\sin\br{\psi_{ij}}\begin{pmatrix}
\sin\br{\theta_{ij}}\begin{pmatrix} 1 & 0 \\ 0 & -1\end{pmatrix}
& \cos\br{\theta_{ij}}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix}\\
\cos\br{\theta_{ij}}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix} &
\sin\br{\theta_{ij}}\begin{pmatrix} -1 & 0 \\ 0 & 1\end{pmatrix}
\end{pmatrix}
\end{align*}
Define
\[M=\begin{pmatrix}1 & 0 & 0\\ -1 & 0 & 0\\ 0 & 1 & 0 \\ 0 & 0 & 1\end{pmatrix}\]
The first piece corresponds to the Hessian of the energy function for lossless systems. We can factor this piece as
\begin{align}
(&2|Y_{ij}|\expb{\rho_i+\rho_j}\cos\br{\psi_{ij}} M \begin{pmatrix} \cos\br{\theta_{ij}} & \sin\br{\theta_{ij}} & \sin\br{\theta_{ij}}\\
\sin\br{\theta_{ij}} & -\cos\br{\theta_{ij}} & -\cos\br{\theta_{ij}} \\
\sin\br{\theta_{ij}} & -\cos\br{\theta_{ij}} & -\cos\br{\theta_{ij}}
\end{pmatrix}\tran{M}\nonumber\\
&=2|Y_{ij}|\expb{\rho_i+\rho_j}\cos\br{\psi_{ij}}M\begin{pmatrix} 1 & 0 & 0\\
\tan\br{\theta_{ij}} & 1 & 0 \\
\tan\br{\theta_{ij}} & 0 & 1
\end{pmatrix} \begin{pmatrix} \cos\br{\theta_{ij}} & 0 & 0\\
0 & -\frac{1}{\cos\br{\theta_{ij}}} & -\frac{1}{\cos\br{\theta_{ij}}} \\
0 & -\frac{1}{\cos\br{\theta_{ij}}} & -\frac{1}{\cos\br{\theta_{ij}}}
\end{pmatrix}\tran{\begin{pmatrix} 1 & 0 & 0\\
\tan\br{\theta_{ij}} & 1 & 0 \\
\tan\br{\theta_{ij}} & 0 & 1
\end{pmatrix} } \tran{M}\\
&=2|Y_{ij}|\expb{\rho_i+\rho_j}\cos\br{\psi_{ij}}\begin{pmatrix} 1\\
-1\\
1+\tan\br{\theta_{ij}} \\
1+\tan\br{\theta_{ij}}
\end{pmatrix}\cos\br{\theta_{ij}}\tran{\begin{pmatrix} 1\\ -1 \\
1+\tan\br{\theta_{ij}}\\
1+\tan\br{\theta_{ij}}
\end{pmatrix} }\\
&\quad + 2|Y_{ij}|\expb{\rho_i+\rho_j}\cos\br{\psi_{ij}}\begin{pmatrix} 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0\\
0 & 0 & -\frac{1}{\cos\br{\theta_{ij}}} & -\frac{1}{\cos\br{\theta_{ij}}} \\
0 & 0 & -\frac{1}{\cos\br{\theta_{ij}}} & -\frac{1}{\cos\br{\theta_{ij}}}
\end{pmatrix}
\label{eq:p1}
\end{align}
Let $\delta_i\leq \frac{\pi}{4}$ be an upper bound $|\theta_i-\theta_j|$ and define
\begin{align*}
s\br{\delta_i}=\min_{|t|\leq \tan\br{\delta_i}} \sigma_{\min}\br{\begin{pmatrix}
1 & 0 & 0\\
t & 1 & 0 \\
t & 0 & 1
\end{pmatrix}}
\end{align*}
Then, the \eqref{eq:p1} is bounded below by
\begin{align*}
2|Y_{ij}|\expb{\rho_i+\rho_j}\cos\br{\psi_{ij}}M \begin{pmatrix} s\br{\delta_i}\cos\br{\theta_{ij}} & \begin{pmatrix} 0 & 0 \end{pmatrix}\\
0 & -\frac{1}{\cos\br{\theta_{ij}}}\begin{pmatrix} 1 & 1 \\ 1 & 1
\end{pmatrix}\end{pmatrix}\tran{M}\\
= 2|Y_{ij}|\expb{\rho_i+\rho_j}\cos\br{\psi_{ij}} \begin{pmatrix} s\br{\delta_i}\cos\br{\theta_{ij}}\begin{pmatrix} 1 & -1 \\ -1 & 1 \end{pmatrix} & \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \\
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & -\frac{1}{\cos\br{\theta_{ij}}}\begin{pmatrix} 1 & 1 \\ 1 & 1
\end{pmatrix}\end{pmatrix}
\end{align*}
The second piece can be bounded blow as
\begin{align*}
&2|Y_{ij}|\expb{\rho_i+\rho_j}\sin\br{\psi_{ij}}\begin{pmatrix}
\sin\br{\theta_i-\theta_j}\begin{pmatrix} 1 & 0 \\ 0 & -1\end{pmatrix}
& \cos\br{\theta_i-\theta_j}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix}\\
\cos\br{\theta_i-\theta_j}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix} &
\sin\br{\theta_i-\theta_j}\begin{pmatrix} -1 & 0 \\ 0 & 1\end{pmatrix}
\end{pmatrix} \\
&\succeq
2|Y_{ij}|\expb{\rho_i+\rho_j}\sin\br{\psi_{ij}}\begin{pmatrix}\cos\br{\theta_{ij}}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix}
& \cos\br{\theta_{ij}}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix}\\
\cos\br{\theta_{ij}}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix} &
\cos\br{\theta_{ij}}\begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix}
\end{pmatrix}\\
&=
-2|Y_{ij}|\expb{\rho_i+\rho_j}\sin\br{\psi_{ij}}\cos\br{\theta_{ij}}\begin{pmatrix}
1 & 0 & 1 & 0\\
0 & 1 & 0 & 1\\
1 & 0 & 1 & 0\\
0 & 1 & 0 & 1
\end{pmatrix}
\end{align*}
where the second inequality follows because $|\sin\br{\theta_{ij}}|\leq \cos\br{\theta_{ij}}$ as long as $|\theta_{ij}|\leq\frac{\pi}{4}$. Thus, overall the symmetrized Jacobian is larger (in the psd) sense than
\begin{align*}
& 2|Y_{ij}|\expb{\rho_i+\rho_j}\br{\cos\br{\psi_{ij}} \begin{pmatrix} s\br{\delta_i}\cos\br{\theta_{ij}}\begin{pmatrix} 1 & -1 \\ -1 & 1 \end{pmatrix} & \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \\
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & -\frac{1}{\cos\br{\theta_{ij}}}\begin{pmatrix} 1 & 1 \\ 1 & 1
\end{pmatrix}\end{pmatrix}-\sin\br{\psi_{ij}}\cos\br{\theta_{ij}}\begin{pmatrix}
1 & 0 & 1 & 0\\
0 & 1 & 0 & 1\\
1 & 0 & 1 & 0\\
0 & 1 & 0 & 1
\end{pmatrix}}\\
& = 2|Y_{ij}|\cos\br{\psi_{ij}}D \begin{pmatrix} s\br{\delta_i}\cos\br{\theta_{ij}}\begin{pmatrix} \expb{\rho_j-\rho_i} & -1 \\ -1 & \expb{\rho_i-\rho_j} \end{pmatrix} & \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \\
\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} & -\frac{1}{\cos\br{\theta_{ij}}}\begin{pmatrix} \expb{\rho_j-\rho_i} & 1 \\ 1 & \expb{\rho_i-\rho_j}
\end{pmatrix}\end{pmatrix} D\\
& \quad\qquad-2|Y_{ij}|\cos\br{\delta_i}\sin\br{\psi_{ij}}D \begin{pmatrix} \expb{\rho_j-\rho_i} & -1 \\ -1 & \expb{\rho_i-\rho_j} \end{pmatrix}\otimes \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}D \end{align*}
\end{proof}
where
\[D=\mathrm{di}{\begin{pmatrix}\expb{\rho_i}\\ \expb{\rho_j}\\ \expb{\rho_i}\\ \expb{\rho_j}\end{pmatrix}}\]
\end{comment}
\section{Monotonicity of the Power Flow Operator}\label{sec:Montone}
In this Section, we study the monotonicity of the PF operator $F$ \eqref{eq:F}. As described in Section \ref{sec:Mon}, zeros of $F$ (solutions to the PF equations) can be found efficiently if $F$ is monotone. Thus, if we can prove that the PF operator is monotone, the PF solutions can be found efficiently. Since PF equations can have multiple isolated solutions, it is not possible that the PF operator is globally monotone because this would imply a unique solution to the PF equations. Thus, we focus on characterizing domains over which the PF operator (or a scaled version of it) is monotone. Proofs of all theorems in this section are deferred to the appendix Section \ref{sec:App}.
\subsection{Characterization of Domain of Monotonicity of the Power Flow Operator}
We now derive our main results on the monotonicity of the PF operator \eqref{eq:F}. In order to state the result succinctly, we will need to define some matrices that are functions of the network topology, locations of (P,V)~buses and of the network impedance matrices.
\begin{definition}
Define the following row vectors:\begin{align*}
G^i &=\begin{pmatrix}G_{i1},G_{i2},\ldots,G_{in} \end{pmatrix} \\
B^i &=\begin{pmatrix}B_{i1},B_{i2},\ldots,B_{in} \end{pmatrix} \\
G^i_{\mathrm{pq}} &=\begin{pmatrix}G_{i1}\Ind{1\in\mathrm{pq}},\ldots,G_{in}\Ind{n\in\mathrm{pq}} \end{pmatrix}\ \\
B^i_{\mathrm{pq}} &=\begin{pmatrix}B_{i1}\Ind{1\in\mathrm{pq}},\ldots,B_{in}\Ind{n\in\mathrm{pq}} \end{pmatrix}
\end{align*}
Let $e_i$ denote the $i$-th column of the $n\times n$ identity matrix, so $e_i$ has zeros everywhere except the $i$-th entry.
\end{definition}
\begin{definition}
Define the following matrices:
\begin{subequations}
\begin{align}
M_i &= \begin{cases}
\begin{pmatrix}
\diagb{G^i}+e_iG^i & \diagb{B^i}-e_iB^i \\
-\diagb{B^i_{\mathrm{pq}}}-e_iB^i_{\mathrm{pq}} & \diagb{G^i_{\mathrm{pq}}}-e_iG^i
\end{pmatrix} & i\in\mathrm{pq}\\
\begin{pmatrix}
\diagb{G^i}+e_iG^i & \diagb{B^i}-e_iB^i \\
-\diagb{B^i_{\mathrm{pq}}}+2e_i\tran{e_i} & \diagb{G^i_{\mathrm{pq}}}
\end{pmatrix} & i\in\mathrm{pv}
\end{cases} \\
N_i &= \begin{cases}
\begin{pmatrix}
-\diagb{B^i}+e_iB^i & \diagb{G^i}+e_iG^i \\
-\diagb{G^i_{\mathrm{pq}}}+e_iG^i_{\mathrm{pq}} & -\diagb{B^i_{\mathrm{pq}}}-e_iB^i
\end{pmatrix} & i\in\mathrm{pq}\\
\begin{pmatrix}
-\diagb{B^i}+e_iB^i & \diagb{G^i}+e_iG^i \\
-\diagb{G^i_{\mathrm{pq}}} & -\diagb{B^i_{\mathrm{pq}}}+2e_i\tran{e_i}
\end{pmatrix} & i\in\mathrm{pv}
\end{cases} \\
M_0 &= \begin{pmatrix}
\diagb{G^0} & \diagb{B^0} \\
-\diagb{B^0_{\mathrm{pq}}} & \diagb{G^0_{\mathrm{pq}}}
\end{pmatrix} \\
N_0 &= \begin{pmatrix}
-\diagb{B^0}& \diagb{G^0}\\
-\diagb{G^0_{\mathrm{pq}}} & -\diagb{B^0_{\mathrm{pq}}}
\end{pmatrix}
\end{align}
\end{subequations}
\end{definition}
We now state our main technical result, which shows that the PF equations can be solved by solving a monotone variational inequality (for which there exist efficient algorithms).
\begin{theorem}\label{thm:Monotone}
Let $W \in \mathbb{R}^{2n \times 2n}$ be an invertible matrix and $m>0$. There is at most one solution of the PF equations $F\br{V^c}=0$ over the domain:
\begin{align}
\mathcal{C}\br{W}=\left\{\begin{pmatrix}V^x\\V^y\end{pmatrix}: \sum_{i=0}^{n} \Sym{W\br{M_iV^x_i+N_iV^y_i}}\succeq m I\right\}
\end{align}
Define $F_{W}\br{V^c}=W F\br{V^c}$. $F_{W}$ is strongly monotone with modulus $m$ over the set $\mathcal{C}\br{W}$. Let $\opt{V^c}$ be the unique solution to the monotone variational inequality:
\begin{align}
&V^c\in\mathcal{C}\br{W}\\
&\inner{F_{W}\br{V^c}}{\alpha-V^c}\geq 0 \quad\forall \alpha:\alpha\in\mathcal{C}\br{W}
\end{align}
If $F\br{\opt{V^c}}=0$, $\opt{V^c}$ is the unique solution to the PF equations in $\mathcal{C}\br{W}$. Otherwise, there are no solutions to $F\br{V^c}=0,V^c\in\mathcal{C}\br{W}$.
\end{theorem}
\begin{remark}
We implicitly assume existence of a solution to the variational inequality above. This is guaranteed (by theorem \ref{thm:VI}) if $\mathcal{C}\br{W}$ is compact. Magnitudes of voltage phasors in practical power systems are always bounded, and one can simply pick a large positive number $b>0$ such that all power flow solutions satisfy $\norm{V^c}\leq b$ and define $\mathcal{C}\br{W}$ with this additional constraint, ensuring it is a compact set.
\end{remark}
\subsubsection{Illustration on 2-bus network}
We consider a 2-bus network with admittance matrix
\[Y=\begin{pmatrix}
.05-\mathbf{j} 1.11 & -.05+\mathbf{j} 1.11 \\
-.05+\mathbf{j} 1.11 & .05-\mathbf{j} 1.11
\end{pmatrix}\]
We fix $=I,V_0=1+\mathbf{j} 0$. Let $V_1-V_0=V^x+\mathbf{j} V^y$. By varying $W$, we can find two disjoint monotonicity domains for this system:
\begin{align*}
W_1=\begin{pmatrix}
-6.75 & .31 \\
0 & .1
\end{pmatrix}, W_2=\begin{pmatrix}
-6.75 & .31 \\
0 & -.1
\end{pmatrix}
\end{align*}
It can be verified that these two monotonicity domains cover the space of $\br{V^x,V^y}$ and there is at most one solution in each domain. In fact, in this system, as long as there is a solution, there exist two (one in each domain).
As the loading increases, the two solutions move closer to each other and eventually disappear (at the point of the saddle-node bifurcation). Note that the boundary between the two solutions is observed exactly at $V_1-V_0=-\frac{1}{2}$. Note that letting $V_1=V\expb{\mathbf{j}\theta}$, or equivalently
\[V\cos\br{\theta}\geq \frac{1}{2}\]
which is a well-known classical criterion for voltage stability in the two bus example.
\begin{comment}
\begin{figure}
\begin{center}
\includegraphics[width=.8\columnwidth]{TwoBus.pdf}
\caption{Two Bus System: Montonicity domain corresponding to $W_1$ (in green) and corresponding to $W_2$ (in cyan). $x=\Rep{V_1-V_0},y=\Imp{V_1-V_0}$. The two power flow solutions for the zero injection case are plotted as red dots. $\br{0,0}$ corresponds to voltage phasors at the two buses being equal, while $\br{-1,0}$ corresponds to the voltage at the (P,Q)~bus dropping to $0+\mathbf{j} 0$.}\label{fig:TwoBus}
\end{center}
\end{figure}
\end{comment}
\subsection{Selection of the Monotonicity Domain}\label{sec:MonCC}
Theorem \ref{thm:Monotone} shows that PF solutions in $\mathcal{C}\br{W}$ can be found efficiently. However, the matrix inequality characterizing $\mathcal{C}\br{W}$ is not intuitive and does not have a simple interpretation. Further, the choice of $W$ would affect the domain of monotonicity. Thus, it is important to pick $W$ so that $\mathcal{C}\br{W}$ contains the ``operationally relevant'' PF solutions. In this Section, we describe a technique to achieve this goal.
We consider the following class of operational constraints:
\begin{align*}
|V_i-v_i|\leq \delta_{i}
\end{align*}
where $v$ is a ``nominal voltage profile. Intuitively, one can think of this as the ``center'' of the monotonicity domain. Stated in terms of $V^c=\begin{pmatrix}
V^x\\ V^y
\end{pmatrix}$, the constraint becomes
\begin{align}
&\sqrt{|V^x_i-{v^x_i}|^2+|V^y_i-{v^y_i}|^2}\leq \delta_{i} \quad i=1,\ldots,n\label{eq:Flim}\nonumber\\
&\C_{op}\br{\delta}=\nonumber\\
&\left\{\begin{pmatrix}
V^x\\ V^y
\end{pmatrix}: \sqrt{|V^x_i-{v^x_i}|^2+|V^y_i-{v^y_i}|^2}\leq \delta_{i}\quad i=1,\ldots,n\right\}
\end{align}
We now state a theorem that gives a sufficient condition to guarantee that $\C_{op}\br{\delta}\subset\mathcal{C}\br{W}$.
\begin{theorem}\label{thm:MonotoneC}
Let
\begin{align}
K = \begin{pmatrix}
1-\sqrt{2} & -1 &-1 & 1-\sqrt{2} \\
1 & \sqrt{2}-1 & 1-\sqrt{2} & -1
\end{pmatrix}
\end{align}
Suppose $\exists W,X_1,\ldots,X_n\in\mathcal{S}^{2n}$ satisfying
\begin{subequations}
\begin{align}
\sum_{i=0}^n\Sym{W\br{ M_iv^x_i+N_iv^y_i}}\succeq mI+\sum_{i=1}^n X_i\label{eq:CCa} \\
X_i \succeq \delta_k\br{-K_{1l} M_i-K_{2l} N_i}, l\in\{1,\ldots,4\}\label{eq:CCb}\\
X_i \succeq \delta_k\br{K_{1l} M_i-K_{2l} N_i}, l\in\{1,\ldots,4\}\label{eq:CCc}
\end{align}\label{eq:CC}
\end{subequations}
Then $\C_{op}\br{\delta}\subset \mathcal{C}\br{W}$. Further, this is a convex feasibility problem in $W$, $X_1,\ldots,X_n$.
\end{theorem}
Theorem \ref{thm:MonotoneC} gives us a principled way to choose $W$ so that $\C_{op}\subset\mathcal{C}\br{W}$. However, the system of constraints \eqref{eq:CC} may be infeasible. In this situation, we can try to see if a scaled version of the constraint set $\mathcal{C}\br{\delta}$ lies within $\mathcal{C}\br{W}$. Specifically, we look for the largest possible $\rho>0$ such that $\mathcal{C}\br{\rho\delta}\subseteq\mathcal{C}\br{W}$.
We then formulate the following problem:
\begin{subequations}
\begin{align}
& \maxi_{\rho\geq 0,W\in\mathbb{R}^{2n\times 2n},X_i \in\mathcal{S}^{2n}} \quad \rho \\
&\text{Subject to } \nonumber\\
&\sum_{i=0}^n\Sym{W\br{ M_iv^x_i+N_iv^y_i}}\succeq mI+\sum_{i=1}^n X_i\label{eq:CCa} \\
& X_i \succeq \rho\delta_k\br{-K_{1l} M_i-K_{2l} N_i}, l\in\{1,\ldots,4\}\label{eq:CCb}\\
& X_i \succeq \rho\delta_k\br{K_{1l} M_i-K_{2l} N_i}, l\in\{1,\ldots,4\}\label{eq:CCc} \end{align} \label{eq:ConvFeas}
\end{subequations}
\begin{lemma}\label{lem:ConvFeas}
\eqref{eq:ConvFeas} is a quasi-convex optimization problem and can be solved efficiently. Further, if the matrix
\[\sum_{i=0}^n M_iv^x_i+N_iv^y_i\]
is full-rank, the problem is always feasible and the optimal solution satisfies $\C_{op}\br{\rho\delta}\subseteq \mathcal{C}\br{W}$.
\end{lemma}
\begin{remark}
The condition that $\sum_{i=0}^n M_iv^x_i+N_iv^y_i$ is non-singular means that the Jacobian of the power flow equations at the nominal voltage profile $v$ is non-singular. This is generically true, except for very special choices of the $v$ and the network admittance matrix. Further, power system voltage stability criteria are often formulated in terms of the ``distance to singularity'' of the Jacobian matrix, so enforcing a non-singular Jacobian is a reasonable restriction.
\end{remark}
\section{Introduction}
Power systems are experiencing revolutionary changes due to various factors, including: Integration of renewable generation, distributed generation, smart metering, direct or price-based load-control capabilities. While potentially contributing to the long-term sustainability of the power grid, these developments also pose significant operational challenges by making the power system inherently stochastic and inhomogeneous. As these changes become more widespread, the system operators will no longer have the luxury of large positive and negative reserves. Moreover, operating the future power grid will require developing new computational tools that can assess the system state and its operational margins more accurately and efficiently than current approaches. Specifically, these new techniques need to go beyond linearized methods of analysis and ensure that the power system is safe even in the presence of large disturbances and uncertainty. In this paper, we focus on the fundamental equations of the power system -- the Power Flow (PF) equations. The equations constitute a system of nonlinear equations and are known to exhibit complex and chaotic behavior \cite{araposthatis1981analysis}\cite{varaiya1992bifurcation}. In the past, when the power systems were operated well within their security margins, the PF equations were solved without difficulty using standard techniques like Newton-Raphson and its variants. However, changes in the power system mentioned above mean that this may no longer be possible. Thus, Newton-Raphson techniques which rely on good initialization may fail to converge. In such a situation, it becomes difficult to assess whether the system is actually operationally unsafe or the Newton-Raphson method failed because of numerical difficulties or bad initialization. In this paper, we propose an approach to remedy this problem. Our approach is based on the theory of monotone operators. Just as a convex optimization problem can be solved efficiently, one can find zeros of a monotone operator efficiently. (In fact, the gradient of a convex function is a monotone operator.) Thus, if we can show that the nonlinear PF equations can be described by a monotone operator, then they can be solved efficiently. It turns out that the PF operator is not globally monotone, however it is monotone over restricted domains.
Our main technical result is a description of the domain over which the power flow operator (whose zeros are solutions to the PF equations), is monotone. In fact, we introduce a family of monotonicity domains, parameterized by a matrix-valued parameter. Each monotonicity domain is characterized by a Linear Matrix Inequality (LMI) in the real and imaginary components of the voltage phasor at each bus. Within each of these monotonicity domains, there can be at most one solution of the PF equations. Further, the solution of the PF equations within each domain can be reduced to the solution of a \emph{monotone variational inequality}, for which there exist efficient algorithms. The algorithms run in polynomial time and terminate either by finding a solution to the PF equations or a certificate that no solution exists to the PF equations within that domain.
The choice of monotonicity domain is critical, since different domains cover different parts of the voltage space. Ideally, one would like to find a monotonicity domain that covers all the solutions of interest, i.e. solutions that satisfy typical operational constraints on voltages and phases. In general, this is a hard problem. We deal with this problem by proposing a sufficient condition to ensure that voltages satisfying some bounds are constrained within the monotonicity domain. Finding the largest bound can then be cast as a quasi-convex optimization problem. We use this technique to pick the monotonicity domain. Numerical tests show that this approach is able to generate a sufficiently large monotonicity domain for several test networks.
The rest of this paper is organized as follows. Section \ref{sec:Intro} covers relevant background on power systems and monotone operators. The main technical results are presented in Section \ref{sec:Montone}. In Section \ref{sec:Related}, we discuss how our approach compares to related work on conditions for existence and uniqueness of PF solutions. In Section \ref{sec:Num}, we present numerical results illustrating our approach on some IEEE benchmark networks.
\section{Conclusions and Future Work}
We have presented a novel approach to solving the PF equations based on monotone operator theory. Our main technical contribution is a characterization of the family of domains over which the PF operator is monotone. Within any of these domains, there can be at most one power flow solution. The approach leads to efficient algorithms for determining existence and actually finding solutions to the PF equations within the monotonicity domains. In spite of the progress reported, there still remain many unanswered questions. First, the numerical experiments show that our approach to selecting $W$ based on solving \eqref{eq:ConvFeas} is potentially conservative and misses some solutions that could be captured by other choices of $W$. Figuring out the relationship between the monotone-operator approach developed h`ere and the energy function approach of \cite{DjEnergyFun} is another important direction for future work. Finally, developing algorithms that scale well and allow these techniques to be applied to larger systems is another item in our path forward.
\section*{Acknowledgments}
The work at LANL was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396 and it was partially supported by DTRA Basic Research Project $\#10027-13399$. The authors also acknowledge partial support of the Advanced Grid Modeling Program in the US Department of Energy Office of Electricity.
\section{Numerical Illustrations}\label{sec:Num}
This Section presents numerical experiments illustrating theoretical results presented above. We start by illustrating monotonicity domain on a 3 bus system example, and then discuss numerical experiments performed on the case9 and case14 systems available with the MATPOWER \cite{zimmerman2011matpower} software. For solving the convex optimization problem \eqref{eq:ConvFeas}, we use the parser-solver CVX \cite{cvx}\cite{gb08}. For solving the variational inequality, we implement our own solver based on the extra-gradient method described in \cite{boydmonotone}. The implementations used here are not optimized and currently do not scale to larger systems. Algorithmic developments that would enable applications of these ideas to larger network will be an important direction for future work.
\subsection{Illustration of Monotonicity domain for 3-bus network}
We consider a 3 bus network with bus $0$ being the slack bus, bus $1$ a (P,V)~bus and bus $2$ a (P,Q)~bus. The voltage phasor at the slack bus is taken to be $1+\mathbf{j} 0$ and at the (P,V)~bus to be $\expb{\mathbf{j}\theta}$. The phasor at the (P,Q)~bus is parameterized as $1+\mathbf{j} 0+V^x+\mathbf{j} V^y$ where $V^x,V^y$ represent the \emph{deviations} from the reference voltage. The variables to be solved for in the PF equations are $V^x,V^y,\theta$. We pick a nominal voltage profile by setting all voltages equal to $1+\mathbf{j} 0$. We use \eqref{eq:ConvFeas} to find a monotonicity domain $W$. We then plot the monotonicity domain in $\br{V^x,V^y}$ space for multiple values of $\theta$ in Fig.~(\ref{fig:ThreeBus}).
Fig.~(\ref{fig:ThreeBus}) shows that for small values of $\theta$, the monotonicity domain covers a fairly large space in $V^x,V^y$. As $\theta$ increases, the domain shrinks and ultimately, before $|\theta|$ hits $\frac{\pi}{2}$, it becomes empty. This is consistent with the idea that all voltages ``close'' to the nominal voltage profile are contained within the monotonicity domain. Fig.~(\ref{fig:ThreeBus}) also shows that the domain actually includes a fairly large region around the nominal voltage profile.
\begin{figure}[htb]
\centering
\begin{subfigure}[b]{0.35\columnwidth}
\includegraphics[width=.8\textwidth]{ThreeBusA.png}
\caption{$\theta=0$}
\label{fig:ThreeBusA}
\end{subfigure
\begin{subfigure}[b]{0.35\columnwidth}
\includegraphics[width=.8\textwidth]{ThreeBusB.png}
\caption{$\theta=.23\pi$}
\label{fig:ThreeBusB}
\end{subfigure
\begin{subfigure}[b]{0.35\columnwidth}
\includegraphics[width=.8\textwidth]{ThreeBusC.png}
\caption{$\theta=-.23\pi$}
\label{fig:ThreeBusC}
\end{subfigure
\begin{subfigure}[b]{0.35\columnwidth}
\includegraphics[width=.8\textwidth]{ThreeBusD.png}
\caption{$\theta=.45\pi$}
\label{fig:ThreeBusD}
\end{subfigure
\begin{subfigure}[b]{0.35\columnwidth}
\includegraphics[width=.8\textwidth]{ThreeBusE.png}
\caption{$\theta=-.45\pi$}
\label{fig:ThreeBusE}
\end{subfigure
\caption{Monotonicity Domain for a $3$ bus system}\label{fig:ThreeBus}
\end{figure}
\subsection{Computation of Voltage Phasor Bounds}
We use the methodology of Section \ref{sec:MonCC} to find the maximum possible deviation from a nominal voltage profile contained within a monotonicity domain. We choose $v_i=V_0$, so that every bus has a voltage phasor equal to the reference at the slack bus. For a system with only (P,Q)~buses, this is in fact a solution to the PF equations for the case of no, $0$, injections. In practical power systems, large deviations from the slack bus voltage are relatively rare.
Therefore, it is reasonable to seek a monotonicity domain that includes all solutions in some neighborhood of this special (nominal) one.
We choose a uniform bound $\delta_{i}=1$ and solve \eqref{eq:ConvFeas} to compute $W$. We report the bounds for our test networks in the Table \ref{tab:Bound}. These bounds easily suffice to cover typical voltages observed in practical power systems operations. However, these domains may be insufficient to describe solutions in the case of extreme injections used in planning studies and contingency analysis. Our numerical experience suggests that these bounds are are conservative. More specifically, there are many $\br{V^x,V^y}$ that do not satisfy the bound given by $\rho$, but still lie within $\mathcal{C}\br{W}$. The results of the next section establish this numerically.
\begin{table}[htb]
\vspace{.8em}
\begin{center}
\begin{tabular}{| c | c |}
\hline
System & Limit on $|V_i-V_0|$ (p.u system) \\
\hline
Case 9 & .2 \\
\hline
Case 14 & .25 \\
\hline
\end{tabular}
\caption{Bounds on $V^c$ guaranteeing $V^c\in\mathcal{C}\br{W}$}\label{tab:Bound}
\end{center}
\end{table}
\subsection{Scaling Loads}
In this Section, we use the monotonicity domain obtained by solving \eqref{eq:ConvFeas}, but instead of relying on the computed bound $\rho$, we test numerically whether existence of a solution of the PF equations implies existence of a solution in the monotonicity domain. Of course, determining existence of a solution to the PF equations is a hard problem, so we instead rely on sufficient conditions for insolvability developed in \cite{molzahn2012sufficient}. We use the implementation available with the MATPOWER package \cite{molzahn2013implementation}.
Our experimental approach is as follows: We take the injections given as part of the Matpower test case, and scale each injection by a complex scalar: $\tilde{S}_i=\alpha S_i$. By scaling the magnitude of injections, we reach a point where there are no solutions to the power flow equations (maximum loadability). By scaling by a complex factor, we effectively achieve different scaling for the real and reactive parts of the injections. We pick the magnitude of $\alpha$ uniformly distributed between $1$ and a maximum value and the phase uniformly distributed between $\pi/6$ and $\pi/3$. (We observe that once we scale beyond a certain { threshold} there are very few cases where the PF equations have a solution.) These choices create a space of injections that include at least part of the solvability boundary (injections beyond which the PF equations have no solution). For a uniform grid of the $\alpha$ space described above with $100$ points, we compute the number of points at which there are no PF solutions (that is in this case we have a certificate of infeasibility based on \cite{molzahn2012sufficient}) and the number of points at which there are no solutions in $\mathcal{C}\br{W}$. The results are shown in Table (\ref{tab:Scale}).
\begin{table}[htb]
\begin{center}
\begin{tabular}{| c | c | c | c |}
\hline
System & $\mathcal{C}\br{W}$ & $-\mathcal{C}\br{W}$ & NoSol \\
\hline
Case 9 & 38 & 6 & 56 \\
\hline
Case 14 & 40 & 49 & 11 \\
\hline
\end{tabular}
\caption{Existence of Solutions in the Monotonicity Domain: The first column denotes the number of instances (out of 100) such that a PF solution within $\mathcal{C}\br{W}$ was found. The second denotes the number of instances for which a PF solution within $\mathcal{C}\br{W}$ was not found, and there is no certificate of insolvability of the power flow equations based on the sufficient condition from \cite{molzahn2012sufficient}. The last column denotes the number of instance where we have a certificate of infeasibility.}\label{tab:Scale}
\end{center}
\end{table}
The results show that for the 9 bus network, most cases where a solution exists lie within the monotonicity domain. However, for the 14 bus system, there exists a significant number of cases for which the solution does not lie in the monotonicity domain, if it does exist. It turns out that there are larger monotonicity domains that contain the original one (we checked this post-hoc by solving a feasibility problem to find a $W$ such that $\mathcal{C}\br{W}$ includes all the solutions found using Newton-Raphson). Thus, it seems like the choice of $W$ based on \eqref{eq:ConvFeas} is not optimal and larger monotonicity domains could be found. How one might do this in a principled way constitutes a comprehensive direction for future work.
\subsection{Comparison to Energy Function Approach}
In this Section, we consider a lossless modification of the 9 bus and 14 bus networks and perform the same experiment as described in the previous Section. This allows us to compare the approach developed in this manuscript with the energy function based approach described in \cite{DjEnergyFun}.
The results (table \ref{tab:EF}) show that for these networks, existence of a solution seems to imply existence within $\mathcal{C}_{EF}$ but not within $\mathcal{C}_{W}$. This suggests that $\mathcal{C}_{EF}$ is a superset of $\mathcal{C}_{W}$ and that potentially choosing $W$ based on \eqref{eq:ConvFeas} does not cover all the solutions. Closing this gap and designing approaches to ensure that $\mathcal{C}_{W}$ would contain all the solutions in $\mathcal{C}_{EF}$ is a direction for future work. We anticipate that development of this approach will likely suggest improvements applicable to lossy networks as well.
\begin{table}[htb]
\begin{center}
\begin{tabular}{| c | c | c | c | c | c |}
\hline
System & $\mathcal{C}\br{W}$ & $\mathcal{C}_{EF}$ & $-\mathcal{C}\br{W}$ & $-\mathcal{C}_{EF}$ & NoSol \\
\hline
Case 9 LL & 50 & 56 & 6 & 0 & 44 \\
\hline
Case 14 LL & 62 & 92 & 30 & 0 & 8 \\
\hline
\end{tabular}\caption{Monotonicity vs Energy Function: The first, third and final columns have the same meaning as table (\ref{tab:Scale}). The second column is the number of instances where a PF solution within $\mathcal{C}_{EF}$ was found, and the final column the number of instances where a PF solution within $\mathcal{C}_{EF}$ was not found and there is no certificate of infeasibility.}\label{tab:EF}
\end{center}
\end{table}
\section{Related Work}\label{sec:Related}
Several papers have studied conditions for existence of solutions to the PF Equations \cite{bolognani2014existence}\cite{lesieutre1999existence}\cite{wu1982steady}. In \cite{molzahn2012sufficient}, the authors propose a sufficient condition for the insolvability of the PF equations based on a convex relaxation.
Our approach differs from these in the following important ways:
\begin{itemize}
\item To solve the PF equations in $\mathcal{C}\br{W}$, we provide necessary and sufficient conditions, that is, our approach finds a solution in $\mathcal{C}\br{W}$ if there exists one, and a certificate of non-existence if there is no solution.
\item Our approach is algorithmic, that is, we provide an algorithm (based on solving a monotone variational inequality) that is guaranteed to find the solution efficiently, i.e. in polynomial time.
\item If there are additional operational constraints $\br{V^x,V^y}\in S$, where $S$ is a convex set and $S\subset \mathcal{C}\br{W}$ , e.g. corresponding to line protection \cite{singh2001direct} and/or line flow limits, we can additionally answer the question of whether there exists a PF solution with $\br{V^x,V^y}\in S$. This is an important contribution, since most of the time system operators are interested in finding PF solutions that additionally satisfy operational constraints.
\item We can find multiple PF solutions by choosing different nominal voltage profiles $v$. This is relevant for a number of important power system applications, such as assessing distance to voltage collapse and transient stability (computation of the so-called controlling unstable equilibrium point).
\end{itemize}
In \cite{bolognani2014existence}, the authors also propose an algorithm based on a contraction mapping. However, the algorithm only works in a small ball around the origin in the $\br{P,Q}$ space. This was extended to other kind of sets in \cite{KostyaExist}. On the other hand, our results are stated in terms of a convex constraint in $\br{V^x,V^y}$ space. Understanding the set of $\br{P,Q}$ for which the solution $\br{V^x,V^y}\in\mathcal{C}\br{W}$, and conversely the set of $\br{V^x,V^y}$ for which $\br{P,Q}$ lies in a certain set, is still an open problem, even for the special case where all buses are (P,V)~buses. This setting was studied and the results were extended and connected with results on synchronization in coupled oscillators in a series of recent papers \cite{dorfler2012synchronization}\cite{dorfler2013synchronization}\cite{dorfler2014synchronization}. These authors provided distinct sufficient and necessary conditions on the injections for the existence of power flow solutions with phase differences satisfying certain bounds.
In recent work \cite{DjEnergyFun}, we have shown that for the special case of lossless networks (and networks with constant ratio of inductance to resistance) the PF equations can be solved analyzing a convex optimization problem. Specifically, we minimize the so-called energy function over a restricted domain (the convexity domain of the energy function). The optimization problem in \cite{DjEnergyFun} was formulated in polar coordinates, i.e. in terms of the voltage magnitude and phase at each bus. In that setting, we get a single domain characterized by a nonlinear but convex matrix inequality, and any solution within this domain can be found efficiently. In fact, if one writes the PF equations in polar coordinates, one can show that the monotonicity domain coincides precisely with the convexity domain of the energy function. However, this polar-coordinate monotonicity domain of \cite{DjEnergyFun} is not equivalent to monotonicity domain in the Cartesian coordinates discussed in this manuscript. In this context, work reported in the present manuscript was inspired by our earlier attempt to extend the polar-coordinate based approach to lossy networks. Even though we were not able to find a simple convex characterization of the monotonicity domain in the polar coordinates, it lead us to discover that in the Cartesian coordinates the monotonicity domain can be described using LMIs. Numerical tests show that the domain of convexity of the energy function is a superset of the monotonicity domain computed by \eqref{eq:ConvFeas} for lossless networks. Furthermore, in that setting, we were able to prove a stronger result for tree networks showing that there exists a PF solution if and only if there exists one in the convexity domain. The condition characterizing the convexity domain also had a simple physical interpretation - it simply requires voltage magnitudes and phases at the neighboring buses to be ``close'' to each other.
However, the approach reported in the present manuscript is more general. It allows one to tune the monotonicity domain to compute multiple solutions. Furthermore, the monotonicity domain is expressed as an LMI here and can be handled using off-the-shelf software, while the nonlinear matrix inequality from \cite{DjEnergyFun} requires specially designed solvers. Understanding the relationship between the approach of this manuscript and the one from \cite{DjEnergyFun}, in particular, the relationship between cartesian and polar parameterizations, is an important direction for future work.
\section{Modeling Power Systems}\label{sec:Intro}
\newcommand{\sim}{\sim}
\subsection{Notation}
$\mathbb{R}$ is the set of real numbers, $\mathbb{C}$ the set of complex numbers. $\mathbb{R}^n,\mathbb{C}^n$ denote the corresponding Euclidean space in $n$ dimensions.
Given a set $\mathcal{C}\subset\mathbb{R}^n$, $\mathrm{Int}\br{\mathcal{C}}$ denotes the interior of the set. Given a complex number $x\in\mathbb{C}$, $\Rep{x}$ denotes its real part and $\Imp{x}$ its imaginary part. $\herm{x}$ denotes its complex conjugate. If $X\in\mathbb{C}^{n\times n}$ is a square matrix with complex entires, $\herm{X}$ denotes the conjugate transpose. $\norm{x}$ refers to the Euclidean norm of a vector $x\in \mathbb{R}^n$ or $x\in\mathbb{C}^n$ and $\inner{x}{y}$ to the standard Euclidean dot product. Given an vector $x\in\mathbb{R}^n$, $\diagb{x}$ denotes the $n\times n$ diagonal matrix with $\br{i,i}$-th entry equal to $x_i$. $\mathcal{S}^k$ denotes the space of $k\times k$ symmetric matrices.
Given a differentiable function $f:\mathbb{R}^k\mapsto\mathbb{R}^k$, $\nabla f$ denotes the Jacobian of $f$, a $k\times k$ matrix with the $i$-th row being the gradient of the $i$-th component of $f$.
For $M\in\mathbb{R}^{n\times n}$, $\Sym{M}=\frac{M+\tran{M}}{2}$. $\Ind{p}$ is the indicator function:
\begin{align*}
\Ind{p}=\begin{cases}
1 & \text{ if } p=\text{True}\\
0 & \text{ if } p=\text{False}\\
\end{cases}
\end{align*}
\subsection{Power System Model}
The transmission network is modeled as a graph $\br{\mathcal{V},\mathcal{E}}$ where $\mathcal{V}$ is the set of nodes and $\mathcal{E}$ is the set of edges. In power systems parlance, the nodes are called buses and the edges are called lines (transmission lines). We shall use these terms interchangeably in this manuscript. Nodes are denoted by indices $i=0,1,\ldots,n$ and edges by ordered pairs of nodes $\br{i,j}$. We pick an arbitrary orientation for each edge, so that for an edge between $i$ and $j$, only one of $\br{i,j}$ and $\br{j,i}$ is in $\mathcal{E}$. If there is an edge between buses $i$ and $j$, we write $i \sim j,j\sim i$.
Edges correspond to transmission lines. The transmission network is characterized by its complex admittance matrix $Y \in \mathbb{C}^{n\times n}$. $Y$ is symmetric but not necessarily Hermitian. Let $G=\Rep{Y},B=\Imp{Y}$.
Let $V_i$ be the voltage phasor, $P_i$ and $Q_i$ denote active and reactive injection at the bus $i$ respectively. $V$ is the vector of voltage phasors at all buses. Buses are of three types:
\begin{itemize}
\item\underline{(P,V)~ buses} where active power injection and voltage magnitude are fixed, while voltage phase and reactive power are variables. The set of (P,V)~ buses is denoted by $\mathrm{pv}$. The voltage magnitude setpoint at bus $i\in\mathrm{pv}$ is denoted by $v_i$.
\item\underline{(P,Q)~ buses} where active and reactive power injections are fixed, while voltage phase and magnitude are variables. The set of (P,Q)~ buses is denoted by $\mathrm{pq}$.
\item\underline{Slack bus}, a reference bus at which the voltage magnitude and phase are fixed, and the active and reactive power injections are free variables. The slack bus is denoted by $\mathcal{S}$ and its voltage phasor by $V_0$. We choose bus $0$ as the slack bus as a convention.
\end{itemize}
\subsection{Background}
\subsubsection{Power Flow Equations}
The PF equations model the flow of power over the network. They are a set of coupled nonlinear equations that follow from Kirchoff's laws applied to the AC power network. Circuit elements in the standard power systems models are all linear, if one ignores discrete elements like tap-changing transformers. Even though Ohm's laws and Kirchhoff's laws are linear in voltages and currents, power is a product of a voltage and a current and hence quadratic.
PF equations are static and as such the equations model the regime when the network is balanced, that is, the net sum of power consumptions, injections and power dissipated is zero. This relies on the assumption that at the time-scale where the PF equations are solved (every few minutes), the system is in a quasi-steady state, i.e. the dynamic disturbances have been resolved through actions of the automatic control (voltage regulators, power system stabilizers and primary and secondary frequency control systems).
The complete set of PF equations over the graph $\br{\mathcal{V},\mathcal{E}}$ is formally stated as
\begin{align*}
P_i & =\Rep{V_i{\herm{\br{YV}}_i}} \quad i\in\mathrm{pq}\cup\mathrm{pv}\\
Q_i &=\Imp{V_i{\herm{\br{YV}}_i}}\quad i\in\mathrm{pq}\nonumber \\
|V_i| & = v_i \quad i\in\mathrm{pv}\\
V_{\mathcal{S}} & = V_0
\end{align*}
It will also be convenient, for what follows, to utilize the Cartesian parametrization of voltages: \[V_i=V^x_i+\mathbf{j}V^y_i, i\in\mathrm{pq}\cup\mathrm{pv}.\]
Let $V^c=\begin{pmatrix}V^x \\ V^y\end{pmatrix}$ denote the stacked vector of real and imaginary voltage components, so that $V^c_i=V^x_i,V^c_{n+i}=V^y_i$.
\begin{definition}
Define the power flow operator as $F:\mathbb{R}^{2n}\mapsto \mathbb{R}^{2n}$
\begin{subequations}
\begin{align}
[F\br{V^c}]_i & =G_{ii}\br{\powb{V^x_i}{2}+\powb{V^y_i}{2}}\nonumber\\
& \,-\sum_{j \sim i} B_{ij}\br{V^y_iV^x_j-V^x_iV^y_j}\nonumber \\
& -\sum_{j\sim i} G_{ij}\br{V^x_iV^x_j+V^y_iV^y_j}-P_i ,i\in\mathrm{pv}\cup\mathrm{pq}\label{eq:F2a}\\
[F\br{V^c}]_{n+i} &=B_{ii}\br{\powb{V^x_i}{2}+\powb{V^y_i}{2}}
\nonumber\\ & +\sum_{j\sim i}B_{ij}\br{V^x_iV^x_j+V^y_iV^y_j}\nonumber\\
&+\sum_{j\sim i}G_{ij}\br{V^y_iV^x_j-V^x_iV^y_j}-Q_i ,i\in\mathrm{pq}\label{eq:F2b} \\
[F\br{V^c}]_{n+i} &=\powb{V^x_i}{2}+\powb{V^y_i}{2}-v_i^2,i\in\mathrm{pv}\label{eq:F2c}
\end{align}\label{eq:F}
\end{subequations}
Then the PF equations can be written as
\[F\br{V^c}=0.\]
\end{definition}
\subsection{Monotone Operators}\label{sec:Mon}
We now review briefly the theory of monotone operators, as is relevant to the approach developed in this paper. For details and proofs of the results quoted in this Section, we refer the reader to the recent survey \cite{boydmonotone}.
A function $H:\mathbb{R}^k\mapsto\mathbb{R}^k$ is said to be a monotone operator over a convex domain $\mathcal{C}$ if
\[\inner{H\br{x}-H\br{y}}{x-y}\geq 0 \quad \forall x,y\in\mathcal{C}\]
A monotone operator is a generalization of a monotonically increasing function (indeed, if $k=1$, the above condition is equivalent to monotone increase: $x\geq y \implies H\br{x}\geq H\br{y}$).
$H$ is said to be strongly monotone with modulus $m$ (or simply strongly monotone) if
\[\inner{H\br{x}-H\br{y}}{x-y}\geq \frac{m}{2}\norm{x-y}^2 \quad \forall x,y\in\mathcal{C}\]
for some $m>0$.
A common example of a monotone operator is the gradient of a differentiable convex function.
\begin{definition}[Monotone Variational Inequality]
Let $\mathcal{C}\subset \mathbb{R}^k$ be a convex set and $H$ be a monotone operator over $\mathcal{C}$. The variational inequality (VI) problem associated with $H$ and $\mathcal{C}$ is:
\begin{align}
\text{ Find } x\in\mathcal{C} \text{ such that } \inner{H\br{x}}{y-x}\geq 0\quad \forall y\in\mathcal{C}\label{eq:VI}
\end{align}
\end{definition}
The following result shows that monotone variational inequalities with compact domains always have a solution and can be solved efficiently.
\begin{theorem}\label{thm:VI}
If $H$ is strongly monotone operator over a compact domain $\mathcal{C}$, then \eqref{eq:VI} has a unique solution $\opt{x}$. Further, an approximate solution $x_\epsilon\in\mathcal{C}$ satisfying
\begin{align}
\norm{x_\epsilon-x}\leq \epsilon\label{eq:VIapprox}
\end{align}
can be found using at most $O\br{\logb{\frac{1}{\epsilon}}}$ evaluations of $H$ and projections onto $\mathcal{C}$.
\end{theorem}
\begin{remark}
In this manuscript, we are interested in finding zeros of the PF operators introduced above.
We can use monotone operator theory for this as follows: Suppose $H$ satisfies the hypotheses of theorem \ref{thm:VI}. If there exists a point $\opt{x}\in\mathcal{C}$ with $H\br{\opt{x}}=0$, then this is the unique solution of the variational inequality. Conversely, if the variational inequality has a solution with $H\br{\opt{x}}\neq 0$, then have a certificate that there is no solution of $H\br{x}=0$ with $x\in\mathcal{C}$.
\end{remark}
The next result provides a simple characterization of monotonicity for differentiable operators:
\begin{theorem}\label{thm:VIcond}
Suppose that $H$ is differentiable. Then $H$ is strongly monotone with modulus $m>0$ over $\mathcal{C}$ if and only if
\[\Jac{H}{x}+\tran{\Jac{H}{x}}\succeq m I \quad \forall x \in \mathcal{C}\]
\end{theorem}
|
{
"redpajama_set_name": "RedPajamaArXiv"
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**Begin Reading**
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To Amy Lovell
# AUTHOR'S NOTE
_Huntress_ is set in the same world as _Ash_ , but it takes place many centuries earlier. There are some significant cultural differences between the time periods.
# PRONUNCIATION GUIDE
In multisyllabic names, the emphasis is on the italicized syllable. In some cases, both syllables should be given equal weight. In human names, the letters _ae_ are pronounced like the _a_ sound in _mate_ and _skate_ ; the letters _ai_ are pronounced like the _i_ sound in _kite_ and _site_. Xi names (designated with asterisks) have different pronunciation rules.
Ailan: _Eye-lahn_
Anmin: _Ahn-min_
Cai Simin Tan: Tsai Sih- _meen_ Tan
Con Isae Tan: Con _Ee-_ say Tan
Ealasaid*: _Ay-_ lah- _sed_
Elowen*: _Ell-_ oh- _when_
Farin: _Fahr-_ in
Kaede: _Kay-_ dee
Kaihan: _Kye-hahn_
Maesie: _May-_ see
Maila: _My-_ lah
Maire Morighan*: Mare _Mor-_ ih- _gahn_
Mona: _Mo-_ nah
Nara: _Nah-_ rah
Niran: _Nee-rahn_
Noa: _No-_ ah
Ota: _Oh-_ tah
Parsa: _Par-_ sah
Pol: Pole
Raesa: _Ray-_ sah
Raiden: _Rye-den_
Shae: Shay
Sota: _So-_ tah
Suri: _Soo-ree_
Taeko: _Tay-ko_
Taisin: _Tie-sin_
Tali: _Tah-lee_
Taninli*: _Tan-_ in- _lee_
Tanis: _Tan-_ is
Tulan: _Too-lahn_
Xi*: Shee
Yuna: _Yoo-_ nah
Yuriya: _Yoo-_ ree-ah
# PART I
Clouds and thunder arise:
The sage brings order.
Those who chase deer without a hunter
Lose their way in the Wood.
— _Book of Changes_
# Chapter I
he saw a beach made of ice, and she felt her heart breaking.
The ground where she stood was frozen white, but twenty feet away, cold blue ocean lapped at the jagged shore. Someone there was climbing into a rowboat, and she knew that she loved this person. She was certain of it in the same way that one is instantly aware of the taste of sweetness in a drop of honey. But she was afraid for this person's life, and the fear raised a cold sweat on her skin and caused a sick lurch in her stomach, as though she were on a ship during a violent storm.
She opened her mouth to call the rower back—she couldn't bear the loss; it would surely cripple her—and at that moment she realized she could hear nothing. All around her was an eerie, unnatural silence. There was no sound from the ocean. She could not even hear herself breathing. She felt her tongue shaping the syllables of the person's name, but she did not recognize what the name was until the rower turned to face her. _Kaede_.
The rower was Kaede, and she looked back with dark, troubled eyes. Loose strands of black hair whipped around her pale face; there were spots of red on her wind-roughened cheeks. Her lips parted as though she would speak. But then Kaede reached down into the boat and lifted out a long oar, dipping it into the azure sea to propel the small craft away from the shore. The droplets of water falling from the blade of the oar were tiny stars, extinguished as quickly as they burned into being. The boat cut through the water, leaving the shore behind, and just before the destination came into view, the vision ended.
She was wrenched out of the icy landscape and back into her body, where she was sitting in the empty practice hall, alone on her cushion.
She opened her eyes, blinking against the light of the single candle she had lit on the altar. Her heart was pounding, and there was an acrid taste in her mouth. Her hands, folded in her lap, were trembling and chilled. A trickle of sweat ran from her temple down her cheek.
She drew her knees up and hugged them close, burying her face in the crook of her elbow, and because there was no one to hear her, she let out the sob that reared up in her throat. The sound echoed in the vaulted ceiling of the practice room, and for once she gave in to the overwhelming feelings rushing through her. She felt gutted. She felt powerless.
She had never seen so clearly before, and her teachers would praise her for it. But she felt no satisfaction, for she could not rejoice in the vision of someone she apparently loved departing on a journey to her death.
# Chapter II
aede was working in the cliff garden when she received the summons. This was her favorite part of the Academy—the crescent-shaped patch of earth carved out of the edge of the island, facing the mainland. On a clear day, she could see the brownish-green hills behind the crooked roofs of Seatown. But there had not been a clear day in a little over two months; only this constant gray light and scattered drizzle. Yet, as much as she hated it, it was better to be outside in the brisk sea air than trapped indoors behind the Academy's suffocating stone walls.
She continued down the row of stunted carrots, working in the rich fertilizer that Maesie, the Academy's cook, had given her at the start of her shift. A hard winter had been followed by no sign of spring, and Maesie had delayed planting at first, hoping for sunshine and warmth before she subjected her seedlings to the cold earth. But one morning she announced that she would wait no more, and the seeds went into the ground that day, followed by biweekly applications of the thick black fertilizer she concocted in the evenings. And despite the lack of sunlight, the seeds sprouted, though they were thinner and weaker than usual.
Kaede had just finished the row and was about to drag the jug of fertilizer to the next when Maesie came out of the kitchen, an odd look on her face. She held a wooden spoon in her hand as if she had come straight from the stove. Kaede straightened, brushing off her dirty hands on her cotton trousers. "What is it?"
"I've just had word from the Council," Maesie said. "They want to see you."
Kaede was puzzled. What would the Council of Sages want with her? She was hardly one of their favorite students. "What? When?"
"Now. You'd better leave your things there. I'll have someone else finish up for you."
She blinked at Maesie. "Now?" She wasn't sure she had heard correctly.
"Now. But you should clean up before you go—you don't want to track mud all over their chambers."
Kaede had not been to the Council chambers since her first visit to the Academy of Sages when she was eleven, to apply for admission. In the ensuing six years, there had never been a reason for her to make the long trek to the North Tower, for the only students invited into that inner sanctum were those who could perform the rituals they were taught. Although she had read the _Book of Rituals_ several times, Kaede had never successfully completed even the simplest of blessings. She knew she had only been allowed to remain at the Academy because her father was the King's Chancellor, and her mother—before she married him—had been a sage. Now she wondered if her time at the Academy was finally coming to an end, for why else would the Mistress have called for her, if not to dismiss her at last?
To reach the Council chambers, she had to climb a lengthy, circular flight of stairs. Carved in every step were the words to a different verse from the _Book of Changes_. She knew that if she read each step in order from the ground floor up, she would find the entire first folio there, comprising the core teachings that every student was required to learn during her first year. But Kaede only glanced down at random, and the verses made little sense out of context.
> _In disorder, misfortune._
>
> _In sincerity, fear gives way._
>
> _Dragons battle on the plain: yellow and black blood spills._
>
> _Fire in the mountain lake: grace brings success._
The phrases irritated her, reminding her of countless hours spent huddled over her books, feeling as though they were only mocking her. By the time she reached the landing outside the iron doors to the Council chambers, she was eager to be done with it. Whatever form her dismissal might take, she would welcome it.
She reached for the rope hanging from the mouth of the iron dragon embedded in the stone wall, and pulled. Several minutes later the left-hand door was opened by Sister Nara, the youngest of the three Council members. Her black hair, which was normally coiled in two careful braids tucked against the nape of her neck, was coming loose as though she had rushed through her morning rituals. Two small vertical lines appeared between her brown eyes as she said, "Come in."
Kaede followed Sister Nara through the circular antechamber to the inner redwood doors. Each was hung with a round gold shield. On the left was a phoenix, its tail feathers curling toward its beak, wings extended: the sign of harmony. On the right was a unicorn, the symbol of justice; its deerlike head was lowered so that its curving horn pointed down, while its goatlike tail curled up.
Sister Nara opened the doors, and the moment that Kaede entered the Council chamber, she knew something was wrong—she could not have been called there merely to be dismissed. For there were two men seated at the long wooden table along with the Council members and the Mistress of the Academy: One of them was her father, Lord Raiden, the King's Chancellor; the other was King Cai Simin Tan himself. What could have possibly brought him all the way from his palace to the isolated Academy?
Out of long habit, she folded her hands and bowed to the King, but she did not acknowledge her father. The last time they had spoken, they had argued heatedly, and the memory of it still made her face burn with suppressed anger.
At the head of the table, Maire Morighan, the Mistress of the Academy, said, "Kaede, please sit down."
As she walked to the table, her cloth shoes making no sound on the cold stone floor, her pulse quickened with curiosity. She saw the three Council members: Sister Nara, who was just pulling out her chair; Sister Ailan; and Sister Yuna. She saw Maire Morighan, her hands clasped on the table before a small wooden box. And, unexpectedly, she saw another student seated beside Sister Ailan. Kaede recognized the girl's face, but she couldn't remember her name. They had arrived at the Academy the same year, but after that first year, they had never had any classes together. She was supposed to be extraordinarily gifted, and she took all her classes in private with Sister Ailan. Kaede had never given much thought to her, but now she wondered why she was here. The girl's cheeks darkened a little under Kaede's gaze, and she turned deliberately toward the Mistress. And then Kaede remembered: Her name was Taisin.
Maire Morighan said: "You must be wondering why you have been called here. But before we can tell you that, you should know a bit more about why His Majesty has visited us so unexpectedly." She inclined her head toward the King. "Would you like to tell the tale, Your Majesty?"
King Cai glanced at Lord Raiden before turning his attention to Lord Raiden's daughter. He had seen her before, of course, when the Chancellor brought his family to the palace, but the King had never done more than keep track of her as a potentially useful tool. She was not the beauty her mother was, though she resembled her in spirit, at least, for she raised her eyes to him boldly. He ran a hand over his triangular beard, considering where to begin.
"One month ago," the King said, "a visitor arrived at the palace in Cathair. He demanded an audience with me, but he was in a wretched state—looked as if he'd been traveling for months, clothing all torn up. I thought he might be mad. Of course, I refused to see him. I couldn't risk it. This year alone my guards have uncovered three assassination attempts—those southern lords are getting more brazen by the day. So I waited until Lord Raiden—until your father returned from his visit to the South. That was about two weeks ago."
Kaede finally let herself look at her father, whose face was carefully blank as he regarded the King. He was wearing the plain black cap and robes of his station, but they were made of the finest silk, embroidered all over with phoenixes in black thread. The last time she had been home in Cathair, her father had been preparing for the trip to the southern provinces that the King had mentioned. The past two years had delivered extremely harsh winters followed by particularly poor harvests, especially in the South. This year, the strange, lingering winter, combined with the unexpected spoilage of much of the Kingdom's food stores, had led to growing panic among the people. The Academy was largely insulated from such things, but Kaede knew that some in the Kingdom were already going hungry, and hunger led to unrest—especially when the wealthy continued to eat well.
The King continued: "Your father met with this visitor as soon as he returned. He—I could hardly believe this when I first heard it—the man claimed that he had been given something by the Fairy Queen, and she had ordered him to deliver it to me. We have heard nothing from her people, the Xi—at least nothing _official—_ in generations." He leaned forward, stabbing a heavily ringed finger against the table to emphasize his point. His blue silk sleeves ballooned. "I thought it was a hoax at first."
Kaede asked, "What do you mean, nothing official?"
Irritated by the interruption, the King answered brusquely, "There have been some sightings—nothing definite, mind you—but it seems that some of the Xi have been coming across the borders into our lands."
"It may not be the Xi who are crossing over," Maire Morighan said.
"Then who—or what—are they?" the King snapped. "They're unnatural, these creatures, whatever they are, and they don't belong here."
Lord Raiden said mildly, "Your Majesty, perhaps we can discuss the identity of these creatures later. Let's continue."
The King relented. "The man brought a box with him; he said it had come from the Fairy Queen herself. Inside the box there was a medallion and a scroll. The scroll was written in the language of the Xi, which we could not read. Lord Raiden informed me that the scroll appeared to be genuine, and in that case, we had no choice but to bring it here. This morning, the Council deciphered it. It appears to be an invitation to me to attend the Fairy Queen at her palace in Taninli at midsummer."
"This is the box," Maire Morighan said, gesturing to the small rosewood container before her. She placed her finger in the center of it, and the top opened like the petals of a flower. From within, she removed a tiny scroll and a medallion on a long silver chain. "We have read the scroll, and it is indeed an invitation. It seems that the Fairy Queen, at least, still abides by the laws of our treaty."
Kaede was puzzled. "What treaty?"
"Many generations ago, our kingdom negotiated a treaty with the Fairy Queen that established the border between her lands and ours," said the Mistress. "It was also agreed that we would each keep to our side of the border, and that no one—human, Xi, or other races of fay—would cross it without an invitation from the other land's sovereign. It has been so long since the Borderlands Treaty was signed, and no invitations were ever issued, I believe, until now. So this is quite unexpected."
Everything Kaede had been taught led her to believe that the Xi had no interest in humans anymore. Some traces of them remained—especially here at the Academy, where each Mistress took on a name in the Xi language—but Kaede had always had the impression that the Kingdom was better off without the Xi. "Why do you think they're contacting the King now?" she asked.
The Mistress's eyes flickered to the gray sky outside the windows. "We believe that the unchanging seasons—and even those creatures who have been crossing into our lands—we believe that these are all connected. You have learned, in your lessons here, that we are all part of one vast motion of energies. Something is disrupting the natural flow of things. The meridians that run across our world have been... bent... somehow. We suspect that the Fairy Queen may be aware of this, too. It is very important that we accept her invitation." Maire Morighan's lips narrowed briefly, as if in disapproval. "However, the King is not able to go on the journey, for it will take many months and may be quite dangerous. He will send his son, Prince Con Isae Tan, in his stead."
"I remind you that my hands are full dealing with the chaos in the southern provinces," the King said defensively. "They're nearly ready to launch a civil war. I cannot leave my kingdom for months just to gallivant off on an invitation to the Fairy Queen's court—an invitation that says nothing about why she's inviting us after all this time, I might add."
"With all due respect, Your Majesty," Maire Morighan said, "it is the Council's strong belief that the Fairy Queen may know why the seasons haven't changed, and _I_ remind _you_ that all the storms and droughts and food spoilages have been the primary cause of all that unrest. We need to reestablish relations with the Xi; it is a matter of supreme importance."
"His Majesty and I agree that we must answer the Fairy Queen's invitation," Lord Raiden put in, trying to smooth both King Cai's and Maire Morighan's ruffled feathers. "But he cannot travel now. Not only are we on the verge of war, the Queen is pregnant."
"I dare not leave her," the King said stiffly. "She has had a difficult pregnancy." Kaede remembered that the King's first wife had died more than a decade ago, but he had not remarried until last year, when he chose a much younger bride. It had been something of a scandal, for the new Queen was the same age as Prince Con, the King's son from his first marriage.
"We understand," Maire Morighan said, as though they had argued over this many times already. She looked at Kaede. "We have also consulted the oracle stones about the invitation, and they called for Taisin, your classmate, to accompany the prince."
Kaede shifted in her seat, confused. "But what does this have to do with me?"
The Mistress leaned forward slightly, her dark eyes focused on Kaede. "You have been called, as well."
Kaede stared at her for a moment, dumbfounded. "Me?" It made no sense to her.
And then Taisin, who had been silent until now, said: "I had a vision. I had a vision, and you were in it."
# Chapter III
ord Raiden watched his daughter's face as Taisin spoke. Kaede was startled, curious, but guarded. She lifted a hand to tuck a strand of hair behind her ear. He had noticed the minute she entered the Council chambers that she had cut off her hair at chin-level since the last time he had seen her. She should be wearing it in a cylindrical roll at the nape of her neck in the manner of a proper sage-in-training—like Taisin. It was a small rebellion, but an unmistakable one, and Lord Raiden felt a familiar frustration rising in him. He had thought the Academy would discipline his daughter, force her to act in accordance with her station. But instead, it seemed to have only encouraged her to run wild. He could see traces of dirt on her hands, and he frowned.
"Taisin is a true seer," Sister Ailan was saying, "and we consulted the oracle stones. They confirmed what she saw. Kaede must also go on this journey."
"But the stones are not always clear," Lord Raiden objected. "There are hundreds of stones with thousands of marks on them. Perhaps they've been read incorrectly. And Taisin is so young—"
Sister Ailan said crisply, "I have not read them incorrectly, Lord Raiden. And Taisin may be young, but she is our most gifted student in a generation."
Lord Raiden looked pointedly away from Sister Ailan to Maire Morighan. "Mistress, I must question the wisdom of sending my daughter on such a mission. You yourself admitted it might be dangerous. I know the state of our kingdom right now, and I can assure you it is not a place of peace. I refuse to risk my daughter's life."
"Raiden," the King said, "you know we would send as many guards with them as necessary."
"Of course, Your Majesty, but you know as well as I do that Kaede is not gifted in the way that Taisin apparently is. Nor is she trained to defend herself as your son is. And Kaede is only a child; she is not yet eighteen." Lord Raiden glanced back at Maire Morighan. "You should be sending an experienced sage, not a couple of students. You heard my daughter—she isn't even familiar with the Borderlands Treaty."
Kaede's cheeks burned at the dismissive tone in her father's voice. Resentment seethed inside her, acidic and sour. She wanted to lash out at him, but Maire Morighan gave her a warning look, and Kaede reluctantly bit her tongue.
"Lord Chancellor," the Mistress said, "I understand your concern for your daughter's safety, but the matter is no longer in our hands. Taisin's vision was exceptionally clear, and when we consulted the oracle stones about Kaede, they were decisive. Kaede is meant to accompany Taisin, and no other sage may go. That is the word of the stones. Even if we don't always understand why the oracle stones say what they do, there is a reason. They have never steered us wrong. We must trust in them."
"Wait," Kaede interrupted, frustrated. She turned to Taisin, whose brown eyes were shadowed as though she had not slept well. "What was in this vision?" Kaede asked. "What was I doing there?"
Taisin glanced at Sister Ailan as if to ask permission, and when her teacher gave an almost imperceptible nod, she said haltingly, "I—I saw you on a beach—a beach made of ice." The memory of it washed through her; she felt the same loss and fear she had felt that night in the practice room, and beneath it all, she remembered the deep ache of love. It was disorienting, for in her life at the Academy, she had rarely noticed Kaede before, and now, sitting there across the table, Kaede was simply another girl in a black Academy robe, the plain stone buttons marching across her left shoulder as they did across her own. Taisin was sure she had no feelings for her—not here in the Council chambers. The emotions in the vision seemed to belong to someone else, and Taisin couldn't reconcile them with the present.
"What were we doing on this beach?" Kaede asked.
Taisin took a deep breath. "The vision was very clear, but it was also quite limited. I only saw the beach, and the ocean... and you. You were important." Taisin colored, and she lowered her eyes to her lap. "I had the vision the night after the Council told me the oracle stones called for me to go to the Fairy Queen. I knew that the vision was about this journey, and I knew it was telling me that you must be a part of it."
"Kaede," Lord Raiden said, addressing his daughter for the first time that day. "You know that you have duties that you cannot shirk." Kaede's stomach dropped; she should have known he would bring that up. "This is not the best time for you to be absent."
"When would be the best time, Father?" Sarcasm twisted her words. "Should we ask the Fairy Queen to wait until you're finished with me?"
The Chancellor's face darkened with suppressed rage. "You disrespect your King, and I will not tolerate that," he snapped.
"I think you are the one who is disrespecting _me_ ," Kaede countered, hot with anger.
The King frowned, but before he could speak, Lord Raiden pushed his chair back from the table, the legs scraping loudly against the stone floor. He stood, towering over the table. "You are behaving like a spoiled child, Kaede, which only goes to show that you are not prepared to take on the responsibility that this journey would entail."
"If I'm so irresponsible, why do you want to marry me off to some lord from the South?" Kaede demanded. "Why would you trust me with a political alliance if you think I'm such a child?" The words seemed to echo in the room, and she heard her own heartbeat thudding in her chest. When her father had first presented her with his plan last winter, they had argued over it for hours. He wanted her to marry a complete stranger just to keep the man's province under the control of the King's Guard. The idea of it sickened her.
"We are trying to prevent a _war_ , Kaede," Lord Raiden said coldly. "Surely you are not so selfish that you would send your kingdom to war just because you don't wish to settle in the South?"
"It's not about where I wish to _settle_ , and you know it. And who's the selfish one? You only want me to marry him because it would be good for _you_."
Maire Morighan rose abruptly, cutting into their argument. "Enough," she said. "Lord Raiden, please sit down."
"Mistress—"
" _Sit down_ ," the Mistress ordered. The Chancellor's face was nearly purple with frustration, but he sat, the chair legs scratching across the floor again. "Lord Raiden, with all due respect, this is not your decision to make."
For one brief, glorious moment, Kaede felt vindicated, but then her father said, "She is my daughter. She is not of age. She does not go where I do not permit."
Kaede fumed, but before she could rebut him, the Mistress said coolly, "Undoubtedly that is true. But this journey is every bit as important—perhaps even more important—than your plans for her. You must give her up to us. She has another duty that comes first now."
"Don't I have any say in this?" Kaede asked. She looked at Maire Morighan, who seemed exasperated with both her and her father. "Mistress, you can see that I have no desire to do what my father wants me to do. But you aren't giving me a choice, either." Maire Morighan frowned, but before she could speak, Kaede rushed on. "I have been a student here for almost six years. Not the best student, but I have paid attention. And the one thing that has always made sense to me is the teaching that every individual has the right to make choices about their lives. Every minute of every day, we make choices. Why would you take that away from me now?"
Kaede knew she was taking a risk by speaking so forcefully to the Mistress of the Academy. But the anger she felt at her father boiled within her, driving away any fear of offending Maire Morighan.
The Mistress was not surprised by Kaede's willfulness. That had always been the one quality that hampered Kaede's ability to work through the rituals. But she was taken aback by Kaede's appeal to the Academy's teachings. From across the table, Sister Yuna said softly, "She is right. She deserves to choose her own path."
Maire Morighan looked at Kaede, whose face was filled with desperate determination. At last the Mistress said, "All right. You have until the evening meal to make your decision."
# Chapter IV
aede's entire body was tense as she hurried down the stairs away from the Council chambers. The unexpected encounter with her father had rattled her, and she needed to shake it off. Her teachers would have advised her to go to the practice hall, to sit quietly, but she wanted to go outside and breathe the fresh air.
She took the empty corridor behind the kitchens, avoiding the students at their work shifts. The kitchen cat, curled in his basket by the back door, stretched lazily as she unlatched the door and slipped outside. The rain had lightened to a drizzle, but the cobblestones of the path down to the beach were slick, and she walked carefully. The sea, visible ahead of her in a gray swathe only a few shades darker than the sky, moved in giant, undulating swells. She could hear the crash of the surf below.
When she reached the edge of the kitchen garden, she went down a narrow stone staircase toward the sand. A stream of smoke curled up from the groundskeeper's workshop huddled against the retaining wall ahead. Fin was in. Kaede hesitated only a moment before heading for the workshop. She knocked on the wooden door, and hearing a gruff answer from within, she pushed it open, the hinges creaking slightly.
Inside, the workshop was a warren of crates and sandbags, wood scraps and tools. A lamp was lit in the back, where Fin called out, "Who is it?"
"It's me," Kaede replied. She threaded her way through the shop toward the sound of Fin's voice.
Fin was seated on a stool at her workbench, mending a gardening tool. Her short gray hair curled over her ears and forehead, which was marked with black oil as if she had pushed her hair aside with dirtied fingers. She had once been tanned dark from the sun, but without a clear day in months, her skin had paled. She was still as vigorous as ever, though, despite the fact that she had celebrated her half-century mark the previous winter. She glanced at Kaede with quizzical brown eyes. "What are you doing down here? Your work shift with me isn't until tomorrow. Maesie has you today, doesn't she?"
Every student at the Academy spent several hours each day working in the kitchens or the library, cleaning the practice hall or sweeping the corridors. During Kaede's first year, she had been assigned a task suitable for a Chancellor's daughter: sitting in the library and marking down the names of every student who came and went. The duty had left her so restless that she had soon been reassigned to Fin, the Academy's groundskeeper, who set her to work sweeping the Seawalk or filling sandbags. On slow afternoons, Fin would take her out to the North Beach and set up a target, teaching her how to toss the knives she kept in a tooled leather case, evidence of her former life with the King's Guard.
Fin saw the nervous energy in Kaede's stance, and she asked, "What happened?"
Kaede took a deep, shaking breath. "My father is here. And the King. When did they arrive? Where is their ship?" She hadn't seen or heard any ship in the harbor that morning, and she knew it would have caused an uproar, for the only ships to come and go were scheduled months in advance.
Fin put down the tool, wiping her oily fingers on a rag. "They came in the middle of last night. The ship sailed back to Seatown as soon as the King disembarked. They wished to keep it secret." But there could be no secrets from Fin; she had been roused by Sister Nara herself, bearing a candle and urging her to come down to the dock. She looked at Kaede's agitated expression and said, "We should take a walk out to the North Beach."
Startled, Kaede said, "Now?"
"Now is as good a time as any. I could use a break." Fin levered herself up from the stool, reaching for a long leather case on the shelf bolted to the wall above her head. She slung the case over her shoulder. Her joints were a bit stiff from sitting still in the damp air, yet she moved with the measured gait of the former soldier she was.
Kaede followed Fin out into the misty afternoon. "Did you know they were coming?" she asked as they walked across the wet sand.
Fin shook her head. "I didn't. They sent word by carrier to the Council, but only an hour or so before they arrived. You've spoken to them?"
"Yes. The Mistress summoned me to the Council chambers."
"Ah. What did they want?"
Kaede explained what had happened, and recounting the argument with her father caused her anger to flare again. "I can't do what my father asks—I just can't," she said vehemently.
"Are you—" Fin hesitated, glancing sideways at Kaede, who had a fierce scowl on her face. "Are you in love with someone else? Is that why you refuse to marry this man?"
Kaede almost laughed. "No. I'm not in love with... anyone." She wasn't sure if she ever had been in love, although she remembered the rush of emotions that accompanied her first kiss, with her classmate Liya, up in the crescent garden. It had been almost two years ago, on a sunny early summer afternoon. They had been clumsy and shy at first, but the giddiness that flooded through her after the kiss had plowed through all those nerves. She had felt exhilarated—free. But had she been in love? She didn't think so. There was no heartache on either side when their little romance ended a few months later.
Kaede and Fin rounded an outcropping of rock that jutted from beneath the Academy's iron foundation and stepped onto the North Beach, a crescent of unmarked, light brown sand cradling the sea. About a hundred feet out, waves crashed against submerged rocks that created a breakwater. When it had been warm, Kaede had often come here with classmates to swim in the sheltered cove. Fin set the case down on the sand and unlatched it, asking, "Who does your father want you to marry?"
Kaede paced back and forth, her footprints sending long trails across the sand. "One of the lords in the South. Someone named Lord Win."
"Is it a political alliance?"
"Yes."
"Your older brother made a political marriage, didn't he?" Fin unfolded the wings of the leather case; within it were about a dozen knives. The smallest—an ornately jeweled dagger—could fit into an ankle holster; the largest was more accurately a small sword.
"Kaihan? Yes. He married the King's niece."
"And how is that marriage working out?" Fin straightened, carrying a square target toward the stony cliff wall that sheltered the cove. Years ago, she had affixed hooks into the wall and punctured holes in the target to hang it.
"I don't know. I haven't heard anything out of the ordinary." Kaede stopped pacing and squatted down by the knife case. She was about to select her favorite throwing knife—a bright steel dagger with a black leather grip—but Fin bent down and pointed to a different one.
"Why don't you try this one today?" Fin suggested.
Kaede was surprised. "Why?"
Fin shrugged and moved off. "It's time for a change, I think."
So Kaede picked up the dagger that Fin had pointed out. The blade was just shorter than the length of her forearm, and though it was made of a darker metal than the other knives, it was simple, straightforward, and ground very sharp. Her fingers slid over the nubbly surface of the grip, and it fit comfortably enough in her hand.
She rose, counted out twenty paces from the target, and shifted the hilt in her hand so that the blade was pointing backward toward the sea. Then she flung it, extending her arm in the direction of the target. This dagger flew differently than the ones she was accustomed to. It was heavier, and she hadn't adjusted her technique to the weight yet, so it struck the very edge of the target and tumbled to the sand.
Fin went to pick it up and asked, "Do you think Kaihan objected to his marriage?"
"I don't think so. His wife—we've known her since we were children. But even if he did object, it wouldn't have made a difference. My father doesn't take no for an answer."
Fin handed the dagger back to her. "Again. The flight of the blade was unsteady last time. Be centered in your body when you throw it."
Kaede curled her fingers around the grip again, and this time, she felt the core of her belly engaged in the movement of her arm. When the knife left her hand, she felt her fingers reaching after it, and the dagger struck the center of the target.
"Good. It's not so different from the other knives, you see."
Kaede sighed. "I can't marry this Lord Win."
"Why not?" Fin's expression was blandly curious.
Kaede pulled a face. "Fin, I could never marry any man, you know that."
Fin gave her the dagger again. "Kaede, you should realize that the chances of your making a political marriage with another woman are—well, it is unlikely. It has happened before, but you know that it's rare."
Kaede reddened. "I don't want to make any political marriages with anyone."
"That is your birthright, and it is your burden." Fin stepped out of the way. "Try it again."
The dagger clanged against the cliff, several inches off the target.
Fin asked, "Did you talk to your mother about it?"
Kaede grimaced. "Yes. She said that I should be open to the possibility that I could love a man. That I was being too narrow-minded." She pushed her hair behind her ears as the wind came up, blowing a salty, wet breath across her face. "And beyond that, she said that plenty of married women have lovers—and sometimes their husbands die young, especially in a time of war. Can you believe that?"
"Well, your mother is a politician's wife," Fin said, smiling slightly.
"Yes. But I don't want to be a politician's wife."
"What do you want to do, then?"
Kaede held the knife in her hand again, feeling the weight of it. It was made of iron, she realized. Solid iron. "I don't know," she said slowly. "I don't want to be a politician, either. Marrying this man is just a way for me to establish myself at court. It cements an alliance, and I would be expected to do my best to make sure it stays strong. I'd have to be pregnant within a year. I don't want that. I want to do something else with my life. I'm not like Kaihan, who just wants to have a family and stay in Cathair. I want to see the world."
"You could see it. If you go with Taisin to answer the invitation of the Fairy Queen."
Kaede had never even considered the possibility of seeing Taninli, the Fairy Queen's city. It was only a legend to her. A thrill ran through her as she thought about it: What would it be like to set foot on those streets? They were supposedly built of diamonds. But a nagging worry tugged at her. "Fin, I don't understand something. Yes, the idea of going on this journey—it's exciting. At the very least, if I go I can put off the marriage my father wants to arrange. But the vision that Taisin had..." She trailed off, struggling to put her finger on what was bothering her. "I think she's hiding something," Kaede said at last. "I have no talents as a sage, but Taisin said that I'm important. Why? It doesn't make sense to me. But visions—I don't think they can be avoided. I'm not even sure if I truly have a choice."
Fin studied her student, with her serious expression and windblown hair. She noticed Kaede's fingers cradling the hilt of the iron dagger as if it had always been hers. After a long moment, Fin said, "The teachers here know much more about visions and fate than I do. But what I know is that in every moment of your life, you have a choice. Every choice leads to another, and another after that. You can only make a decision based on what you know now."
Kaede laughed. "That's almost exactly what I said to Maire Morighan. But what if what I know now is not enough?"
"Making a decision isn't about knowing every potential consequence. It's about knowing what you want and choosing a path that takes you in that direction."
Kaede shifted the knife from her right hand to her left, and back again. "I guess I know what I want, then." She lifted the knife; it was heavy, dependable. She felt every muscle in her arm engage as she threw it. The dagger struck the very edge of the target and clung there, quivering slightly. She sighed, opening and closing her fingers. "At least, I know what I don't want. And I'll delay that marriage as long as I can."
Fin put her hand on Kaede's shoulder and squeezed it gently. Then she went back to the target and retrieved the knife, bringing it to Kaede. "This is for you," Fin said. "It's forged from one piece of iron. I have had it since I left my mother's home; it used to be my father's dagger. It will now be yours."
"I can't take your father's dagger," Kaede objected, trying to give it back to Fin.
"Yes, you can. This dagger is as powerful a thing as I have ever had." Reluctantly, Kaede took it. "If you go on this journey, you're likely to encounter the Xi. They don't like iron. Most blades these days are made of steel, but this one is all iron. And it has survived for many generations. You should keep it on you."
"I thought the idea that the Xi don't like iron was only an old wives' tale. Is it true?"
"This Academy would not be built on iron if it were only a tall tale. Do you realize how much effort—how much magic it took to raise this place?"
Kaede looked at the Academy's iron foundation, sunken into the top of the rocky cliff. Above the dark gray iron, stone walls formed the North Tower.
"No Xi will ever set foot on this island," Fin said. "That's proof enough for me."
"Have you ever seen the Xi?"
Fin nodded. "When I was with the King's Guard in the Northerness. I was young. The Xi came out of the Great Wood one afternoon while we were securing one of the villages up in the hills, and they watched us." Fin voice was urgent. "You keep an eye out, Kaede. They're not like you and me. Bear that in mind."
Her words reminded Kaede of something else the King had said. "Have you heard the news of creatures coming out of the Wood in recent months? The King spoke of them, but Maire Morighan did not explain. Is it the Xi?"
Fin furrowed her brow. "I don't know. Your teachers have told you nothing about it?"
Kaede shook her head.
"What I know is only hearsay," Fin said. "Some strange bodies have been found in the villages bordering the Wood. Some folk have said they're the bodies of monsters. All I know is that the Xi don't look like monsters, and that's why they're so dangerous. If you're going into the Wood, it won't be an easy journey. You must keep that dagger with you at all times."
The intensity in Fin's tone was sobering, and Kaede said, "I will."
She stepped back, lifting her arm, and threw the knife again and again, until all she could hear was the iron ringing as it flew through the air, the sharp strike as it hit the wall, and behind her, the rising-and-falling groan of the sea.
# Chapter V
aisin saw Kaede arrive late at the dining hall for the evening meal, and she knew it meant that Kaede had just come from Maire Morighan's chambers. They did not speak, for all meals were taken in silence, but they looked at each other from their opposite corners of the sixth-form students' table. There was a new sense of intention in Kaede's demeanor, and Taisin was certain that Kaede would be coming on the journey. It made her nervous all over, anxiety and anticipation prickling across her skin.
After the meal, a servant was waiting for her in the corridor with a message: Sister Ailan wished to see her in her study. Taisin went immediately, hoping to avoid Kaede for as long as possible. She didn't know what to say to her; she didn't know what she _could_ say to her.
She had barely knocked on Sister Ailan's door before it opened. Her teacher ushered her into a beautifully appointed room lit with two globe-shaped oil lamps, one on the desk, one resting on a dark wooden stand carved with lotus flowers. One wall of the rectangular room was lined with windows, but umber-colored curtains were pulled across them to block out the night. Beside the windows, two simple, elegant armchairs faced each other across a low round table on which a tea tray rested. A black earthenware pot of tea steamed there, and Sister Ailan gestured to Taisin to take a seat while she poured the tea.
"Tomorrow morning, you will depart," Sister Ailan said.
Taisin lifted the warm teacup in her hands, inhaling the scent of jasmine flowers. It had been many months since she had smelled such fragrance; the jasmine, these days, was reserved for special occasions.
"I have one item to give to you before you go," her teacher said, and she went to retrieve something from top drawer of her desk. She placed it on the table before Taisin: the wooden box that had come from the Fairy Queen. "Go ahead and open it."
Taisin set down her teacup and leaned forward to look at the box. The carving was exquisite; the lid looked exactly like a chrysanthemum. She had never touched anything made by the Xi before. Until the King's arrival she had never thought the Xi would come into her life at all, except through the pages of history books. The idea of going to their land was strange and wonderful—and frightening, if her vision was true.
As Maire Morighan had done, Taisin placed her fingertip in the center of the carved chrysanthemum and felt the wood give slightly, like a bed of moss. She lifted her hand away and the petals folded back smoothly. Within the box she saw the scroll and a black velvet pouch.
"That is the medallion," said Sister Ailan. "Take it out."
Taisin emptied the pouch into her hand, and the medallion tumbled into her palm. The links of the chain gleamed in the lamplight. There were faint colors in it: slight streaks of azure and emerald coiling through the silver. The same colors were repeated, though faintly, like a watercolor, in the silver metal that held the stone, and symbols were engraved around the rim. When she touched the symbols, the stone seemed to shimmer as if there were something living within its depths. "What do these symbols mean?" she asked in a hushed voice.
"We are not sure. It is not the language of the Xi—or if it is, it is something more ancient than we can read. But you shall take it with you."
Taisin was surprised. "Me?"
"Yes. It will be entrusted to you. It may be a talisman of some sort—to mark you as a proper guest of the Xi."
Taisin slid the chain around her neck, and when it touched her skin it was cold for only an instant, and then it felt as though she had always worn it. She cupped her hand around it in astonishment, and looked at her teacher. "It feels like it's mine."
Sister Ailan's brow wrinkled just slightly. "You must keep it safe, Taisin."
"I will."
Sister Ailan sat back in her chair, lifting her own teacup. As her right arm rose, the dark green silk of her robe's wide sleeve fell back, exposing the sage's mark on her forearm. Every sage who took the vows was given a mark just above her wrist: a stylized symbol slightly larger than a gold coin. Though it was tattooed in black ink, Taisin had always seen colors in it, as she did now in the lamplight—shadow colors, as indistinct and shifting as dusk over the sea.
She had looked forward to receiving the sage's mark on her own skin since she was a child, but remembering her vision, her face burned. "Teacher," she began in a hesitant voice, "I must ask you something." When she had first told Sister Ailan about her vision, she omitted the feelings that had been so upsetting, fearing they were a sign of weakness or inexperience. But they had come back to her again and again, and now she could not ignore them.
Sister Ailan regarded her gravely. "Yes?"
"In my vision, I felt something." Taisin clutched the teacup with both hands, as if that might hide her self-consciousness, but she was afraid it was written plainly on her face.
"What did you feel?"
"I felt—I think that I"—she looked away, biting her lip, and finally she blurted it out quickly—"I think that I was in love with Kaede. In my vision. But that is—that can't happen, can it? I want to be a sage, and I know that all sages take vows of—of celibacy. Does this mean that I—that I will never become a sage?"
Sister Ailan heard the anxiety in Taisin's voice. She answered carefully: "Your vision is not the same as a fortune foretold by a traveling mystic. It is not a prediction of the future, Taisin."
"No, but visions—the one I had—isn't it a glimpse of the truth? A truth that exists already within the energies of the world? Everything I do—everything that Kaede does—will bring those energies into the form they took in my vision. Isn't that what you taught me?"
"You are thinking about this too analytically. Your vision is the truth, but it is not the future. It may be that you don't yet understand what you saw."
Taisin put down the teacup, curling her fingers into fists. "Teacher, I want to be a sage more than anything I've ever wanted in this world. I don't want to jeopardize that by falling in love with anyone."
Sister Ailan considered Taisin's flushed face, her renitent posture. She asked, "How did it make you feel, this... love?"
Taisin was taken aback by the question. "I—I have been trying to forget it."
"Why?"
"Because it can't happen," she said miserably. "It can't. If Kaede comes on this journey—if my vision comes true—then—" She broke off, remembering the dreadful fear roiling in the pit of her stomach when she saw Kaede leaving the beach behind. At last she said, "I don't want her to die."
Sister Ailan leaned forward and took Taisin's hands in her own, curving her warm, dry fingers over Taisin's fists. She looked into her student's dark brown eyes. "Love is not what you fear, is it? You fear the loss of it."
Taisin's eyes filled with tears; she was mortally embarrassed. She should not cry in front of her teacher. She wanted to pull her hands away, but Sister Ailan held them fast.
"It is true," her teacher said in a low voice, "that sages take a vow of celibacy. If you wish to be a sage, you will have to walk that path alone. It is a wondrous path, Taisin, and I know that you wish to follow it. That is a choice you will make later, when you are ready. You are not a full sage yet. Now you have a different path to take. Don't let your fear of the future overshadow your decisions in the present. You must remember that."
She let go of Taisin's hands, and Taisin folded her arms across her stomach, looking uncertain. "What should I tell Kaede, then?" she asked in a small voice. "How can I tell her what I felt?"
"Why do you need to tell her?"
Taisin shrugged. "I don't know. I thought—she is the only other person in my vision. Shouldn't she know?"
Sister Ailan leaned back in her chair, running her hands along the armrests. "Taisin, sometimes it is better for others to not know what we have seen in our visions. You see how much it has distracted you. Think of how much it will distract Kaede."
"Then you think I should not tell her?"
"You must determine that on your own. Just know that whatever is meant to happen will happen, whether she knows what you saw or not. It might be better for her to make her decisions without the additional... suggestions that your vision would give her."
Taisin nodded. "I understand."
"Good." Sister Ailan gave her a rare smile. "Then shall we continue? I have a few other things to tell you."
"All right." Taisin listened as Sister Ailan gave her instructions on what she would need to do when she reached Cathair, but beneath it all she felt an upwelling of emotions that threatened to engulf her. How could she keep her feelings secret? Was there any way to prevent what she had seen from happening?
She resolved, at least, to try.
# PART II
A tree grows on the mountain.
The wild goose flies near:
It seeks the flat branch.
— _Book of Changes_
# Chapter VI
he next morning, the King's ship came to ferry Kaede, Taisin, the King, and his Chancellor to Seatown. Kaede remained out on the deck for the three-hour crossing, preferring the salty sting of the wind in her face to the cramped warmth down below. The spray soaked through her cloak, but she didn't mind. She wanted to remember this day: when she left behind the life her parents had built for her. She watched the Academy diminishing as they sailed away until it was only a small gray speck, indistinguishable from the vast dark sea.
In Seatown, a contingent of the King's Guard was waiting to escort them through the crowded, noisy wharves. It stank of fish and seawater, but all Kaede saw were the black uniforms of the guards around her, their thick leather boots splashing through slimy puddles. They soon arrived at two black carriages, their doors emblazoned with the mark of the King, and Kaede and Taisin were quickly ushered into the second one. The carriage lurched as it turned away from the wharves and began the ascent up the steep road into Seatown proper.
Kaede watched out the window as they drove past an open-air kitchen with an old woman ladling out steaming broth to a line of young men—sailors, with their hair tightly plaited in single braids. They passed long brick walls dividing the compounds of Seatown's wealthy traders from the common folk who did the work of the city. And soon enough, they left Seatown behind and struck out onto the King's Highway.
The journey to Cathair would take a little over a week, and every mile of it was carefully scripted. Every place they stayed was first secured by the King's Guard, and every meal they ate was first tasted by the King's chief taster to ensure that the food was not poisoned. Kaede and Taisin rode in the fifth black coach in a line of eight. Lord Raiden and the King rode separately in the third and fourth carriages; two were reserved for the King's servants and were loaded with his wardrobe trunks; and they were all preceded and followed by guards.
Neither Kaede nor Taisin had traveled with the King before, and at first all of it was strange and overwhelming: the guards who rode with their hands on their swords; the rituals of greeting each evening when their hosts prostrated themselves before the King, holding their empty hands out to him for his blessing. And they ate better than they had in years, for no landlord would serve the King anything less than his finest offerings, even if that meant butchering a tenant farmer's last suckling pig. The King, who wore a different silk robe to each meal, ate it all with gusto, but Kaede, who had grown accustomed to the simpler food at the Academy, found all the rich sauces and succulent meats to be excessive. The King's appetite turned her stomach.
During the day, she and Taisin sat mostly in silence within the cushioned confines of their carriage, each staring out her window at the countryside. They passed a farmhouse burned to the ground, its roof about to collapse. They drove through a village that was empty but for a few hollow-eyed beggars lurking in the abandoned market street. And they passed many people in torn cloaks walking down the side of the road toward Cathair. Sometimes the travelers ran after the coaches for a short distance, but the caravan stopped for no one.
"Where are they going?" Kaede wondered aloud.
"To search for food," Taisin answered, startling Kaede. Taisin rarely spoke, and Kaede had not yet determined whether it was because she was disinterested in conversation or merely shy.
"How do you know?" Kaede watched Taisin struggle to contain some kind of emotion, fidgeting with the edges of her cloak.
"It has been a difficult year. Two difficult years. My family's farm—we have done better than some. My family has received travelers for some time now, seeking food. We send them on to Cathair, for we have heard that there are provisions there for the needy."
"Your family has a farm?"
Pink crept up the curve of Taisin's cheeks. "Yes."
Kaede realized that Taisin was self-conscious about it, and that made Kaede feel tactless, clumsy. She changed the subject awkwardly. "Do you have any brothers or sisters? I have three brothers. They're all older than me."
Taisin seemed surprised by the question. "I have a younger sister, Suri. She is twelve."
"Is she as gifted as you are?"
Taisin turned red, the color streaking across her throat and face, and she stammered, "M-my sister is gifted in her own way."
Kaede was taken aback by Taisin's reaction. She wanted to tell her she hadn't meant to embarrass her, but her classmate had turned away to stare out the window, her eyes fixed on the changing landscape. Kaede didn't understand why Taisin seemed so uncomfortable around her. Had she done something wrong? She tried to find something to distract herself in the carriage, but there was nothing new to see in that small, dark space. She suppressed a sigh. It might be a very long journey indeed.
On the fourth day, it rained. It was a heavy, unwelcome downpour that turned the dirt road into a muddy mess. At a crossroads that had seen better days, the caravan had to stop entirely while the drivers climbed down and dug the first carriage out of a rut that had trapped the wheels in several inches of sludge. Taisin had almost nodded off to sleep in her seat, the sound of the rain soothing away the bumpy discomfort of the King's Highway. When Kaede cried out in alarm, Taisin jerked awake, her head knocking against the window.
There against the glass was a man's angry face, his mouth open as he shouted at them, raising his fist to bang against the door.
Taisin screamed; she scrambled back as the force of his blows caused the coach to sway. Her shoulder slammed against Kaede, who was also pushing herself away from the door. In their haste they tumbled onto the floor, their bodies pressed together in the narrow space between the seats.
The man outside raised his hand again, and this time there was a rock in it, and it smashed against the glass so hard that it cracked. But before he could strike again, a guard grabbed him, pulling him away with a force that yanked his shoulder back at an unnatural angle. Another guard joined the first, who pinned the struggling man's head in the crook of his leather-armored elbow, and the second guard struck him full in the face, blood flying out as the man's nose was crushed. A third guard appeared, and the man, who was thin and weak from hunger, had no chance at all. One of the guards drew his sword, and before the man could take another breath, the guard slit his throat. He doubled over, his life spilling down his chest, mingling with the rain that still fell, unceasingly, from the sky.
It was a crime punishable by death to attack the King, and the royal mark was painted on every one of the coaches in that caravan.
Inside the battered carriage, huddled on the floor, Taisin felt her heart pound from shock. Kaede was crowded so close to her that Taisin could feel the other girl's muscles as tense as a drawn bowstring. Suddenly the door was wrenched open, and Kaede's father was standing outside, the rain running down his face. He hadn't bothered to put on a cloak. "Are you all right?" His voice was rough with panic. Behind him three guards stood with their swords drawn, and beyond them the body of the attacker was slumped on the muddy road.
"We're fine," Kaede said, her voice shaking.
"Blasted idiots!" Lord Raiden shouted, and spun toward the guards. "You paid no attention!" he snarled. "This cannot happen again. Next time it will be one of you who is dead." He slammed the door of the carriage shut, and the cracked glass shattered completely, letting in the rain. Lord Raiden threw up his hands and ordered, "Fix this!"
Kaede began to get up, and Taisin realized that she was gripping Kaede's hand with white fingers. Heat rushed through her and she dropped Kaede's hand as if it were a live coal. Kaede turned to her, a strange look on her face, and then the guards came to sweep the glass out of the carriage. Taisin pulled herself onto her seat, avoiding Kaede's eyes. A man had just been killed scarcely ten feet away, and yet all she could think of was the jolt that went through her when she felt Kaede's hand in hers. She had reached for her without any awareness of what she was doing. Was it already happening? Was her vision already coming true?
Taisin set her jaw stubbornly to prevent it from trembling. She deliberately gazed out the broken window, where the guards were carrying the body of the dead man toward the side of the road. Others approached with shovels, and they began to dig a grave in the soft ground. None of them had any idea who he was, and they would never find out. After the guards rolled him into the earth, they marked the grave with a circle of stones, and the caravan departed.
Eight days after they left the Academy, the road widened and flat paving stones replaced hard-packed dirt. The coaches picked up their pace, and the King's guards were able to relax just slightly. After the attack, there had been repercussions all around. The guards had been ordered to increase their vigilance, and now no one was allowed to leave the caravan unprotected. Kaede and Taisin were sent off with two female guards if they needed to stop at the side of the road, and though the guards turned their backs, Taisin especially chafed at the indignity of it. Kaede, who was more accustomed to being followed by servants, still had never experienced this level of interference in her daily life. She did her best to pretend as though it was entirely ordinary: traveling with the King, being surrounded by armed guards at every moment, riding in a carriage with a window covered by an oilcloth where it had been broken by a starving bandit. If she paused to think about it too closely, the significance of it all frightened her, and she would rather go blindly forward than dwell on what it all meant.
By the time they saw the stone walls of Cathair in the distance, Kaede had almost convinced herself that this new existence was normal. After all, the crenellated guard towers of the city were as tall and warlike as ever. Nothing had disturbed them, so far. But then they encountered a sight that she had not anticipated: a growing collection of tents pitched on the barren fields on either side of the road. As they drew closer to the city walls, the tents appeared more and more like permanent fixtures, the canvas walls dirtied with grime from fires burning in hastily dug pits. Kaede realized that the people camped closest to Cathair had been there the longest. They stood up as the King's caravan passed, but though some children ran toward the coaches, most remained still, gaunt as specters, knowing that nothing would come their way.
The sight of all these desperate people overwhelmed Kaede. The world had changed so much since she had last been outside the Academy walls six months ago. She hardly recognized this city that she had grown up in. The streets were thick with guards, and all the guards carried weapons. Half the shops seemed closed; the ones that remained open had new bars over their windows. When the carriage rolled to a halt outside her family's compound, Kaede was absurdly relieved to see that her home was the same as ever—red gates and dark red tiled roofs rising behind the wall.
Taisin was continuing on to the palace, where she would stay until they departed a week from now. Kaede looked back at her before she exited the carriage, feeling oddly reluctant to leave her. She said, "You can send word if you need anything."
Taisin was surprised by the offer, but also a tiny bit pleased, and it was the pleasure that made her feel awkward. "Thank you," she said formally.
Then Kaede heard the red gates open, and her mother's voice calling her. Giving Taisin a small smile, she climbed out of the carriage, carefully closing the door with the oilcloth tacked over the broken window.
# Chapter VII
here was a strange man in her father's study. Kaede paused in the doorway, her hand on the latch. He was tall, and he wore an uncommonly fine dark blue silk tunic embroidered with white-capped waves, but his hair was as short as a guard's. He turned at the slight creak of the door that Kaede pushed open, and broke into a smile. A single dimple creased his left cheek.
"Kaede," he exclaimed. "It's good to see you."
"Con?" she said, recognizing him at last. He had been a regular guest in her parents' home when she was a child, for he was close in age to her brothers Taeko and Tanis. She bowed to him. "What did you do to your hair?" The last time she had seen him had been at Kaihan's wedding last year, and Prince Con Isae Tan—like all young men of rank—had worn his long black hair in a topknot.
The prince grinned, running a hand over the prickly ends of his black hair, now barely half an inch long. "I cut it off."
She laughed. "Why?"
He shrugged. "I wanted to look ordinary."
Behind her, Kaede's father said, "Ordinary? What did your father think of that?"
Kaede stepped aside as Lord Raiden entered his study, carrying an account book under one arm. He set it down on his desk and took his seat behind it, flicking back the wide sleeves of his black robe. "Kaede," he said, glancing perfunctorily at his daughter, "the prince and I have business to attend to. You may leave us."
The smile that had lit Kaede's face upon seeing Con disappeared. The prince glanced from father to daughter and said, "Lord Raiden, perhaps Kaede might join us."
"What? I don't think so."
"Lord Raiden, she is part of this business." The prince's voice was gentle but firm.
Lord Raiden met the prince's gaze. There was a brief silence. "Fine," he said gruffly. "Kaede, close the door when you come in." He did not wait for her to sit down before opening the account book and paging through to a section marked with a ribbon. "As I was saying earlier, the King has ordered a contingent of guards to accompany you, as well as several wagonloads of supplies. I've no idea how long this trip will take; all the maps are confoundedly inaccurate."
Kaede realized they were discussing the journey she was about to embark on—and that her father had had no intention of telling her anything about it. She bit back the flaring anger inside her and sat down in the empty chair next to Con. The prince said, "Lord Raiden, I know that my father always travels with a large number of guards, but I think we would be better served by a smaller party."
"It is dangerous out there, Your Highness. The people are restless. Our caravan was attacked on the way back from the Academy."
Con nodded. "I know. But I think we would be more likely to slip by, unnoticed, if we were fewer in number. Consider this: If we travel with one guard each, we can stay at inns along the way instead of requiring shelter from my father's loyalists. It will allow us to gain information, as well. I can send word to you by carrier or messenger if necessary."
Lord Raiden frowned. "One guard each is not much. The King will not support it."
Con leaned forward, putting a flattering smile on his face. "Lord Raiden, my father will support anything that you recommend."
Kaede's eyes flickered from Con to her father. She could see that he wanted to believe what the prince said.
"Your Highness, that is kind of you to say, but I'm afraid it will be too dangerous." Lord Raiden glanced at his daughter, who was watching him with a stony expression. "And besides, my daughter is traveling with you. I want her to be safe."
Kaede choked back a laugh; he had never been so concerned for her safety before she was called to go on this journey. When she was a child, he had rarely seemed to notice her at all. She was convinced that his worry, now, was only a pretense; he was just frustrated that she was not doing what he wanted. When her father saw the disbelief on her face, he glared at her, and she glared back.
Con saw the exchange but made no mention of it. "No one will know who we are if we travel lightly, Lord Raiden. But if we travel with a caravan of guards, we will be a slow-moving target."
"What about the Xi? They aren't to be trusted. It would be better to send more guards with you."
"The more people we send, the more the Xi can turn with their glamours. We should bring only the guards we can trust."
Lord Raiden tapped the tips of his fingers together. "Whom would you propose to take with you? Which guards?"
Con relaxed a bit. He could sense that Lord Raiden was about to give in. "Tali, of course," Con said. Tali had been his personal guard since he was a boy, and he was trusted by both the Chancellor and the King. "He is completely loyal to me."
Lord Raiden nodded. "Tali would be going with you anyway. I agree he is a good choice. Who else?"
Con had already consulted with Tali on this, and he had two names ready. "Pol should go. He is one of Tali's favorites and has been in the King's Guard for ten years now. He is from the Northerness, and he is a skilled hunter. He would be a valuable asset. And I think we should also bring Shae, from the Third Division, though she is fairly new to the Guard." Tali had suggested the woman, who had only been a guard for two years. "She's from the village of Jilin; grew up near the Great Wood. She'll know it better than any of the other guards."
"So there would be six of you," Lord Raiden said. "You, Taisin, Kaede, and three guards."
"Yes."
"You'll need six horses?"
"I would suggest four riding horses, and two to pull the supply wagon."
"No servants?"
"Tali will do the cooking," Con said with a grin.
Lord Raiden let out a short laugh. "You won't eat well."
"We don't need to eat well. We just need to survive the journey."
Lord Raiden nodded slowly. "All right. I'll speak to the King about your wishes."
"Thank you." Con looked over at Kaede, who had listened to their conversation in silence, and asked, "Does that sound all right with you?"
Kaede blinked. "With me?" She hesitated. Her father was watching her. Hearing the prince and her father discuss the details of the journey had made her feel largely irrelevant. Six years at the Academy behind her, and she was utterly unprepared for this sort of thing. She felt both useless and irritated by the uselessness. But she would never allow her father to see her misgivings, so she said nonchalantly, "Of course. It all sounds fine." But the palms of her hands were clammy, and Con's words rang in her ears: _We just need to survive the journey_. What was he expecting? She began to wonder, seriously, what she had gotten herself into.
The night before their departure, the King hosted a private banquet in their honor, and even Queen Yuriya, her belly swollen in the seventh month of pregnancy, joined them in the dining room. In addition to the King and Queen, Taisin's family was present: her father and mother, with somewhat awed expressions on their faces; and her sister, Suri, with large dark eyes that seemed to look right through a person.
Kaede's family had been invited, as well. Her mother, her hair twisted into the shape of a spiraling shell, sat at the King's right hand. Her father sat next to Prince Con, who suffered the good-natured ribbing of Kaede's three brothers for cutting off his hair. Kaede was between the prince and her middle brother, Tanis, who had recently returned from the South and only wished to discuss politics with the prince. Caught between them, Kaede fell silent, watching Taisin across the table. She was seated next to Kaede's brother Taeko, who was the closest to her in age and had become something of a flirt in the last few years. Taisin had a small smirk on her face as Taeko attempted to impress her, and Kaede liked Taisin the better for it, as few were immune to Taeko's charms.
The broad, circular table was laid with a cloth of pale gold silk printed with twining crimson and green flowers, and there were eight courses. There was cold salad and clear soup, with translucent mushrooms floating within the broth in cloudlike clusters. There was roast duck and sweet, brined pork and tender, spiced lamb. There were tender cabbage leaves sautéed with ginger; there was an entire river fish with its mouth propped open on a carrot; and at the end there were bowls of sweet bean soup, with candied plums sinking to the bottom like treasure. Kaede couldn't help but feel as though it were a last meal of sorts, and the forced joviality of it all made her uneasy. It seemed wrong to eat like this when people were going hungry in that tattered tent city outside Cathair's walls.
At the end of the evening, the King stood up and toasted them as if they were about to depart on a holiday, and Kaede almost winced as she was forced to raise her glass along with everyone else. When she glanced at Con and Taisin, she saw that they, too, had sober looks on their faces as they listened to the King's booming, slightly drunken voice. She was relieved when the toast was over. She did not know what lay ahead, but she was ready to find out.
# Chapter VIII
aisin lay awake on the platform bed, gazing up at the wooden canopy. The silk sheets were cool and slippery beneath her, and when she shifted, her skin slid across them with a whispering noise that sounded abnormally loud in the hush of her chamber. Her family had been given rooms adjoining hers, but the palace was so large that she could hardly believe they were sleeping under the same roof. The last few days with them had been precious, though. She would see them in the morning once more, but she already missed them.
She tried to relax; she knew she should get as much sleep as possible, because tomorrow would be a long day. But she was anxious and unsettled, and the palace was too grand to be comfortable. When she first arrived, she had stared wide-eyed at everything. She had never seen furniture as fine as the dark red lacquered armchairs and tables in these rooms; she had never slept in a bed as magnificent as this one, with a frame carved into the shapes of singing birds on branches. At night, there had been a phalanx of servants to bathe her in jasmine-scented water, and in the morning, more servants came to dress her in clothing so exquisite she was almost afraid wear it.
But all the luxury in the palace did nothing to dull the sharp clarity of the emotions that gripped her every time she remembered her vision.
Since the first time she had envisioned that beach of ice, she had seen it twice more in dreams. Each time she awoke feeling torn up with loss, the sight of Kaede departing as painful as a fresh wound. Tonight in the palace, she was still awake when the vision began to pull at her, like fingers gently tugging her toward a deep blue pool. Part of her did not want to go, but part of her experienced this tugging with a kind of intellectual detachment. She had never encountered this kind of Sight before; it was like there was someone or something leading her forward. It was not unpleasant or frightening; it was merely quietly insistent. She knew it would win eventually, and so she gave in, allowing her mind to open up to what it wanted to show her—and then she was there: standing on the beach as always, her feet planted on the snow, looking out at the boat that Kaede rowed away from the shore.
For the first time, she sensed another person with her. She knew, somehow, that if she turned around, Con would be standing behind her. And she realized that she could feel some of what he was feeling: pain, physical pain, and beneath that a knotted rope of worry. He was moving toward her, and his fingers wrapped around her shoulder as if to restrain her. She saw Kaede leaving; her stomach twisted with dread. But this time there was more: a hot wash of guilt, spreading a bitter taste in her mouth.
The Taisin lying beneath silk sheets in the palace twisted her body, curving it as though she were running after Kaede, but the one standing on the beach did not move beneath the press of Con's hand. Instead she looked up, past Kaede's receding figure, and there she saw something that took her breath away. In Cathair she gasped out loud, crumpling the sheets into her fisted hands. There before her in her mind's eye was a fortress rising up from the frigid sea like a mountain of snow. It was as though an iceberg had been carved with a giant knife, shaped into towers and walls; and cut into those walls were glass windows that winked in the brilliant sunlight like a thousand sparkling diamonds.
The fortress was on an island—or perhaps it was simply a particularly large ice floe—and Kaede was rowing toward it. Each stroke took her farther from the beach Taisin stood on, her feet growing colder by the second, and now she heard a sound for the first time: Con speaking in her ear, an urgent tone in his voice. _Come back_ , he was saying to her. _Come back._
Taisin awoke well before dawn, the vision still clear in her mind, her nightgown soaked with sweat. She shivered; the silk sheets held no warmth. She sat up, shaking, and climbed down from the platform bed to retrieve her knapsack. She pulled it open and rifled through it in the dark until she found her woolen traveling cloak. It had been laundered by the palace servants, and now she wrapped it around herself, the scratchy fabric a welcome contrast to the cold silk.
What had Con meant? Come back from what? The image of the ice fortress loomed in her memory, monstrous and beautiful. Who—or what—could have built that? The only thing she was sure of was the way her heart constricted every time Kaede left, and every time she felt it, she was more determined to make sure it never happened. But now the guilt confused her. Why hadn't she felt it before? She was bewildered; she was frustrated. She didn't understand the version of herself in the vision. That Taisin had emotions that the present-day Taisin—the one clutching her cloak to her chest in the King's palace—couldn't relate to. Was she fated to become that other Taisin?
Restless, she went to the windows overlooking the courtyard and unlatched them, curling up on the window seat. She tried to remind herself who she was right now, at midnight, in this grand, noiseless palace. She was a student at the Academy of Sages; she was in her sixth year, nearly ready to receive the mark. She was the daughter of two farmers; she was an older sister to Suri. She was not in love with the daughter of the King's Chancellor.
She repeated these facts to herself over and over as if they were a mantra until she fell asleep, her head leaning against the window frame.
# Chapter IX
aede awoke the morning after the banquet with a thrill of excitement inside her: Today was the day. She couldn't wait to leave Cathair behind. Her earlier misgivings were forgotten; now she tasted the allure of adventure.
Three guards were waiting with Con and Taisin in the palace stable's south courtyard when Kaede and her father arrived. Though a few stable hands were standing nearby with the horses, no one else had come to see them off, and the small group was dwarfed by the vast expanse of carefully raked gravel around them. Even Taisin had arrived alone, having already said good-bye to her family. Kaede supposed they were already following Con's plan to draw as little attention to themselves as possible.
The prince introduced Kaede to Tali, a burly guard with a salt-and-pepper beard and hair shot through with gray. The second guard, Pol, moved with the stealthy grace of a dancer. He was older than Con but younger than Tali, and he spoke with a northern accent. The third guard, Shae, was Con's age or perhaps a year or two older, and like the other guards and Con, she wore her black hair cut very short. She had expressive dark brown eyes, and there was a liveliness in her that Kaede liked immediately.
There were four riding horses, and two hitched to a supply wagon. Taisin would ride with Pol on the wagon seat; Con, Tali, and Shae would ride their own horses; and Tali led a chestnut mare to Kaede. "Con tells me you can keep up with us," the guard said.
She had to crane her neck to look up at him. "I can."
"Good." Tali gave her an unexpectedly encouraging smile. "The mare's name is Maila." He left her with the horse and went to talk to her father and Con.
When everything had been checked one last time, Kaede's father came to kiss her formally on both cheeks. The press of his lips was so dry and light that she might have imagined them. "Go safely," he said.
She felt a twinge of disappointment at how distant he was. She did not see that he turned his face away to hide the worry that lined his forehead.
They exited Cathair through the North Gate, passing a short line of travelers waiting to be admitted into the city. There was no encampment outside this gate, only brown fields with patches of moss growing over the ground. Every so often they passed a family walking toward Cathair, their belongings dragged behind them on a handcart or piled onto their backs. At noon they stopped by the side of the road to eat steamed bread stuffed with salty pork.
"From the palace kitchens this morning," Tali said as he passed around the buns. "We won't get much of this from now on, so enjoy it while it lasts."
Kaede took a bite as a gust of wind blew around them. The horses stamped. In the distance she saw smoke rising from a farmhouse chimney, and two figures moved slowly in the empty field as if cataloguing their losses. "The road wasn't so empty south of Cathair," she observed.
"The winter was much harder north of the city," Tali said. "I think that those who wished to seek shelter in Cathair have already come; most of the rest refuse to leave their villages."
Con squinted up at the sky. "It's going to rain." He looked at Kaede. "North of here is the Great Wood. People believe that the trouble comes from that direction—I don't think anyone wishes to seek it out. With few people coming or going, it makes for an empty road."
"Then won't we be highly noticeable?" Kaede said. "What about maintaining some secrecy?"
Tali frowned. "We'll be all right. There are travelers on the road—just not many. And we're such a small group that we shouldn't attract too much attention."
"What will we say is our purpose?" Taisin asked. The damp wind whipped back loose strands of her hair.
"Sir," Shae said to Tali, "if I might make a suggestion?"
Tali gestured with his half-eaten bun. "Go ahead."
"If we are asked, we could say that we're going to visit my family. That will take us to Jilin, and beyond that is the Wood itself—we won't need a story then."
"It's a good idea," Tali said. "We can do that if we need to, but I don't think we'll need to tell much of a story." He turned to Con and added, "Let me do the talking, Your Highness, and no one will ask."
"All right," Con said. "But you don't need to address me so formally. None of you do—in fact, you shouldn't while we're on the road. What happens to one of us happens to us all. We are all equal in this."
As if to underscore his words, at that moment the sky opened, and Kaede stuffed the last bite of her bun into her mouth as they all scrambled for their rain gear.
It rained for little more than an hour—not heavily but steadily, sliding down their oil-slicked cloaks and dripping onto chilled hands. When it stopped, there was no sun to dry them off, and they were still damp when they arrived at the hostel they planned to sleep at that night.
It was in a small village built right up to the road, a way station for merchants. The hostel itself was tiny, and all but two of its half-dozen rooms were taken. After a supper cooked over the shared stove in the courtyard, they separated to go to their rooms for the night, Kaede with Taisin and Shae, Con with Tali and Pol. Each room had a single platform bed that looked particularly hard and unyielding.
"There's not much space," Kaede said. Gauging the width of the bed, she judged that there was just enough room for the three of them. She guessed that in Con's room, one of the men would have to sleep on the floor.
Shae lit the murky oil lamp on the wobbly bedside table and said, "There's no heater, either. We may as well get to know one another."
Kaede laughed. "I'll take the side closest to the wall." She began to spread her blankets out.
"I'll be closest to the door," Taisin said quickly.
Shae shrugged. "That's fine with me—I'll be the warmest one." She and Kaede grinned at each other, but Taisin seemed to color a little and would not meet their eyes. She turned her back on them to unlace her boots and pull off her outer tunic. As Taisin lifted her hands to her hair to unpin her braids, Kaede caught herself watching. She looked away and saw Shae observing her with a small smile. Kaede flushed. "So," Shae said, "you have brothers. Three of them, I understand?"
Grateful for the change of subject, Kaede answered, "Yes. All older than I am."
"I have an older brother myself, and an older sister."
"Are they both still in Jilin?"
"Yes. My entire family is."
Taisin tried to ignore them, setting up her bedroll on the edge of the platform. Kaede asked Shae, "Did you grow up there, then? What was it like?"
Shae pulled a leather-bound flask from her knapsack and sat down on the dusty wooden floor, cross-legged. "It was a good childhood," she answered, taking a swig from the flask and offering it to Kaede. "You're not too young for this, are you?"
Out of the corner of her eye, Taisin saw Kaede sit down, leaning her back against the cold wall. "Do you think I'm too young?" Kaede said.
"One never knows. Would you like some?"
"Not for me. At the Academy, we don't indulge."
"You're not at the Academy anymore."
"True," Kaede agreed, but she did not take it.
"Taisin," Shae called. "None for you, either, I imagine?"
"No, thank you," Taisin answered, feeling uncomfortable. She didn't know what to make of Shae. They had said very little to each other all day, and they didn't seem to have much in common. But she could tell that Kaede liked her, and that made Taisin feel oddly jealous of the guard. Annoyed at herself, Taisin pulled out the _Book of Rituals_ from her knapsack, telling herself that she should review it. She climbed onto the bed and opened the book in her lap, squinting at the page in the dim light.
"There are stories about the Great Wood," Kaede was saying.
"What have you heard?" Shae asked.
"I've heard that things work differently in the Great Wood. That people get lost, even if they have a map. That magic goes awry there; rituals go bad. That sort of thing."
"I've heard those things, too."
"Are they true?"
Shae did not answer immediately, and when she did speak, her words were measured. "Every story, I think, has a grain of truth to it. But sometimes, people are misled by what they believe, and they see what they think they should see, not what is actually there."
"That could be said of almost anything in life."
"That doesn't mean it's not true." Shae paused for a moment. "I'll tell you this much. The Wood is a special place. It was difficult for me to leave it. Every day I spend away from it, I miss it. For me—for my family—things make more sense when we are at home there beneath the trees."
"Then why did you leave?"
"There was nothing for me to do at home. My family is not rich, and King Cai offers a steady wage to his guards."
There was no shame in her voice, only a matter-of-factness that made Taisin wish she could be as easy about her own family background as Shae was about hers. But Shae was a guard in service to the King; it didn't matter who her parents were. Taisin wanted to be a sage, and few of them were lowborn. Taisin knew she was lucky that the Academy had taken her, for her family could not afford to pay for her education. It was a compliment to her talent, yes, but it was also a reminder that she owed the Academy a great debt.
"Why did you decide to become a guard?" Kaede said.
"I like action," Shae said, a smile in her voice. "I had no talent for the sagehood, and besides, the King makes it easy to join his Guard. When the recruiters came to Jilin two years ago, it seemed like a good thing to do." Shae shrugged. "I've liked it well enough so far, though I didn't think I'd be away from home for so long." There was a pause, and Taisin heard Shae putting the flask away, lacing shut her knapsack. "How old are you, then?" the guard asked.
"I will be eighteen at midsummer," Kaede replied.
"You'll celebrate your birthday at the Fairy Queen's palace."
"I suppose so."
Shae yawned. "I'm exhausted. There are many nights ahead of us; we can talk more later. I'm going to sleep."
"Would you like me to turn down the lamp?" asked Taisin, blushing when she realized her question showed that she had been listening.
Shae smiled at her, and it was such a friendly smile that Taisin was ashamed for feeling jealous. "I can sleep in broad daylight," Shae said, getting up and gathering her bedroll. "Don't bother to stop your reading for me. But perhaps Kaede has a preference?"
Kaede shook her head. "Stay up as late as you like," she said, and stood to change out of her traveling clothes.
Taisin looked away, trying to focus on her book. She shifted over to make room as Shae and Kaede climbed onto the creaking platform and settled in for the night. At home, Taisin always shared her sister Suri's small bed; indeed, she probably had less space there than she did tonight, but it was not the same. She could have curled up against Suri's back, sharing her warmth. Here, her body was tense, trying to avoid inching too close to Shae's slumbering form.
Taisin sat up past midnight, feeling awkward and self-conscious, staring at the page before her but not reading a word. Her ears rang with the sound of Shae's and Kaede's breathing in that small room, and beneath it, the flutter of her heartbeat seemed as loud as a drum.
Kaede awoke very early, eager to get back on the road. Her eyes opened to dim light coming through the small window, and beside her she felt the warmth of Shae's body. She sat up too quickly and winced; she was not used to riding a horse all day, and her muscles were paying for it. The hard bed hadn't helped, either, and she gingerly eased herself out of it, trying to avoid waking Shae and Taisin. She dressed as quietly as she could, and after a moment's hesitation she buckled the dagger that Fin had given her onto her belt. It made her feel a little self-conscious to wear a weapon like that, but the guards—and Con, too—were all armed. Feeling the hilt pressing gently at her ribs, she picked up her boots and took them outside to put them on. It was chilly in the courtyard, and from the color of the sky above she could tell that it was just barely after dawn. She decided to head to the stable and look for breakfast among their provisions instead of waiting for the others to wake up.
Just as she was rounding the corner of the hostel she heard the swift passage of an arrow followed by a thud as it struck its target. She flinched. Pol was standing in the stable yard and shooting at a tree. He looked over his shoulder at her and said, "You're up early."
"So are you."
He went to pull the arrows out of the tree. "It's too cramped in that room. Tali's a big man."
She smiled. He shot again and again, sending a series of arrows fleet and sure to the center of the trunk, just below a branching limb. She marveled at the way he made it seem so effortless: lifting the long bow, nocking the arrow, loosing the string so that his right hand arched back gracefully, echoing the flight of the arrow itself. She wanted to be able to do that.
"Will you show me how to shoot?" she asked.
He looked at her as if gauging her potential. "The bow is a bit long for you."
"Let me try. At least it'll be something to do while we wait for the others to wake up."
"All right."
The bow, made of a springy, yellowish-brown wood, was as tall as she was. Pol took off his shooting glove—an odd, three-fingered leather glove with a bulging, padded thumb—and showed her how to strap it onto her right hand. The first time she tried to pull back on the string, she could feel the muscles of her neck and shoulder straining at the effort. The arrow she had nocked slipped and fell, flailing like a downed bird, to the ground at her feet. It was not, she realized quickly, like throwing a knife. Pol seemed amused by her attempt, but said kindly, "My father gave me my first bow when I was a boy of six. It'll take some time before you get the hang of it."
He corrected her stance and told her to breathe in as she raised the bow; to press that breath down within herself as she stretched the string; to allow the arrow and her breath to loosen simultaneously. But the more she tried, the less she succeeded, and she began to sweat from the effort.
"You are too willful," Pol said, observing her latest failed attempt. She reminded him of a young bird flapping her wings, unable to gain the lift needed to take off.
"What do you mean?" Kaede's arm and shoulder ached, and the bowstring had snapped loudly and painfully against her left forearm enough times that she was sure it would leave a red welt there.
"If you think about it too closely, you will choke the energy of the arrow. Your body—and your thoughts—are getting in the way. Try to let go of your thoughts when you shoot. You do not have to force the arrow to fly; it wants to fly."
His words reminded Kaede of her teachers' instructions at the Academy, but hearing them applied to archery was like hearing those lessons in a different language—one that was maddeningly familiar but as elusive as a slippery fish.
Pol saw the growing frustration on her face, and he took the bow from her and showed her, again, the smooth rhythm of the draw, the arrow in flight, his hand in the air. "Stand like this," he told her, spreading his feet wider. "Put your hand here." He moved her left hand down on the grip.
Bit by bit, the bow began to seem less foreign to her, though she knew she was far from being as skilled as Pol was. By the time Tali came out to the stable yard to fetch their breakfast supplies, Kaede was sweating and famished, her right shoulder aching, and still the arrow had not struck the target.
Pol said, "We'll practice every morning—how about that?" He seemed excited by the prospect.
"Delightful," she said, smiling weakly, and he laughed at her. But she handed the bow back to him with some reluctance.
Before she left the stable yard, she couldn't resist unsheathing her dagger and tossing it at the tree, just to remind herself that she wasn't completely inept. It flew out of her hand so easily—she didn't have to think about it—and struck the tree with a solid thunk. She flexed her fingers thoughtfully. Her hand knew what it was doing. Perhaps it was her body that needed to learn this new language, not her mind.
She went to retrieve the dagger from the scarred tree trunk and went inside for breakfast.
# Chapter X
wo days after they left Cathair, the road curved east as it followed the bend in the river Nir. In better times, fishing vessels trawled the river, but now there was little to catch, and what could be caught was better left uneaten. Word had spread through the roadside hostels of a fisherman who had brought in a giant carp—a rarity in any season, but especially abnormal now—only to discover that the fish's belly housed hundreds of tiny stinging eels.
There were other rumors, too. One traveler, a thin man with a nervous black horse, told them he had seen a strange creature lurking behind one of the riverside taverns: half woman, half animal, with a fox's red-gold tail and sharp teeth. A young man had been found dead nearby, his body bruised and bitten.
"All of this trouble comes from upriver," the thin man said, jerking his thumb toward the Nir. He ran his eyes over the group of travelers and their gear—their wagon still full of supplies, the fine workmanship on their horses' saddles—and suspicion flickered over his face. He glanced at the burly, gray-haired man, who was clearly their leader, and asked, "Where are you headed?"
"To Jilin," Tali answered, his tone not inviting further questions. Jilin was at the southwestern edge of the Great Wood, where the Nir originated.
The thin man eyed the group's wagon; the wheels were especially well made. There weren't many travelers heading north, and even fewer who were so well outfitted. But a kind of unspoken camaraderie had developed among travelers on the King's Highway in the last two years, for dark times gave cover to dark deeds, and it was better to pass on one's news without learning too much about anyone else. So the thin man said only, "I've heard that something's not quite right at Ento. I haven't been there recently, but as you're headed in that direction, you might ask about it."
Tali said, "We will."
Two nights later, they lodged in a tiny village perched on the banks of the Nir, and Ento was the only subject of conversation in the village's lone tavern. Crowded with out-of-work fishermen, the dark, low-ceilinged room smelled of river water and spirits. The locals had glanced at the six travelers when they first entered, but made no effort to lower their voices to keep their gossip private.
"A man came through the other day," a fisherman was saying. "He told me people are deserting the place as quick as they can."
Built on an old crossroads, Ento had once been home to a major marketplace. But now there was little to sell, and the town had fallen on hard times.
"That family who was here last week said the same thing," said another man.
"I hope whatever's happened in Ento doesn't move south to us."
"Not likely to be so lucky," said one man bitterly. "Wind blows south from the Great Wood—we're right in the line of it."
Tali turned in his seat and said casually, "We're headed in that direction. What happened?"
Taisin kept her eyes down, but she was curious, too. The more they heard about Ento, the more she was convinced there was something there that she should see. Her instincts were tugging on her in a way she had never experienced before. She turned slightly toward Tali, hoping he would ask the right questions. Earlier in the day, he had told them he would find out as much as he could about what was going on in Ento, and Taisin twitched with impatience.
The fishermen all swiveled around to stare at Tali, and one of them—a man with a long, scraggly gray beard—said, "You'd be better off avoiding that place."
"Why?"
The fishermen looked at one another uneasily before one of them spoke, his missing front tooth flashing like a dark eye. "It was little things at first—goats gone dry, wells turning bad."
"Same things have been happening all over the Kingdom," said the gray-bearded man.
"That was bad enough, but now folks are saying that the Xi are taking our children," said the man with the missing tooth. His voice was harsh and loud, and the common room fell silent.
Taisin glanced up in surprise; she had never heard of the Xi having much interest in human children before. Across the table, Tali just barely shook his head at her, and she swallowed her question.
"It's only one child, and no one knows if it's true," objected a man from across the room.
"Has a child been taken or not?" Tali asked bluntly.
The man with the missing tooth scowled. "The mother says it's still her babe, but the father came through here just yesterday. Looked as though he'd lost everything. He said the child is a monster, and his wife has gone mad."
"It's dark magic," said the graybeard. "If you can avoid Ento, you should. Take an alternate route."
The room erupted with men arguing whether the town was safe to travel through. "Thank you for the information," Tali said, his voice nearly drowned by the din.
Taisin tried to focus on her meal, but the fisherman's words rang in her mind. What kind of dark magic? Her pulse raced. She wanted to know.
The rumors came more quickly as they approached Ento. The child was one of the Xi, cursed to inhabit the body of a human to atone for a crime; the child was the reincarnation of a legendary sorcerer; the child was a demon who had eaten the human child. After hearing the tale of the demon, Tali suggested, "Perhaps we should bypass Ento altogether." They were in the stable yard of another inn in another fishing village, unpacking their gear for the night.
"It will lengthen our journey by several days," Pol said.
Taisin, who had just finished feeding the horses, came around the corner of the wagon. "I think..." She hesitated as they all turned to look at her. She took a breath and said: "I think we should continue the way we planned. The rumors are... they're just rumors."
"They're rumors, yes," Con said, "but, Taisin, I traveled north with Tali last fall, before the worst of the winter storms. The things we saw there were—well, they make me inclined to believe these rumors."
"Nobody seems to have been hurt by this child," she said with studied nonchalance.
"That's true," Tali agreed.
"Then we might as well travel through Ento," Taisin said. "It will be inconvenient to avoid it, and there is no guaranteed benefit." She saw Kaede watching her with interest. She could tell that Kaede wondered why she was so adamant about this, for she had never indicated her opinion on their route before. She still couldn't explain it; she only knew that she needed to see this creature, whatever it was. She lowered her eyes, trying to hide her excitement. Tali would be suspicious if she appeared too eager.
Shae said: "She has a point, Tali. And we'll only be there one night."
He relented. "All right. Ento it is."
A little over two weeks into the journey, the rhythms of travel had settled into Kaede's body. She woke early, met Pol in a stable yard or at an empty patch of dirt near their hostel, raised the bow, and loosed arrows until breakfast. Her arms and shoulders grew stronger, but still she could not strike the target. They rode all day, stopping only for a noon meal at the side of the road, eaten cold. She came to know her horse, Maila, who was both sweet-tempered and energetic. She grew accustomed to falling asleep with the sound of others breathing nearby, and at times she wondered how she had ever lived another way. She thought of her small chamber in that great stony Academy, and her parents' luxurious Cathair home, where she had entire assortments of rooms to herself, but she did not miss them. She realized that she loved the road: Every day was new and unexplored.
Kaede especially enjoyed talking to Shae, who told stories about her training as a guard; about learning to fight and to ride with a sword. Her life was so different from Kaede's years at the Academy that she was always eager to hear more. She began to wonder if she could join the King's Guard when she returned from this journey. Then she would never have to face the dreary politics of court life; she could be on a horse all day, going to places she had never been before.
Shae always included Taisin when she told her tales, even if Taisin was pretending to study, as she often did. It was noticing Shae's kindness that caused Kaede to gradually become aware that Taisin watched her, often, with hooded eyes. She would look away as soon as Kaede glanced at her, so initially Kaede wondered if she were imagining things. But as the days passed, she began to watch Taisin, too. Her classmate was quiet, reserved; she spoke when spoken to, but rarely entered into any conversations on her own. Con tried to draw her out by joking with her, and sometimes Taisin seemed to appreciate it, but she quickly retreated back into a state that seemed to hover between anxiety and frustration. Once, when Kaede caught Taisin looking at her, she had the odd impression that Taisin thought of her as a problem to solve, but she did not know how to do it.
The day they were due to reach Ento, Kaede spent nearly the whole afternoon puzzling over the enigma of her classmate. She had just resolved to speak to Taisin about it directly when they caught sight of the town gates in the distance. They hung open as though abandoned, and as they approached they saw there was no one in the gatehouse.
"You're sure you want to stay here tonight?" Pol said from his perch on the wagon seat.
Tali said: "We'll just sleep here and make an early start in the morning. Let's go."
They were the only guests at the hostel that night, which meant that, for once, there were enough vacant rooms for each of them to sleep alone. After supper, Tali, Con, Pol, and Shae went upstairs, but Kaede lingered behind in the common room waiting for Taisin, who had taken their empty bowls to the innkeeper in the kitchen. When Taisin returned several minutes later, she was startled to see Kaede still there.
"I thought you went upstairs," Taisin said, picking up her cloak from where she had left it, slung over a chair.
"I wanted to talk to you." Kaede stood up, but hesitated. What should she say? All her words seemed to flee from her; she felt awkward.
Taisin suddenly looked nervous. "Now? Now is not—I can't talk now."
"Why?" Kaede eyed Taisin's cloak. "Where are you going?"
"I'm going to see the child."
A chill rushed through her as Kaede realized which child Taisin meant. "The child—the one they say is a monster?"
Taisin began to move toward the door, pulling the cloak over her shoulders. "The innkeeper told me where the mother lives."
"You're going now?"
"Yes."
Fear prickled across Kaede's skin. "I don't think that's a good idea. Tali wouldn't like it."
Taisin stopped and looked back at Kaede. "I haven't yet seen any of these strange creatures that people keep telling us about. Don't you want to see what we're dealing with?"
"What do you mean, 'what we're dealing with'? Why are you so eager to go?"
"It's all related," Taisin insisted. "The weather. The rumors we've been hearing about these... creatures. The Fairy Queen's invitation."
Kaede remembered Maire Morighan's theory that these disparate events were all connected, but Taisin spoke with an assurance that was surprising. "How do you know?" Kaede asked.
"I can feel it. Every day on the road—I feel something pulling me. I don't know what it is, but I have to find out. I know it's important."
Kaede was doubtful. "I don't think you should go alone. Let me get Tali, or Pol—"
"They won't let me go," Taisin objected. "They barely even agreed to stay in Ento for one night. They certainly won't let me go look for the child. You can't tell them."
"But—"
"I have to go. Now." Taisin's hand was on the doorknob as she added, "Do you want to come with me?"
Kaede glanced at the empty stairs uneasily. She knew she should tell the others, but Taisin was right. Tali would never allow her—or Kaede—to go, and Taisin's urgency had sparked Kaede's own curiosity. She wanted an adventure. Perhaps now was the time to get it.
Just as Taisin was pulling the door open Kaede said, "Wait. All right. I'm coming with you." She ran back to grab her own cloak from where she had left it at the table, and pulled it on as they left the hostel.
# Chapter XI
hey took the lantern hanging at the entrance to the hostel courtyard, and it shed a small pool of light as they went down the road. "The innkeeper told me that she lives in a house on the edge of town," Taisin said, but beneath her briskness was a note of trepidation.
The buildings they passed on either side were dark, and some of their courtyard gates were wide open. There would be nothing inside to tempt any thieves; Ento had been deserted as if it were the host of a plague. At the end of the paved road they turned left down a rutted dirt lane; only the last house seemed to be occupied. A dim glow emanated from a curtained window, and from within they heard a baby crying.
Taisin strode up to the front door and raised her hand to knock, her knuckles ringing on the wood. The door was pulled open by a woman with haunted eyes and thin, oily black hair. "What do you want?" she asked defensively.
"May I see your child?" Taisin asked.
The woman's eyes flicked back to Kaede, who was standing behind Taisin. "Who are you?"
"I may be able to help," Taisin said. "Please, let me see your child."
"I won't let you take him away from me," the woman warned her.
"We are not here to take him," Taisin reassured her.
"What can you do? You're only a girl."
For a moment Taisin wavered. What exactly was she planning to do, anyway? The baby cried again, and the sound of it jerked at her gut. She forced down her self-doubt and said: "I am training to be a sage. Please—I've come a long way, and I want to help you."
The woman eyed the two girls on her doorstep. They were both young and obviously inexperienced. The girl who had spoken was so eager to prove herself, while her silent companion seemed reluctant to be there at all. These days, the woman was suspicious of almost everyone who came to her door, but these two girls, with their artless faces, made her feel hopeful for the first time in weeks. Perhaps this girl really was a sage in training, but even if she was lying, what harm could a couple of girls do? She stepped back and allowed them to come inside.
The house, consisting of one room, was small but clean. A fire burned on the stone hearth, and nearby was a rocking chair and a cradle. There was a platform bed against the far wall, its blankets mussed as though someone had slept there recently. A little shrine was built into the corner; Taisin saw the scroll listing ancestors' names, a spray of dried flowers, a small pot of incense. It did not look like the house of a madwoman.
"When was your baby born?" Taisin asked.
"Three months ago." The woman's eyes darted toward Kaede, who said nothing. "He is healthy," she insisted.
"Where is your husband?" Taisin asked.
Tears filled the woman's eyes, and she began to rub her left arm nervously, as if it were a lucky stone. "He has gone," she answered, and her voice broke. "He has gone."
"Why?" Taisin asked.
"He—he believes I have betrayed him." She rubbed her arm more quickly.
"Why would he think that?"
"He says the baby is not his." As she spoke, the baby opened his mouth and wailed. She knelt down and picked him up, rocking him in her arms until he quieted. "But I never betrayed my husband. I was with him every night. This is our baby." Tears trickled out of her eyes, leaving shining rivulets on her cheeks.
Taisin walked to the woman and put her hand on the baby's blanket. "Let me see him."
At first the woman clutched her baby closer, but as Taisin waited calmly, she slowly relaxed and allowed Taisin to pull back the blanket. The child looked perfectly normal: a sleeping baby boy, fine new hair in a black cap over his head, a small nose, a bow of a mouth.
Kaede approached them, unease rising in her. The mother's eyes were skipping about the room, looking everywhere but at Taisin or her son. The boy let out a small coo as he awoke, reaching for Taisin's hand. He wrapped his little fingers around her thumb and tugged. Taisin's eyes widened; a shudder went through her.
"What is it?" Kaede asked. This did not feel right.
"How wondrous," Taisin breathed. The baby's eyes were black as coal, without a glint of light in them. They were unnatural.
"Taisin," Kaede said warningly. She could see the boy's eyes now, and a knot of horror clenched in her belly. No human had eyes like that.
"It's all right," Taisin said, but Kaede didn't know if she was talking to the baby, his mother, or herself. Taisin seemed entranced by him.
He let go of her thumb and reached up with chubby fists, trying to grab the strands of Taisin's hair that had come loose from her braids. She leaned closer, and the medallion that Sister Ailan had entrusted her with tumbled out over the collar of her tunic, as if it had been pulled. It was shiny and bright, and the stone was like a magnet to the child's hands. When he touched it, he and his mother and Taisin shone for an instant as long as one blink—and then Taisin was clutching at the child's fists, which were firmly clasped around the medallion.
"Let go," Taisin hissed, and the child would not obey. There was an eerie smile on his face as if he were mocking her, his black eyes wide and staring.
"What are you doing to him?" the mother demanded, trying to back away, but he would not let go of the medallion, and it tethered the both of them to Taisin.
"Let go!"
"He doesn't understand you. He's only a baby!" the mother pleaded.
"He understands," Taisin said, and the baby's mouth yawned open in a soundless cry.
Kaede wanted to intervene, but she didn't know what to do. Panic raced through her frozen body.
Taisin put her hands on the baby's forehead and said, "Reveal your true spirit—I command you to come forth!" The baby let out a growl, raising the hairs on Kaede's neck.
The child strained toward Taisin while his mother tried to pull him back, and it was almost as though he was suspended in the air between the two of them. Kaede wondered if her eyes were playing tricks on her, for he seemed to be lengthening. Taisin said again, her voice harsh and deep, "Reveal your true spirit! I command you to come forth."
And then the child began to change. His hands were growing, his head was enlarging, and where baby fuzz had once covered a pale new scalp, now long tentacles were emerging. Parts of his body were dissolving into mist and then re-forming into a greater thing: a creature made of scales and feathers both, as if it could not decide exactly what kind of being it should be. Its hands were still pulling on the medallion around Taisin's neck, and the woman was still trying to hold this creature that had moments before been her baby but was now kicking back at her with clawed feet that tore gashes into her arms. Blood erupted on the woman's skin, and the creature screamed, fury distorting its face.
Kaede was rooted to the spot, stunned by what was happening in front of her. She felt useless; her limbs would not obey her. She saw the creature's taloned hands stretch toward Taisin's throat. Kaede realized that it was going to rip that medallion from Taisin's neck, and her neck would come with it. Instinctually, Kaede felt for the dagger that Fin had given her. The touch of the iron hilt seemed to unstick her feet from the floor at last, and she moved through what felt like thick mud toward the monstrous child.
The woman was clinging to the thing that had erupted from her baby; she was screaming at Taisin; Taisin was still trying to pull the medallion out of the creature's hands; and Kaede took the last few steps, her muscles straining against unseen weights, and plunged the iron into the monster's chest.
After the viscous density of the air, there was little resistance; it was suddenly like carving through fog or mist. But the monster felt it. It turned its horrible black eyes toward her, and for a moment, Kaede lost her breath looking into those bottomless depths. They were as dark as a thousand starless midnights, and she was dragged down with despair; she was sure that she would sink so far into the earth that her body would be crushed at any moment by the mass of the world above it.
And then she felt something give. Warmth seeped over her skin, and time sped up again with a great whoosh like a blast of winter wind, and the monster shriveled up until there, in the woman's bloody arms, was a baby with an iron knife protruding from its still belly.
Along the side of the baby's face was an iridescent fringe of feathers, grown out of its skin like a strange mane, the only sign that it had ever been anything other than a plump little boy.
# Chapter XII
he woman collapsed onto the floor, and the lifeless creature rolled out of her arms, leaving a glistening crimson trail down the front of her dress.
Taisin's body hummed with a jumble of emotions—awe at witnessing the child's frightening transformation; terror that it was going to kill her. But Kaede had saved her. She was alive. And then the full force of what had just happened—what she had barely avoided—swept through her.
She sank to her knees, taking a deep, ragged breath. She was as cold as if she had been submerged in icy water. She wrapped her arms around herself; she was shaking. She became gradually aware of the heart-wrenching sound of the mother's sobs: She was crying. And Kaede stood as still as stone, her face ashen, her right hand streaked with the creature's blood.
Taisin pushed herself up; her knees wobbled. She touched Kaede's arm. "Kaede, it's over."
Kaede's dazed eyes flickered to Taisin. As if she were coming awake after a disorienting dream, awareness flooded into her. She saw Taisin's face, drained of color; her dark, anxious eyes. Taisin could have been killed. Kaede reached for her, cupping Taisin's face in her hands, pulling her closer as her thumbs pressed into Taisin's cheeks. "Are you all right?" she asked urgently.
Taken aback, Taisin said, "Yes."
"It didn't hurt you?"
"No."
Kaede's face was tight with worry, and Taisin realized that the worry was for her. All at once, she wasn't cold anymore. She backed away, flustered, and Kaede's hand left a smear of red on her left cheek.
They heard a voice behind them: "What's going on?"
They spun around to see Con standing in the open doorway.
"Are you all right?" he asked, taking in the sight of Taisin and Kaede, the queer little body on the floor, the keening mother.
Taisin swallowed; she tried to gather herself together. The strange pull she had felt before was gone. Had the child been the source of it? Had it called to her? And what was that creature? She had certainly never heard of anything like it at the Academy, and her lack of knowledge frightened her.
She saw Con still watching her, waiting for an answer. "The child that we have been hearing about—it was not human," she said. Her voice was steadier than she expected it would be. "We must destroy it." Saying the words turned the horror into a task, an assignment.
"Why?" Kaede asked. She still felt a bit muddled, and seeing the iron dagger still protruding from the creature's belly made her shudder. She went to it and pulled the dagger out. The blood was bright on the blade, and it made her stomach clench. She could have thrown the weapon into the fire, never to see it again, but Taisin came to her side and held out a torn rag.
"Use this," Taisin said. Kaede hesitated, but finally took the rag and ran it over the edge of the blade. The blood came off in long dark streaks. Taisin knelt down beside the tiny body. The eyes were still open, reflecting the firelight with an eerie liveliness. She shivered. "We must burn the body."
"Can't we just bury it?" Kaede asked.
"I don't know what kind of magic created it. Burial will only allow it to take root and spring up again."
Kaede imagined tiny, gnarled fingers reaching up through the soil like a strange new plant. "Fire, then," she agreed quickly. "Where?"
They wrapped the body in a canvas cloth that had been discarded in the corner, and Kaede tucked the bloodied rag inside. The mother lay like a broken doll on the floor, paying no attention to them. Con saw Kaede's worried expression and said, "We won't leave her alone; I'll tell the innkeeper about her."
Behind the woman's small house there was a bare dirt yard, and in the light of the lantern that Con held, they found the woodshed. He helped Kaede assemble the funeral pyre, and then they laid the small, wrapped body on top of it. It was light as a feather.
Kaede had taken flint from inside the house and was about to light the fire when Taisin said, "Wait. Let me bind the body to the earth first." She went back inside and returned a few minutes later carrying a saltcellar.
Con saw her fingers tremble as she fumbled with the coarse white grains. "Have you done this before?" he asked, not unkindly.
She wouldn't let herself look at him; she didn't want to see the doubt that must be in his eyes. "I know how it is done," she said. At the Academy she had learned about the appropriate rituals for a funeral, but only from books. And her knowledge of binding a malevolent being to the earth was entirely theoretical; she had never before encountered such a creature. She began to circle the funeral pyre three times clockwise, trying to quell the apprehension bubbling inside her. She didn't want to think about what could go wrong if she performed this ritual incorrectly.
She sprinkled the salt on the earth; she breathed deep into her belly. The night smelled of dampness, mud, and smoke from the small house's chimney. She halted at the head of the shrouded body, completing her three circles, and set the saltcellar down on the ground at her feet. She folded her hands together just below her breastbone and felt the rapid thrumming of her pulse, her whole body taut with nerves. She tried to slow down her breathing, to calm herself, but her voice still shook a little as she said, "As earth calls to earth, we bind you here: May you rest in peace and disturb us no more." She repeated it twice, then stepped back and said to Kaede, "You can light the fire."
The wood was slightly damp from the rain, and Kaede had to kneel down to blow on the spark until the kindling caught fire. Ever since she was a child, she loved to watch the flames dance; she and her brothers would build giant bonfires on the beach outside Seatown in the summer, adding driftwood until the fire roared like a dragon. But as these flames licked at the shrouded body, it turned her stomach to see it eat away the cloth. When the creature's skin began to catch fire, she turned away, pressing her hand over her nose to block out the smell. She felt a deep pain within her. Even if that creature had been a monster when she killed it, she had still killed it. The knowledge of it was oppressive; her heart felt like iron.
It was past midnight before the fire consumed all the remains. Taisin's eyes stung from the heat, and she felt weak, exhausted—as though something wild had been dragged through her body. "When the ashes have cooled, we'll have to bury them," she said.
"I'll stay," Con said. He saw the weariness on Taisin's face and the dull remains of shock on Kaede's. "You're both worn out. You should go back to the hostel and sleep if you can."
"Are you sure?" Taisin asked.
He squeezed her shoulder. "Yes."
Kaede rubbed at her eyes and asked, "What about the mother?" They hadn't heard her crying in some time.
"I'll bring her back with me if I can," Con said. "Just go back with Taisin. You look as if—well, you need some rest."
Kaede blinked. Her eyelashes felt clogged with smoke. "How did you know where to find us, Con?"
He seemed surprised by her question. "I noticed when you didn't come upstairs—I promised your father I'd look out for you. So I asked the innkeeper if he knew where you'd gone, and he told me."
Taisin touch Kaede's elbow. "Come on. Let's go."
Con's brown eyes reflected the embers of the funeral pyre. He nodded at her gently. "You should go. I'll see you in the morning."
Kaede and Taisin walked back to the hostel in the dark, having forgotten to bring the lantern with them. Kaede felt confused and tired; she felt guilty. Whenever the dagger at her side brushed against her thigh, it sent a shock through her.
She was startled when Taisin spoke, her voice only slightly louder than the sound of their footsteps on the dusty road. "Thank you. I owe you my life."
"You don't owe me anything." Kaede was overcome by a wave of despondency. If the night were not so black already, she would have closed her eyes to block out any light. The smell of the funeral pyre seemed to be burned into her nostrils.
"Kaede, you did the right thing—you did the only thing you could."
She knew that Taisin was trying to comfort her, but it only made her feel worse. "Let's just go back. I'm tired."
They walked the rest of the way in silence.
Kaede could not fall asleep. The bed was hard and cold, and she missed the sound of Shae and Taisin breathing nearby. All she could see, over and over in her mind's eye, was the hilt of her iron dagger protruding from the still form of that creature. It looked disturbingly like a human baby. She wondered if she would be haunted by that image forever.
After what seemed like hours, she threw off her blankets and packed up her bedroll, dressing quickly. She went downstairs and out to the stable. It was still dark. She rifled through the wagon until she found Pol's bow, taking it out to the courtyard. She nocked an arrow and let it fly at the wooden hitching post.
She missed.
It made her angry. Her skin flushed at her own incompetence. What good was she? She would never be a sage, and she had no other skills. Why was she even trying to shoot a bow? Did she actually expect to become a guard like Pol or Tali or Shae? Her father would never allow it. And she couldn't even kill a monster—a _monster_ , she told herself—without feeling like a monster herself.
She jerked the iron dagger out of its sheath at her waist and threw it savagely at the post, but as soon as it left her hand, she knew it was a bad throw. She heard it clanging to the ground beyond the post. She let out a frustrated groan and stalked across the dirt yard to retrieve it. Her knees shook when she squatted down to pick it up. Her whole body was worn out, but she was too tightly wound to rest. She shoved the dagger into its sheath and went back to the bow.
When she had shot all the arrows, she went to where they lay and picked them up, stuffing them back into the quiver. Then she returned to where she had been standing at the opposite side of the courtyard and raised the bow again. She couldn't keep feeling this way. It would drive her mad. She breathed in, trying to loosen the knot of frustration and self-loathing inside herself.
The arrow's feathers brushed against her gloved hand as she pulled back on the string. She told herself that the only thing in the world was this arrow. There was no stable yard; there was no village of Ento; there was no Kaede, even. Everything melted away like fog in sunlight. She was riding on the sharp point of the arrowhead itself; she was flying through the predawn stillness.
The thud as it struck the hitching post surprised her.
She pulled another arrow, and another, and sent them all, more or less, into the post. Some shivered a bit before tumbling down, not having been sent with enough force. When she saw one fall, she pulled back harder on the next one. She felt emptied of everything; she only existed to hold the bow and to ready the arrow for its task.
She did this repeatedly until the sky brightened into gray. She did it until her shoulders and arms were aching and her eyes stung from staring so fixedly at the target. She did it until the gate to the stable yard opened behind her and she heard Con's voice say, "You're getting pretty good at that."
She turned to look at him, and it all came back to her: the woman, the child, the dagger in its belly. "My father asked you to look out for me," she said.
He was taken aback by the sharpness in her tone. "Yes. And your mother. And your brothers."
"They think I'm incapable of taking care of myself," she said bitterly. "They must think I'm a child." Her arms burned from holding the string taut, and the bow that had felt so light moments before now became heavy in her hands.
He frowned, shaking his head. "That's not it. They want you to be safe."
She looked down at the ground. The numbness inside her was being pushed away by hot emotion: resentment at her father, a sudden ache for her family—she missed them, she realized. There was a sludgy black sadness at the bottom of it all. She yearned for the clarity, the nothingness that had flooded her when she was shooting. She tried to draw some memory of that into her now, to smooth away the rawness. She remembered the creature's human mother. She asked: "What happened to the mother?"
"I brought her back with me. She inside. She's—she's had a shock." When Kaede only stared morosely at the arrow clutched in her hand, he said, "Come inside and eat some breakfast."
She nodded. There was an emptiness inside her, but she did not think it was due to hunger.
# Chapter XIII
veryone told Kaede that she had done the right thing, but she felt hollow inside. When Fin had given her that dagger, it had been like a toy to her. Now she knew what a weapon was.
Two days after leaving Ento, the road narrowed and became packed dirt instead of paving stones. They had reached the end of most of the farmland, and now low hills began to rise in the distance. They were far from Cathair, and yet they still had more than a week of travel before they would reach Jilin and the Great Wood. Kaede felt the lack of sun with a brutal sense of futility: The whole world was gray, colorless. Her fingers were cold where they gripped the reins, and though she rode beside Con, who had been trying all morning to engage her in conversation, she felt alone. She knew he meant well, but he had no idea what she was going through. In the distance the road curved around a hill, and she was overcome by the desire to run, to leave them all behind.
She leaned over the neck of her horse and urged her into a gallop, pushing past Shae and Pol. She heard them calling after her, but she didn't answer. On the left the road sloped down toward the river Nir; on the right it curved up a brown hillside. She caught sight of a lone tree at the top, stripped bare of its leaves, and then she was rounding the hill and there was only more road.
She loved the whip of the wind in her face. It was cool and faintly wet. She remembered the first time she had ridden a galloping horse: She had been a child, barely eight or nine, trying to keep up with her older brothers. They were at a family friend's country home, and her brothers had taken their host's horses out for a run in the morning. Her mother had told her she was too young to go with them, but she hated being left behind. She had sneaked down to the stables and taken out a fat little pony and somehow forced him into a gallop, chasing those boys down to the riverbank. When she arrived, flushed and proud of herself, only their host's son was surprised; her brothers laughed and chided her for taking so long.
Now she let her horse gallop at full speed until she felt her begin to tire, and then she gently slowed her down to a walk. When the road curved close to the river, she turned Maila toward the water, leaning back in the saddle as they went downhill the short distance. She dismounted at the riverbank and watched as Maila lowered her head to the water. The Nir was wide and deep here, sliding with a dim roar south toward Cathair. At this time of year, it should have been full of fishing vessels and ships carrying goods from the north—woolens, lumber, stone from mountain quarries. But the river was empty. Not even a waterbird floated on its surface. Trade had halted last fall when the storms began, and business had not returned to normal. The empty river should have been a peaceful sight, but instead it drove home something that Kaede hadn't fully understood until now: The Kingdom would die if the seasons did not change.
She sucked her breath in sharply. This was why she was here, standing on the banks of the Nir so far from the protection of the Academy walls and her family's influence. She was here because the Council of Sages believed the Fairy Queen knew something about why their kingdom was turning into a wasteland—a place where crops spoiled overnight, where farmers couldn't replant because there was no sunlight. Where monsters crawled out of their dark places and were found dead in northern villages, or were somehow reborn in the soft little bodies of human babies. She was here because the oracle stones said she was part of this journey to discover what the Fairy Queen knew. Did that mean that what she had done in Ento was meant to be?
Behind her she heard a horse on the road. When it began to descend the hillside to join her, she turned to see that the rider was Shae.
"Did they send you to bring me back?" Kaede asked.
"No." Shae dismounted and came to stand beside her. "To keep you safe."
"Safe. I don't think we've been safe for a long time."
"Does that worry you?"
"Should it?"
Shae shrugged. "I don't believe in worrying. It's a waste of energy."
They stood for a while in silence, gazing out over the river. Dried grasses rustled as a wind gusted down the barren slope, raising several strands of Kaede's hair. She tucked the ends behind her ears and looked at Shae, whose face was open, waiting. "Shae," Kaede said, and she felt the words come tumbling out of her: "When I chose to come on this journey, I thought—I thought it was going to be an adventure." Kaede grimaced at her own foolishness, but Shae gave her an encouraging smile.
"I like a good adventure myself," Shae said. "Why else do you think I wanted to join the King's Guard? I needed a living, yes, but I could have done something less... life-threatening. Some of us need adventures."
"But in Ento—" Kaede stopped, rubbed her hands over her face as though she could wipe the memory away. "It's not an adventure anymore. If it ever was."
Shae reached out and squeezed Kaede's shoulder. Several heartbeats later, she bent down, pulled up a dry stalk of grass, and began to shred it with her fingers. "I killed someone once," she said in a low voice.
"As a guard?"
"Yes. It was in one of the southern provinces, my first year as a member of the King's Guard. There was trouble at a border village, and I was sent with a contingent of guards to... to quell the resistance." Though her tone was calm, there was an undercurrent of tension in her words. It was clear that the memory was not an easy one. "At first it seemed as though the villagers would comply with our orders. Everyone was obeying. But then several men attacked us just as we were preparing to depart, and there was a—a scuffle. It turned out later they were sent by a neighboring lord to protect his stores, and they had been given the order to keep us out of the village for fear that we would take his grain." She paused, and plucked another long brown blade of grass from the ground. "Grain was never on our list."
"What were you sent to do?"
"We were supposed to make sure that the people of that village accepted the lord whom King Cai had instated as governor of that province. Because they were complying, there was no need to use force."
"But you did."
"Ultimately, yes. The men who attacked us were well armed and strong, and they took one of our guards quickly. I saw him beheaded not a foot in front of me. That's not a sight I'll ever forget." Shae let go of the torn shreds of grass. They fluttered out over the hillside like dandelion blossoms on the wind. "After that, the men who attacked us smelled a potential victory, and they—they charged us. I reacted before I could think." Her eyes were fixed on the distance as though she were seeing that day again. "One of them came at me, and all I knew was that if I did not kill him first, he was going to kill me. So I did."
"You were defending yourself."
"Does that make it all right?" They looked at each other, and the guard's dark brown eyes were troubled. "I knew that to be one of the King's Guard meant that I might have to kill. But I wasn't prepared for it when it happened. I wasn't prepared for the way it changed me. It was weeks before I could talk about it, though all my fellow guards praised me for what I had done. On the battlefield, they said, there is no time for anything but instinct. And yet, I can't help but wonder if perhaps our instincts are sometimes wrong."
"Do you regret it?"
Shae sighed and looked away. "How can I regret what I did, when it kept me alive?"
# Chapter XIV
hat night, they camped on the side of the road for the first time. There would be no hostel for another two days' journey. Taisin and Shae tended to the horses as usual, rubbing them down and feeding them. Taisin enjoyed the work; it reminded her of home. When she was a little girl, her father had given her the task of brushing down the farm horses at the end of the day, and she had loved being in the barn at twilight, the smell of hay and horses all around her. Those were things she had truly missed at the Academy: the warmth of animals, and the simple honesty of their energies.
Focused on the horses, the feel of their muscles beneath her hands, she was startled when Kaede appeared by her side, a cup of tea in her hand. "Tali says supper will be ready soon," Kaede said, offering her the warm drink. Kaede seemed more relaxed now than she had been earlier in the day; Taisin wondered what had soothed her.
"Thank you," Taisin said. She began to tuck the brush under her arm, but then Kaede held out her hand.
"I'll trade you," Kaede said, smiling.
The smile made Taisin's cheeks burn. She was glad it was dark. "All right." She handed the brush over in exchange for the tea. It smelled of barley, nutty and hot, and it tasted wonderful.
"It's the last of it. I didn't want you to miss out." Kaede tilted her head briefly at the campfire, where Con and Pol were sitting on their bedrolls, joking with Tali as he prepared whatever concoction they would be eating tonight.
"What about Shae?" Taisin looked at the guard, who was working on the wagon horses several feet away.
"I already brought her a cup."
"Oh." Taisin raised the tea to her lips again, the steam wafting into her eyes. It reminded her of wintry nights at the Academy, curled up in her tiny room with her bed strewn with books. She felt a deep tug of homesickness inside her.
"I wanted to tell you something."
"You did?" Taisin's stomach fluttered. She often felt nervous around Kaede. It frustrated her, but she didn't know what to do about it. She was doing everything she could, she told herself, to avoid the fate in her vision—but she was afraid she was losing that battle.
"Yes." Kaede took a deep breath, steeling herself. "I didn't really understand, until today, even, what was at stake on this journey. Now I do. You were right, in Ento—we need to know what we're dealing with, or as much as we can know. So I have to ask you: What did you see in your vision, Taisin? You haven't told me—not exactly. But the way you look at me sometimes, I have to know: What did you see me doing?"
Taisin clutched the battered metal teacup with both hands and swallowed. All she could think was that Kaede had caught her staring at her. She was mortified that she had been so obvious; she was terrified that she would have to tell her the whole truth.
Kaede saw Taisin's distress. Even in the dark, the way her shoulders had stiffened betrayed her. "Is it so bad?" Kaede's own anxiety began to rise. "What did you see me do?"
Taisin shook her head swiftly. "No—no, it's not anything—you didn't do anything awful. That's not what I saw."
"Please. Please just tell me."
She knew she had to tell her something. "I saw you—and I—we were on a beach. An icy beach." Her voice shook a little, remembering. "You stepped into a rowboat, and you rowed away. I saw you leaving." She stopped, hoping that Kaede would ask for nothing more.
"A rowboat?" Kaede was puzzled. "And I was leaving? That's all?"
"Yes," Taisin said, and pressed her lips together.
As Kaede mulled over her words, Taisin saw that she didn't seem to realize that anything had been held back. But why should she? Taisin knew she had done her best to keep her emotions hidden. She had even tried to keep them hidden from herself, though it was becoming increasingly difficult.
Kaede asked, "Where is this beach?"
Taisin was startled. It had never occurred to her to wonder about that at all. "I don't know. I just saw it. It's part of this journey—that's all I know."
They heard Tali calling to them; supper was ready.
"You go ahead," Taisin said, taking the opportunity to change the subject. "I'll be there in a minute. I just want to put away the brushes." She held her hand out for the brush Kaede had taken from her, and for a moment Kaede didn't seem to want to give it to her. She was looking at Taisin closely, searching her face. Taisin tried to school her expression into one of calm blankness; she had the irrational fear that Kaede could see right through her.
But Kaede only said, "All right," and handed over the brush. "Don't be long. The food will get cold."
Taisin clutched the brush with one hand, the teacup with the other, and told herself that she shouldn't be so silly. It was dark, and besides, Kaede couldn't read her mind.
Around the campfire that night, they told stories. What had happened in Ento had left them all unsettled, and tale-telling was a welcome distraction. Con, it seemed, had heard every story ever told, and he regaled them with the legendary exploits of King Rin Tai, who traveled to the clouded mountain to face the sinuous green dragon who had terrorized the people of six provinces.
"And when he returned, I suppose he married the most beautiful highborn lady in the land and had a dozen children," Shae said drily.
Con shrugged. "You object to a happy ending?"
Shae leaned forward, poking at the fire with a stick. The flames roared. "I'd like to hear a tale about an ordinary person for once. Not all of us are born princes." She softened the sharpness of her words with a smile, but Con was chagrined.
Tali laughed. "She has a point. Do you have a story in your head for us common folk?"
"Is that a challenge?" Con asked.
"Yes," Tali said. "A challenge."
"All right, then." Con flexed his fingers and thought for a moment. "Have you heard the tale of Farin and Anmin?"
Taisin smiled. "I have."
"Good. Then you can correct me if I get it wrong. Farin was a blacksmith—a noble enough profession, to be sure, but one that kept him hard at work day and night. His village was located near the King's Highway, and his smithy was adjacent to the town's best inn, which was always busy with travelers. One autumn, a wealthy merchant and his family were passing through Farin's village and boarded at the inn. The merchant had a daughter, whose name was Anmin. She, they say, was as beautiful as a spring morning."
Tali whistled. "I haven't seen one of those in a while."
Con gave him a stern look. "Anmin, as I was saying, was a beautiful girl. Her father had aspirations for her. He was a merchant, but he hoped to marry her to a wealthy lord and thereby increase his standing in the court."
"Here come the nobles," Shae said.
"Wait until you hear the whole story," Con objected. "Anmin was more than beautiful; she was also intelligent, and she knew what her father's plans were. But she had other goals in life. She had heard from her father that there were other lands across the sea, and she wanted to explore them. She knew that to become an explorer she would have to learn how to ride and defend herself—talents that no lord's wife needed—so every chance she had, she would practice swordplay or horsemanship. One afternoon while she was in the village, she discovered that her sword had a knick in it, and she decided to bring it to the blacksmith nearby. When she and Farin saw each other, they knew immediately that they had found their one true love."
"How did they know?" Shae asked. "Sparks flew from the anvil?"
Con grinned at her. "Don't you have any faith in the power of love?"
"Do you, Prince Con?" she teased him, and the tone in her voice made a tingle run through him. She was watching him with her head half-cocked, and he noticed a sly smile turning up the corners of her mouth.
He responded, "You're avoiding the question." The expression on Shae's face changed just slightly—he wondered if it was self-consciousness—and she ducked her head and poked at the fire again.
"Tell the story, Con," she said lightly, but she avoided his gaze.
"As you wish," he said, feeling a little surge of anticipation. Shae had always been friendly with him, never anything more or less, and for the first time Con became aware that he might like it if there was something more. While she prodded at the burning coals, he continued: "As I was saying, when Farin and Anmin first saw each other, they fell in love. They resolved to marry as soon as possible, but when Anmin told her father of her intentions, he flew into a rage and told her he had already arranged her marriage to the King's nephew. When she saw that he had no intention of backing down, she decided to elope with the blacksmith. However, the following morning, she awoke to discover that her father had been robbed during the night. All of the goods he had been transporting to Cathair had been stolen, and because soot had been found in the room where the goods had been stored, her father believed that Farin was the thief.
"Farin was brought to the village magistrate, who listened to the merchant's suspicions and found Farin guilty. But Farin insisted he was no thief, and he also knew that the magistrate could be easily bribed. With Anmin's help, Farin appealed to the provincial magistrate, who also sided with the merchant. Farin was about to be thrown into prison when the King's Magistrate agreed to hear his case—thanks to Anmin's hard work—and Farin was so convincing that the King's Magistrate told him that if he could face the judgment of the unicorn and survive, then he would be set free. Of course, if the unicorn found him guilty, he would be gored by the beast and die."
"No one ever survives the judgment of the unicorn," Pol said. "We are all guilty of something; the unicorn never finds anyone innocent."
"In some of the tales they survive," Taisin put in.
"Really? Which ones?" Pol asked.
"Hang on," Con said. "Let me finish this tale first. So: Farin was taken into the Wood to seek out the unicorn."
"In the version I heard, the unicorns were kept in a special enclosure at the palace," Taisin said.
Con blinked. "An enclosure?"
"Yes. There was an enclosure, adjacent to the King's Magistrate's office," she said. "The accused would be brought there and judged."
"I can't imagine the creatures would submit to being enclosed," Pol said.
"Because you've seen them before?" Tali said skeptically.
"No, but they're not horses to be trained. You might as well keep a phoenix as a songbird."
"I'm sure that's been attempted by some king or another," Shae said. "Con, please continue."
When she spoke his name her eyes flickered to him, and warmth spread over his skin. He swallowed. "All right. So, Farin was taken to the unicorn to face his judgment. Of course, Farin was innocent, but his heart was so pure and his love for Anmin so true that the unicorn not only let him live, he showed him who the real thief was: Anmin's own father, who had sought to incriminate the blacksmith to prevent him from marrying his daughter. When Farin returned to his village, he immediately told the merchant that he knew his secret, and he threatened to tell Anmin as well. But the merchant knew that if his daughter found out, she would never again acknowledge him as her father. Faced with the loss of his only daughter, he agreed to drop his accusations, and Farin and Anmin were soon married. Afterward, they both became explorers and lived long and happy lives."
Tali clapped, and the others laughed and joined in. Shae said, "That is a sweet tale, Con. But what's the moral of the story?" She watched him, her face half in shadow.
"Magistrates are generally corrupt," Pol quipped.
"Fathers shouldn't attempt to marry their daughters off to noblemen when there's a handsome blacksmith nearby," Kaede said, pulling a face.
Con smiled. "Those are a couple of ways to think about it." He looked at Shae as he said, "Or, perhaps the lesson is that true love will always prevail."
"How romantic of you," Shae said, and she might have meant for her words to sound wry, but Con heard a thread of wistfulness in her voice.
"I think it's true," he said. "Love knows no limits; it sees no distinctions based on birth or any other characteristic. A prince may love a seamstress as much as any princess."
"But would the seamstress be allowed to love the prince?" Shae asked.
"Love will always prevail," Con said. He thought he saw the hint of a blush on her face, though he couldn't be sure, for she stirred the embers in the campfire again, and the light flared reddish-gold over her skin.
They sat up late telling stories, and by the time Taisin rolled into her blankets by the fire, she was so tired she fell asleep immediately. She didn't know how much later the vision came, but when it began, she could still feel the hard ground beneath her body, softened only slightly by the blankets she had folded into a thin pallet. But she could also feel the cold breath of winter on her face, and she could see the fortress of ice again. This time, she had left the beach behind entirely; she was floating, hovering up high, ascending toward the glass windows set into thick, frozen walls. She had never known that ice could take on so many shades of blue: sharp lines of indigo like the deepest sea, aquamarine shadows, even the glint of blue-green where the sun struck just so.
For the first time, she realized the significance of that. The sun shone here. Wherever _here_ was, it was not locked in the unchanging clouded gray that blanketed the Kingdom. She wanted to look up at the sky, to gaze into the sun's brilliant white-gold eye, but she had no control over her movements, and she had arrived at one of the windows. The glass was like a mirror reflecting the light, and what she saw in the window made her jerk in surprise. A tiny person was hovering there on little feathered wings, like a hummingbird, and Taisin heard the creature speaking some kind of language she did not understand.
A moment later the window opened, and the creature fluttered inside. Taisin was pulled along with her, as if riding in the draft of her wings. The creature flew so quickly that all Taisin could do was follow. She only caught glimpses of what passed: walls of white, glacial floors, and every once in a while, a torch burning with a cold blue flame. She became aware, slowly, that the flying creature's heart was beating as quickly as a tiny war drum, urgent with some kind of duty. And then all of a sudden the way opened wide, and Taisin now understood that they had been flying down a corridor and had just emerged into a great, echoing space. She heard more sounds like the words that the winged creature had spoken. She could not make out the distinct syllables, but they made her heart ache, for they were all sounds of yearning—each being who cried out was crying out for freedom.
Taisin saw the creature's bright orange and emerald wings flutter as she twisted in midair to look down, and Taisin reeled at the sight below her. There were cages, hundreds of them, stacked like crates. She saw golden bars; she saw eyes of different colors peering up at her. The voices she had heard came from within those cages.
The flying creature turned to look back, but she did not seem to see Taisin. She had a tiny, delicate, girl's face, and she wore an expression of dread. Her glittering golden eyes widened with alarm, and then Taisin was thrust out of the vision as though someone had pushed her aside, and she was lying on her back on the hard ground beside a fire that sent golden sparks up into the black night sky. She saw Pol sitting up nearby; he had taken the second watch that night.
Her breath came as quick as that creature's wings had been beating. She knew she had been close to seeing something important. What had pushed her aside? Who was trapped in those cages? The memory of the imprisoned voices made her shiver. Who, she wondered, was their jailer?
# PART III
Dragons battle on the plain:
Yellow and black blood spills.
Where frost is underfoot,
Ice cannot be far.
— _Book of Changes_
# Chapter XV
heir first glimpse of the Great Wood came nearly three weeks after leaving Cathair. It was a dark smudge against the distant hills that blinked in and out of sight as the road curved. And then one afternoon as they rounded another bend, there it was, spreading its fingers out into the valley below, brushing up close to the river, extending to the horizon in waves of brown and green. Kaede had never before seen so many trees.
They camped within a copse of oaks that night. The weather had turned the leaves brown, even though it was midsummer, and a cold wind gusted through the gnarled branches, making the dried leaves rattle.
"We should get to Jilin sometime tomorrow," Shae said, squatting down to warm her hands at the fire while Tali cooked the rice. "Hopefully before dark."
"When was the last time you were there?" Con asked, sitting down beside her.
"Two years, one month ago," Shae answered. "It's been too long."
Shae's eagerness to reach Jilin caused them to push the horses hard the next day. The road took them through the outer reaches of the Great Wood, winding through clumps of oaks and bay trees. As dusk fell, shadows deepened beneath the branches. The road widened ahead, but the murky twilight made it difficult to see.
Shae, who was riding in the lead, called them to a halt. "Something's wrong," she said in a low voice. Beside her, Tali drew his sword.
Kaede felt a prickle of apprehension run down the back of her neck. It was too quiet; they couldn't even hear the sound of insects.
Suddenly a torch flared twenty feet ahead of them, and behind that torch, a half-dozen more burned into life. In the smoky light, Kaede saw men and women approaching with weapons in their hands; some held swords, while others carried long wooden staffs or axes. Fear raced through her. She heard the loud, ringing scrape as Con drew his sword, and she reached for her own iron dagger.
A man stepped out of the crowd of torchbearers, his black beard obscuring half his face, his eyes glittering in the torchlight. "Who goes there?" he called out in a harsh voice.
Shae had drawn her sword as well, and Tali and Pol flanked her. "Noa, is that you?" Shae called out. "What is going on? It's me, Shae."
The bearded man took a step forward, but he still brandished his sword before him. "Shae? Niran's sister?"
"Yes! Don't you recognize me?" She dismounted and sheathed her sword, approaching him with her hands outstretched. "Noa, I'm back. It's me."
For a long, tense moment, Kaede was sure the man was going to deny that he had any idea who Shae was and strike her down, but then he lowered his sword and closed the gap between them, crushing Shae into an embrace. "Shae," he said, his voice heavy with relief. "Why didn't you send word in advance?"
The other torchbearers gathered around Noa and Shae, their voices rising as they pelted Shae with questions about why she was back. She answered with rising concern in her voice: "I will tell you all—I will tell you everything, but where is Niran? Where is my brother? Why isn't he with you?" The crowd fell silent, and Shae turned to Noa and demanded, "Tell me, Noa. What has happened?"
"Your brother, Niran, is fine," he said, but his tone suggested that he was holding something back.
"Noa," Shae said. "What do you mean?"
"I'll take you to him. He's fine," Noa said again.
"Now," Shae said firmly, and Noa nodded.
The village of Jilin was surrounded by trees, and trees marched down Jilin's few streets. The buildings seemed to have been situated to make room for giant trunks and root systems, and in the wavering torchlight, they looked almost as if they had grown out of the trees themselves.
Noa led them to a massive oak outside a long dark building and said, "You should leave your horses here. It'll be easier."
Shae knew the village of Jilin intimately, and she knew immediately that Noa was not taking her to her brother's home. "Where are we going?" she asked him.
"Into the Wood." Most of the other villagers had returned to their homes, but two remained behind, carrying torches. "Let's go," Noa said, and struck off down a small trail.
In the daylight, the path would have been an easy walk, but in the dusk—brightened only by the flickering torches—it was an obstacle course. Even Tali tripped once, cursing under his breath. Kaede kept her eyes on Noa's torch ahead, trying to ignore the strange sensation that there was something out in the dark, watching her. It made the hairs on her neck stand on end, but she told herself she was imagining things.
After they had walked for about a quarter of an hour, Noa paused and called out, "Niran!"
Moments later a man came running down the path; behind him someone followed more slowly, bearing a torch. "Shae?" the man cried. "Is that you?" Niran was a tall man with a closely cropped black beard; his hands and face were streaked with dirt, but it could not disguise his surprise and joy at seeing Shae. He crushed her in an embrace, asking, "What are you doing here? Why didn't you tell us you were coming?"
"I'll tell you everything later," Shae said. "But why are you out here? What's going on?"
"We've found something," Niran said.
The torchbearer who had followed Niran came forward; she was a woman, her black hair hanging in a long braid over her shoulder. "Shae?"
"Parsa," Shae said, and threw her arms around her brother's wife. When they parted, Shae asked, "What have you found?"
"Come and see for yourself," Niran said, and stood aside. There was a clearing just past him, and a long rectangular hole gaped open in the ground. Shovels were leaning against a nearby pine tree, and Kaede realized that she was looking at a grave. A chill ran through her. Beside the grave was a shape wrapped in a sheet. A body.
Niran bent down and pulled back the sheet. They saw the corpse of an inhuman creature, its arms wrapped around bended knees, its head lolling sideways onto the ground. It had long hair that resembled hundreds of tiny vines, some of them smashed and brown. The eyes had been covered by a torn piece of cloth, like a blindfold, and the mouth was stuffed with a black stone. From its fingertips, nails like long green blades of grass extended, curling over mottled, barklike skin. They were the only living things on the creature: It was as if the grasslike nails had sprouted out of a seed and were determined to make a new life out of what had already expired.
Taisin edged past Niran to take a closer look, curiosity vying with aversion. She wondered if it was some kind of fay. There were fay races other than the Xi—she thought the winged girl she saw in her vision must be fay—but she knew little about them. This one looked like it could have grown from a tree. She asked, "When did you find it?"
"Yesterday morning," Niran said.
"Did you place the stone in its mouth?" Taisin asked. It was traditional to put a stone in the mouth of a person who had been murdered, to prevent him from speaking to the living if he returned as a ghost.
"I did," Parsa said. "It is marked with the sign for peaceful rest."
Taisin couldn't see the mark; the stone was wedged in too deeply. The creature's lips were cracked and dry, reminding her of parched earth after a drought. "You were going to bury it?"
"Yes," Niran said.
"It should—it would be better if it were burned," Taisin said.
"We can't burn it," Niran objected. "We would set the Wood on fire."
"And we won't carry it into Jilin; it is polluted with death," Parsa said. Her eyes narrowed on Taisin. "Who are you? What would you know about this?"
Taisin shrank back, feeling stung. Shae said quickly, "We're here for a reason. I didn't send word because, well, our reasons mustn't become widely known. But I will tell you the truth." She glanced uneasily from the body to Taisin. "First, though, I think we should finish what you have started here."
Shae's brother looked them over skeptically, but he nodded. "All right."
He bent down to pull the shroud over the face of the dead creature again. Taisin said nothing. She hoped that the stone and the blindfold would do their jobs and take the place of a funeral pyre. She told herself that if the ghost of the creature could not speak or see, then no real harm could be done. But still, she was uneasy. She had no idea if those traditions would work on something so clearly inhuman. She wanted to know more about it: How had it died? And where had it come from?
Niran and Parsa picked up their shovels, levered them under the body, and tipped it over the edge of the grave, where it fell with a dull thump. Taisin flinched. Beneath her breath, she muttered a blessing ritual meant to keep a body in its grave.
Niran, like his father and grandfather before him, was a blacksmith, and his family's home had been built adjacent to the smithy over the course of many generations. Kaede had the impression that additional wings had been added at random, creating a maze of connecting rooms that opened here and there into sky wells and broader courtyards. Niran led them through the main gate and past the smithy, the forge still smoldering, and then into the main hall, next to a kitchen where a fire burned in an open pit.
Shae's older sister, Raesa, who had heard news of Shae's arrival, greeted them warmly. "The children are asleep," she said. "You must come and eat."
Raesa's husband, Tulan, had brought back two hares from his traps that afternoon, and the rich fragrance of braised meat made Kaede's mouth water. They gathered together in the hall, sitting around two square tables pushed together, and ate salty flat bread and rabbit stewed with aromatic spices. A brown-and-black hound nosed his way around their feet, sniffing for fallen scraps. Raesa poured them hot, bitter tea in small earthenware cups, and Shae told her brother and sister why she had brought five strangers with her to Jilin.
"Please, don't tell anyone else what I've told you," Shae said when she finished.
Niran nodded, and glanced around the table at her companions. "How long do you plan to stay?"
"Not long," Tali answered. "I'm sorry."
"Stay through tomorrow," Parsa insisted. "You have to at least give us time to welcome you back."
"All right," Shae assented with a smile. "As long as nobody else objects."
"I'm happy to have a roof over my head for one more night," Con said, and no one disagreed with him.
"You're traveling into the Wood?" Raesa asked.
"Yes," Tali said. "We're headed north of the river Kell."
Raesa glanced at her husband, who had been mostly silent. But now he said, "When I was a boy, my uncle said he traveled that far, but when he returned there was something off about him. I never could get the whole story out of him."
Tali had brought their map case inside, and now he opened it, pushing aside empty bowls to unroll a map of the Wood onto the table. Kaede scooted her chair closer, wanting to get a better look. Tali had never shared them with her, though she had heard him discussing their route with Pol and Shae. Jilin was clearly noted on the map, and trails splintered off from the village and led into the Wood. Some of them ended abruptly only a few miles in; the longest followed the river Nir north, and then ended just south of where the Nir intersected with the Kell, which flowed east. Above the Kell, the Great Wood continued unabated to the northernmost edge of the map, which was marked with mountains: the Northerness. Tali looked at Tulan and asked, "Is there a way to cross the Kell? A bridge? It is unmarked."
Tulan leaned over the map to examine it, but he shook his head. "Not that I've heard of. I suppose there are stories of folks who have crossed the Kell."
"Where did they cross it?" Tali asked.
"They're stories, not directions," he said mildly.
Tali seemed disappointed.
"I think this map is as good as you're going to get," Tulan said. "It's accurate enough around here. I don't know about the northern part; I imagine that's all a guessing game."
"So how would you advise that we find our way to the Kell?" Shae asked.
"Follow the Nir. I'm fairly certain it does meet the Kell. You'll find it that way. That's as best as I can tell you." Tulan frowned, tugging at his beard. "You're going off the map. No one knows what's up there."
# Chapter XVI
hey slept in their bedrolls on the floor of the main hall, pushing the table and chairs to one side, next to the family shrine, to make room. Kaede found the stone floor as comfortable as a feather bed after days of sleeping on lumpy ground, and she fell asleep so quickly she barely had time to enjoy the flatness beneath her back. She was awakened in the morning by the shrill voices of children—Shae's nieces and nephew—who ran into the room and pounced on Shae's sleeping form, startling a yelp out of her.
At breakfast, Raesa and Tulan announced that they were going hunting, for they planned a celebration that night and hoped to bring back a deer. Pol volunteered to go with them, and when he asked Kaede if she'd like to come along—"You should see the bow in its natural environment," he said—she was surprised but pleased, and said yes.
The hound, whose name was Ota, came with them, his ears perking forward as they left Jilin behind and entered the Wood. It was another cool morning, but the Wood held none of the menace it had the night before, and Kaede wondered if she had imagined the sensation of something watching her. Now there were only trees, their gray-brown trunks scaled with lichen, and every so often the sound of a squirrel or rabbit bounding through the underbrush. Raesa and Tulan, like Pol, had quivers strapped to their backs and hunting knives at their waists; they carried their bows and moved with a stealth that Kaede knew she could not match. Her footsteps sounded like a herd of giants compared to theirs, and she feared that Pol had been wrong to invite her. She didn't want to scare away their supper.
But as they walked, Tulan said to her, "Raesa is a much better shot than I. When we find the deer it would be best if she and Pol move downwind, and then you and I can nudge the deer toward them."
"So you'll take advantage of my clumsy footsteps," Kaede said, smiling.
"You'll get better," Raesa said.
Kaede tried to limit the noise she made. She set her feet down as lightly as she could, imagining that she was a cloud, a mist, snaking slowly but surely around the gnarled oak trees. The Wood smelled of damp things: rainwater soaking into fallen logs, softening the bark until it crumbled back into the ground. In the distance, she heard the caw of a crow, over and over.
It was nearly an hour before Ota scented the deer; when he did, his entire body pointed northwest, his legs quivering in excitement. They had long ago left the well-maintained paths behind and were now picking their way down a tiny deer trail. As soon as Ota gave the signal, Raesa and Pol melted into the trees, moving as quietly as they could to avoid startling the deer. Ota vanished after them, and Tulan and Kaede continued on. Soon afterward Kaede saw the flash of a white tail just off to her left. All her senses came alive, and a thrill rippled through her. It was awe-inspiring to be so near to this animal. And yet—her breath caught in her throat—they were going to kill him. Her knowledge of the buck's imminent death seemed to magnify everything: the beauty of the animal, the smell of the forest, the beating of her heart. Time seemed to slow down. The caw of the crow echoed through the trees like a bell.
Beside her, Tulan crept forward, and the deer began to back away from them. Kaede followed, her pulse racing, and they pushed the deer ahead for some time, always moving in the direction that Pol and Raesa had gone in. With every careful step, Kaede was aware that death was coming closer, and she began to wonder if the buck knew it, too.
And then an arrow struck the deer in his side, and he bolted.
Ota leapt after him, baying, his nose soon dropping to the ground to follow the scent of spilled blood. The deer had been wounded, but it would run in panic for some distance. They could only hope that the arrow had landed deep enough, or else it would be a long and potentially fruitless chase.
Pol and Raesa came out from their cover, and Tulan asked, "Who sent the arrow?"
"Raesa did," Pol said. "You're right—she's a good shot."
"Don't speak too soon," she cautioned him, and they began to follow Ota on a jagged path through the trees.
But they were lucky; the arrow had been true, and it was only another half mile before they found the deer collapsed on the ground, his flanks heaving. Tulan unsheathed his long hunting knife and went to the deer, and before Kaede could catch her breath, he slit the buck's throat.
Raesa held Ota back from the stream of blood while the deer died.
Kaede halted several feet away. The sight of the dying animal brought back the memory of the creature she had killed in Ento, and for a moment she thought her stomach would turn itself inside out. Cold sweat beaded her forehead. Pol saw the expression on her face and said, "The buck will feed many of us tonight, and more tomorrow. It was a necessary death."
She swallowed. She knew that Pol was right. But never had the word _necessary_ seemed so cold.
They strapped the deer's legs to a long fallen branch and hoisted it up on their shoulders, each taking turns to bear the weight on the way back to Jilin. Ota ran between their legs excitedly; he had been given a piece of the warm liver, but he smelled the meat and was eager for more.
When they reached Niran's home, Kaede slipped away. She felt bruised somehow, as though someone had smashed a fist into an old wound, and she wanted to be alone. There was a garden behind the smithy, and when she saw the rows of low green shoots, a pang went through her as she remembered working with Maesie. There were some things she missed from the Academy: the sea, and Maesie and Fin, and her friends. Beyond the garden, a small path led into the Wood, weaving between bay trees. It was gloomy now, but seeing the way the branches arched overhead, Kaede suspected it would be beautiful beneath the sunlight. She imagined a green tunnel, the leaves whispering in a warm breeze. She ached for the warmth of summer. Though it was now nearly midsummer, it was still as cool as late winter.
The path ended in a small clearing with a stone bench. Opposite the bench was a statue that appeared to have been shaped out of the oak stump rooted there in the ground: a deer's head. She sat on the bench and stared at it, wondering who had made it, who had imbued such life into the way the ears tilted.
She heard the footsteps some time later, and glanced up to see Taisin coming down the path. She looked a bit nervous, and she held out something wrapped in a white cloth. "I brought you some bread," she said tentatively.
"Thank you," Kaede said. It was flat bread fresh from the pan, still warm.
Taisin sat on the far edge of the bench beside her. "They're eating, if you want to go back."
The flat bread was good, slightly charred and salty. "I'll go back in a little while," she said between bites.
"They're butchering the deer. I think that Parsa intends to invite all of Jilin here tonight." Taisin glanced sideways at Kaede. "How was the hunt?"
Kaede's fingers were smeared with salt and lightly greased with oil from the bread. She wanted to lick them, but thought it might be impolite. She scrubbed them on the cloth and said, "It was successful. No help from me." She grinned, but there was no joy behind it. "I just followed."
Taisin could feel the forced cheer coming from Kaede, who regarded her with serious brown eyes, her mouth slowly turning down at the corners as the grin faded. Taisin asked, "Are you all right?"
The question caught Kaede off guard. "All right? I'm—" She hesitated, the words stuck in her throat, and she looked down at her hands, twisting the cloth into a knot. "I didn't like seeing the deer die," she said at last. "It is—I thought hunting would be... normal, somehow. But something has to die."
Taisin wasn't sure what to say. She thought about telling Kaede that she had seen her first pig butchered when she was a baby; that she had helped every autumn—until she went to the Academy—when her father harvested their meat for the winter. She could say that the deer had died so that they might live, or that its spirit had been released into the world and it would return, again and again, transformed each time into a different being. But it did not change the fact that death came and took things that were not yet ready to leave the world of the living.
She reached out and covered Kaede's hands with her own, and Kaede looked at her in surprise. Taisin felt Kaede's fingers loosen on the cloth; her hand turned upward into Taisin's. Their fingers interlaced. Taisin's heartbeat quickened; a flush crept across her neck. She saw, as if from a distance, that her feelings were changing whether she wanted them to or not. She sensed that she was about to tip over the edge, and at some point, she wouldn't care if she was doing the right thing anymore.
But today, she was still in control. She pulled her hand away, taking a quick, determined breath. "We should go back. I told Parsa I would help her."
Kaede nodded, seemingly unfazed. "Yes. Shae's family has been very kind to us." They stood, and Kaede pocketed the cloth. "I don't think we'll eat so well once we leave."
"We should enjoy it while we can," Taisin said, and immediately felt ridiculous trying to make small talk about surviving the next leg of their journey. But Kaede didn't seem to notice her discomfort. She had started back down the path and turned to wait for her. Kaede was always polite; she was the daughter of the King's Chancellor, after all. Taisin suddenly felt every inch the farmer's daughter—clumsy and foolish.
Taisin balled her hands into fists at her side and followed, keeping her eyes on the ground to avoid betraying her self-consciousness. The path was well maintained, though narrow; the dirt was hard packed in the center, and tufts of brown grasses grew along the edges. And then she saw something that made her stop and turn back. She knelt down on the trail. There was a limp flower bud there, tucked behind a clump of grass—the only splash of purple anywhere in sight. Normally at this time of year, the Wood should be dotted with them, and the sight of this solitary blossom was almost as saddening as it was miraculous.
"Look at that," Taisin whispered. Kaede turned to see what she had found.
Taisin stroked the flower with one finger and bent her head down close to it, trying to breathe in the air around the tiny growing thing. For as long as she could remember, she had been sensitive to all the shifting meridians of energy around her, and her years at the Academy had sharpened and honed her awareness of them. The last two years, with their summer droughts and winter storms, and now the unending grayness, had been heartbreaking. Before, she had been able to sense the life all around her—in the waving sea grasses that grew on the beach below the Academy; in the oak trees that climbed so slowly toward the sky on her parents' farm. It had been a steady hum underlying everything; a feeling of constant renewal. But in the last two years, the hum had faded; the lines of energy had become increasingly sluggish. Even the plants in the ground seemed to have given up. It was like seeing all the color leeched out of the world bit by bit. So, given the faintest whiff of rebirth in the form of these wilted, half-opened petals, Taisin could not resist.
She cupped the flower in her hand and called to it, and as Kaede stood over her, watching, the flower grew plump; the stalk lifted itself from the earth as though sunlight poured from Taisin's breath into its green leaves. The petals opened one by one, each a perfect violet teardrop, and at the center, the flower's black eye gazed unblinkingly up at Taisin, whose face glowed with the energy unfurling through her.
Kaede could have chastised her, for their teachers at the Academy had taught them from day one that such a display of power was reckless. It was the equivalent of lighting a signal fire on the tallest mountain to announce one's presence during a war. But at the same time, Kaede understood why Taisin had done it, for it was written clear as day on her face: It made her whole.
Afterward, when Taisin was too weakened to walk back immediately, Kaede sat with her on the forest floor, watching as the purple flower, gloriously open to the air, bobbed in the wind.
That night it seemed as though everyone in Jilin stopped by Shae's family home. Parsa and Niran seared thin slices of venison and served it with onions cooked until they were sweet. Other villagers brought more of the flat bread, some stuffed with pickled greens or mushrooms culled from the Wood; and one family brought two jugs of home-brewed spirits. Kaede avoided them, for the fumes alone made her eyes water. There was no talk of bad harvests or strange creatures; it was as if everyone had tacitly agreed to pretend that nothing was wrong, and the only thing on their minds was celebrating Shae's brief return home.
Kaede was grateful for the holiday feel; it drove away the shadows that had clung to her since Ento. She played a game of tacks with Shae's nephew; she joked with Tali about how much venison he could eat; she watched Con flirting shamelessly with Shae, who laughed at him and said loudly—so that everyone could hear—that he had no chance with her. But the way she turned her eyes back to him gave a different impression, and Kaede suddenly wondered whether there was something between them. The thought was surprising to her, but also a bit funny. Kaede simply couldn't imagine Shae in court dress at the palace with Con. She grinned to herself and glanced around the room, taking in Pol talking with Tulan, Parsa's two daughters racing out the door with rock sugar in their fists. Taisin was seated at the table chatting to Raesa, a smile on her face. The smile transformed her. Her cheeks were pink from the warmth of the room; her eyes were shining. She was a young woman still unaware of her own beauty, and Kaede could not look away.
Con pushed his way onto the bench beside Kaede and said, "She's lovely, isn't she?" He threw his arm around her shoulders with a brotherly squeeze.
"What?" she said, startled.
"Shae," he whispered in her ear. "Look at her!"
Kaede gave him a sidelong glance. "Are you being serious?"
"I'm always serious," he said, ruffling her hair. It had grown long enough now that she usually tied it back, but tonight she had had the opportunity to bathe, and it fell loose, still slightly damp, to her shoulders.
"Stop it," Kaede said, swatting his hands away and tucking the ends behind her ears. He reminded her of her brothers, and all of a sudden she missed them fiercely.
"Do you think I have a chance with her?" Con asked.
It took a moment for Kaede to remember what he was talking about: Shae. She tried to swallow her homesickness and said with forced lightness, "You have every advantage. Who wouldn't fall in love with you?"
His eyes sparkled as he gave her a mischievous grin. "Do I detect a hint of jealousy? Are you going to fight me for Shae's love?"
Kaede gaped at him. "Now you truly must be joking. Why would I do that?"
"You don't want her for yourself?" He elbowed her. "I know you enjoy her company."
Kaede shook her head. "I take it back," she said, laughing. "You're too much of a fool—Shae will never love you."
He pulled an exaggerated frown. "You wound me, Kaede. Your brothers told me I could trust you—I shouldn't have believed them."
"That's good. I never believe them, either." They laughed together, and Kaede felt the tightness within her relaxing. She would see her brothers when she returned, she told herself.
Con's arm was still around her shoulders, and he whispered in her ear, "I saw you looking at Taisin. She's especially pretty tonight."
A flush spread over her face. "You must have been looking at her, too, then," she said, and Con raised his eyebrows at her in a sly smile.
She glanced away, her eyes seeking out Taisin almost automatically. Taisin was watching them, a thoughtful look on her face. When Kaede's gaze met hers, Taisin colored as though she had been caught stealing sweets. Kaede broke into a smile, and Taisin quickly turned away, ducking her head as if she wanted to hide. But scarcely a moment later she glanced back as though she couldn't help it, and Kaede felt a tremor inside herself as the blush on Taisin's cheeks deepened.
Con squeezed her shoulder. "I see I won't have to fight you for Shae," he said in an amused tone.
She gave him an exasperated look. "She's not going to fall in love with you if you stay here all night with _me_."
He grinned at her. "Good point." He stood up and straightened his tunic. "We must take advantage of tonight, for who knows what shall come tomorrow?"
Kaede watched him head toward Shae, but she did not make a move to go to Taisin. She finished her tea, one ear tuned to the conversations around her, occasionally glancing out of the corner of her eye at Taisin, who had pulled a little boy onto her lap to play a game of peekaboo with a red wooden ball. Kaede hadn't felt that tug toward another person in a long time. She certainly hadn't expected to feel it for Taisin, who was usually so distant and self-contained that any possibility of a deeper connection had seemed impossible from the beginning. But this afternoon, the sight of Taisin's face after she urged that flower to bloom—she had been luminous. It was as if a door had briefly opened, and behind it there was sunlight, warm and rich and seductive.
But Taisin was going to be a sage, and sages made vows of celibacy. Kaede had learned this in her earliest days at the Academy. Students were not permitted to form romantic attachments to each other—at least not officially, though Kaede had not been the only one to break the rules. But Taisin had always adhered to those guidelines. No one had even whispered about her in the dormitory.
Kaede told herself that what she felt was only a little seed; she would simply not water it. It wouldn't grow any larger than this tiny prickle of attraction. She wouldn't let it.
But that night after everyone had left, and they had all spread their blankets on the floor of the hall, Kaede lay awake for some time, trying to make out the sound of Taisin's breathing in the dark.
# Chapter XVII
t began to rain scarcely an hour after they left Jilin. They pulled out their oilskin cloaks, but as the day wore on with no sign that it would let up, Kaede began to feel the wet weight of it like a burden on her back. That morning, Shae's family had seen them off with as much good cheer as they could muster, but it was obvious they had a difficult time fighting their fear that Shae would never return.
Niran had convinced Tali that their wagon would never make it through the narrow trails carved into the Wood, and he traded them two sturdy packhorses for the wagon itself. Pol and Taisin rode the two wagon horses, outfitted with saddles that Tali bought from one of Niran's neighbors. As they picked their way through the dim, drenched Wood, Kaede peered out from beneath the hood of her cloak at the surrounding trees. She felt, again, the eerie sensation of another presence. The farther they rode into the Wood, the more she noticed that there was a peculiar awareness to this place. The oaks might be half dead, but something else was distinctly alive out there.
When it began to grow dark, they set up camp just off the trail; downhill, the river Nir was pregnant with rain. Tali and Pol struggled to set up their tents in the downpour, staking them out between trees as best they could, while Shae and Con took the empty water skins down to the river to be filled. Taisin volunteered to search for bits of dry wood, and Pol called, "You'd better take Kaede with you." He stuck his head out from one of the half-constructed tents. "I don't have a good feeling about this place."
Even though the day had been one long, wet slog through an increasingly muddy forest, Kaede was absurdly pleased about the prospect of taking a walk through the Wood with Taisin. Taisin herself looked momentarily alarmed at the prospect of Kaede accompanying her, but the expression vanished almost instantly, making Kaede wonder if she had imagined it. As they struck off down the trail, Kaede glanced at Taisin, but Taisin kept her eyes to the ground, seeking out sheltered places that might have kept fallen wood dry.
They found a few branches here and there, and piled them into their arms beneath their oilskin cloaks. As Taisin pushed her way through thickets and into hollows, Kaede was surprised by her classmate's apparent disregard for mud. Taisin had always seemed so neat and orderly, not a hair out of place. Now she pushed back a stray lock with dirty fingers, leaving a dark streak on her face.
They came to a clump of hollyberry trees sheltered by a giant overhanging oak, and they bumped shoulders and hips as they reached for kindling beneath the brush. Taisin backed out a bit breathlessly. "You go first," she said, her face flushed. Kaede tried to stuff down the warmth that flared in her when Taisin's body had snaked past hers, and she began to haul out handfuls of twigs, handing them to Taisin.
When their arms were full, they headed back to the camp, and Kaede said with a grin, "You're covered in mud."
Taisin pointed out, "So are you."
Kaede glanced down at herself and laughed; the entire front of her, from her chest down to her knees, was smeared with dark brown. Taisin began to giggle, and then they were both bent over double, clutching the twigs and branches to their chests as they guffawed, their voices ringing in the twilight Wood. Kaede felt a little delirious; she was soaked through, muddy, and darkness was falling. The whole situation should be terrifying, but she felt a kind of helpless surrender to it. Here she was on this journey to a place that didn't exist on their maps, and all around unseen things seemed to stare out at them day and night. But there, not two feet away from her, was a girl who made her feel light-headed.
As their laughter faded they looked at each other, and there was an openness in Taisin's face—a kind of camaraderie—that Kaede had not seen before. It made her skin tingle. She did not think she was doing a good job of letting the seed die.
The rain clung to them for several days. Sometimes there would be a break in the middle of the afternoon, or the rain would turn to mist for a while, but their belongings began to have an exasperating dampness that could not be burned off by their smoky campfire.
On the morning the rain finally stopped, they awoke to a world covered in fog so thick it was difficult to find one another in their small camp. It curled around the trees in ghostly white, seeping through their clothes and into their bones with its chill. But the fire burned hot that morning, and they drank their tea standing up, turning around slowly to warm their backsides. The fog clung to the river Nir all morning, making the trail difficult to see, and it did not burn off until afternoon. That evening, her teeth chattering from cold, Kaede stood so close to the campfire that when the wind gusted, it sent flames dangerously close to her face. She jumped back in alarm, and Tali laughed at her as he eased the iron kettle into the fire.
"Watch out," he warned her. "This wind is not like any I've encountered before. Sometimes it seems to have a mind of its own." The two of them had stayed to set up camp while the others went to gather more wood and refill their water skins.
Shae and Con returned from the river as Tali spoke, and Shae set her heavy water skin down on the ground and sighed, stretching her arms. "I'll take the wind over the rain any day—or night."
"At least the rain drowns out the sound of the wind," Tali said. "Sometimes I swear I hear it calling my name." He shuddered. "I don't like it."
Con looked at him curiously. "What do you mean? Are you hearing things, Tali?"
The guard squatted down and stirred the pot with a long-handled wooden spoon. "I must be. This Wood gets to me; I don't think it wants me here."
"Don't be ridiculous," Shae said. As if her words were an invitation to prove her wrong, the wind whipped around them, ruffling Shae's short hair and making the flames roar.
Kaede felt it like a silken scarf sliding quickly around her neck. She shivered.
Shae glanced at her sharply. "Did you feel something?"
Kaede put her hand to her throat, touching her skin with cold fingers. "I don't know. It was so fast."
They didn't notice, at first, that Tali had cocked his head a little, as if he were listening to someone whisper in his ear. His eyes were slightly glazed, and his entire body seemed pulled in a direction even he was not aware of.
"Tali!" Con called, alarmed.
Tali blinked and let go of the wooden spoon in surprise, and it fell into the fire. "Blast," he said, standing up. "I don't have another one."
"What did you just hear?" Kaede asked.
He looked confused. "Just now—did you hear it as well?"
"I don't know," Kaede said, disquieted. "I felt something, though." She looked at Shae and Con. "Did you hear anything?"
"No," Con answered.
Shae seemed worried. "Not really. The wind seemed a little... odd, but I don't know why."
Tali said grimly, "It's only talking to me, then."
"Who's talking to you?" Taisin asked. She was coming back toward the fire, Pol following her. She dropped an armful of wood on the ground.
"The wind," Tali said. His broad shoulders were stiff with tension as he added, "The Wood itself."
Taisin's eyes widened. "You must not listen. Do you understand? Whatever you hear—whatever they tell you—you must not listen to them."
Tali was taken aback by her intensity. Pol, laying his firewood down, asked, "What's going on?"
Tali said gruffly, "We're just hearing noises in the dark."
Taisin's forehead wrinkled. "Has anyone else heard anything?"
They all looked at one another, anxious faces turned gold by the firelight. The black night beyond the camp had never felt so heavy; the branches of the trees leaned above them like ghosts. For a moment, the only sound was the crackle of the fire. The strange wind had left them.
Kaede finally said, "I felt something."
"What?"
"It—it felt like the wind was tightening around my neck."
Taisin stared at her, fear plain in her eyes. She turned to Tali. "Tell me what you heard."
"It wasn't speaking our language," Tali said, scrubbing a hand through his gray hair. "But it wanted—it wanted me to follow it." He had broken into a nervous sweat, and he wiped his forehead on his sleeve.
"You mustn't follow it," Taisin said.
He seemed a bit affronted. "Of course I'm not going to follow it."
"I just—I'm just trying to keep you safe," she stammered.
"Taisin," Con said, seeing the distress on her face, "have you felt something, too?"
"Yes," she said reluctantly. Whatever it was had been increasing in strength the deeper they traveled into the Wood. At first it had been merely a whisper, as if a feather were lightly brushing against her, but now it came more insistently, like a child pulling at her hand.
"What is it?" Tali asked.
Taisin hesitated. She hadn't known what to make of it in the beginning, for the Wood was full of energies she had never encountered before. It was difficult to separate out this presence from the others, but she was increasingly convinced that this spirit—if that is what it was—had a goal. It reminded her of something she had felt once, but the memory eluded her, like an itch in the middle of her back that she couldn't quite reach. It was irritating and frightening all at once, for she sensed that this presence was not benevolent.
She said carefully, "It is intelligent. There is a purpose to this creature—or this presence. I don't know what it is. But it seems... it wants something. It seems malicious."
"Is it the Xi?" Pol asked.
Taisin thought back to what Sister Ailan had told her and what she had read. It was so bizarre to apply those dry teachings to the eerie reality of this Wood. "Sister Ailan—my teacher—she always described the Xi to me as possessing a presence of great purity. Powerful, of course, but pure. Not hot or cold; not emotional; simply _there_. Pure. This presence that I feel is not pure. I don't think it is the Xi."
Tali asked, "What do you think it wants?"
"I don't know."
"How can we protect ourselves, then?" Con asked.
Taisin turned to Tali, expecting him to answer, but the guard was looking at her with a reluctant expression on his lined face. "Taisin, you know the most about this of any of us."
Taisin realized he was relying on her now, and she felt paralyzed. She hadn't even been marked yet. She might be the most gifted in her class, but she was still a student. All at once the gaps in her knowledge seemed too great, and a cloud of panic engulfed her. How could her teachers think she was ready for this? She was only a frightened schoolgirl. She felt faint, and pressed her fingers between her eyes. She took a deep breath, and another. She could not crumple into a puddle of fear—that was not why her teachers had believed in her.
"We must stay together," she said, her voice wavering at first. "If you hear anything speaking to you—in the wind, in your ear, whatever—just ignore it. And tell someone. Don't leave the camp alone." She looked over her shoulder at the dark. It was alive with energies she hadn't yet teased apart, but one of them was waiting and listening. Taisin turned back to the others. Her mouth was dry as she said, "Promise me. Don't leave the camp alone."
They all agreed, and their nodding shadows rippled across the trees.
Wrapped in her bedroll that night, the chilly air seeping through the thin canvas walls of the tent, Kaede longed for the dry heat that used to bake the streets of Cathair in the summer. She dreamed of sunlight spreading like honey over her skin; she dreamed of sweat sliding down between her shoulder blades as she ran down sweltering alleyways behind the palace. She dreamed of Taisin, standing in the shade of a stone building at the end of a maze of narrow streets, a bouquet of flowers in her hands like the prize at the end of a race. But no matter how fast Kaede ran, she couldn't quite reach her. The muscles in her legs groaned with the effort; her lungs heaved; she woke with a jerk, gasping.
Beside her Shae shifted, turning her back to Kaede. It was the middle of the night. Kaede's heart was pounding, her skin flushed as if she had truly been running. She flung off her blanket, feeling overheated. What had awakened her? She wanted to go back into that dream world. She wanted to reach Taisin, take the flowers out of her hands, touch her. A wave of longing rushed through Kaede's body.
She turned over, looking past Shae toward Taisin. She could barely make out her silhouette in the dark, but she could hear her breathing. It was uneven. Was Taisin awake, too? The thought made Kaede's skin prickle all over with excitement. It seemed impossible that Taisin could sleep through this—every nerve in Kaede's body was screaming for her to notice—but there was no answering sound or movement from Taisin.
Kaede lay awake for some time. She was tense from her dream. She counted her breaths, attempting to make them regular. She lost count. She listened to the sound of wind in the trees, remembering Taisin's warnings, but she heard nothing out of the ordinary. She did not realize she had fallen asleep again until she was awakened by shouting outside. Someone was calling for Tali.
Shae scrambled up first, pushing aside the tent flap and stumbling into the dim morning, pulling on her boots as she went. "What is it?" Shae asked, and outside Con and Pol were standing, dazed, near the ashes of the fire.
"Tali is missing," Con said, panic thick in his voice. "When we woke up this morning, he was gone."
# Chapter XVIII
t was Shae who found him. He was lying in a clearing barely fifty feet from their camp on the other side of the trail. Dried leaves encircled his body as if blown by a great whirlwind. He lay on his back, arms and legs spread-eagled, his face expressionless. A strange gray dust was trapped in his salt-and-pepper beard, and a thin white film had crawled over his open brown eyes. He was cold to the touch, and there was not a mark on him.
Con knelt on the ground next to Tali's body and lifted the older man's hand. His fingers were stiff. Con was stunned; he couldn't believe that Tali was dead. He had survived so many military campaigns; how could he have been taken so easily, so silently, by—Con didn't even know what had taken him. "Who—what did this?" he demanded.
All the color had drained from Taisin's face. She knelt beside Tali's head, stretching her hand out over his eyes. She felt nothing. There was no life energy left within him; his body was only a shell now. And she did not know whether his soul had safely traveled to the other side. The thought chilled her to the bone, and she muttered to herself, "I should have done it."
Con looked at her. "You should have done what?"
Guilt washed over Taisin, hot and sour. "I could have—I should have done a protection ritual. Around the camp."
Con's mouth opened, but he couldn't speak. A torrent of emotion battered at him: disbelief, grief, anger. Was Taisin saying she could have prevented this? He felt like he had been punched in the gut, and he had trouble breathing.
Shae squatted down beside him and squeezed his shoulder. She asked in a carefully measured voice, "Why didn't you?"
Taisin gulped, her heart pounding. She said in a rush: "My teacher told me that I shouldn't use that ritual except as a last resort. I didn't know this could happen. I thought we would be safe enough if—if we didn't leave the camp." Tears pricked at the corners of her eyes, and she blinked them back fiercely.
"Can you do that ritual now?" Pol asked. He stood at Tali's feet, his arms crossed.
"I can do it tonight when we set up camp. I can't protect us as we are moving."
"Wait," Shae said, frowning. "Taisin, why did your teacher warn you about the protection ritual?"
Taisin drew in a trembling breath. "Because it—it might draw attention to us."
"What do you mean?" Pol asked.
"Weaving a protection ritual around our camp would... rearrange the natural meridians. Those who are sensitive to the lines of energy would—if they are near enough or powerful enough, they would notice."
"The creatures we've seen," Con interjected, struggling to make sense of what she was saying. "Can they sense these things?"
"I don't know. I suppose... it's possible."
Kaede understood, suddenly, the reason for the hesitation in Taisin's voice. "You think that by doing the protection ritual, you'll draw them to us."
Taisin met her eyes somberly. "It has occurred to me."
"But what's the alternative?" Con asked. "Tali was—" His voice broke, and Shae slid her arm around his shoulders. Con wiped away the tears that burned down his face. "Tali was stronger, I thought, than all of us. For this to happen to him... We can't let it happen again." He looked across Tali's still form at Taisin, and he noticed how young and vulnerable she looked today, with purple shadows beneath her eyes and her narrow shoulders slumping. He realized that he had been on the verge of blaming her for Tali's death, but he couldn't. She was only seventeen. She had done the best she could. He felt a yawning ache inside him as he said to her, "You have to do it tonight, Taisin. Whatever protection ritual you can. We'll deal with the consequences when they come."
Taisin's lips trembled, but she squared her shoulders. "All right. I will do it tonight. But first, we must leave this place. And we must bury Tali."
"Here?" Con said.
"No. This place is—it isn't right. We must take him with us, but we have to bury him before nightfall."
None of them disagreed. It was the worst kind of luck to leave a dead body in the open overnight—especially when the person died of unnatural causes. And though there were no signs of struggle on Tali's body, there was no doubt in any of their minds that his death had been far from natural.
When they broke camp, they strapped Tali's body, shrouded in his woolen blanket, onto his horse. Tali had always ridden in the lead before, but today Shae took his position and his map case. Con followed her, leading Tali's horse, and Taisin and Kaede came after him. Pol went last as usual, keeping one hand on his sword.
As they rode, Taisin stared at Tali's body, hanging facedown over his horse's flanks. Part of her still couldn't quite grasp it. How could _Tali_ , of all people, have been lured away so easily? He was so solid, so dependable. Why had the Wood—or whatever was in the Wood—chosen to take him? And if it could take him, what would it do to the rest of them? The questions made her increasingly nervous, and the queasiness in her stomach rose until she abruptly pulled her horse to a halt and dismounted, running off the trail to bend over, retching. Nothing came up, but she felt like she was turning inside out, and her throat burned.
A moment later she felt a hand on her back, and Kaede was leaning over her. "Are you all right?"
"I'm fine," she gasped.
"Here," Kaede said, handing her a water skin. Taisin tried to breathe more slowly. She was panicking. She knew she had to calm down. She heard Kaede saying to the others: "Just give us a minute."
Taisin straightened up, feeling woozy. Her face was flushed, and her hands shook as she raised the water skin to her lips. The liquid trickled into her mouth, and she swallowed carefully. "I'm sorry," she muttered.
Kaede shook her head. "There's nothing to be sorry about."
"Yes, there is. If I had done the protection ritual, Tali would still be here." Taisin spoke without thinking, and now that the words were out, she was both ashamed and relieved.
"You don't know that," Kaede objected.
Taisin turned to face her. The dull gray daylight carved deep shadows beneath Kaede's eyes and darkened the hollows in her cheeks. She didn't look like the same girl who had argued with the King's Chancellor in the Council room, demanding that she be given a choice. She looked bruised. She looked sad. "What are we going to do, Kaede?" Taisin whispered. "This wasn't supposed to happen. What if Maire Morighan was wrong? What if I can't do whatever it is I'm supposed to do? What if I don't know enough?"
Kaede heard defeat hovering at the edge of Taisin's words, and it tore at her. "You know enough," Kaede insisted. "The oracle stones would not have chosen you if you didn't know enough. And what's 'enough,' anyway? You don't know everything, but nobody can." She heard herself repeating what Fin had told her on the beach at the Academy: "All you can do is make your decisions based on what you know now."
"What I know now," Taisin repeated. What she knew now was that this journey was much more dangerous than she had anticipated. Perhaps she had not wanted to acknowledge that before. In Ento, she had called that creature out of the baby's body, but it was Kaede who had faced the consequences. Now Tali's death had driven home the fact that there was a malignant force out there, and she knew she had to open her eyes and look it in the face. It frightened her, but she had never fled from something because she was afraid. Going to the Academy alone when she was eleven, leaving her family behind, had terrified her. The vision of Kaede on the beach still scared her. But she knew what to do with fear: She fought it.
"You're right," Taisin said to Kaede. "Thank you."
Before she could doubt herself again, Taisin headed back to the trail, ignoring the panic that still churned in her stomach.
Just before noon, they found a roughly rectangular clearing a few feet off the path, with soil that looked like it could be broken with their makeshift tools. Taisin fitted one of their few remaining candles into a lantern and lit it, setting it on the ground where the head of the grave would be. The light was meant to guide Tali's soul to the land of the dead. Usually sages did not perform funerary rites; that responsibility typically fell to village greenwitches or, in the cities, to specialists. But there were no specialists here. Everyone did their part.
Taisin helped Shae and Kaede dig the grave while Con and Pol wrestled with Tali's body, dressing him in his cleanest clothes. The mysterious nature of his death was unlucky enough, but it would be even worse for him to be buried in the clothes he was wearing when he died. They lugged water from the river and washed his hands, but they could not remove the dirt from beneath his nails. They sponged off his face and neck, closing his eyes and covering them with a blindfold torn from Tali's cloak. And then Taisin found a stone on the riverbank that had a particularly peaceful energy, and she handed it to Con.
"His death was not... natural," she said awkwardly. "It would be best to place this in his mouth."
He looked sick to his stomach, but he nodded. Tali's body had stiffened by now, and it was difficult to pry his jaw open. Con feared for one awful moment that he might have to break it, but then, at last, Tali's mouth opened just enough, and Con slid the stone between his cold lips.
Afterward, Con had to sit still, holding his head in his hands, trying not to throw up.
It was late afternoon by the time the pit was deep enough, and the light was becoming dim. Dirt smudged all of their faces where they had wiped away sweat that had risen while they dug. Tali's body had been wrapped into his blanket again—the closest they could come to a shroud—and Con and Pol rolled it as gently as they could into the grave. The candle flickered within the lantern as if a breath had blown against it.
Con sat back on his heels and looked at the rest of them. "It's time."
They each scraped up a handful of dirt and, beginning with Con, sprinkled it into the grave. The sound of dirt pattering onto Tali's body reminded Con of rain on the roofs of Cathair: hard and cold. A wave of loss threatened to engulf him; he curled his fingers into fists, feeling his nails pressing into his palms. The others began to push the loose soil back into the grave. In the background, he heard Taisin murmuring. The words were familiar; he had heard them before, at funerals. As she repeated them, Kaede echoed her, and then Pol and Shae. Their voices, low and sorrowful, lifted the words of the lament into the heavy stillness of dusk in the Great Wood.
> _This fleeting world:_
>
> _Life passes as quickly as the morning star,_
>
> _As a rumble of thunder,_
>
> _A gust of wind over the grasslands._
>
> _This fleeting life:_
>
> _Brief as a spark,_
>
> _Ephemeral as a dream._
>
> _Soon enough we are ghosts upon the cloud._
# Chapter XIX
hey left the lantern burning at Tali's grave while they set up camp. Taisin walked in a circle around the perimeter, marking it with stones or branches. "Bring everything we'll need into this circle," she told them, "because after I set it up, no one will be able to leave without breaking the boundary."
"What about Tali?" Con said. "I want to sit vigil with him tonight."
Taisin had taken out her small brassbound trunk and opened it, but now she paused with her hand on a glass vial. "It's not safe, Con."
"Tali was like a father to me," he said. "I owe him that respect."
Taisin saw the sadness that dragged at his shoulders; his ashen face, drawn with grief. She knew that he would do it whether or not she agreed with him, so she said, "Then I will sit with you."
"Will you extend the circle of protection to the grave?" Con asked.
"I can't. The space around it must be open, so that Tali's soul can travel freely." She didn't tell him that she suspected that Tali's soul had departed long before any of their burial rituals.
Con eyed her closely, as if he guessed that she was holding something back, but he didn't question her further. "All right. We'll sit vigil together. Let me know when you're ready." He went to help Pol set up their tent, leaving Taisin kneeling on the ground.
Her fingers shook slightly as she took out the herbs that she would need for the ritual. Sister Ailan had given her these supplies for this very reason, but Taisin had never actually believed she would need them. Milk-vetch root, dried and ground up in yellowish-brown crystals, for strength. Fox nut, pounded into a pale powder, for life energy. The barest sprinkle of dragon bone scrapings, like minuscule white petals, for power. Taisin combined them all in an iron bowl, stirring them together with her index finger. The powders seemed to glitter a bit, just as Sister Ailan had told her they would. The mixture was ready.
She asked Con to stand just outside the perimeter, and she placed Shae, Pol, and Kaede at three places along the interior of the circle. It would have been better if there were a fourth person, so she could create a full compass, but they would just have to make do with three points tonight. Holding the iron bowl in her hand, Taisin walked to the northernmost edge of the circle and closed her eyes, standing still. She had performed smaller protection rituals before, but never one this major, or as important. Sister Ailan had explained it to her and assured her that she could do it, but this was no Academy examination, where she might be forgiven for making a mistake or two. Taisin's heart raced as her nerves nearly got the better of her, making her hands clammy. She took a deep breath and tried to calm herself.
First, she had to find the way in. That was how her teachers always described it: being sensitive to all the currents of energy around her until she discovered the one that called to her—the one that was her own special path into the unseen world. Meridians of energy ran through every human being and animal and plant; they lay in limitless lines in the earth and the air like a vast web. Every living thing had its place in this field of energies. The protection ritual would reshape portions of that field, reweaving the net into a barrier around their camp.
If only she could do it. Every time she thought she had found the way in, it slid away from her. She was like a fisherman trying to reel in his catch, but it leapt away from him time and time again, splashing back into the sea.
And the wind that had whispered in Tali's ear was everywhere, distracting her. It slipped beneath her collar, tickled her earlobes, caressed her skin in cool, lingering breaths. It took every effort to ignore it, to focus instead on the elusive thread of energy that had come so easily to her when she had seen that purple flower. The thought of the flower helped, and she envisioned it in her mind's eye; she could feel the life of it, pulsing. And then she had it. She felt the humming threads of life all around her, and they were different here, deep in the Wood. There was still something not quite right about them, but they were a thousand times more vibrant than they had been in Jilin. She plucked one strand out—easy as tucking a lock of hair behind her ear—and began to weave it around their camp as she walked, eyes closed, for she didn't need to see the ordinary world when she could see, instead, the extraordinary one.
At the north, south, east, and west points of the circle, she sprinkled some of the powder on the ground. She said, "Peace within, darkness without." The powder burned into the ground like fox fire. Taisin walked around the perimeter of the camp three times, and each time she felt the web of protection tightening. It was exhilarating. She felt all of the energies she controlled at her fingertips: such incredible power. She was connected to the heartbeats of every living creature in the Great Wood; everything wanted so fiercely to live, even the trees that seemed half dead.
On her third circle, Taisin stopped before each person. She opened her eyes, looking directly at them, touching her fingers to their hearts, murmuring, "Peace within, darkness without." Pol's heartbeat was strong within him. Shae was worried; her breathing was quick and anxious. Kaede was tense as well, and when Taisin reached out to touch her, she felt a jolt pass between them. Taisin was so startled she almost faltered in the ritual.
To her surprise, Kaede reached up and covered Taisin's hand with hers. Taisin pressed her palm against Kaede's heart. She felt it speeding up until it matched the pace of her own. She was breathless. Kaede's eyes were light brown; Taisin saw her pupils dilating as they looked at each other, dusk spinning out around them, cloaking them in shadow. She wished she could stay there forever, the space between them freighted with possibility.
But she had to complete the ritual. She whispered, "Peace within, darkness without."
And then, reluctantly, she closed her eyes again. She saw Kaede, Pol, and Shae bound within a circle of energies like creatures caught in a spider's web. She pulled herself away from Kaede, feeling the link between them stretching like a gossamer thread. She made her way back to the place where she had begun, and she set down the iron bowl, pressing it into the ground.
When she straightened, she folded her hands before her lips and bowed first to the circle, then to the dark Wood beyond. It was done.
At the head of the grave mound, the candle still burned. Taisin sat on one side of it with her hands folded in her lap, and Con sat across from her. She had never kept overnight vigil at a grave before, and she knew she was not in the best condition for it. She was drained from the protection ritual and from the day itself. The hard, cold ground pressed sharply into her shins, and the dreadful wind was worrying at her hair.
Con shifted in the dark, uncrossing his legs and trying to find a more comfortable position. As time passed, he began to nod, weariness overcoming him. "Con," Taisin whispered, and he jerked himself awake.
"I'm sorry," he said. His tongue felt heavy and thick; his senses dulled.
"It's all right," Taisin whispered. "Just—don't fall asleep." She spoke as much for her own benefit as for his, for the air here was ripe with magic. Some of it was residue from the circle of protection she had woven, but some of it was darker, more malevolent. She was not certain, but she thought she recognized a thread or two of this other magic. It had a very distinct, unusual scent: like winter. It was the smell of that fortress of ice.
The visions had come more often since she entered the Wood, and sometimes they came at particularly inopportune moments. When she was riding, sometimes she would suddenly glimpse dark brown skin, mottled like lichen. Or when she was gathering firewood, she would catch sight of that winged creature again, flying high against icicles hanging like teeth from a cavernous ceiling. It would only be the briefest glimpse, and then she would snap back into reality, knocked slightly off balance, and Pol or Kaede or Tali would ask her if she was all right. Her heart sank at that memory. Tali would never speak again.
She looked across the grave at Con; his body was rigid, and his wide-open eyes reflected the flicker of the candlelight. He no longer seemed in danger of falling asleep. He shivered as if someone had run a finger down his back, and for a moment, he cocked his head to the right, listening. "Con," Taisin said, her voice a whip crack in the stillness.
He jerked. "What?" he said hoarsely.
"Look at me." Taisin was almost certain that something was trying to lure him away, just as it had done to Tali. "Are you hearing something?"
"I don't know." He felt a caress on his cheek; he wanted to turn his face into it. It was as seductive as the sleep that had dragged at him earlier. But he struggled against it, trying to fix his eyes on Taisin. The tiny light of the candle only served to make the Wood beyond seem blacker, a spill of ink on black paper. How could it possibly be enough light to guide Tali's soul to the other side?
Taisin could sense the energy around Con; it was charged with frustrated desire. She felt it gathering in strength, like massing thunderclouds, and then it turned its attention, abruptly, to her.
She was nearly knocked over by the power of it: a gale-force wind, ice-cold, biting into her face and pulling at her clothes. Long, wordless screams buffeted at her, and she clapped her hands over her ears to protect herself from the sounds. She stared in horror across the grave, trying to anchor herself to Con, who was gaping at her. He said something, but she could not hear him. She wanted to run, but she did not dare leave the light of the candle, and she would not leave Con.
She remembered, suddenly, what had been so familiar about the wind that had come teasing at her hair earlier. Now she had only a younger sister, but there had been a time when she also had a younger brother named Sota. He was Suri's twin, and when Taisin was ten years old, Suri and Sota fell sick. Suri recovered, but Sota did not, and died. After his death, her father and mother sat vigil beside his still little body all night. Four-year-old Suri hadn't understood what was going on, and Taisin had been charged with taking care of her. She crawled into bed with her, listening while Suri mumbled the name of her brother in her sleep: _Sota, Sota, Sota_. The word was a hypnotic rhythm. It lulled Taisin into an uneasy sleep of her own, cuddled next to her little sister.
She woke later that night to hear voices—despairing, yearning voices. She felt fingers running along her arm, touching her. If the wind could form itself into hands, that was what it felt like. She went rigid with fear, goose bumps rising all over her body. Suri was still asleep, but sweat dampened her brow as if she had broken into a fever. Suri's hair was being lifted as though someone were running their fingers through it, smoothing it back from her face. Taisin was terrified. She muttered her sister's name; she gripped Suri's shoulder and shook it.
Suri opened her eyes, and the wind ceased. Warmth flooded into the room, and Taisin realized that it had been freezing before—how could Suri be sweating?
"Sota?" Suri whispered.
Taisin put her arms around her sister, trying to rock her back to sleep. "Shh," she murmured.
"Ghosts," Suri said. "Ghosts."
Those ghosts, frightening though they were, were nothing compared to what circled Taisin now. These were different. These were much more powerful. They had been wronged.
But now that she understood what they were, she felt calmer. She knew what to do.
She removed her hands from her ears. They shrieked at her, their voices pounding into her head. "Stop it!" she cried.
"Taisin!" Con was calling her name. He was trying to stand up, but he could not move. Something was pinning him down.
"It's all right," Taisin said. "It's all right." And then she said to the circling ghosts: "I will listen to you."
Instantly, the Wood disappeared; she plunged into a world of vivid color. Everything was richly green: the color of newly budded leaves, of luminescent moss, of every possible shade of pine needle. And then she was in the middle of the ocean, carried by warm currents, the water changing from sea green to midnight blue as she sank from the surface into the depths. She had fins; she was as slick as a porpoise. She broke into the air; she was on top of the tallest tree; she was the tree itself.
The images were confusing at first, until she finally understood that she was experiencing the lives of each of the ghosts speaking to her. These were not the lives of humans, and she knew with absolute certainty that they were not the lives of animals, either. These were fay, creatures who inhabited the trees and the rivers, the seas and the hills. They had lived lives that were full of wonder, and now their lives were over.
She was thrust into darkness. When she could see again, she was cold all over. She saw golden bars. She heard the dragging shuffle of someone pacing in a tiny cage. She had never wanted to be free so badly. She wanted to strike at the bars with her bare hands, but the metal cut her skin. Black blood dripped from the wounds in her side. Something had been torn out of her. She bent over, falling onto her knees, feeling the icy floor beneath her.
They had been wronged.
Taisin's eyes flew open. She was still standing beside Tali's grave. The night was not over. She gasped for air as if she had been underwater.
Con had moved; he was now standing directly in front of her. His hands gripped her shoulders.
"Taisin," he said. "Taisin."
"I'm here," she whispered, dazed.
He loosened his grip on her just slightly. "Are you all right?"
She shuddered. "Yes."
"Did you see something?"
She realized he had no idea what she had just experienced. "They're ghosts," she said.
A shiver ran down Con's spine. He looked beyond Taisin, but there was nothing but darkness.
Taisin reached up and pulled his hands from her shoulders, holding them in hers. "It's all right," she said. She felt the energy of the ghosts dissipating. She had satisfied them for now, but ghosts always returned until their wrongs had been righted. She only hoped they would not return tonight.
"Is it safe here?" Con asked.
She almost laughed. "Safe? No. But we must stay. We must stay with Tali until dawn." He began to pull away from her, but she did not let him go. "Sit here, right here, with me."
And so they sat together until the dawn light came, pallid and gray, and they saw that the soil of Tali's grave was newly rimed with frost.
# Chapter XX
hen Taisin and Con returned to camp, Shae had brewed strong black tea for them, and Kaede and Pol had already disassembled the tents. While they waited for the rice porridge to cook, Taisin told them what had happened the night before.
"Ghosts," Pol muttered. "Just what we need."
"There are many of them," Taisin said. Her legs ached from sitting all night in the cold. "It's still not safe for us out there. We have to stay together at all times."
"Is that what took Tali?" Pol asked.
"I don't know," Taisin said. "Maybe. They were not happy spirits."
Before they departed, Taisin had to release the space where they were camped back to the Wood. She retraced her steps around the perimeter of the camp three times, grinding the remaining powders into the forest floor. She felt the meridians of energy springing back like strings snapping into position; it made her skin feel red, chapped, as though she had been scoured by a dry wind.
The days that followed were gray and heavy, as if Tali's death was a dark cloud surrounding them. They decided to set one of the packhorses free; Shae believed he would find his way back home to Jilin. They transferred the supplies to the wagon horse that Pol had been riding, and Pol rode Tali's horse instead. On the mornings that Kaede found time for target practice, Pol pushed her harder than he had before. She understood why: The bow was a weapon, and without Tali, they were one guard less.
For Kaede, the one bright moment in each day came at the end, when Taisin wove the circle of protection around their camp. Every time Taisin put her hand on Kaede's heart, warmth bloomed between them, pushing back the dark night just enough to give them room to breathe together. Kaede found herself waiting for Taisin's touch all day, turning the memory of it over and over again in her mind as they rode through the wild Wood. Every night, she felt the link between them thickening, ripening: at first a slender shoot, and then a vine that curled around them, strengthening each day. She began to wonder if Taisin might feel it, too, but Taisin never said a word about what happened between them during the ritual.
Taisin was afraid to acknowledge it. From the very first time she performed the ritual, she had known that the connection between the two of them was different than what she felt with the others. As the days passed, she became gradually aware that Kaede knew it, too. The realization thrilled her, but it also raised the specter of her vision. It shook her to know that this ritual that should protect them all was also doing the one thing she wanted to avoid. And yet, part of her—a growing part of her—wanted only to nurture the delicate bloom between them.
Sometimes that desire would subside, and Taisin thought she might succeed in preventing her vision from happening, but then her feelings returned at the most unexpected moments. When Kaede brewed tea for everyone, she took care to hand a cup directly to Taisin. Their fingers brushed together against the hot metal, and the thread between them drew tight. Taisin turned away with studied casualness, trying to hide the rising color on her cheeks. She tried to remember that she did not want to fall in love with Kaede, but more and more, she forgot. She forgot to avoid lingering near Kaede when they paused to rest during the day. She forgot to put space between them when they sat by the campfire at night.
One morning Kaede awoke to discover—her head still full of the mustiness of sleep—that Taisin had curled up beside her in the tent they shared with Shae. The warmth of her body was comforting, for the dawn air was cool and slightly damp. As she turned onto her back, Taisin moved, too, burrowing her head into Kaede's shoulder, and Kaede blinked her eyes open, feeling suddenly, acutely aware of Taisin breathing so close to her. And then Taisin shifted, stretching as she awoke, and her entire body slid against Kaede's side. At first, still half asleep, Taisin levered herself up on one elbow and looked at her, and at that moment Kaede could have reached up and pulled her back down again—but then Taisin woke completely, and she blushed so deeply that the tips of her ears went pink.
She scooted away as quickly as she could, mumbling something apologetic, and almost tripped over Shae as she stumbled out of the tent.
Shae, who was just waking up, rubbed her face and muttered, "What's going on?"
"Nothing," Kaede whispered, closing her eyes. Maybe if she didn't get up right away, she could slide back into those delicious moments before Taisin awoke. Her whole body was tingling. What would she have done if Taisin hadn't left so abruptly? She would have kissed her. Even with Shae right there beside them, she would have done it. The thought made her feel like fire had erupted over her skin.
She threw off the blankets. She needed to get out into the cold morning. She crawled out of the tent, ignoring Shae's protests as she climbed over her.
Outside, her breath misted into the air; the whole camp was surrounded by fog. There was no sign of Taisin.
Con was stirring the fire. He looked up at Kaede's abrupt arrival. "Good morning." His brows drew together. "Are you all right?"
"What? I'm fine." She shoved her feet into boots, bending over to lace them as she asked, "Where did Pol and Taisin go?"
"To get more water."
"Oh."
Con grinned at her. "She'll be back soon enough. Would you like a cup of tea?"
Kaede turned red. But she accepted the battered metal cup with as much dignity as she could.
Pol and Taisin took much longer than expected, and by the time they returned, Con, Shae, and Kaede were standing nervously beside the fire, staring down toward the river and thinking uneasy thoughts. "We were beginning to worry," Con said, unable to hide his anxiety. Taisin set down the heavy water skin she was carrying, and her eyes flickered immediately to Kaede, who looked relieved to see her.
"I apologize," Pol said, kneeling to pour water into the kettle. "I saw something, and I had to find out what it was. Taisin wouldn't let me go alone."
"What did you see?" Con asked.
"Something is following us," Pol said.
"Something?" Shae repeated, eyeing the trees warily.
"Yes. I don't know what it is. But it's not human."
# Chapter XXI
n the third night after Pol's announcement, their followers finally showed themselves.
It had been drizzling all afternoon, and lighting the fire was an ordeal that put everyone in a bitter mood. They ate their supper in silence, huddled beneath oilskins as the rain dripped down, hissing, into the fire. They slumped over their food, tired and vulnerable. Even Pol, who had been so vigilant, did not notice that they were slowly being surrounded. It was Kaede who looked up after finishing her meal and saw the eyes in the dark. She stiffened just like a deer noticing he was being hunted.
"Pol," Kaede said in a harsh whisper.
He looked around sharply. Several pairs of yellow eyes glowed in the dark, reflecting the light of the fire. Shae and Pol reached for their weapons at the same time, standing up to face the dark.
"What are they?" Taisin asked in a small voice.
"Wolves," Pol said. "Will the circle of protection keep them away?"
"I don't know," Taisin said. "The circle is meant to keep out harmful magic, not—not wolves."
"But it's also meant to protect us," Pol said. "Isn't it?"
"Yes. We should stay within it while they're out there."
They sat up all night, looking out at the eyes looking in at them. Their initial fright turned inevitably to weariness, for the wolves did not seem to be interested in advancing. Kaede had the eerie suspicion that they were merely there to watch them, to assess their strengths and weaknesses. Sometimes one of them looked directly at her, and she was startled by how intelligent the gaze was.
As morning approached, the wolves began to melt away, and when dawn finally broke and there was light enough to see beyond their campfire, there was no sign of them. But all around the circle of protection that Taisin had woven were long paw prints in the rain-dampened ground, where the wolves had paced.
They had barely been in the saddle for an hour that morning when Kaede caught sight of the wolves running through the trees about fifty feet away, roughly paralleling the path. They stayed downwind of the horses, who had not yet noticed them. Pol, who was bringing up the rear, sped up briefly to ride alongside her. "Take this," he said, handing her his bow and quiver.
"What about you?" Kaede said, slinging the quiver onto her back.
He drew out his sword. "I'll need more mobility. You stay with Taisin."
Kaede nodded, trying to ignore the fear that bubbled in her stomach as Pol dropped back again. The trail was so narrow that they were riding single file. Shae was first, followed by Con, who was leading one of the packhorses. Next came Taisin, also leading a packhorse, and then Kaede; Pol rode last, his sword resting on his thighs.
As the morning wore on, Kaede began to suspect that these wolves were not entirely ordinary. They were practically flaunting themselves now; every once in a while one of them would break away from the pack and come closer to the path, either to get a better look at them or to demonstrate how bold they were. Kaede counted at least a dozen wolves, though she could not be sure, for they blended into the mottled brown of the Wood as if their coats had been made for this purpose.
Being constantly on guard after a sleepless night was a good way to render one's muscles stiff and clumsy, and that was the way Kaede felt when the wolves finally moved in. She wasn't sure what she had expected, but she knew she had not thought they would go after Pol first. He was clearly their strongest member, and he was riding Tali's horse, a great black stallion trained for battle. When she heard his horse cry out, she was so startled that she almost dropped the bow. By the time she fumbled an arrow out of the quiver and twisted in Pol's direction, he was already slashing his sword down at the wolves that had surrounded him in a ferocious, snarling wave, isolating him from Kaede and the others. One wolf sank his teeth into the horse's neck, and another bit into Pol's thigh, releasing a thick stream of red blood. He screamed, but he kept fighting, clinging to the back of his horse.
Kaede's fingers trembled on the fletching of an arrow. The wolves' brindled backs were a sea of matted fur and muscle between her and Pol. She knew that all those mornings in empty stable yards came down to this instant: the instinctual motion of hand to arrow to string—and release—and the arrow plowed into a wolf's chest, knocking him down. Kaede's blood pounded in her ears. There was no time to think; the wolves did not stop coming. She nocked another arrow, and another. Her nostrils filled with the beasts' stench.
Out of the corner of her eye she saw the packhorse tied to Con's saddle tear free from his lead rope, fleeing into the trees. Two wolves sprinted after him, and he never had a chance. They brought him down as easily as they might bring down a much smaller deer, and they howled their victory.
Con's stomach reeled as he watched the wolves tear into the packhorse; they had split into two mobs, one surrounding the horse, the other surrounding Pol. Kaede was trying to pick off the wolves around Pol, but she couldn't shoot too close to him. Con's fingers were sweaty on the hilt of his sword. Pol needed help.
"Stay with Taisin!" Con shouted at Shae, and doubled back through the trees parallel to the trail, heading toward Pol. As he approached the melee, a wolf charged him. Yellow teeth bared, she launched herself at Con's horse, who reared and struck at her with his iron-shod hooves. Con's own blade whistled in the air. He held on to his horse with his knees and slammed his sword into the wolf's shoulder. The beast's snarl turned into a whimper; Con ripped his weapon out and struck again, drops of hot blood stinging his hands. The creature collapsed, her rank scent filling the air. When Con looked up to find his next target, he saw two wolves yanking Pol from his horse onto the ground, and the guard's body disappeared beneath the pack.
"Pol!" he screamed.
Taisin heard him, and she twisted in her saddle to see Con trying to fight his way closer to the fallen guard. Terror engulfed her. Kaede was shouting at her; she was raising the bow, and an arrow flew frighteningly close to Taisin, making her flinch. It lodged in the flank of a gray wolf scarcely twenty feet away. That was when she noticed more of the beasts emerging from the trees and loping almost casually in her direction.
She could feel them: They were all hunger and vicious need. They were meant for this—to hunt and to kill—and there was a frightening beauty in their sharp golden eyes and powerful jaws. It was the beauty of a creature fulfilling her exact purpose in the world, being the precise thing she had trained her whole life to be.
The moment the first wolf leapt at her, Taisin acted entirely out of instinct, driven by panic. She had never used her knowledge of magic as a weapon before, and she knew there were proscriptions against it. None of that mattered when faced with a slavering wolf.
She forced her way into the fields of energy around her, tearing out fistfuls of the power that lived in every plant and animal, and she flung it at the wolves, knocking them down like paper dolls.
It was as easy as plucking ripe fruit from a tree. She felt like she had been born to do this. Her entire body thrilled with the power running through her. All the meridians of energy that ran across the Great Wood buckled beneath her touch. And the wolves began to run from her, yelping in fear.
Kaede stared at Taisin in amazement as she slid down from her horse, striding off the path toward the wolves. She raised her arms, flinging something at them that Kaede could not see. Whatever it was, it struck them like great punches, and Kaede saw one wolf's rib cage collapse, while another's snout was smashed, blood arcing through the air.
Taisin's eyes were shining, her hair coming loose. White light pulled at the ends until they swirled around her head in a black cloud. She looked like she was possessed by something as ferocious as the wolves themselves, and Kaede was chilled by the expression on her face. Taisin looked inhuman—powerful and frightening and hard as ice.
The wolves outside the radius of Taisin's power lifted their heads, looking in her direction. They backed away with deep-throated growls. It was as if a lightning storm had settled over her, and they wanted no part of it.
As the wolves retreated, Shae left the path to ride back toward Con and Pol, her blade dark with blood from the wolves that had left the fallen packhorse to find new prey. She did not see the ones who ran silently out of the trees east of the trail, and within an eyeblink, dragged her off her horse.
Shae screamed as the wolf bit down on her ankle; she tried to kick at him. Her horse reared, but it only loosened her from her saddle. She slid awkwardly, one foot caught in the stirrup, one hand tangled in her reins, and she tried to drive her sword into the wolf who had bitten her. It glanced off his shoulder, and then she was on the ground, her free hand scrabbling in the slightly damp earth, her cheek scraping against the soil. The wolves, their saliva dripping from hungry jowls, came for her.
Shae was fifteen feet away from Kaede when she was attacked. The space between them was a straight shot, and as one of the wolves raised his head to look at Kaede, she sent an arrow directly into his yellow eye.
He collapsed, but his pack mate turned in Kaede's direction and growled. She shot again, and the arrow lodged itself in the wolf's shoulder. He yelped and abandoned Shae, bounding toward Kaede instead. She loosed another arrow, but it only glanced off his flank. Then he was less than ten feet away from her, and before she could think she pulled out the iron dagger and hurled it squarely into his throat.
Finally he fell, his jaws nearly touching Maila's hooves when he slumped onto the forest floor. Hot relief flooded through Kaede's body. Her lungs heaved.
Through the buzzing of blood in her ears, she heard the wolves howling. When she looked up from the dead wolf, she saw his pack mates fleeing. The path toward Pol was clear at last, and Kaede saw that the guard's neck was bent at an unnatural angle, and his left thigh had been torn into a mass of bloody flesh.
But Shae was still alive, and as the wolves' howls faded into the distance, her gasps of pain filled the air. Con slid from his horse, dropped his bloody sword on the ground, and ran to her. Kneeling beside her, his face turned gray at the sight of her wound. Shae looked up at him, reaching out for his hand, muttering something that he could not understand.
"You're not leaving us, Shae," he said fiercely. "You're not leaving us."
# Chapter XXII
aede ran toward Taisin, who had collapsed on the ground surrounded by dead wolves. Her lips were faintly blue, and she was breathing shallowly, her forehead glistening with sweat. Kaede was afraid Taisin had been injured, but she couldn't detect any physical wounds. She knew that Taisin might have sustained other, less visible, injuries, but she had no idea how to treat them. In all the years she had studied at the Academy, she had never heard of anyone doing what Taisin had just done, and she was fairly certain that it was forbidden.
But she would not let herself think about what that meant. All she wanted right now was to make sure that Taisin was not hurt. She knelt on the ground and lifted Taisin's hand. Her pulse raced within her wrist. Kaede leaned forward, pushing back damp strands of hair from Taisin's forehead. Her eyes suddenly opened, her pupils so huge they made her brown eyes seem black. She began to shake violently, and Kaede gathered her into her arms to quell the tremors, concerned that she would harm herself. At last the shaking subsided and Taisin asked in a hoarse voice, "Are the wolves all gone?"
"Yes." Kaede was relieved; Taisin sounded mostly normal. "Are you all right?"
Taisin squinted up at her. "I don't know." Her whole body felt bruised, and the pain was excruciating. But she also remembered the way she had held all of that energy in her hands: as muscular as a snake, as powerful as a fistful of iron.
Her stomach heaved with the memory, and she scrambled away from Kaede, doubled over on her hands and knees as she threw up. She might have been invincible against those wolves, but now she was weak as a newborn, shuddering her way into a strange new world.
When she had breath to speak she asked, "How are the others?"
"Shae is wounded. Pol—I don't know—"
Her voice broke off, and Taisin looked at Kaede and saw the fear on her face. Taisin took a deep, uneven breath. She pushed herself up onto her feet, wobbling like a colt taking his first steps. She surveyed the scene: the wolves' bodies splayed in a circle around them; the mauled packhorse, with their gear strewn across the forest floor; their four skittish mounts huddled together; Con bent over Shae on the ground. Down the trail she saw Pol's body; his horse had been dragged off by the wolves.
"We should go to them," Taisin said. She had to keep moving, or the gravity of what she had just done would overwhelm her. "We have no time to lose."
Shae was seriously injured. Her leg was in horrible shape, and she had sustained some ragged slashes on her side. They bandaged her wound, but there was nothing else they could do until they set up camp, and none of them wished to remain here, surrounded by the stinking corpses of dead wolves. Kaede retrieved her dagger and most of the arrows she had shot, but she didn't have the stomach to pull out the one lodged in the wolf's eye.
There was no saving Pol. They wrapped his broken body in his blanket and slung him as gently as they could over the back of the remaining packhorse, redistributing their supplies across all the horses. Con helped Shae climb back onto her own mare; she stubbornly refused to faint and instead had to grit her teeth over every bump in the road. They managed to put an hour's slow walk between themselves and what remained of their attackers before Con insisted they stop to tend Shae's wound. The bone in Shae's shin was exposed where the wolves had torn out her flesh, and Con had to hold her down while Taisin and Kaede wrapped her leg with a clean cloth. The cuts on her side where a wolf's claws had dragged across her body were jagged, and although they cleaned them as thoroughly as possible, Taisin had a bad feeling that the wounds would become inflamed. She brewed a bitter tea that would send Shae to sleep for the time being, which was the best she could do for the pain, and then they measured out just enough space for another grave.
Con broke up the ground with his sword while Kaede and Taisin dug with their battered metal bowls. Every time his blade bit into the ground, he remembered the way it had cleaved into the wolf's shoulder. He had killed that one, but he had been too late to save Pol. He had been too late to prevent Shae from being attacked. Seeing her on the ground, bleeding, had ripped him open, too. It made him realize that he had so much to say to her. Sweat broke out on his skin despite the cool air. He did not want to even consider the possibility that Shae wouldn't survive her wounds. He rammed his sword into the earth, making Taisin and Kaede jump out of the way.
"I'm sorry," he said. They kept digging.
Night fell before the grave was deep enough. The candle they had lit for Pol's soul did nothing to push back the dark. Taisin suggested they light a fire so that Shae would not get chilled. "You two will have to gather firewood," Taisin said. "I should stay here with Shae and Pol."
"Alone?" Kaede said. She straightened, standing in the grave itself. "Con should stay with you; I'll go alone."
"No." Taisin rubbed her eyes wearily with the back of her hand. "I'll be fine here. I can protect myself, but it's not safe for either of you to be alone in the Wood."
"Come on," Con said, offering his hand to Kaede. "Let's get it over with. We should have done it earlier."
Kaede frowned, but she took Con's hand and scrambled out. The lip of the grave crumbled beneath her foot as she climbed, sending clods of dirt tumbling into the pit. Taisin began to climb in.
"You shouldn't do that," Kaede said, her skin prickling. "Wait till we return."
"There's not time," Taisin said, picking up her bowl to dig. "We have to bury Pol as soon as possible."
Con and Kaede did not stray far from the path as they foraged for fallen branches. The Wood seemed particularly malignant that night. Kaede could have sworn she saw the eyes of wolves peering out at her from the cover of darkness. And it was so cold. She had been warmer when she was digging, but now she felt the wind on her face, and it smelled sharply of snow.
When they returned to their camp, they could hear Taisin chanting to herself as she dug. She didn't stop when they returned. Kaede built the small fire as quickly as she could, and Con pulled Shae's sleeping form toward it, pillowing her head on a rolled-up blanket.
As soon as the grave was deep enough, they rolled Pol's body into it. There had been no time to wash him or to change him out of the clothes he had died in. Taisin knew it was bad form, but she didn't know what else to do—it was already too late at night for proper burial rites—and she was so exhausted that she could barely say the words of the funeral lament. But Kaede and Con helped her, and together they laid Pol to rest.
In the morning, Shae awoke feverish and in pain. Taisin had learned some rudimentary healing practices at the Academy, but she was not trained as a healer, and Kaede had never reached that far in her studies. Con refused to give up; his stomach churned at the thought of losing Shae. "We'll just keep going," he said. "We'll find the Xi in time. They'll help." He heard the desperation in his voice, and he turned away so that he didn't have to see the awful sympathy in Kaede's face.
They were nearly packed and ready to go when the dog came trotting down the trail toward them. At first Kaede thought it was another wolf, and her dagger was in her hand before she realized it was not a wild animal. Though he was tall as a wolf, he moved differently, and his brown eyes lacked the feral sharpness she had seen in those beasts. He barked at them, and Taisin and Con jumped at the sound. When they were all staring at him, the dog began to wag his tail.
Behind him, coming down the trail, was a white-haired woman. She walked with a slight limp, leaning on a horned staff, and as she approached she called out, "Good morning, travelers! That's my dog, Cavin; he's harmless enough." When she was standing at the edge of their camp she paused and smiled. "On a little journey, are we?" she said lightly.
The three of them were silent. Con did not know what to make of the strange old woman. She looked innocuous, but he knew that a helpless old woman could never survive on her own in the Great Wood. Tali would not trust her. Con could almost hear him warning them: _Don't be fooled by the appearance of weakness_.
Con stepped forward, putting himself between her and the others. "Who are you?" he asked.
The woman cocked her head at him, hearing his defensiveness. "I am only here to help. I saw the wolves yesterday, running past my cottage. I thought that someone might be in need of my assistance."
"What kind of assistance?" Con asked.
"One of your party is injured, I see. Perhaps I can help."
Despite his doubts, hope flared inside him. "How?"
"Let me see her, and I will tell you what I can do."
# Chapter XXIII
er name, she told them, was Mona. She was blind in her left eye, but she seemed to have no trouble examining Shae's injuries. Con watched her carefully, noting the practiced way she handled the bandages, her touch light and quick. When Mona suggested they bring Shae back to her cottage where she could treat her, he agreed.
Taisin, who had said nothing during the exam, now asked, "Are you a healer?" A note of skepticism could be heard in her voice.
Mona looked at her out of her one good eye—it was startlingly blue compared to the filmy white covering the other—and said, "I am a greenwitch."
Taisin was surprised. "And you live here in the Wood, alone?"
The old woman smiled crookedly. "Solitude, young one, teaches many things not found within the walls of your Academy."
Taisin stared at her, startled, for she had not mentioned the Academy of Sages. But it was obvious that Mona had guessed Taisin was a student there. Before she could ask how Mona had known, the woman got up. "We'd better go," she said. "Your friend must not wait any longer."
Mona's cottage was about an hour's walk into the Wood, away from the river Nir. It was a roughly built log cabin with mud plastered into the cracks, and there was one door and one square window covered with greased paper. But the interior was unexpectedly cheerful, with a colorful quilt thrown over the bed in the corner and dried herbs hanging from the ceiling. On one wall was a fireplace in which the remains of a fire glowed; on the other wall was an ironbound trunk surrounded by stacks of leather-bound books. The sight of them astonished Taisin. A cottage like this one was the last place she would have expected to find so many books. They were costly items and difficult to obtain.
Mona told them to put Shae on the bed, and then asked them to build up the fire. "There's wood out back, behind the lean-to," she said. "And I would much appreciate it if one of you could bring me some water. You'll see the well by the woodpile. And you"—she motioned to Taisin—"I could use your help."
Shae was shivering. Mona had built up the fire until it roared, but though the heat of it sent sweat trickling between Taisin's shoulder blades, it seemed to have no effect on the guard, who was lying on the bed beneath several heavy quilts. Mona had given Shae something to make her sleep before she treated her wounds, but even asleep she was restless and agitated. Her face was white, her lips almost blue, and she breathed shallowly.
"Will she recover?" Taisin asked, watching the old woman touching Shae's forehead and cheeks with the back of her hand.
"She has a fever. There is poison inside her."
"From the wounds?"
"From the wolves. They're dirty beasts."
"Can you save her?" Taisin was afraid to know the answer, but she had to ask.
"I don't know yet." Mona left the bedside and went to the stack of books piled near the trunk. She pulled out a thick volume bound in black leather and propped it open on the mantle above the fireplace, holding it in place with a heavy pewter candlestick. Taisin came closer to look; on the page was a recipe listing at least two dozen ingredients. She recognized a few of them—milk vetch, aralia root, sage. But she didn't know many of the others: goldthread, blue aralia, skullcap.
"What is this for?" Taisin asked.
"Your friend is very weak. She has suffered a great shock." Mona opened the trunk, and inside there were dozens of little boxes and vials stacked one upon the other. "Her energies have been severely depleted. She has bled quite a bit. Her body could overcome the injury to her leg on its own if she were strong and healthy, but the wolf's bite has drained her." Mona began to pull out a number of boxes and handed them to Taisin. "Put them on the table by the clay pot."
"Are you making a tonic?" Taisin had learned about healing tonics at the Academy, but her knowledge of them was limited to the relatively harmless brew she had made for Shae the night before. It had not kept the pain away for long.
"It is a kind of tonic," Mona said, pushing herself up from the trunk to set down two more vials on the table.
"What will it do?"
"If it works, it will restore her vigor and strengthen her blood, and drive out the infection." Mona opened one of the boxes and pulled out dried flowers, rusty brown in color, and dropped them into the clay pot. She added little round seeds and the scrapings of a gnarled, flesh-colored root; furry, blue-gray leaves and pale orange blossoms. When all of the ingredients had been combined and crushed into a fine powder, she drew a small knife from her pocket and bent down to hold it in the hottest part of the flames.
"What is that for?" Taisin asked.
"There is another ingredient," Mona said, and a moment later she straightened, waving the knife in the air to let the blade cool off.
Something in Mona's voice made Taisin recoil. "What is it?"
"Your blood."
Taisin stepped back, her foot banging into the trunk. "What?"
Mona did not move; she held the blade lightly. It was only a paring knife. "Your blood," she said again. The woman's blind white eye moved as if it could see. "The tonic will not work without it."
"No tonics require human blood," Taisin objected, her skin prickling.
"Do you know every tonic?" Mona asked mildly. "What a scholar you are."
Taisin flushed. "No, I—" She clenched her fingers into fists. "I'm not saying I know everything. But I have never heard of blood as an element in healing rituals."
"Blood is the water of life. Your friend has been drained of too much of hers." Mona took a step closer to her, and Taisin had the impression that the old woman could see right into her mind. It was unnerving. "You are young, and I know that the energies run strong within you," Mona continued. "I felt it yesterday, when you defended yourself from those wolves. I felt the way you pulled and stretched the meridians to do your bidding. That is not something the Academy teaches its pupils, is it? And yet you knew how to do it."
Taisin stared at her, shocked. "You—you felt that?"
Mona gave her a shrewd look. "You should know better, Taisin. You know that when you do something like that, others can sense it."
"The wolves would have killed me—"
"And your friend will die if you don't give her your blood."
Taisin's heart pounded. She glanced at Shae, at her white face and heaving chest. When she turned back to Mona, the woman was watching her with a patient expression. "How much do you need?"
"Not so much. You are strong enough that a little will go a long way."
Taisin took a deep breath. "All right."
"Come here, then, and give me your arm."
Taisin went to her, knees shaking, and rolled up her left sleeve. Mona held her arm steady over the bowl of herbs, their bitter scent wafting up to her nostrils. Mona placed the knife against Taisin's skin, and with a short, quick move, sliced into her forearm. Taisin gasped; it stung. She watched as blood welled up in the cut, and let out a short moan when Mona wrapped her fingers above it, squeezing. The blood dripped, hot and red, onto the herbs.
Mona was saying something, but Taisin couldn't understand her. The words were in another language—something brutal and dark, like a knuckle scraping against stone. She felt light-headed as her blood drained from her, making a slight hissing sound when it struck the mixture in the clay pot. She couldn't look at the cut anymore; it was a mouth on her arm; it screamed at her.
She turned her eyes away, feeling sick. She stared at the fire, at the hearthstones, at the candlestick holding the black leather book open, the words crawling like worms across the page.
And then Mona was smearing an ointment over the cut, and she pressed a cloth against it. "Hold it there," Mona ordered, and began to crush the herbs into the blood. She poured in water from a black bottle; she knelt before the hearth and shoved the pot into the coals. She made a sign in the air—a circle—and she folded her hands together and touched them to her forehead, her mouth, her heart. A log fell with a crash, sending up sparks.
After several moments Mona stood again, and Taisin asked nervously, "Is it ready?"
"No, not for at least another hour. The herbs must absorb the blood fully." Mona looked tired, and she sat down in the rocking chair. "Let me see your arm."
Taisin had almost forgotten about it, but now she peeled back the rag. The ointment had left an oily residue on the cloth, which was now stained red, but the cut itself had stopped bleeding. She didn't resist when Mona wrapped a strip of linen around it, tucking the ends into place firmly. Her arm throbbed a little, and Mona said, "You should sit down. You've lost blood now, too."
Dazed, Taisin sank down to the floor. As Mona rocked nearby, Taisin stared at the iron pot in the fire, wondering if she had been right to let the greenwitch take her blood.
# Chapter XXIV
on paced back and forth in the clearing outside the cottage, his shoulders taut with worry. Earlier, they had heard Shae crying out in pain, but hours had now passed with no sounds from within. Taisin was still inside with Mona, who had shooed Con and Kaede away once they delivered the firewood and water. "You'll just be in the way," the old woman had said. "You'd best wait outside."
So they tended to their horses. They built a small fire in the stone-lined pit in the middle of the clearing, and they boiled water for tea. They cooked a cup of rice to eat, but neither Con nor Kaede had much experience with cooking, and the rice began to burn. They added more water, and then it became too wet. They ate it anyway, feeling gloomy and tired.
Afterward, Kaede pulled out her bedroll. She was so worn out she was sure she could sleep in broad daylight, but Con was too wound up, and he began to pace. His agitation was contagious, and she was about to give up on sleeping when he sat down on one of the logs beside the fire pit, demanding in frustration, "Why haven't they come outside yet? This woman must not know what she's doing. I was too eager to believe in her."
Kaede rolled over, pillowing her head on her bent arm to look at him. "She said she's a greenwitch."
He put his head in his hands. "But what do we really know about her?" he asked, his voice muffled. "Mona, is that her name? Who would want to live out here alone?"
"She has a dog," Kaede pointed out drily. Cavin was lying just outside the cottage door, apparently asleep.
Con let out his breath in an exasperated sigh. "You're making jokes, Kaede?"
She groaned, lying back again and blinking up at the gray sky. It seemed unusually bright today. "I'm sorry, Con. You know I'm worried about Shae, too."
He nodded briefly. "She seems unusual, though. This greenwitch."
"Do you know many?" Kaede rubbed her hand across her eyes. Yes, she was positive: The cloud cover was thinner today.
"A few. I met a few when I went up north last year. Aren't they women who never passed the tests required to become sages?"
"Some of them are. But I've heard of others, in recent years, who have rejected the sagehood and chosen to call themselves greenwitches instead."
"Why?"
She glanced over at the cottage. The door was still closed. "There are some greenwitches who claim that the Academy—and the Council—are too distant from the people of this kingdom," Kaede explained. "They believe that sages should be among the people, not removed from them."
He was surprised. "I haven't heard anything about this."
"I don't think the Council wants it to be widely known."
He quickly understood. "It would stir up trouble if people knew that some are resisting the Council's orders."
"And there are fewer sages made every year," Kaede pointed out. "They don't want to lose anyone."
"What about you? Aren't you due to join their ranks?"
"I will never be a sage," she said, and she realized that the idea of it no longer made her feel inadequate. It felt, instead, perfectly ordinary.
"But you've been a student there for six years."
"I've read the classics, but I'm not meant to be a sage. I don't have the skill."
"Why didn't you leave the Academy earlier, then?"
She turned back onto her side, propping her head on her hand, and gave him a tiny smile. "I have a powerful father, Con. He—and my mother, who would have been a sage if she hadn't married him—wanted me to be there. I'm sure they hoped I'd develop the abilities, but... I don't think it's something you can learn."
"What are you going to do, then? When we return."
The question startled her. They had been on the road for almost five weeks now, but it felt like years. Her life before—the Academy, her family, her obligations—was a different world, one she could barely believe she had ever lived in. The real world was here and now: this clearing, where the clouds overhead were thin enough to remind her what a blue sky might look like. The dirt under her nails, the healing scars on her hands, the ache in her shoulders and back from digging Pol's grave. Returning to her previous life seemed impossible. What would she do?
"I don't know," she said at last. "My father wants me to marry someone."
"Who?"
"I haven't met him." She grimaced. "Someone named Lord Win."
His eyebrows rose. "Really? I've met him. He's—"
"Don't tell me," she interrupted, sitting up. "I don't want to know anything about him. I don't intend to marry him."
Con's lips twitched as though he were amused, but he only said mildly, "I didn't expect you would."
Kaede sighed. "Tell that to my father."
"All right, I will."
She gave him a skeptical look. "What do you mean?"
"When we return, I'll talk to your father."
"My father won't listen to you."
"Why not?" He waggled his eyebrows at her. "You don't believe in my powers of persuasion?"
She rolled her eyes. "My father is the most stubborn man alive. He usually gets what he wants."
"Have a little faith in me." He grinned at her. "I am your future King."
She smiled faintly. She knew he was joking with her, but the thought of the future was sobering. Tali and Pol, both dead, and now Shae hovering on the edge. She said quietly, "I hope Shae will be all right."
Con stiffened; his grin vanished. "Shae is going to be fine," he insisted. He picked up a stick and began to poke at the fire.
"Of course she is," Kaede agreed. Con's brows were knitted with worry again, and she was sorry she had brought it up. If she had doubted his feelings for Shae before, she no longer did.
She watched Con run a hand through his hair; it had grown at least an inch since they had left Cathair, and now it stuck out everywhere, as if he were a porcupine. Kaede noticed he had grown a beard, too, and she wondered when he had stopped shaving. It had been some time, she guessed. Wearing dirty, bloodstained clothes, he looked more like a highway bandit than a prince. But when they returned— _when_ , she told herself, not _if—_ he would also return to his obligations, and they did not include falling in love with a guard.
Kaede asked, "Has your father spoken to you about marriage?"
"No." Sparks flew up as Con broke apart one of the burning pieces of wood. "He has been busy with his new bride," he said bitterly. "And by the time we return, I suspect I'll have a new half brother or half sister." He stared at the fire with a dour expression. "I'm guessing it'll be at least another year before my father realizes he could use me that way."
At that moment, the cottage door opened, and Taisin came outside. "We're finished," she said. She looked exhausted, with purple smudges beneath her eyes and yellow and red stains on the front of her tunic.
Con stood up and asked immediately, "How is she?"
Taisin sat down on the log, rubbing at her tired eyes. "She is as well as she can be, given the circumstances."
"Is she in pain?" Con asked.
"She is sleeping. Now all we can do is wait."
They slept away the afternoon, curled up around the fire pit, and even Con dozed a little. When Taisin awoke, evening was falling in lush, soft shadows around them, and Mona was pulling an iron teapot out of the fire.
Taisin pushed herself up, blinking in the firelight. "How is Shae?" she asked, her voice thick with sleep.
"She's resting," Mona answered.
Con was holding a small iron cup of tea. "She looks a little better," he said. He had gone inside the cottage as soon as Mona came out, and he had been relieved to see some improvement. Shae's fever had cooled somewhat, although she was still hot to the touch.
Mona poured another cup and handed it to Taisin. "Be careful. It's hot."
Taisin took it gingerly, holding it by the rim. The fragrance of summer flowers wafted up at her. "Where's Kaede?" she asked.
"She'll be back soon. Ah! There she is now."
Kaede came from the lean-to behind the cottage carrying an earthenware jar. "Is this what you were looking for?" she asked, handing it to Mona.
"Oh, yes," the woman said. Her smile spread wrinkles across her whole face. With a deft twist, she opened the jar. "I haven't had visitors in so long." She sounded both eager and a bit uncertain. "The occasion deserves something special, doesn't it?" She handed the jar back to Kaede, who sniffed it: honey. Her mouth watered instantly; it had been so long since she had tasted something sweet that she wanted to upend the entire jar into her mouth. Mona laughed at her. "Use this, my dear," she said, and handed her a wooden spoon and a steaming cup of tea. Then she turned to Con and added, "Although I'm afraid I can't offer you anything to compete with the King's table."
He paused, teacup half-raised to his mouth. He hadn't told her who he was. "How did—do you know who I am?"
"I have seen your face before, Your Highness," she said.
"Where?"
She shook her head, clucking her tongue. "I cannot reveal my secrets. I know you and your companions are embarked on a very important journey, and I am so pleased that I have been able to do my part in it."
"Did you know to expect us?" Kaede asked.
"Expect?" Mona repeated. "I don't think that is the right word, exactly. Although I have been seeing pieces of you all for years, you know."
Kaede considered the old woman's impish expression. "Do you have the Sight?"
"It is not what you would call the Sight," Mona said, clucking her tongue again. "No, not what you would know. Young Taisin here may have an idea... she has visions I would never dream of having." Mona gave Taisin a smile that was almost proud, and Taisin looked nervous. "Do not be afraid of your visions," Mona said to Taisin, speaking as if she were addressing a small child. "You must be open to them—open to everything under the sun and the moon, though these are both obscured to us now... sadly."
Con set his teacup gently on the ground and said, "Madam, you are undoubtedly a wise woman. May I ask how many years you have lived here in the Great Wood?"
She turned her head toward him almost coquettishly. "I am not averse to some flattery, indeed I am not, young prince. I have lived beneath these trees for longer than you have been alive, certainly."
He smiled at her. "Then you must surely know much about this Wood that I—that _we_ do not. Will you look at our maps and share your knowledge about the land here?"
"Oh, maps," Mona said, her voice lilting. "What have maps to do with anything? They do not show the true path." She sighed. "But of course I will look at them, though I assure you they are useless."
Puzzled, Con went and retrieved the maps from their long carrying case. He spread them out on the ground near Mona, taking care to avoid the fire. The light flickered over the paper as the old woman crouched down and stared at the lines demarcating the Great Wood, the river Nir, the Kell. Con pointed at a spot south of the intersection of the two rivers and said, "Is this where we are?"
Mona squinted down at the map and said, "That may be. Yes, that may be." She gestured broadly at the northern portion of the map, which was largely unmarked forest. "All of that is wrong. All wrong."
"Have you been north of the Kell?" Con asked.
"No, not I," Mona objected, as if affronted. "I stay to my side of the boundary."
"So there is still an agreed-upon boundary?" Con said.
"Well, _I_ have agreed to my own boundary." Mona laughed as if she had told a joke. Then her face grew serious, and she pointed at the line of the Kell. "This," she said. "This is the boundary I have agreed upon. I stay on my side, and they don't bother me."
"Who?" Con asked.
"The fay, of course," Mona said.
"You mean the Xi?" Kaede said.
"The Xi are only one of many races of fay peoples," Mona said. She added with an arch smile, "Perhaps the most arrogant ones. The Fairy Queen, of course, purports to rule them all."
Kaede asked curiously, "What other fay races are there?"
Mona shook her head. "It is not so simple, young one. Many of them have died out. There were wars between many races; few survived." But then she seemed truly delighted as she added, "And yet life moves in its cycles, doesn't it? I believe some fairies survived after all. I saw the loveliest little sprite the other day—moving just like a hummingbird. Do you know those? So pretty."
A thrill ran through Taisin as she heard Mona describe the sprite. Was that the name of the creature she saw in her visions? She burned with questions, but Mona picked up her staff and levered herself to her feet. "Nonetheless, it makes no difference to you," she said. "You won't see anything that doesn't want to be seen."
Con said, "Madam, we must travel north of the Kell. We'll surely encounter the Xi, won't we?"
She gave him a measuring look and answered, "It is unwise of you to cross the river."
"We have an invitation from the Fairy Queen," Con said.
"An invitation?" Mona said, her white eyebrows rising. "A true invitation?"
"Yes," Con said.
Mona shrugged. "Then perhaps all will be well."
"Do you know where we should cross the river?" he asked. "Is there a bridge?"
"I have been to the river, but never forded it. You will be safe enough on this side if you keep quiet about your destination—the Wood listens, you know. But on the other side, it is not a place for humans." She paused for a moment as if considering whether or not to tell them something. At last she said, "When I visited the Kell some years ago, I saw the Xi. They guard the border, I think. A great phalanx of them, hunters all. With bows and swords and grand horses. They kindly allowed me to leave without an arrow in my back."
And then Mona looked up at the darkening sky and seemed to remember something. "Oh, my, it is growing late! Taisin, you had better come with me; I'll need your assistance sitting up with our invalid tonight."
# Chapter XXV
y now, Taisin recognized parts of the fortress—the long, sloping corridor; the cavernous ceiling hung with icicles sharp as swords; the endless ranks of golden cages. And then there were the creatures she had seen, each one equally strange and beautiful. Some had scales like fish, and they slipped beneath still pools. Others, with fingers as gnarled as tree roots, nevertheless moved with the grace of leaves in a summer breeze. But the only creature she had seen whole was the winged fairy, who repeatedly flew down that corridor as if she were doomed to traverse the same small space for eternity.
It wasn't until late at night in Mona's cottage, when Shae was finally resting peacefully, that Taisin saw the other woman. Mona was asleep in her chair by the fire, and perhaps it was the greenwitch's presence that made it possible for Taisin to finally see her. One moment Taisin was lying on the pallet she had made on the floor next to the bed, and the next she was moving swiftly down the same corridor she had floated through countless times before—but this time, she was walking.
She could feel the contours of her body—this woman's body—and she wore a gown of some kind of heavy fabric. A cloak of ermine was draped around her shoulders. The floor was cold beneath the thin soles of her shoes, but she was used to the cold; it no longer bothered her. Taisin felt a fierce protectiveness for the ice, and it surprised her. This woman was in love with the mountain she had raised, block by block, from the frozen northern sea. She was no one to be toyed with, for she could shape icebergs into towers so high they scratched the sky. Taisin felt the power in the woman's veins, and she was awed by the strength of it. The way Taisin herself had felt when she had ripped into the fabric of the world to kill those wolves—that was only the beginning of what this woman could do.
She walked briskly to the end of the corridor, and Taisin saw her hand pushing open a door. The sight that greeted her made the woman swell with pride and determination. It was a nursery. On a dais, as if it were a throne, was a cradle made of crystal. Small hands reached up from within, and the woman went to the cradle and lifted out a baby. It was a perfect child in many ways. It had soft, sweet skin, and tiny fingers and dimpled knuckles. Verdant green eyes looked up at her from beneath long black lashes. Then the child opened its mouth and turned its head, and sank a row of pearly little fangs into the woman's arm.
Taisin felt the pain herself; it was as though she had been stabbed by a half-dozen little needles, each one poison-tipped. She jerked on the floor of Mona's cottage, and in the fortress the woman snarled at the baby and threw it, hard, against the edge of the cradle.
Blood smeared against the crystal, and Taisin was stunned by the strength of the woman's rage. It boiled out of her: pain and anger and choking, bitter disappointment.
And then, in a jarring, disorienting lurch, Taisin felt Mona's hand on her, shaking her, calling her name, and she awoke on the floor of the cottage.
The old woman was standing over her, that one milky eye fixed on her as though it could see into her mind. "Where did you go?" Mona muttered, prodding at her with the end of her staff. "No use in flying off to unsafe places. Keep your wits about you."
Taisin pushed her hair away from her eyes; her hand came away damp with sweat. "I will," she said. "I do."
Mona gave her a skeptical look. "You are walking a fine line."
Taisin was confused. The vision of the ice fortress still clung to her, making this world seem hazy, unreal. "What do you mean?"
Mona shook her head as if Taisin were a rebellious child. "What you did yesterday to those wolves—I haven't felt anything like that since... well, not since I was a very young girl. You had better keep an eye on yourself. These things have a way of turning."
Taisin went cold all over. Mona's blue eye was icy as she gazed at her, unblinking, and Taisin felt utterly exposed, as though Mona were peeling back layer upon layer of her defenses and examining each one. Taisin remembered how it felt to bend the meridians of energy to her will: like she was invincible. She realized—half ashamed, half defiant—that she yearned to feel that way again. To hold the webbing of the world in her hands, and to use it.
Mona bent down and clutched Taisin's chin in her bony hand and nearly spit in her face as she said, "You listen to me, young Taisin. You have a strong heart, but even the strongest heart can be tempted."
Taisin tried to pull back, but Mona's iron grip was bruising in its strength. It seemed to reach through her—within her—and smothered the flame of that desire until all that remained was a hard, hot little ember.
Mona let go, and Taisin fell back, gasping and weak. The old woman gestured toward Shae, pushing up her sleeves. "She's ready for her next infusion. Will you bring the herbs?"
Taisin was transfixed by the sight of Mona's bare forearm: There was a mark there, but though it was roughly the same size and shape as a sage's mark, it was a solid black circle, not the symbols that Taisin had seen before. It was as though Mona had once been marked, but had since chosen to efface the symbol—or to erase it. Mona saw her eyeing the mark, and she said shortly, "We don't all make the right choices when we're young."
"What do you mean? Are you a marked sage?"
"No."
"But what is that—"
"I might have once been marked, but I am no longer."
Taisin was incredulous. "How could you reject your station like that? It is an honor to be marked." Another possibility came to her, and the idea that the Council might have stripped Mona of her marking made her look at the greenwitch uneasily. It could only be a horrible thing that would cause the Council to revoke a sage's status.
Mona's eyes narrowed and she leaned down so that she was peering directly into Taisin's eyes with her single good one. "Not everything they teach you is true. I have chosen my own path. So must you." She backed away and returned to Shae's bedside. "Now will you bring me those herbs?"
Later that night, Mona slept again in her rocking chair, gently snoring. But Taisin couldn't sleep anymore; her thoughts circled endlessly around Mona's strange words, the awful vision, and the black mark.
Shivering, she wrapped her blanket tighter around herself and crawled over to the hearth to stir the coals. The flaring light illuminated the books stacked around the trunk nearby, and as the shadows leapt over the bindings, she began to wonder what was in them. She glanced at Mona, who was still asleep, and then reached for the closest volume, pulling it down as quietly as possible and opening it in her lap. It was a journal of some sort containing long lists of what looked like herbs or plants. The last quarter of the pages were blank, and she realized they must be Mona's own records. She closed the book and pulled out another, and another, motivated by a rising compulsion she did not understand. She felt as if she were searching for something. But book after book disappointed her—they all seemed to be journals of plant life, notations about tonics or medicines. In every one, the handwriting was the same: tiny, precise, taking up no more room than was necessary. Taisin assumed it was Mona's work, and it made sense, for she had known precisely what to do for Shae's injuries. Mona had spent her whole life, apparently, studying the medicinal properties of herbs.
The last book on the stack nearest to Taisin was the largest yet, and Taisin opened it expecting more of the same. But this time, there were illustrations, too, and they were not illustrations of plants. The drawings—sometimes crude, but always lifelike—depicted creatures like the ones she saw in her visions. Holding her breath in excitement, she stopped at a picture of a being with wings just like a hummingbird's. There were notes there, too, in Mona's handwriting. _Sprite_ , Taisin read. She turned the page. A slender woman with hair like sea kelp: _asrai_. _Found in the icy waters of the north._ A dwarflike being with legs as thick as tree trunks: _knocker_. And another creature that looked as if it had been sprung from the limbs of an oak tree: _wood nymph_. Taisin stared at it, her mouth open, remembering the body they had buried outside of Jilin.
"Find something interesting?" Mona said.
Taisin started, looking up at the greenwitch. "Are these creatures... are these all fairies?" Taisin asked, her heart racing.
Mona cocked her head, reminding Taisin of a bird with a very sharp beak. For a moment Mona's shadow seemed to arch overhead malevolently, but then Mona settled back into her chair, and she was just an old woman again. "What a silly question," Mona finally said, though there was no sting in her voice. "What else could they be?"
Taisin looked back at the drawing of the wood nymph. Notes were scrawled around the picture. "Is this your handwriting?"
"Some of it is. Some of that book was wrong. I had to correct it."
"You mean this book was..." Taisin trailed off, thinking. "Where did this book come from?"
"I rescued it from the Academy," Mona said, and she sounded almost cheerful about it.
"You _rescued_ it?"
Mona leaned down, the birdlike look back in her eye. "You trust your teachers, do you?"
"Yes," Taisin said, feeling defensive. "Why shouldn't I?"
"Did they teach you about these fairies?"
Taisin hesitated. "No, but—"
"But what, my dear? They have sent you on this journey through the Great Wood without even telling you about the creatures you might encounter?" Mona put her bony hand on her chest, a look of sorrow sweeping over her face. "I wouldn't trust anyone who did that to me. Why should you?"
Taisin was disconcerted. Was Mona right? She thought of Sister Ailan, who had always seemed to be so honorable and honest. She thought of Maire Morighan and the other teachers, who had all been generous and kind to her, and answered every question she posed, no matter what it was. Had she been asking the wrong questions?
Mona seemed to see the confusion in her face, for the old woman said, "You read that book tonight. And when you return to the Academy, perhaps _you_ will have something to teach your teachers."
# Chapter XXVI
hey spent two nights at Mona's cottage. Taisin showed Con and Kaede the book of fairies, and they pored over its yellowed pages for hours. By the second night, Shae's fever was gone, but she was still too weak to travel. When Mona offered to shelter Shae until she was recovered enough to return to Jilin, they knew they had to move on. Midsummer—and their appointment with the Fairy Queen—was less than a fortnight away, and they had no idea if they would arrive in time.
Con lingered by Shae's bedside on the morning of their departure. She drifted in and out of a drugged sleep, and all he could do was hold her hand. "We're coming back," he whispered, as much for himself as for her. His eyes were hot with suppressed tears. "I promise you."
They left Shae's horse behind, along with her gear and a tent, but they took all the remaining food supplies. There wasn't much, and Kaede began to wonder if she would have to attempt to hunt on her own. She felt extremely vulnerable now, traveling only with Taisin and Con. The two days at Mona's cottage had been a reprieve from cold reality, but now, as they made their way down an overgrown trail that surely hadn't seen human traffic in generations, that reality returned. They had lost their leader in Tali. They had lost Pol and Shae, who knew how to survive in the wilderness. Now they were only three, and Kaede was terrified that the Wood might demand another sacrifice. They took care to stay within sight of each other at all times, and Kaede carried Pol's bow across her lap.
She watched Taisin's back as they rode, wondering what she was thinking. She had been a little distant since the wolf attack, and it made Kaede anxious. What if the things that Taisin had done to those wolves had changed her? There were warnings, rules against using the energies to harm any living being. But had she done anything worse than what Kaede had also done, using Pol's bow?
When the time came for Taisin to perform the protection ritual around their camp, Kaede was tense, wondering if there would be something different in Taisin tonight. And when Taisin's fingers pressed firmly against Kaede's chest, something _had_ changed. But it was not what Kaede expected. There was a new strength to her; there were no hesitations in her movements. And the connection that had grown between them was still there. It had slackened a bit in last few days, but now it tightened again. Perhaps because of Taisin's new confidence, today the connection opened up, and for the first time, each could see a tiny part of the other.
In the breathless moment before Taisin realized what she had done, Kaede saw some of the truth that Taisin was hiding from her. Taisin was falling in love with her—the emotions were as clear and hot as a summer sky. But beneath them was the bitter tang of fear.
When Taisin broke the connection, Kaede staggered. She was overjoyed, but she was also confused. She reached out for Taisin's hand, but she had already turned away to finish the ritual. When it was done, her face was a carefully controlled mask; she would not meet Kaede's eyes.
Con saw the tension between them, and he came to Kaede as Taisin put away her supplies and asked, "What happened?"
Kaede looked up at him, dazed. She couldn't tell him. She wasn't even sure what it meant. And had Taisin seen her own feelings as well? She reddened to think of it.
"Kaede?"
"It's nothing," she said. But her heart hammered in her chest, and she trembled as she went to light the campfire.
In the middle of the night, Taisin woke Kaede to take over the watch, shaking her shoulder gently. Kaede pushed herself up, and Taisin pulled back. Con was asleep in his bedroll on the other side of the low-burning fire, and the trees arched above in a rib cage of bare branches.
Kaede fumbled for words. Her mouth was clumsy, fogged with uneasy sleep. "What did—tell me—"
She half expected Taisin to flee from her, but when Taisin remained where she was, her face pale and tense, Kaede tried again.
"Why—why are you afraid of your feelings?" she whispered.
Taisin bit her lip. She looked away from Kaede; she looked down at her hands; they twisted together as if she were trying to weave a rope around her wrists. She said something so softly that Kaede could not hear it.
Kaede pushed aside her blankets, leaning toward Taisin. "You can tell me."
Taisin touched Kaede's cheek very gently. Her fingers were cold. Kaede reached for her, but Taisin drew back, flushing. Kaede waited. Taisin's eyes, reflecting the firelight, looked like tiny burning stars. Finally she said in a low voice, "I'm going to be a sage."
"I know that."
"I can't—I can't be with anyone." Her words were full of regret. "I'm sorry. I'm so sorry."
The misery in her voice made Kaede ache. She wanted to ease Taisin's pain, but she had no idea how.
Taisin turned away, wrapping her blankets around herself, and then lay down with her back to Kaede. The distance between them, though it was only a few feet, had never seemed so great.
The third day after leaving Shae behind, they came to the river Kell. It was a grand sight to behold. The Nir and the Kell branched off from a wide, tumbling rush of water coming from the north, the Nir continuing south and the Kell running east. Both rivers were swollen with rainfall and thick with boulders that created dozens of small, swift waterfalls. The rains that had doused the travelers repeatedly on their journey had fed into the rivers, making them particularly treacherous to cross.
They agreed to travel east to search for a better place to ford the Kell, and when they came to a shallow beach in the early afternoon, Con stopped. "Perhaps we should just cross here. There are fewer boulders in the river, and who knows how far we'd have to go to find a calmer spot."
Taisin looked out at the river. He seemed to be right—the way was mostly clear. On the far side, the trees looked just like they did on this side. There was no sign of the Xi. "It will be cold," Taisin said.
"We'd better cross soon, then," Kaede said, "or wait until morning. It'll be difficult to dry off after night falls."
Con squinted up at the hard, bright gray sky. "We have time. I don't think we should wait."
They unwound the longest coil of rope they had, tying each horse to it. They secured their bedrolls and supplies as well as they could.
"Hold on to your horse if you lose your footing," Con advised, trying to remember what Tali had taught him. "They will swim." As soon as he was ready, before he could second-guess himself, he led his horse into the river. The packhorse went next, followed by Taisin and her horse, and finally Kaede stepped into the water, leading Maila.
At first, it was just cold. Kaede shivered when the water rose above her boots and began to seep through the fabric of her trousers, but she was not prepared for the icy wash of it when she was chest-deep in the river. They were barely twenty feet from the bank at that point, and there was more than three quarters of the way to go. She began to wonder if this had been a wise choice, but Con was already too far ahead to turn back. She gritted her teeth and plunged deeper into the Kell.
She quickly realized that though the river had appeared to be unobstructed here, the boulders were merely underwater, and the river itself was deeper than it seemed. The closer she swam toward the center of the Kell, the colder it became and the swifter it flowed. Her knee smashed into a submerged boulder and she cried out at the impact. River water gushed into her mouth, nearly choking her. She felt like she was struggling in the embrace of a slippery, suffocating beast, and for a moment it pulled her down below. When she fought her way back to the surface, her eyes stung and everything was askew. She saw the trees on the far bank at a strange angle; she saw the gray sky lurching above; she saw Maila battling against the current. Kaede lunged toward her horse, grabbing onto the stirrups beneath the water and kicking back with her legs.
This was not like swimming in the ocean by Seatown. The water there would rise up and buoy her before the waves crested over her head. She knew how to float on those waves, how to close her eyes and pinch her nose shut when the wave came toward her. She knew that those waves would push her inexorably toward the beach, and she and her brothers used to laughingly skim along their crests until they were spit out on the sand. But here the river was pulling her downstream, and she was trying desperately to elude its powerful grip. Ahead of her she saw Con approaching the opposite bank, and Taisin was almost through the wide, fast center. Kaede kept her eyes on them, and she had just crossed the halfway point when Taisin's head went underneath and did not come up again.
It happened so swiftly—as if she had simply been swallowed. Kaede felt as though she had been punched in the gut.
"Taisin!" she screamed, and freezing water went down her throat. She spit out, coughing, floundering, the entire world heaving with the rush of the river.
Kaede sucked in as much air as she could and dived down after her. The water was clear, but there was very little light beneath the surface; all she could see of Taisin was a murky fluttering ahead of her, as if someone were spinning, struggling to escape a trap. She kicked forward, her lungs beginning to burn, and miraculously, she found Taisin's hand. She gripped her fingers as firmly as she could and lunged up toward the light. When she broke through she gasped, desperate for air, and yanked again at Taisin.
She bobbed up to the surface, limp, her body still pulled downstream, her face pale and her eyes closed.
Con had already climbed out of the river, and two of the horses stood shivering on the bank, but now he saw Kaede and Taisin struggling. He pulled out another rope, tying one end to his horse's saddle and then wrapping it around his waist before he began wading back into the water. Kaede tried to sling Taisin's arm around her, but the river was too strong. All she could do was drag her while keeping Taisin's head above water. When Con was waist-deep in the river he threw the rope in Kaede's direction. At first it missed them entirely, and Kaede just stubbornly pushed on toward the bank. She no longer felt the cold; it was as if all the blood in her body had turned to ice. Now there was only one thing to do: overcome the river, and she had no intention of giving up.
The second time Con threw the rope Kaede caught it, rough and wet, in her right hand. She struggled to wrap it around Taisin's waist, and several desperate minutes later, after they had been dragged another twenty feet downstream, she succeeded, and Con began to pull them onto the bank. When her feet touched the riverbed again, Kaede put her arms around Taisin's motionless body and picked her up, the weight of her partially supported by the water, and carried her until Con met her and helped lay Taisin down on the riverbank. They pushed at Taisin's chest, hard, until water bubbled out of her mouth and her eyes opened. She coughed, rolling over, and Kaede helped her up onto her hands and knees, her body convulsing as she spit the water out of her lungs. Taisin began to shake with cold, and Kaede said to Con, "We need to build a fire."
He pulled a mostly dry bedroll out from within the gear packed onto his horse and tossed it to Kaede. "I'll find firewood," he said. "You need to get her out of those wet clothes." He had stripped off his own shirt and was pulling on another, drier one, but he did not bother to change out of his wet trousers before heading off into the trees.
Kaede began to unbutton Taisin's tunic, pulling the heavy, wet cloth away from her chilled skin. Goose bumps rose on Taisin's shoulders when she felt the air, and she shivered more violently. Kaede pulled the blanket toward them and draped it over Taisin, who attempted to unlace her boots with numb fingers. "Just sit there," Kaede ordered, throwing the wet tunic aside. "I'll do that." She listened to Taisin's chattering teeth as she worked the wet laces, wanting to curse at the knots Taisin had tied. But at last she had them undone and pulled the soaked leather off, and as she reached for the clasps that fastened Taisin's trousers, Taisin put her hands on Kaede's to stop her.
"Thank you," Taisin said. Her lips were bluish-purple, her fingers like icicles.
All of a sudden, Kaede realized she was she was staring at Taisin, stripped to the waist, the medallion like a black eye hanging around her neck. Her face was white as snow but for rough red spots burning on her cheeks, and Kaede felt herself flush in response.
They heard Con returning, his footsteps seeming inordinately loud. Taisin pulled the blanket around her bare shoulders, covering herself, and Kaede backed away, sitting on her heels. "You don't have to thank me," she said awkwardly. She looked away; she looked at the river that had almost taken Taisin away from them. From her.
It was deceptively beautiful, for being such a monstrous thing.
They staked out the horses close to the fire, where Taisin sat huddled in the blanket. Kaede hung the kettle over the flames, and before night fell she had brewed tea for them all to sip, crouching close to the blaze.
"Everything's going to be wet for days unless we stay here tomorrow," Con said. "We'll have to lay everything out on the riverbank and hope they dry."
"Is it safe to stay here?" Kaede asked. "What was it like in the Wood?" She glanced at the trees nearby; the low light turned all colors into shadows upon shadows.
"It looked no different than the Wood south of the river. It might be a good idea to stay here and scout around a bit—see if there is a trail. We can leave our things here to dry while we explore this bank."
"Tonight, at least, all we have to do is eat and sleep," Kaede said. "That was not an easy crossing." She put down her cup and went to retrieve supplies for supper. But just at the edge of the camp she saw something that made her halt. There was a horse and rider, nearly obscured by the twilight. And then she saw another beside him. "Taisin," Kaede said in a low voice. "Con. Look."
Taisin and Con scrambled to their feet. Con's sword rang as he pulled it out of its scabbard.
More riders emerged out of the dusk, ghostlike, until they had surrounded the camp. As they came closer they seemed to take on something of a glow. They were tall and pale, with white clothing and eerie, sparkling eyes. Some of them wore swords on their belts; others had quivers of arrows strapped to their backs. There were men and women both, but they all shared the same otherworldly beauty: hard and cold and perfect.
One of the riders pushed his horse a few steps closer to the three humans. He asked in a peculiar accent: "Who are you, and why have you crossed over into our lands?"
# PART IV
Some seek to act upon the world,
But success will not follow.
The world is inviolable:
It has no beginning and no end.
Those who seek to change it will be changed;
Those who grasp onto stones will find water.
— _Book of Changes_
# Chapter XXVII
aede couldn't tear her eyes away from the riders. They were the most foreign-looking people she had ever seen, and she didn't feel fear so much as curiosity and a rising excitement. Were these the Xi at last?
In answer to their question, Con stepped forward, squaring his shoulders. "I am Con Isae Tan, prince of the Kingdom. Are you representatives of the Xi?"
The rider who had spoken inclined his head. "We are. Why are you here?"
"I have come at the invitation of your queen. Will you allow me to show you the invitation?"
"Show us, then."
Con went to his saddlebags to retrieve the invitation, still ensconced in its intricately carved box. He handed it to the rider, who opened it and unrolled the scroll. "This is an invitation for King Cai, not you."
"I am his only son," Con said. "He has sent me in his stead."
The rider gazed at him, expressionless, and Con felt perspiration rising on his forehead. The man's blue eyes were so penetrating that Con had difficulty maintaining his composure. Finally the rider said, "Come closer, princeling."
Con moved toward him, and to his surprise, the rider dismounted. Con halted, unsure of what to do, and the rider walked slowly around him, examining him as if he were a new dog, acquired for a particular purpose. Con had the disconcerting feeling that the man might pry open his mouth and examine his teeth, but then the rider only asked, "Who are your companions?"
Con let out his breath in relief. He had apparently passed some kind of test. "They are representatives from the Council of Sages."
"The Council of Sages," he said. "I have not heard of them in... many of your generations."
All the riders' eyes flickered to Taisin and Kaede, and Kaede felt as though she had just been buffeted by a strong wind. She stepped back, startled by the force of their gaze. Their leader came to look at her, circling her as he had done to Con. His eyes narrowed on her as if he saw something odd, and for a long moment they locked on hers. She stared back, fascinated—she had never seen eyes of such deep blue—and just as she began to wonder why he was so interested in her, he turned away and moved on to Taisin.
Taisin had watched with growing anxiety as he examined Con and Kaede as if they were fantastical creatures. When he approached her, she felt his curiosity ripple through the meridians between them, and then it sharpened, his eyes focusing on her. He came closer and extended a hand until his fingertips nearly touched her chest. She felt the medallion, hidden beneath her tunic, suddenly burning against her skin. "What do you have there?" he asked.
Wordlessly, her skin buzzing where the medallion radiated heat, she pulled the chain over her head and held it out to him. In his hand, the stone took on a dull light as if it were awakening at his touch. He gazed at it, and she saw him clench his jaw just slightly. "This is not yours to keep," he said. "But you shall wear it until our queen tells you otherwise." He placed it over her head so quickly she barely had time to notice how close he was—a glimpse of the paleness of his throat—and then he moved away and the chain was warm around her neck again.
Behind him several of the riders dismounted and moved toward their belongings as if to take them. "What are you doing?" Con asked, startled.
The man turned toward him and said, "You and your companions will come with us."
"Where?" Con demanded.
"We will take you to your meeting with our queen."
"Right now? It is nearly full night."
The man gave him a tiny smile. "Your meeting is scheduled for Midsummer, and that is scarcely one week from now. We've no time to waste."
"Wait," Taisin said.
The leader turned. "Yes?"
"Who are you?"
He did not answer at first, and even looked back at the other riders as though they were sharing a secret. At last he said, "We are the Fairy Hunt. You may call me the Huntsman."
They set off as soon as the horses were saddled, with the Huntsman riding in the lead. Though the Wood was pitch-black all around them, the riders of the Fairy Hunt stood out against the dark. Kaede thought that it wasn't exactly as if they glowed, but rather there was a lightness about them. Their skin was almost translucent, and she could swear she saw the texture of their muscles moving beneath it. She wondered if their blood was red like hers, or if it was some other queer color. Did it flow as thickly as mercury, or was it thin as water? She had never felt so different from someone in her life.
The Xi stopped only to allow their human charges to relieve themselves, and they would have continued without further pause until Con insisted that they be allowed to rest their horses and to eat. Dawn was breaking by then, and the Wood was slowly coming into light. Kaede was exhausted and her stomach growled, and she felt almost too tired and light-headed to find her way from her horse to their supplies. The Hunt had dismounted, too, and the riders were ranged around the three of them in a loose ring, as if to prevent them from running away. Kaede did her best to ignore them as she pulled out their food. They were down to eating biscuits, now, dried hard and nearly tasteless. She took one and handed the tin to Con and Taisin, who looked as tired as she felt. "Tea," Kaede muttered to them. "I'll start the fire."
The Xi watched her curiously as she began to gather wood, but as she approached the edge of their ring, one of them stopped her and asked, "Where are you going?"
"I need to find more wood to build a fire," she said, raising her eyes to the slender man's blue ones. She shivered.
The rider looked behind her and said something to one of the others in a language she did not understand, then turned back to Kaede. "Fire is all you need?" he said, his eyebrows raised as if he were amused. He opened his hand and there, in his palm, a flame danced for her.
She backed away. "I—I want to boil water."
He cocked his head at her. He was younger than the one who led them, she noticed. His face was smooth as a baby's; his hair like white silk capped over his shapely head. His full, pale pink lips curved upward in a smile, and she felt distinctly uncomfortable. He extended his arm, holding out the burning golden flame, and went toward the small pile of wood she had left on the forest floor, and set the pile alight.
Swallowing, Kaede set up the iron tripod and hung the kettle over the fire. It was as hot as any natural fire, but it did not eat away at the wood; instead, it licked at the fallen branches, almost caressing them. But it still caused the water to boil—perhaps more quickly, even—and the tea tasted no different than it had the day before. Con, Taisin, and Kaede squatted on the ground around the fire, for it was good to feel its warmth, and Kaede tried to soften her biscuit in the tea before she ate the rest of it.
Some of the Xi came a bit closer to observe them, but most seemed to rapidly lose interest in their activities and began to pace back and forth, eager to move on. The young one who had started the fire came close enough to lean over Kaede's shoulder and look at the biscuit in her hand. He asked, "What is that called?"
There was a disconcerting gleam in his eye, as if he wanted to have a bite of her rather than the biscuit. Before she could answer, the Huntsman called to him in a sharp tone of voice, and the young one looked briefly petulant before he withdrew, going back to the edge of the circle of riders.
When they finished eating, they packed their cups and kettle back into their saddlebags, and the Huntsman snuffed out the fire. He passed his hands over the flames once, and then the woodpile was bare and cold, not burned at all. Kaede wondered if it would even be warm if she touched it. "It is time to leave," he said, and though his voice was barely louder than a whisper, all of the Hunt turned in unison to their horses, prepared to go.
They rode steadily that day, stopping only when Con or Kaede or Taisin requested it. The Xi did not seem to eat; nor did their horses seem to need any rest. Kaede felt Maila tire as the day progressed, but she continued on as if compelled. The trees around them began to change as they left the river behind. Oak trees gradually gave way to evergreens. The evergreens grew taller and taller. By late afternoon, they were riding through a forest of trees with trunks wider than the length of the wagon they had left behind in Jilin. The branches drooped down at them, heavy with soft, dark green needles. The colors here were richer than they had been south of the river, where half the trees had turned brown from lack of sunlight. The sky was still gray here, but there was something different about the quality of the air. It was warmer, for one thing, almost as warm as it should be at midsummer. But there was something else, too, and it visibly affected the members of the Fairy Hunt. The farther they rode from the Kell, the more the Xi seemed to shine. They were coming home.
At nightfall, worn to the bone and feeling as though she might fall asleep in the saddle, Kaede was relieved when the Huntsman stopped and told them they could set up camp. He had chosen a clearing near a brook that ran over a rocky streambed, and when Kaede knelt by its side to refill her water skin, the liquid was shockingly cold on her hands. The icy taste of it made her throat momentarily numb. She came fully awake and saw Con and Taisin, too, reeling from the water's chill.
"We should drink _that_ in the morning," Con said, and Kaede laughed. Even Taisin, who was so tired she felt like her body had been dragged across that rocky streambed, couldn't help but smile. The three of them looked at one another, and for a moment they felt entirely human again. Weary, hungry, and cold, but human. Kaede felt her muscles begin to relax. For all the strangeness of their escort, she had Con and Taisin with her, and they would do all right.
They slept soundly that night, curled up in their blankets near the Xi's magical fire, the ghostly riders spread around them, again, in a ring. When she woke the next morning, Kaede lay there in silence for a while, blinking her eyes at the early light. Some of the riders were gone. Those who remained did not look like they had slept at all, but nor did they look tired. One of them saw that Kaede had awoken, and he nodded to her almost pleasantly—as if this were an entirely normal thing, for him to be guarding a group of sleeping, worn-out humans in the middle of the Great Wood. And she realized that yes, that was what they were doing—these Xi were _guarding_ them. She and Taisin and Con were not prisoners. They were being protected.
The idea startled her. She rolled over onto her back, looking up at the sky cupped by the circle of trees around their camp. She thought there was something wrong with her eyes at first, and she blinked several times, but it was still there: On the edges of the bowl of sky, there was the faintest trace of blue.
# Chapter XXVIII
hey traveled for a week in the company of the Fairy Hunt. Kaede often watched the riders surreptitiously, marveling at the grace of their movements. They were like dancers, sinuous and light on their feet, yet there was always something about them that marked them as plainly inhuman. There was a curious play of light and shadow in their faces that made it difficult to understand their expressions. And when one of them looked at her, Kaede found it almost impossible to look away. It was disturbing.
One evening the Huntsman came and sat with them, and at first Taisin, Con, and Kaede simply stared at him, for none of the riders ever joined them at the fire. Finally Kaede, who had just finished eating her tasteless biscuit, blurted out, "Do you ever eat?" Immediately she colored, and Con and Taisin tensed.
But the Huntsman only raised his eyebrows, and Kaede thought she recognized his expression. He was amused. "We eat," he said. "But not while we are on duty."
"Duty?" she repeated, her mouth dry.
"We eat when you sleep," he explained.
"Oh."
They all sat in silence for several more minutes, and then the Huntsman stood and walked away. Con, Taisin, and Kaede looked at one another in confusion.
"Why did you say that?" Con whispered.
"I don't know," Kaede whispered back. "Aren't you curious?"
He gave her an exasperated look, and then Taisin reached out and put a hand on Kaede's arm. Her skin tingled at Taisin's touch. The Huntsman was returning, and he had something in his hand.
He held it out to them with something of a flourish. "Would you like to try some of our food?" he asked. Lying on an unfolded cloth was a square of something that was yellowish-white in color. To Kaede, it looked like a white bean cake, but there was something different about its texture.
"What is it?" Kaede asked. Taisin's hand fell away, leaving a palpable sense of absence behind.
"Cheese," he answered. With a bone-handled knife, he sliced off a small piece and offered it to her.
It tasted nothing like what she expected. It was savory rather than bland; it was chewy rather than soft. The sharp flavor lingered on her tongue after she swallowed it. She wasn't sure if she liked it or not, but she tried to smile at the Huntsman and said, "Thank you."
The corners of his mouth twitched.
As they traveled north, the trees became taller, greener, stronger. And the quality of the light changed. It was as though all those layers of cloud were gradually being peeled away until, at last, on the sixth day they rode with the Xi, they saw the sun.
It had been so long since Kaede had felt its warmth that its first touch brought tears to her eyes; she wanted to strip off all her clothes and stand naked in the light. Taisin had forgotten the way it infused every leaf with vibrant color, causing the veins to stand out in sharp relief against the tender green. And Con could not remember if he had ever seen a sky so blue: robin's egg blue, smooth as glossy porcelain, untouched by clouds.
That same day, they came to a long row of trees planted on either side of the path. In the morning, the path had been only dirt covered in fallen pine needles, but by midmorning, the pine needles were swept away, and by noon the horses stepped onto pavement. It was not like the pavement used in any human city; this was white stone, perfectly cut in long rectangles. At intervals, diamonds of black stone were inlaid in the road, polished until they sparkled in the sunlight. The road became as broad as the largest square in Cathair, with elegant, gold-leafed trees marching down the center. In the distance the Xi city, Taninli, glimmered.
When at last they saw the crystal gates ahead of them, the Huntsman pulled his horse to a halt and turned back to look at his human charges. "We will ride directly to the palace," he told them. "Some of our people may turn out to look at you, but do not be alarmed."
Kaede glanced at Taisin, who seemed slightly ill. As the Huntsman rode ahead, Kaede pushed her horse toward Taisin's and asked, "Are you all right?"
"I'm fine," she said, but she sounded hesitant. Taisin had felt the city coming as early as two days ago; it was an unmistakable knot of energies coalescing together all at once. The closer they came, the more light-headed she felt, and she only hoped that she would be able to adjust to it quickly. So far, though, it was making her feel queasy.
Kaede wasn't affected the same way that Taisin was, but she, too, felt a bit out of sorts as they rode through the gates. The world seemed askew somehow; the shadows fell in the wrong places here, or perhaps her eyes simply weren't accustomed to the angles in the buildings and streets. And the buildings themselves were so strange and exotic. The stone was too smooth to be carved from a mountain, the glass too clear to come from an ordinary forge. The walls were perfectly straight or miraculously curved. Giant windows, cut into facets that held the light like prisms, climbed up the tallest towers. And every structure seemed to fit into the one beside it like a puzzle piece; the only spaces must have been deliberately left open.
In those spaces, the Xi waited and watched. They peered out from balconies, or from beneath archways between houses, or from meticulously landscaped parks that opened onto the white stone boulevard. At first Kaede gazed back at them. In the sunlight, their skin was no longer deathly pale; it was like new-fallen snow, bright and pristine. Their hair, she realized, was a thousand different shades between white and silver; their eyes were sharp, glowing jewels. The pressure of so many eyes on her made her a bit breathless, and after several minutes, she had to look down at her hands, fingers tightly gripping her reins, so that she no longer saw them.
That was when she realized that all the sounds she normally associated with a city—the noise of wagon wheels and beggars and merchants hawking their wares—were absent here. There was only the rise and fall of whispering in the language of the Xi, a kind of hypnotic music. The more she listened to it, the more it made her feel disconnected from her body. But gradually the boulevard climbed out of the heart of the city, and as they left the crowds behind, the whispering faded. At last Kaede allowed herself to look up again, and she saw that they were nearing the glittering crest of Taninli, and before them was the palace of the Fairy Queen.
When they reached the palace gates, the sun hung straight overhead, beaming down hot on their heads. They rode into a grand, circular courtyard, over paving stones set with a mosaic of gold and green in a pattern of swirls. Their horses, lulled into a half doze by the very air around them, were led away by silent-footed Xi clad in tunics the color of fallen autumn leaves. The Huntsman led them inside the palace through doors as tall as a three-story building, and inside it was cool and comfortable beneath ceilings so high Kaede was sure she saw birds flying above her. The Huntsman took them down wide, empty halls filled with light, and Kaede wondered where everyone was. Was the Huntsman taking care to avoid the inhabitants of the palace, or were the inhabitants avoiding them? A bead of sweat trickled down her forehead. It was warm as midsummer, and she realized with a jolt that it _was_ midsummer. Tonight was Midsummer's Eve, and tomorrow would be her eighteenth birthday.
They arrived at a set of smaller doors made of a fine-grained white wood, and the Huntsman turned the round crystal handles and said, "You will be very comfortable here."
Inside there was an apartment of many rooms furnished with chairs carved out of polished tree trunks, with cushions of rose and gold and green silk. The floor was covered in soft carpets, and at the far end of the room tall glass doors opened onto a broad balcony. Sunlight streamed through the windows, filling the room with a lovely midday glow. Con turned to the Huntsman and asked, "When will we see the Fairy Queen?"
"Tomorrow. Tonight is Midsummer's Eve, and we have other matters to attend to." He paused in the doorway and added, "It would be best if you remain here tonight."
"Why?" Con asked.
"It is a night of great celebration for my people. It would be unfortunate if anything were to befall you on the night before your audience with my queen." He looked at each of them to make his point clear. "I ask you to stay here." And then he left them alone, closing the door behind him. Though he had phrased his words as a request, Kaede had a feeling that they would not be able to open that door until he let them out.
# Chapter XXIX
aede chose a round room with walls lined with windows. The vista of the city below was astounding—hill upon hill of buildings formed out of the same white stone that built this palace, every window sparkling. Far below she saw the Wood, a sea of trees all around Taninli. Though it was bright as midday inside, she lay down on the round bed in the middle of the round room, and as soon as her head fell upon the silken pillow, she was asleep.
Con took a square room with a balcony running along two entire walls. He opened the doors, letting the filmy white curtains flutter out into the afternoon. The breezes smelled of jasmine. He stood outside for some time, gazing down at the city, and his eyes were dazzled. The longer he looked, the more his mind became filled with a delicious fog. All the pain of the journey could be erased if he just gave in to this extraordinary place. But he felt a persistent, nagging worry in the back of his mind, and as he leaned forward into the sunlight, he closed his eyes. He saw his red-veined eyelids, the colors of countless ordinary human campfires that had warmed his hands night after night. He remembered Tali, and Pol, and Shae, who had looked at him out of pain-filled brown eyes in Mona's cottage. He had promised her he would come back for her. The worry turned to impatient determination; his hands clenched into fists. He turned his back on the glamour of the city and went back inside, where he began to pace.
Taisin's room was filled with trees; they seemed to grow out of the very floor, with smooth, polished bark the color of rust. Glossy leaves, amber on one side and bright green on the other, shaded her bed from the sun that poured in through windows in the ceiling. Tall glass doors opened onto a little round balcony, and when she stepped outside she looked out over a lush, wild garden. In the midst of all the sculptured buildings, the sight of trees and stones and running water was surprising, but as she looked closer, she could see that even this garden had been cultivated with the utmost care. She yawned, and raising a hand to her mouth she went back into the room, stretching. The bed was inviting. After weeks of sleeping on the ground, the feather bed beneath her back was like clouds. She sank into it and slept so soundly that for the first time in weeks, she did not dream of the fortress.
Kaede awoke after dark, and when she opened her eyes there were lights dancing on the ceiling, reflected from the city below. She pushed herself up, feeling groggy, and went to the closest window. Down below, Taninli was ablaze with fairy lights: thousands upon thousands of them, winking like fireflies in a summer evening.
She left her room, walking down the short, curved corridor that led to the sitting room, and found Con at a table that had been laid with enough food for twenty. He looked up at her with glazed eyes. "Welcome," he said in a thick voice, "to our banquet."
She sat down across from him, gaping at the spread before her. She could not identify most of what she saw. There was a silver tureen of some kind of fragrant soup; plates piled high with colorful fruits; breads that were round and baked with golden-brown crusts. "What is this?" she asked, picking up an oblong fruit, its bright pink skin shading into orange.
"I don't know, but I recommend it," Con said, and handed her a wooden-handled knife with a blade made of thin, strong stone.
She tested the edge with her finger; it was sharp. When she peeled the skin of the fruit she held in her hand, the flesh that emerged was soft, juicy, and golden. She bit into it and the sweetness startled her; it was like liquid sugar with a tart, lingering tang. She discovered that there were several different kinds of cheese, and she especially liked the soft white one that crumbled in her fingers. She ate until her stomach was full, and then Con poured something from a decanter shaped like a bird into the crystal goblet at her elbow. "I have never tasted anything like this," he said.
She looked at him dubiously. "What is it?"
"I think it's wine."
It smelled like newly budding roses. The fragrance itself was intoxicating enough, and she put it down and looked at Con. "Is there water?" she asked.
He laughed at her, and she realized that he had drunk the wine—perhaps he had drunk too much of it. He had shaved off the beard he had grown during their journey, and it made him look younger and more vulnerable. "There," he said, pointing to a crystal pitcher down the table. "I think that is water."
She stood up to fetch it as Taisin came in from the balcony. The sound of celebration followed her through the open doors—music and voices, all mingled together in a joyous crescendo. "It's midnight," Taisin said, joining them at the table. She picked up a chunk of bread, but like Kaede, she avoided the wine.
Kaede poured water into two goblets, handing one to Taisin. "How do you know?"
"The celebration," Taisin said, gesturing toward the balcony. "It's turned a corner. It must be Midsummer Day now."
Kaede took her goblet of water out to the balcony. Below, among the winking fairy lights, she thought she could see the Xi themselves flooding through the streets. She rubbed her eyes, not sure if they were playing tricks on her. Everything here—Taninli, the palace, the food they ate—seemed obscured by a thin but persistent fog. It was as though some of her senses had been dulled, but others had been sharpened. She was more conscious than ever of the rhythm of the blood in her veins, but she felt oddly disengaged from her breath. Every now and then snatches of music floated up to her, played on instruments she had never heard before. It was so beautiful that it made Kaede's heart ache. She longed to be a part of it, to dance among the Xi, and she realized she was gripping the balustrade with white fingers, her goblet tipping precariously until water splashed down on the white stone. She righted it, stepping back, and blinked, pressing her fingers to her temples.
The door behind her opened with a scrape. It was an unexpectedly ordinary sound for Taninli. She looked over her shoulder and saw Taisin coming to join her. "Happy birthday," Taisin said.
"Thank you." Kaede had not expected Taisin to remember, and she felt inordinately pleased about it.
Taisin stood beside her, looking down at the sea of celebrants. The lights glowed on her skin, making her seem gilded. Kaede could not stop staring at her, and she wondered if even the water in those pitchers was somehow thickened with magic, for nothing seemed usual tonight. The Huntsman might have warned them to stay in these rooms, but he could not prevent the air from carrying the scent of their celebrations up to them, a potent, alluring perfume. Taisin turned to look at her, and her lips parted.
Kaede straightened, taking one step forward, and Taisin seemed to lean toward her just enough—and Kaede saw, then, that what she had hoped for could come true. If she wished it, if she reached out and touched her, Taisin would come to her easily; she only wanted a bit of suggestion. The space between them hummed. It was the most natural thing in the world to slide her finger beneath the strand of hair that fell across Taisin's eyes and tuck it behind her ear. Heat suffused Taisin's cheeks, and Kaede drew her closer, her breath a soft tickle across Taisin's lips, and kissed her.
Everything focused.
Taisin felt every place their bodies touched, and she felt every place they did not. Kaede slid her hands down Taisin's back. Taisin felt the blood singing in her veins; all of her was surging up to meet Kaede, who pressed her closer. They moved, clumsy with desire, and one of them bumped against the crystal goblet, knocking it off the balustrade to shatter, loudly, at their feet.
They broke apart, staring dazedly at the fragments of crystal. The lights below were sharp as diamonds.
Taisin recovered first. "I'll get a cloth," she said, her voice husky, and departed abruptly.
Kaede squatted down and picked up the stem, taking care to not cut herself on the jagged edge. Her breath was ragged in her throat; her limbs felt weak, as though she had just climbed a thousand steps; her hand holding the broken stem shook. A shadow fell over her, and when she looked up, it was not Taisin but Con who handed her a cloth.
"What happened? Taisin told me you needed this, and then ran off."
Below them they heard the roar of the crowd in celebration. Her heart was pounding as loudly as the crowd. "I dropped—I dropped the goblet," she muttered. She took the cloth from him and began to sweep up the broken shards. They glinted in the light spilling out from the sitting room.
"Be careful. You'll cut yourself."
"I'll be fine," she said, but she felt the beginnings of panic whirling in her stomach— _why had Taisin left?_ —and she swept up a piece of glass that nicked her thumb. A small drop of blood welled up through her skin. She pressed the white cloth to it, the red blooming like a rose, and her finger smarted from the cut.
Taisin shut herself in her room and sat on the edge of her bed, and all she could think of was how much she wanted to go back to Kaede. Her whole body quivered from wanting it.
Nothing had prepared her for this. None of her books, none of her teachers had said a single thing about what to do with this wild energy pouring through her. She had no idea how to deal with it. She took a deep, trembling breath, trying to moderate the pulsing of her blood. She could still taste Kaede's lips. She pressed her hands to her eyes, but all she could see was Kaede's face.
She curled up on the bed, clutching a pillow to her chest, and gradually the beating of her heart slowed. She counted her breaths, hoping that it would calm her down. One, ten, one hundred breaths. Again and again, until she could push away the lingering sensation of Kaede's hands on her back.
But what if she couldn't fight this anymore? Had she been a fool to even try?
She stubbornly tried to recall every detail of that first vision she had when she was still at the Academy. The beach, the boat, Kaede's face when she pushed away from the shore. The feeling that the most precious thing in her world was leaving her, and it might never return.
Sister Ailan had told her that her vision was a vision of the truth. But what was the truth? Was it that Kaede would leave her behind? Or was it that she loved her?
She heard the whistle of the wind in her ear, singing across the ice. She could no longer feel the softness of the bed beneath her. Cold seeped through her clothing, into her skin, until she felt the icy floor of the fortress beneath her feet.
Now that she had seen the way that glass could be manipulated in Taninli, she knew that the ice was only a cold imitation. She stood in the ice fortress, her fingers curled into fists, and gazed out the window—yes, this was real glass, hard and unyielding—at the landscape before her. The walls of the fortress descended like a mountainside to the ice fields below. In the distance the ocean was azure blue beneath the ice floes, reflecting the great arc of the sky above. Behind her there was motion: the fluttering of wings, the darting shape of another creature. The sprite. It had a message for her, and when she had heard it she reached out and plucked the fairy from the air, pinning its wings back. She watched the sprite's face stretch out in fear, and she whispered to it, soothing it, stroking its hair. An imperfect thing, this one.
But it would be a pity to blame the messenger.
She let it go, feeling its wings brush against her fingers before it bobbed away. She felt its fear, and it both saddened and exhilarated her. She turned back to the frozen vistas outside the window. Soon, she thought, and it sent a thrill through her. Soon her visitors would arrive.
Taisin sensed the woman's anticipation with a clarity she had never experienced before. Beneath that, she felt the heady rush of the woman's power, as if her veins ran with fire. It filled her body, lying on that soft bed in the Fairy Queen's palace, the same way Kaede had filled all of her senses when they kissed.
# Chapter XXX
aede did not know what to do. She went to Taisin's room and stood outside the door, but she could not bring herself to knock. She could barely believe what had just happened—it was all so surreal, this place with its impossibly smooth walls and intoxicating lights. Perhaps they hadn't really kissed at all; perhaps it was all just an illusion. But she could still feel Taisin's mouth against hers, the bones of her spine beneath her fingers. Kaede's entire body burned at the memory. But Taisin had fled from her. Kaede remembered their whispered conversation in the middle of the night after leaving Mona's cottage. Taisin was promised elsewhere. What had made Kaede think Taisin had changed her mind? Kaede's heart sank. She turned away from the closed door and went back to her own room.
She spent a restless night in bed, dreaming of walking down the corridor between her room and Taisin's. Each time she knocked on the door, and each time she woke up just before it opened, every muscle tense.
When dawn came, she dressed and went into the sitting room. No one was there, but the table was already laden with fresh fruit and warm bread. There was even a strange object that she eventually recognized as a teapot, and when she lifted the hinged lid, a rich aroma was released. She poured a small amount into one of the delicate porcelain cups and sipped it cautiously. It had an unusual, roasted flavor that she immediately liked.
She finished two cups of it before Taisin appeared. Though she made no sound, Kaede noticed her immediately, standing hesitantly in the doorway. When their eyes met, Taisin blushed, and the sight of her flaming cheeks gave Kaede some courage. She would have gone to her at once, but then Con brushed past Taisin, entering the room with a yawn. "Are you sure we're not all dreaming?" Con said in a voice still laced with sleep. He picked up an orange fruit and began to peel it, revealing a light pink interior. He pulled off a segment and sighed with pleasure. "This is much better than camping."
Kaede choked on a laugh, and he smiled at her. She wondered if he had said that on purpose, for she felt the tension in the room dissipate—at least a little.
Taisin sat down and took a piece of bread, stealing a glance at Kaede as she said, "I have to agree with you." Kaede caught the end of her look, and all of her came alive with awareness. She thought: Maybe she has changed her mind after all.
That morning, they each made use of the bathing chamber adjacent to the sitting room; they each dressed in the cleanest of their clothes; and then there was nothing to do but pace the stone floor and wait for the Huntsman to arrive.
After so many weeks on the road, the last hour was the hardest to bear. Kaede surreptitiously watched Taisin, who had braided her wet hair and fixed it with a black comb on her head. Her neck was exposed, scrubbed clean and pink, and every time Kaede glanced at her, the pink crept a little farther up until Taisin turned away and went, trembling, to stand by the window, her back to the room. Kaede sat in a chair and looked down at her hands; she could still feel the small of Taisin's back beneath them. Her heart fluttered in her throat. She didn't know how long she could stand this queer pretense that nothing had happened between them. But when she thought of what she might say to Taisin, the words would not come. Her mouth was dry; her palms were clammy. It was like an illness, she thought, or an enchantment: these feelings that cloaked everything in a fog of desire. Here she was in the Fairy Queen's palace at last, after a journey that had killed two men who did not deserve to die; after her hands had been bloodied more than once; and she could barely even remember why she was here. All she wanted was to kiss Taisin again.
Con, who normally would have been sensitive to the strained silence that gripped Kaede and Taisin, was consumed by his own anxieties. Before leaving Cathair, he had discussed the Kingdom's position on the Borderlands Treaty with his father and Lord Raiden, but now that he was here in Taninli, he realized that all the advice they had given him was worthless. King Cai and Lord Raiden knew every detail of the political machinations that were about to erupt in civil war in the southern provinces, but they had no idea what was going on in the Wood. He wondered if they even truly believed that the Fairy Queen existed. She was a figure lost to the mists of history, and though the Council of Sages took her invitation seriously, Con knew that his father only submitted to the Council because of tradition. His father was a man of action; he did his best to ignore the unseen world that the sages worked in. If the Council ever made a demand on him that challenged his power, Con was sure that his father would deny it.
King Cai had told him to play the diplomat; to flatter the Queen yet promise nothing. Con knew that he would not be able to do this. He had seen too much on the way to Taninli to doubt the significance of the Queen's invitation. This was no mere social call, and he was almost sick from nerves. He had visited governors of distant provinces before; he had attended state banquets and done his best to charm those his father asked him to charm. But he was certain that those experiences had been nothing compared to this. He suspected that the Queen had more in mind than a simple renewal of that ancient treaty, and he did not know if he had the power to give it to her—or the judgment to decide if he could.
When the Huntsman came to the door at last, Con sprang up, agitation vying with relief on his face. "Finally," he said. "It's been a long morning."
The Huntsman gave him a sympathetic look. "Shall we go?"
He led them down long corridors of gray-veined marble, past banks of sunny windows, and through a rotunda in which a statue of a unicorn lifted its head toward the arched ceiling. At its feet a stone phoenix spread its wings. They passed Xi dressed in every shade between white and pale blue, who seemed to melt out of sight as soon as Kaede noticed them. The effect was disquieting; it made her wonder if the whole palace was just an extraordinary illusion.
The throne room was reached by climbing one last wide flight of stairs that culminated in grand redwood doors. They reminded Kaede of the doors to the Council chambers; they even had similar handles set in the very center. They opened into a long, broad hall; windows along one wall overlooked a garden sculpted into a perfect wilderness. At the far end of the room, a low dais supported a crystal throne cushioned in green silk. Seated there was the Fairy Queen. When she saw them enter, she leaned forward slightly, laying her right hand on the armrest.
It was a long walk to the dais, and their footsteps echoed in the high-ceilinged room. The Huntsman reached the Queen first and bowed deeply before introducing the humans. He spoke in his own language, but Con recognized their names, and when the Queen's eyes flicked over him, he shivered. The Queen's face was glowing, ageless; her eyes were the color of gold. She was beautiful, but it was a fearsome kind of beauty, like the mirrored edge of a finely crafted blade.
Con swallowed; his mouth was so dry. He stepped forward and bowed to the Queen. "Your Majesty," he said formally, "I come as a representative of my father, King Cai Simin Tan. He regrets that he is personally unable to respond to your invitation."
The Queen spoke in his language: "Why have you come in his place?"
"Our kingdom is suffering through a difficult time, and my father could not be spared."
"Tell me about this difficulty," the Queen said. She studied him intently, and Con had to look away to avoid her eyes. He realized that there was no furniture in the entire room except for her throne; all visitors had to either stand or kneel before her. It was an old trick; his father employed the same strategy. The thought galvanized him. But he allowed himself to look slightly past the Queen as he spoke, so that he would not have to withstand the full force of her gaze.
"For the last several years, Your Majesty, our winters have been... extremely hard. Many of our provinces have experienced storms that have been extraordinarily fierce. Livestock have died; food stores have been destroyed unexpectedly. We have survived these winters, but each summer the harvests have been increasingly poor. This year, summer has not come. My people are starving. Several of the provinces are on the verge of insurrection. This is why my father could not be here." He paused, taking a deep breath. "And there have been other things. There have been sightings of strange creatures near the border of the Wood. Creatures that are not human. We have encountered them ourselves on our journey here."
"What have you seen?"
He told her about the reports his father had received about creatures, possibly fay, entering the Kingdom in the north. He told her about the creature in Ento, and the body that had been found outside of Jilin. The Queen's face remained impassive as he spoke, and when he finished she asked, "Is that all?"
Con bristled. She sounded as if she thought what he had told her was of no consequence. "No, that is not all, Your Majesty. We came here at your invitation, but along the way we lost two of our party. One—Tali, who was a guard to me since I was a boy—he was killed by whatever tortured spirits are haunting the Great Wood that separates your land from mine. And another guard, Pol, was mauled to death by wolves who attacked our entire party. A third, Shae—" Here his voice almost broke, but he continued on with a fresh burst of anger. "Shae was nearly killed as well, and we were forced to leave her behind to make sure we arrived here as you asked, because my people have heard nothing from your kind in generations, and to receive such an invitation during a time of catastrophe—it—" He broke off, trying to compose himself. He looked straight at the Queen. "It could not be a coincidence. We are here, Your Majesty. Why have you asked us to come?"
The Queen swept her eyes over him from head to toe; he felt the hairs on the back of his neck rise. Finally she said, "I am sorry to hear about your companions. And you are correct. My invitation to your king was not a coincidence. But the answer to your question is somewhat... involved." She settled back in her throne and turned her eyes to the long windows.
"Our ties with your people have been mostly severed, but once, it was different. Once, our lands were more closely entwined. Once, our people mingled with each other. But it was not an entirely peaceful commingling. We live so many generations longer than your people do. Some things that we remember, you forget. We could not coexist without misunderstanding each other.
"So, in time, there was war. A long, bloody war. It destroyed countless numbers of my people as well as yours. At the end of it, the survivors on both sides drew up a treaty to prevent such destruction from ever happening again. Afterward, the remaining fay scattered. The Xi remained here in Taninli, but the lesser fay retreated to their own hollows and mountains and forests. And gradually, your people forgot about us. We both kept to our sides of the bargain. Even if there has been isolation, there has also been peace.
"All this happened before I was born. Few of my people were alive when the treaty was signed. And in the intervening years, some of my people have become curious about your kind. You live such short lives compared to ours; we wonder what makes them worth living."
The Queen looked at Con with a trace of regret on her face, and for the first time that day, the glamour she wore cracked. She did not look old in a human sense, but there were centuries in her, and there had been pain.
She continued: "One Xi woman lived near the border between our land and yours. She encountered a human man one summer, and she took him as a lover. She became pregnant. She was terrified, for she knew her halfling child might not be welcome in either of our lands. She came to Taninli and begged for my mercy. I gave her shelter here while she labored, but she did not survive childbirth. The halfling did survive. It was a girl. I raised her as my own daughter."
The Queen's face hardened, and once again she gazed out the windows. "She was given everything, this girl—every delicacy, every bauble, every privilege I could give her—but she always wanted more. She was stubborn. She would never acknowledge that she was not truly Xi. She demanded to be named my heir, but it was impossible. The time has not yet come for me to name an heir, and when it does, I will not choose a halfling."
The words were spoken coldly, but it seemed as if the Queen were holding her emotions tightly in check. A blue vein in her right temple throbbed. Taisin began to tense up; she had a dreadful fear that she knew what the Queen was about to say.
"When she realized I would not change my mind—that she would never rule the fay as she desired—she left Taninli. It has been a dozen years since she walked out of this city's gates. In that time, I have sensed her power growing. I believe she is drinking up the energies of the fay and discarding them when they become too weak to benefit her. The ones who survive have come to me seeking help, but I can do nothing for them. She takes their lives; she becomes stronger with each fairy who dies."
Taisin felt sick. All the cages she had seen in her visions; the glimpses of the fay trapped within them—she knew now that they had been imprisoned there by this woman.
The Queen said, "I believe she has built a fortress for herself in the north."
Taisin's skin prickled. She could see that fortress of ice in her mind's eye as clearly as if she stood before it in the snow.
"The meridians of the world are tangled up there, forced into some kind of knot that she has created. She has gathered winter all around her; I can feel the cold from here. Her actions have altered the seasons elsewhere. I have tried to bring the seasons into alignment here in Taninli, but the chaos you describe in your kingdom—it can only be a symptom of what she has done."
The Queen leaned forward and looked at each of them in turn. "I have called you here because she must be stopped before she does more harm to this world. She has been playing with terrible powers, and soon she will destroy more than can be saved."
Con asked: "How can she be stopped?"
"She must die," the Queen said. "That is the only way the energies she has taken can be returned to the world." A tiny, grim smile twisted her lips. "And only a human can kill her."
The Queen's words rang in Con's ears, and he felt a chill spreading over his skin. "But if she is so powerful, how could any human succeed?" he asked. "Surely this is a task meant for one of your own."
"My people are peaceful," the Queen said curtly. "We cannot take the life of our own kind."
"But she is only half Xi—"
"She is one of us, even if she could never be Queen. That is the truth she has always refused to see. Our blood, just as much as yours, runs in her veins. And there is only one weapon that can kill one of the Xi."
"What weapon?" Con asked. "Why would we have such a weapon?"
"One of you already has this weapon. It is a simple one. You have brought it with you." The Fairy Queen turned her golden eyes to Kaede, who felt a shock run through herself. She remembered Fin handing the iron dagger to her, hilt first. _The Xi don't like iron_ , Fin had told her.
A heavy certainty settled over her, and Kaede said to the Fairy Queen, "You would have us be murderers."
Taisin stepped forward. "I will do it," she said, her heart pounding. She refused to send Kaede to face this woman.
"No," Con objected. "Taisin—"
"You are the Council's girl, aren't you?" the Queen said, looking at Taisin.
She flushed. "How did you know?"
"Everything they know, and many things they have forgotten, I know." The Queen examined Taisin's determined face intently. "But you have seen things even I haven't seen."
"I have seen the fortress of ice," Taisin admitted. Kaede and Con swiveled to stare at her.
"You never said anything about that," Kaede said, stunned.
Taisin's face paled, and she couldn't meet Kaede's eyes. The things she had seen—the cages, the ice, the sea—should she have told Kaede and the others about them? The visions had been so strange; she hadn't understood them.
The Queen asked, "Have you seen _her_?"
Taisin twisted her hands together. She felt guilty and frightened. "Yes. I've seen her."
The Queen's eyes narrowed. "Do not let her deceive you."
"She is so strong," Taisin said.
"I will give you her name," the Queen said, "so that you may see her for who she truly is."
"Her name?" Taisin was confused. "But how—"
"I named her when she was born. Her name is Elowen."
As she said the name, Taisin felt something inside her shift—as if a bolt had been thrown back from a door, and now all she had to do was nudge it open.
"There is power in naming," the Queen said. "And now you have an advantage, however small, against her."
Con asked: "If we do not kill her—if Elowen remains alive—what will happen?"
"She is like a rising storm. She must be stopped soon." The Queen turned to Kaede again. "You have the weapon. You must do this."
Kaede's fingers curled into fists. All of her balked at the Queen's demand. "I am no assassin."
The Queen gave her a measuring look. "I am not seeking an assassin. I am seeking a hunter."
In their sitting room, Con paced back and forth in front of the balcony doors. The Fairy Queen had asked for their decision by end of the day, and Con felt trapped. If what she said was true—and Taisin seemed to believe her—then how could they refuse? Yet Con believed the Queen was asking them to undertake a suicide mission, though Kaede argued that he couldn't predict the outcome. As the hours passed, they talked in circles until Kaede abruptly asked Taisin, "Why haven't you told us about your visions?"
Startled, Taisin responded, "I didn't know what they meant. What use would it have been for me to tell you?"
Kaede looked hurt. "We might have helped you figure them out."
Taisin reddened, feeling chagrined. "I'm sorry. I just—Sister Ailan—" She sat down in one of the armchairs, a miserable expression on her face.
Con stopped pacing and turned to her. "What have you seen?" he asked gently.
She closed her eyes and pinched the bridge of her nose as if her head ached. "I see the fortress, repeatedly. It is made of ice, like a mountain floating on the sea. I see the fay in cages. They can't stand being imprisoned; I think some of them are dying from it. I see her—Elowen. She has a nursery. There was a baby there, like the one we saw in Ento. I don't know what she's trying to do, but it's—" A wave of revulsion swept through Taisin as she recalled the sight of the infant monster smashed against the floor. "She is cruel. She is more powerful than anyone I have ever encountered, except for the Fairy Queen herself."
"Is the fortress guarded?" Con asked.
"I don't think so."
"Then we might have the advantage of surprise," Con suggested.
Taisin frowned. "The fortress is surrounded by open sea. I think we would be visible from quite a far distance."
"Then she could kill us before we even step foot in her fortress," Kaede said. She leaned against the table, her arms crossed.
"True, but..." Taisin trailed off, biting her lip.
"What is it?" Kaede asked. "What are you not saying?"
"I think... I think she will allow us to come." Taisin seemed hopeful and frightened all at once.
"Why?"
"Because she will not think we are a threat. We are three humans with a tiny little dagger."
Con rubbed at his chin, considering Taisin's words. He wondered what Tali would do, and a pang went through him. He looked at Taisin, pale-faced and stiff in her chair carved out of a tree trunk, and then at Kaede, who had dark shadows beneath her eyes. He had known Kaede since they were children; he could remember her in pigtails, chasing him and her brother across the broad palace courtyards. He remembered that her eighteenth birthday was today; she was of age now. But he could not shake the feeling that all of this had come too soon for her, and Taisin was just as young. Tali would never let them take the risk of going after Elowen. Tali would have done it himself.
"Elowen has to be stopped," Con said, "but I will do it."
"What do you mean?" Kaede asked. "The Queen said—"
"I don't care what the Queen said. You've been carrying that dagger, but I can't let you kill her, Kaede. I'll do it."
"Con—"
"You're not going to do it," Taisin protested. "You can't face her. She is very powerful. She'll destroy you."
"If she's so powerful, she can destroy you, too," Con argued.
"I've felt her," Taisin objected. "I'm the only one who has a chance against her. You can't do it." She clenched her hands in her lap stubbornly, but inside, doubt swirled. Elowen was so strong; Taisin had no idea if she could actually defeat her. She only knew that Con—or Kaede—would be defenseless against her.
Kaede was watching Taisin closely. She pulled a chair out from the table and set it in front of Taisin. She sat down, her elbows resting on her knees, and leaned toward Taisin as she looked her in the eye. "You seem to want to do this yourself," Kaede said, "but I don't think that's a good idea." There were only a couple of feet separating them now, and Kaede felt as if that space was pulsing with the beat of her heart. Taisin's cheeks turned pink, but she did not look away. Kaede almost forgot what she was going to say. She took a shallow breath. "If we go, we go together. You and me and Con. We've made it this far; we have to stay together." She looked up at Con. "Do you agree?"
He crossed his arms. "Only if you both promise that neither of you will attempt to face her alone."
"I promise," Kaede said. "Taisin, do you?"
Taisin's stomach quivered. She closed her eyes, rubbing her hand over her face as she remembered the vision of Kaede leaving the shore. Con had stayed on the beach with her. She hoped they would be able to change that future. "Yes," she said at last, reluctantly. "I promise."
"Then we'll go to this fortress," Con said, "and we'll do this together."
When the Huntsman came to their door later, he did not seem surprised by their decision. "I will put things in order," he told them. "We will leave in the morning."
# Chapter XXXI
t had not taken long for Taisin to pack up her belongings. Her knapsack waited by the door, and she lay in bed unable to sleep. Supper had been subdued, and Taisin had fled to her room afterward to avoid Kaede. But now, lying here in the dark, Kaede's face was all she could see.
If she had to describe it to someone else, she would dutifully relate the obvious details: light brown eyes, a pleasant nose and chin, and a mouth that smiled easily. But such a description omitted all of what made Kaede's face so extraordinary to Taisin. The mischievous gleam in Kaede's eyes when she saw something funny; the way her eyebrows arched in exaggerated reaction to Con's jokes; the shape of her lips, and the warm, firm texture of them.
Taisin approached the memory of their kiss gingerly, as though it were a wild beast that might knock her down, and yet part of her hoped it would do just that. If she was to be a sage, she would have to turn away from that beast forever. She would never be able to marry; she would not even be allowed to take a lover. And though she had only had the briefest taste of what she would have to give up, she understood now why sages made that vow. The desire that had awakened within her was like a fog descending on a mountain valley, filling every hollow, slipping between tree limbs, tickling every leaf with its seductive breath. It left no room for the calm contemplation necessary to do a sage's work. And though Taisin had only ever wanted to be a sage, now she wondered how she could possibly deny this feeling inside her.
She splayed her fingers across her heart; she felt the rhythmic beat there, the rise and fall of her lungs beneath. Her body was like a new thing to her; she had never known this ache before. It made her skin flush and her eyes dilate, and some part of her marveled at the focus of the energy that ran through her. All it wanted was one thing: to consume her entirely. To drive her up out of bed in the dark of midnight, to slip barefoot into the corridor between their rooms, and to deliver her, trembling, to Kaede.
Kaede was asleep, dreaming of a hunter running lightly through the Wood, a quiver on her back. She would sight her quarry and draw the arrow as smoothly as if her body were made of quicksilver. The arrowhead was cold as iron. It was Fin's dagger, protruding from the graceful wooden shaft like an eyesore—and then the shaft turned into her hand.
There was a sound that Kaede later recognized as a door closing, and she awoke to find Taisin standing beside her bed.
Confused, her body tingling into awareness, Kaede whispered, "Is something wrong?"
"No," Taisin said, her voice barely audible.
Kaede pushed herself up, heat coursing through her. "Do you need something?" Kaede asked, flustered.
Taisin's hands flew up to cover her mouth, whether to hide embarrassment or laughter Kaede wasn't sure, but a sort of half-choked sound emerged from her, and Kaede said, "Is it about... last night?" It wasn't until the words were out that she realized what they were, and perhaps if she had been awake when Taisin arrived instead of deep in a dream, she might have never had the courage to continue. But now, still shaking off the musty fog of sleep, she said all in a rush, "I didn't mean to upset you, Taisin. I know you'll be a sage, and I'm sorry I kissed you—if I could take it back—"
"Oh, no," Taisin said quickly, firmly. "No." She came to the bed and sat down on the edge of it, and Kaede felt everything sink toward her. "Don't ever say that," Taisin whispered, a catch in her throat, and now Kaede was more awake than she could ever remember. She heard Taisin's breath quickening, and as they leaned toward each other she could smell the scent of her skin. She wanted to put her nose against Taisin's throat and inhale all of it, all of her. She bent her head toward the shadow of Taisin's neck; her mouth brushed over the fluttering of her pulse.
Taisin was wearing an old tunic, the cloth soft with use. Some of the buttons were coming loose, and when she unbuttoned the first one, it hung down on a single thread. She took Kaede's hand in hers and put it on her skin, and gooseflesh rose at the touch of her fingers. Kaede moved her hand, tracing the shape of Taisin's collarbone. She pushed the tunic back, and Taisin's long black hair brushed over her bare shoulders. And then Kaede leaned toward her and they kissed again. Her mouth opened; she breathed her in.
Taisin remembered the way it had felt when she pulled life into that tiny purple blossom, the torrent of energy through her body. She remembered the way that power rippled through Elowen like molten ore, hot and precious. This was even more exquisitely immediate; there was nothing between her and dizzying sensation. Here was the touch of Kaede's fingers on her skin, and there the soft insistence of her mouth. Taisin felt as though there were a thousand purple flowers blooming inside her, a sea of them, each opening her black eye to the sun, trembling to see the wide-open sky.
Taisin slid into sleep so easily; her body was at ease, vulnerable.
The ice fortress swam into focus almost immediately—she was there again, standing at the window overlooking the beach. This time she felt as though she were merging into the body of the woman who stood there. _Elowen._ She formed the name on her lips, asleep in the tower room with Kaede beside her, and she felt the woman in the fortress come alive. Elowen turned her head just slightly, as though she sensed a presence nearby. She left the window and walked toward white velvet curtains hanging against the icy wall. There was a silver cord dangling from the ceiling, and as she pulled it, the curtains parted and revealed a mirror. It was made of glass like all mirrors, but there was something different about this one, though Taisin could not at first discern the difference. All she knew was that she was gazing at the reflection through Elowen's eyes, and she saw a beautiful woman there.
She was tall, willowy, with long, golden-white hair that swept to her waist. She had yellow-brown eyes and sharp cheekbones, and her lips were the color of a bruised pink rose. Her skin was milky white and smooth as a newborn's. She wore a gown of white silk belted with a gold chain, and her fingers were covered with jeweled rings. When she moved her hands, they flashed in the brilliant sunlight: diamonds, rubies, sapphires.
She smiled at herself in the mirror, and Taisin felt her own lips turning up at the corners. Elowen said to her: "You know my name, but I do not know yours." Taisin heard the words as though she were standing in that frozen palace with Elowen; she heard them as though she had spoken them herself. Fear flooded through her as she realized that Elowen could see her, too. As Elowen sensed her agitation, she threw back her head and laughed. The sound echoed.
Taisin did not at first realize that Elowen had begun to push into her consciousness. They were already so close. They were breathing the same breath; their veins ran with the same blood. Taisin felt disoriented; she felt doubled. She couldn't tell where Elowen ended and she began. But in that round tower room in Taninli, her shoulder bumped against Kaede, and Taisin drew a breath all on her own, and she remembered who she was. She nearly awoke, but Elowen reached through that mirror and held her there, transfixed, half asleep, half aware, as she demanded, _Who are you?_
Taisin pushed back. It was like running in quicksand, trying to extricate herself from Elowen's power. It was like struggling against a cold, fierce current, and she was afraid she would drown. But she fought her way up, remembering the grip of the freezing river Kell, and when she came to the surface, just as before, Kaede had her arms around her.
She gasped, drawing breath after greedy breath in the dark of Kaede's tower room.
Kaede was whispering to her, stroking her hair back from her damp forehead.
Her blood was roaring, her heart pounding.
Kaede gathered her close and held her until her lungs felt like they were her own again.
"It was her," Taisin whispered.
"Who?" Kaede asked.
"The Fairy Queen's daughter." She would not say her name.
"What do you mean?"
"I saw her," Taisin said, and she knew that Elowen was angry.
Dawn was breaking, spreading soft pink light across the eastern sky above the city. Kaede propped her head up on her hand, looking down at Taisin's pale and tired face. She ran a finger over the line of Taisin's mouth.
"She knows who I am," Taisin said.
Kaede's hand stilled. "What does that mean?"
"I don't know," Taisin whispered, but fear filled her. She felt tears pricking at the corners of her eyes. She reached up and pulled Kaede down, pressing her face into her neck. She could not forget the way that Elowen had engulfed her, all power and might, and she had no idea how they could possibly kill her.
# Chapter XXXII
hey breakfasted together, sitting at one corner of the table with their knees touching. Despite the shadow of Taisin's vision, they felt enveloped in an enchantment: one in which even the drinking of tea was as magical as any fairy glamour.
When Con came out to join them, Taisin and Kaede hastily scooted apart, but the expressions on their faces were so plain that he laughed out loud. "I see that things have changed," he observed, and Kaede flushed so deeply she couldn't look at him.
The Huntsman came to collect them shortly after breakfast. He told them that the Fairy Hunt would accompany them to the northern edge of the Wood, and then they would have to continue on without their Xi escort. "We will not travel through the lands that she has taken for her own," he explained as he led them through the palace to the outer courtyard.
"But how will we find her?" Taisin asked, hurrying to catch up with his long strides.
"You have a token of hers," he said.
"I do?" Apprehension quivered in her as she tried to think of what she could be carrying that had been Elowen's, and then her stomach dropped. "The medallion," she said, and the alarm in her voice caused the Huntsman to stop and turn back to her. "Is that how—why I have seen so much of her fortress?" she demanded.
The Huntsman regarded her pale cheeks and wide, dark eyes, and said as kindly as he could, "If you were already sensitive, then yes, her medallion may have enabled you to see more of her."
Taisin felt for the chain around her neck and pulled the medallion out. It was black and opaque, as usual, but she felt newly aware of it, and now she wondered how she had ever not known that it once belonged to Elowen. "How did she lose it?" she asked.
Sadness washed over the Huntsman's face. "She left it behind when she left Taninli. It was a gift from the Fairy Queen."
He came toward her and touched the black stone with a gentle finger. A tiny glow burned in the stone for a moment. "It wants to be reunited with her. It will show you the way."
Taisin closed her hand around the medallion, intending to take it off; she wouldn't wear Elowen's chain around her neck. But at the last minute, struggling against an equally powerful desire to keep it, she slid it back beneath her tunic. When she felt the stone pressing coldly against her skin, she was disconcerted by the sense of relief that flooded through her. The Huntsman nodded at her as if she had made the right decision. "The longer you wear it," he said, "the more it also becomes yours."
In the courtyard, half a dozen riders of the Fairy Hunt awaited them, along with riding horses and packhorses loaded with canvas-covered gear. Con did not see their own, ordinary steeds, and he asked, "Where are our horses?"
"They are resting for your return journey back to your kingdom," said the Huntsman. "You shall ride our horses as far as you can. The dogs will take your supplies the rest of the way."
Eight dogs, each with thick gray coats shading into white bellies and paws, had been led into the courtyard by a thin, spry Xi woman. She spoke to the Huntsman in their language, and her green eyes glanced quickly over the humans. She said nothing to them before she left, but she bent down to her dogs and each met her nose to nose in a solemn farewell.
They left Taninli by the same route they had taken through the city when they arrived. At first the few Xi they saw were simply going about their business as usual, but as they descended into the streets, more and more Xi emerged from their homes to watch them ride past. Once again, Kaede had to look down to avoid their eyes. She couldn't bear to see the doubt in their faces—or, even worse, the hope.
Outside the city gates they turned north, leaving the boulevard almost immediately and riding straight into the Wood. The manicured trees quickly turned wild, and within an hour of leaving Taninli and its pocket of summer behind, the air began to carry the bite of cold. The horses and dogs moved swiftly—more swiftly than horses or dogs should move, Kaede thought. When she looked ahead of them the trees were a bit blurry, and the dogs blended into the landscape, running silently over fallen leaves. She felt increasingly detached from her body as the day progressed, and it would have disturbed her if her senses had been more alert, but instead, she felt a kind of haze that prevented her from doing anything but staying in the saddle.
At night they stopped beside a bubbling stream to water the animals, and the Xi set up small, strange tents in the spaces between trees. They were round, like bubbles made of canvas, stretched tight over ingeniously bent poles. Kaede crawled into the one the Huntsman told her was hers, and she slept as soon as she lay down on the fur-covered pallet.
The next morning she emerged from her solitary tent, and one of the riders gave her a horn cup full of a hot, bitter drink. It was shocking on her tongue, and when she looked up she saw a barren landscape around her. Tree branches that should have been heavy with green needles were stripped clean, as if a giant had come and swept them bare with his fingers.
A dog butted against her leg, and she bent down to stroke him. His brown eyes regarded her with gentle curiosity, and then she saw Taisin come out from a nearby tent, and soon Con emerged from another. There was no time to do more than wish one another a good morning, for the Fairy Hunt was readying to go, and they thrust cups of the hot drink into Con's and Taisin's hands and told them to hurry.
They rode again.
Midmorning on the third day after leaving Taninli, the trees abruptly ended. Kaede twisted back in her saddle and stared at the bare trees behind her, trunks the color of ash. Her breath made clouds in the air. The Huntsman was dismounting from his horse, and his boots touched down in snow. She looked north, away from the Wood, and the land was a broad expanse of white stretching toward a faraway horizon. The blue sky arched there in the distance, but above her head the sun was blocked by clouds.
The Huntsman and the other riders were taking bundles down from their horses, and Kaede watched them in confusion, for it was too early in the day to set up camp. They were unpacking long, slim pieces of wood that folded and unfolded in strange ways, and when they put them together, they formed a strong sledge. Stacks of firewood were then lashed onto the sledge, and most of the provisions that had been carried by the packhorses were transferred there as well. The dogs submitted to being harnessed to it, and before she knew what was happening—there was still something wrong with her sense of time—the Huntsman was asking her to dismount from her horse.
"What's going on?" she asked, trying to inhale the chilly air to wake herself up. Con and Taisin seemed as muddled as she was.
"We must leave you here," the Huntsman said. "Your way lies over the ice field."
Kaede shook her head; it felt woolly.
Taisin said, "We are close."
"Yes," the Huntsman said. "I would suggest you put on your warmer clothing."
One of the Xi came to take Kaede's horse away, and she felt the lick of winter against her skin as she looked out over the glacier.
"We have given you everything we can," the Huntsman was saying. He explained how to use the round oil lamps; how to strap the broad snowshoes onto their feet; how to command the dogs.
Kaede blinked again. The light was so odd here. She turned to the Huntsman, willing herself to focus on him. He seemed just slightly worried. "Tell your queen," she said, "that we will do the best we can."
He looked at her gravely and, for the first time, came to her and squeezed her shoulder in the way her father had done once, when she was a little girl and had been knocked down in a fight with her brother Tanis. She had not cried, even though her nose was bleeding, and her father had crouched down to her eye level, his large, warm hand engulfing her shoulder and upper arm, and said somberly, "My little hellion." But she had known that he was proud of her in that moment, and the memory of him suddenly made a lump rise in her throat, and she had to turn away from the Huntsman to stare at the ice.
# Chapter XXXIII
aisin and Kaede walked ahead of the sledge, leading the dogs north, while Con followed behind in their tracks to make sure the load remained stable. Every step across the snow sloughed off a bit of the fog that had clung to them as they traveled with the Hunt, and by midafternoon the vista ahead shone with a clarity that was startling to eyes recently glamoured by Xi magic. The sun was bright overhead; the ice field was broad and unbroken; the air stung their skin with its briskness.
Taisin and Kaede did not speak, for they were wrapped from head to foot in furs, and it was hard going. But more than once they glanced at each other, and each was surprised by the pool of happiness that spread through herself even as she trudged through the falling temperatures and growing dusk.
Their first night on the ice field, they built a small, hot fire in the lee of the sledge, and boiled water for their first hot drinks since morning. The wind had risen and was whipping up the snow in frozen imitations of dust devils, but the night sky was clear and black, with thousands of stars spread in unfamiliar constellations overhead. They crouched as close to the fire as they could, eating a supper of dried fruit and hard, round crackers that tasted, ingeniously, of cheese.
Afterward, as Kaede fed the dogs, Con and Taisin pitched the two tents and unpacked their sleeping furs. Con took five of the dogs into his tent, and Taisin and Kaede took the other three. With the dogs curled up around them, their nest was cozy enough. Kaede slid her arm across Taisin's stomach and nestled her nose into the crook of her neck, and sleep overcame her moments after she lay down. Taisin was awake for only a few minutes more, long enough to wonder if Elowen would come to her tonight, but she was so tired that she couldn't even be properly anxious about it.
Sometime in the hours before dawn, Kaede awoke to hear Taisin speaking. They had shifted apart; Taisin was turned away from her, one arm flung out over the furs. One of the dogs let out a low growl, and Taisin's voice changed, deepening. Kaede could not understand what she was saying, for the words made no sense. The dog beside her tensed up. When she reached out to calm him, she felt his fur rising stiffly down his back.
Kaede shook Taisin's shoulder. "Taisin," she whispered. One of the dogs barked.
Taisin jerked awake, letting out a half-strangled moan. "What? Who is there?"
"It's me," Kaede said.
Taisin pushed herself up. It was too dark to see, but she felt the dogs creeping back to her, their hackles lowered now, and one rubbed his head against her arm.
"Why did you wake me?" Taisin asked, her voice rough. It didn't sound quite like her own.
"You were talking in your sleep."
"What did I say?"
Kaede thought she sounded nervous. "I couldn't understand you. It wasn't... it was not our language." A beat later, Taisin lay down again, and Kaede asked, "Did you see _her_ again?"
"I can't remember," Taisin answered. It was unsettling; her mind was so fuzzy. She lay awake for some time, trying to sort through the hazy memories that kept slipping away from her. But it was no use, and now she could not sleep, and the wind was buffeting the walls of their tent, keening like an army of ghosts.
"Kaede," she whispered, wondering if she had fallen asleep.
She had not. "Yes?" Kaede murmured, and she shifted closer. She heard Taisin's breath grow short; she felt her own skin suffused all over with heat.
Taisin turned to her. How strange and wonderful, she thought, that in the middle of this bizarre journey, there should be this: Kaede, who kissed her.
After a few moments, the dogs slunk off to the foot of the tent, affronted. Kaede stifled a laugh, her hands sliding around Taisin's waist, and later, they slept again.
In the morning, Taisin drew out the medallion and cupped it in her hands. She thought of the fortress of ice; she could imagine the walls of it so clearly, the windows bright in the sunlight, the sea all around it deep sapphire blue. The stone became warm; it pulsed like a tiny heart. Taisin felt it tugging at her until she faced northeast. On the horizon, the blue sky faded into the field of ice, making the land seem endless. "We go there," Taisin said, her voice small, swallowed up by the world of the glacier.
The dogs barked as if in affirmation.
Kaede woke again on the second night to the sound of Taisin's voice. This time she lay still and listened. It might have been the language of the Xi, but Kaede could not make out the different words. They flowed into one another in a singsong pattern that reminded her of chanting, but she had never heard any chanting like this. And then Taisin arched her back and laughed out loud, and the voice that came out of her body sounded nothing like her. The dogs, who had already been stirring awake, backed away and began to growl low in their throats.
"Taisin!" Kaede called, reaching out to touch Taisin's arm.
Suddenly Taisin's body went limp, her eyes blinking open in the darkness of the tent. She let out a weak sigh. "Am I dreaming?" she whispered.
One of the dogs whined and went to lick her face with his rough, wet tongue.
"Am I dreaming?" she asked again, more loudly.
"I don't know," Kaede said, disturbed by the confusion in Taisin's voice.
"I don't want to dream anymore." Taisin sounded as if she were on the verge of tears.
"What were you dreaming of?"
"Elowen," Taisin answered, and the dogs barked. She gave a panicked laugh and added, "She wants to know who you are."
Kaede felt drenched in cold. "What? Why does she want—"
"I don't know. I don't know what she's doing to me," Taisin said, her voice rising.
Kaede pulled her close, pressing her lips to Taisin's hair. "You shouldn't say her name again." She felt useless, and it frustrated her.
Taisin was groggy. She knew that Elowen had been inside her again, but things were different now that Elowen was aware of her. In the past, Taisin had seen the fortress clearly; when she awoke, she remembered. Now she had the feeling that Elowen had been erasing her memory somehow. Her mind felt rubbed clean in some places, and in others it felt like it had been scratched raw. It frightened her.
Kaede fell asleep again; the dogs stretched out, content, on either side of them; but Taisin lay awake thinking for a long time. She could not allow Elowen to take over her mind, and she began to formulate a plan to prevent it from happening.
On the third day, Taisin crumpled in midstep, and when Con and Kaede ran to help her up, she snarled at them. Elowen's voice came spitting out of her: _"Fools."_
They halted, shocked, their hands outstretched to Taisin, lying on the snow. Her face was twisted into a grimace; her eyes were glazed. She began to mutter to herself in the same strange language that Kaede had heard at night. "What is wrong with her?" Con demanded.
"She has been like this before," Kaede said. "The Fairy Queen's daughter visits her when she's asleep." The fact that Elowen seemed to be visiting Taisin now while she was awake was extremely disturbing.
Taisin's eyes were half shut, and her face was so pale it was almost white. Con asked, "What can we do?"
They ended up carrying her to the sledge, making room for her among their tents and blankets. She struggled a bit at first, and Con had to pin her arms to her side while Kaede held her legs. She wondered whether they would have to tie her down, but when they settled her onto the sledge, Taisin's body relaxed. She looked up at them with dreamy eyes and said in Elowen's voice, silky and cold, "It is such a pleasure to meet you both, at last." She laughed, her whole body shaking with mirth while Kaede and Con watched her, horrified.
But as quickly as it had begun, the laughter choked off, and Taisin let out a moan as if she were in pain. She curled up, holding her head in her hands. Kaede stroked Taisin's feverish forehead and asked, "Taisin, what can we do?"
Taisin jerked away from her touch as though it hurt her, and for the first time, Kaede truly wanted to kill Elowen. The anger filled her unexpectedly; her fingers curled into fists.
Taisin, her eyes squeezed shut, said in a shaking voice, "I'll be all right. We just need to go."
So they continued on.
That afternoon they came to a cliff. When Con and Kaede walked to the edge, they saw that the ice field ended in what seemed to be a sheer wall of white. It plunged down a hundred feet to a beach. In the distance, they could see the ocean: intense, cold blue dotted with ice floes.
Con looked in either direction and pointed south. "There. It looks like the cliff is lower there."
Kaede nodded. "All right. Let's go."
After walking for two hours, they found that the ice field did slope down to the beach, but it was a steep descent. "We could continue on," Con said, "and see if there is an easier way down. But we're going farther and farther away from the direction Taisin told us to go."
"We might be able to climb down," Kaede said. "Some areas are not as steep as others. We'll have to be careful, though."
"What about the sledge?" Con asked.
"We can leave the sledge up here. We'll leave half the firewood for the return journey, and the dogs will have no problem."
"And Taisin?"
She glanced back at Taisin, who was sitting on the sledge with a dazed look on her face. The sight of her twisted Kaede's stomach into knots. The closer they drew to Elowen's fortress, the more Kaede wanted to finish this—and finish it quickly. She felt a hard determination growing in her, and though the feeling was new, it was not unwelcome. It gave her courage, and she knew she would need that soon, for she had every intention of making Elowen pay for what she was doing to Taisin.
Kaede met Con's worried gaze and said, "We'll tie her to us. We have rope, don't we?"
He considered it for a moment. "I suppose we have no other choice," he said reluctantly.
Kaede unhitched the dogs, who seemed both surprised and excited at being allowed to roam free at this time of day. Some of them ran along the edge of the cliff, but two sat down behind her as she grimly approached Taisin with the rope. She wasn't sure how Taisin would react to being tied to them; all day she had been slipping further away, and it wasn't clear if she was actually aware of what was going on. But she did not fight when Kaede came with the rope, and just as Kaede knotted it tight beneath her armpits, she gripped Kaede's hand and said fiercely, "I am still here. I am still here. Don't let her tell you otherwise."
Kaede looked into Taisin's dark brown eyes; the sun was reflected in them in bright white spots, and she knew it was Taisin speaking, not Elowen. "I won't," Kaede assured her. "You will have to climb down after Con. Can you do it? I'll stay beside you."
Taisin nodded, though her face was pallid and drawn. "I can do it."
Con descended over the edge first, his belly flat against the snow, and a few of the dogs followed him. They had already bundled their supplies together and pushed them over the cliff, where they slid down the slope until the bundles lodged against an outcropping of ice. Con began to make his way carefully toward the supplies as Kaede helped Taisin begin her descent. From her vantage point on top of the cliff, Kaede kept an eye on Con as he shoved one of the larger packs along. She was reaching for her gloves, which she had removed to tighten the knots in the rope linking them together, when he slipped.
The rope jerked, and Taisin screamed as she was pulled down the cliff face. Kaede reached for Taisin's hand but was just a moment too late, and the rope tightened around Kaede's waist and yanked her toward the edge.
She fell to her knees and dug her fingers into the ice, but the rope dragged her painfully over the lip of the cliff until her legs were dangling over the precipice, her chest flat on the ground, her chin scraped raw against the snow.
Her heartbeat thundered in her ears; panic rushed through her body. She could not see Con or Taisin. The pack leader came and snuffed at her head. She called out, "Con!"
But he did not respond. And the rope continued to pull at her. Dead weights. Fear threatened to overwhelm her.
She let out her breath in a sob. She began to swing her right leg out, searching for footing—searching for anything. She kicked the glacier wall; small pellets of ice and snow rained down the cliffside, but there was nothing to break her fall.
Her fingers were freezing. Her hands began to slip. The ice would cut into her palms any minute now, and she would die leaving bloody handprints in the snow.
# Chapter XXXIV
er cheek was pressed against the ground. She gritted her teeth. Seen up close, the hard-packed snow became glittering ice crystals, sharp as a thousand tiny blades. Her breath steamed out of her; she watched the ice crystals melting. Her hands and arms and back screamed with the strain of clinging to the cliff's edge, but she wasn't about to give up.
And then she slipped again, sliding down a few more inches. Her stomach lurched; sweat broke out on her skin. Her boots scraped against the cliff wall until suddenly—finally—her toe found a tiny outcropping in the glacier wall, no wider than a hand span.
She could hardly believe it. She was breathless with relief. And then she began to drag herself toward the ledge.
It was brutal work. She felt as though her arms might rip themselves out of her body before she was done, and she might even welcome it.
But the ledge was just wide enough to support some of her weight, and when at last both of her feet were dug into it, she allowed herself to rest for a count of five, her face pressed against her arm, still clinging to the top of the glacier. Then she steeled herself and turned just slightly—just enough—and looked down.
The edge of the ice sheet was particularly steep where she had fallen, but just below her, it banked at a shallower angle. Taisin's body was sprawled there, and a splash of red marked the snow near her head. The sight filled Kaede with dread, and she had to force herself to look past Taisin, where the ground plummeted down again. The slope was not as precipitous there as it was near Kaede, but it was steep enough that she couldn't see what had happened to Con, for the rope attaching them together had disappeared into a crevice.
Looking around her, she realized that Con's fall had dragged her over the edge of the glacier at a particularly bad place. He had begun his descent several feet to her left, where the incline was less hazardous. Something had made him slip, yanking him—and Taisin and Kaede in turn—down to the right, where the cliff wall was nearly vertical.
As she pondered how she was going to climb down from her precarious perch, she suddenly felt the rope around her waist slacken. She looked down; Taisin was still motionless on the snow. But the rope that had gone into the crevice was loose now. Con must have cut himself free. Relief flooded through her. She hadn't known how she could continue on with both him and Taisin weighing her down.
"Con!" she shouted.
There was a long silence. But at last she heard his ragged voice below. "I'm here," he called faintly.
"Are you all right?" she yelled.
Again, a pause. There was a scrabbling noise. His voice came again, thick with effort: "I'm climbing out."
"I'm coming down," Kaede called. She took a deep breath and flexed her fingers, for they were chilled to the bone. But there was no other way: She had to climb down, inch by inch.
It was even slower going than before. She had to search out small toeholds in the glacier wall, and then she had to find places to grip in the ice. Below her, Con still hadn't reappeared, but they called to each other regularly, and she had no time to worry about him. Her shoulders burned, and all she could do was focus on each handhold, each step.
At last she came to the place where Taisin had fallen, and the ground was less steep here, so Kaede turned over onto her backside and carefully scooted down to her. Some of her anxiety ebbed when she saw that Taisin still breathed; the snow beneath her nose was slightly melted. The blood seemed to have come from a long, shallow scrape on her chin. Kaede reached out and touched her shoulder. "Taisin," she said. When there was no response, she shook her lightly, and then said her name more loudly. She was about to consider taking more serious action—though she didn't know what that would be—when she felt Taisin stir beneath her hand. And then she let out a low moan, and her eyes fluttered open.
Kaede was elated. "Are you all right?" she asked, and Taisin pushed herself up, putting a hand to her face where the cut on her chin was bleeding. Her fingers came away wet. "It's just a cut," Kaede said, attempting to reassure her. "Is anything else hurt?"
Taisin felt her head gently. "I think... I think I hit my head." Her tongue seemed to have trouble forming words, but oddly, she felt more like herself than she had for days. Perhaps the fall had somehow dislodged Elowen's grip on her. She began to move, and before Kaede could stop her she slipped on the ice, sliding down several inches, and she gasped, scrabbling for hold on the slick surface.
"Slowly!" Kaede called. "Don't move too quickly." Below them there was a crashing sound, and a cloud of snow flew up from the beach. "Con!" Kaede crawled down a few feet, but she could not see him.
"It's just the—the supplies," his voice came back to them. "I'm all right."
Kaede looked at Taisin, who was gradually realizing the severity of the situation, and said, "We must go very carefully, on our hands and knees. Don't try to rush it."
Taisin nodded just slightly. "I'll follow you."
Kaede began to creep down the slope, the rope snaking between them like an umbilical cord.
It was late in the day before they reached the bottom, and it felt as though every last inch of their bodies had been pricked by ice crystals. They were cold and stiff and hot and sweaty all at once, and Kaede would have done anything at that moment for a fire and a bath and a soft bed to collapse into. But there was only the frozen, sandy beach stretching as far as the eye could see, and Con, sitting on the ground propped up against the packs they had pushed over the edge. The bundle that had been packed with firewood had burst open when it hit the ground, and pieces of wood were scattered all over the snow. The dogs, who had climbed down on their own, waited nearby, their breath steaming out in the air.
At first Kaede couldn't understand why Con's left leg was bent at such a strange angle, but as she walked the last few feet to him, she realized that his face was white with pain. He was pressing his hand to his knee, and it was bloody.
"What happened?" she asked, halting.
"My leg," he said hoarsely. "I think it's broken."
Taisin knelt down beside him, holding her shoulder back a little, as if it had been twisted. Kaede rubbed a hand over her tired eyes, leaving streaks of blood across her face. She winced; her fingers were raw and bleeding from the ice.
Taisin bent over Con's leg, and she said hesitantly, "I can set it."
"You don't sound too sure of that," he said, and there was yet a note of grim humor in his voice.
"I saw Mona do it with Shae's leg."
"But you are not Mona."
"I'm as good as you're going to get."
Kaede looked back at the way they had come. The edge of the glacier was jagged, a series of huge steps torn from the earth. She saw that the crevice he had fallen into was a slim slash in the ground—little more than a couple of feet across. There was a smear of blood across the mouth of it. It must have taken a prodigious effort for Con to pull himself out of there. She said to Taisin, "What can I do to help?"
They broke down one of the tent poles and ripped apart the canvas, using it to bind the pole to Con's leg. Kaede had to hold him down as Taisin worked. By the end of it, he had nearly fainted, and Kaede wished she had thought to bring Shae's flask with them.
The dogs were arrayed in a half circle around them, watching attentively. The sky was darkening. Kaede said, "We'll just have to camp here tonight."
Taisin helped her stake out the remaining tent. There wasn't enough room inside for the three of them and all the dogs, but at least the glacier wall created a sort of windbreak. Kaede collected the pieces of wood and built a fire, and Taisin brewed the same tea for Con that she had made for Shae when she was injured. After they ate their cold supper, several of the dogs curled up together, huddling against their packs, and Taisin and Kaede helped Con crawl into the tent. A few of the dogs followed, whining pathetically as the tent flap closed, and Kaede said, "Oh, let them in. We'll be warmer with them inside."
Taisin had been quiet for most of the evening, but now as her two companions readied for sleep and the dogs nosed their way under the furs, she said, "I'll stay up and keep watch."
"Watch for what?" Con asked, grunting as he lay down, trying to prop his leg up at a more comfortable angle.
"I can't go to sleep, Con," Taisin said, though her face was drawn with weariness.
"But you're exhausted," Kaede said. Taisin was still favoring her shoulder, but she hadn't allowed anyone to examine it.
"Yes. But we're too close to... to her. Today—maybe because I was unconscious after that fall—she seems to have left me. At least temporarily. But if I sleep, it would be like opening the door to her again."
"Are you sure you can stay awake? Do you want me to sit up with you?" Kaede asked.
"No. I'll be fine. It's been a long time since I've had the luxury of stillness." She folded her legs beneath her and pulled the furs around her shoulders so that she wouldn't freeze, and as Con and Kaede slept, she sat, her eyes half open, watching the dark.
It took the better part of the morning for them to fashion a sort of sled for Con, for he could not walk long distances, and Kaede refused to leave him behind. They lashed together the remaining canvas from the tent they had torn up to create a sling, and tied it to the dogs' harness. As long as Con held on, he could be dragged, albeit roughly, across the ground. They set off again after a quick noon meal that Taisin ate only because Kaede forced her to; she had sunk into a daze and had begun to murmur to herself. Kaede realized that she was reciting the Thirty Blessings repeatedly from memory, as though that would keep Elowen at bay.
As the day drew to a close and the stars began to shine in the dark blue sky, Taisin was determined to keep going. Kaede suggested that they stop, but Taisin refused. "Just a little farther," she insisted, and she did not wait to see if her companions followed. She knew they would. Elowen was so close to her now; it was like they were in the same room, divided only by a painted screen.
It was pitch-black before Taisin consented to stop. There was a new moon that night, and even the stars seemed to be dimmed. The small fire they lit only served to make everything outside its circle of light seem darker. After they had pitched their tent, fed the dogs, and passed around their own rations for the night, Kaede was so tired she only wanted to crawl into her furs and sleep. But as she burrowed into the warmth of her bedroll, a curious sound began to knock at the edges of her consciousness. In the distance there was a gentle ringing, like two pieces of metal rubbing against each other. She wondered irritably what was making the noise, and why it was bothering her. But the dogs were so warm against her flank and she was so tired that it didn't bother her for long, and soon she was fast asleep.
It wasn't until morning that she learned what had been the source of the ringing sound. As soon as she stepped out of the tent onto the frozen shore, she saw a small dock scarcely twenty feet from where they had set up camp. At the end of the dock was a rowboat tethered with a sparkling silver chain. The boat bobbed gently on the ocean waves curling onto the shore. And there in the distance, like a snow-covered mountain erupting from the sea, she saw the fortress of ice, its windows glinting in the light of the rising sun.
# Chapter XXXV
aisin told them her plan while they ate their morning meal. Though she hadn't slept in days, she felt unnaturally aware, as if all her senses were on high alert. The air here was frigid, but peculiarly exhilarating. "Elowen knows me," she began. "She has been inside me; she has seen through my eyes. I think she expects me to come for her; she's even a little curious."
"You can't go," Kaede said, shaking her head. "You're not well."
"I agree."
Kaede's brows rose. "What?" She had not expected Taisin to give in so easily.
"If I go, I think it will be too dangerous. She could use me." All night, Taisin had agonized over this, initially not wanting to admit it to herself. But Mona's warning echoed in her head: _You have a strong heart, but even the strongest heart can be tempted._ And she had felt the temptation already. Experiencing Elowen's power in her visions had awakened a disturbing hunger to have that power herself. Part of her yearned to go to Elowen immediately; she sensed that Elowen would welcome her as a disciple. Yet everything she had learned at the Academy told her that Elowen's power was a gross perversion of natural law; and even if her teachers had kept some things from her, Taisin believed there had been a reason. She wanted to return to the ironbound fortress and ask her teachers, directly, for the truth.
Last night, sitting awake in the dark tent, everything became crystal clear. If she went to Elowen, she would be tempted to join her and become as corrupt with power as Elowen herself. As much as Taisin wanted to believe she would be able to resist Elowen, she knew she could not take the risk. When she looked hard at herself, examined her deepmost desires, she realized that she did not entirely trust herself. The realization burned at first, but then it made the decision easy. There was one person whom she trusted completely. Someone Taisin knew would do the right thing. She looked at Kaede. "She could use me," Taisin said, "but I don't think she could use you."
"Why not?"
"You're by nature much more closed off to the energies than I am."
Kaede gave a short laugh. "This is why I've never been able to pass the Academy exams."
Taisin smiled faintly. "Yes, well, in this case, I think it will be an advantage. Because even though you are closed off, you've spent many years studying the practice, and I think it has made you quite self-contained. It's like you've built a little wall around yourself."
"Good. Then I'll go."
Con, who had been listening to the two of them silently until now, interrupted: "You can't go alone. I'm coming with you."
Kaede protested, "Con, your leg—"
"Damn my leg," he said, frustrated. "You can't go alone."
"She's not going alone," Taisin interjected. "I'm going with her."
Kaede's forehead wrinkled. "You just said—"
"Listen," Taisin said fiercely. "Elowen has been inside me. But I haven't just been helplessly letting her in. I've learned some things from her."
Con was uneasy. "What have you learned?"
"I can do it, too." She turned to Kaede. "I can be inside you, to help you fight her."
"Inside my mind?" Kaede said uncertainly.
"Yes."
Con said: "Taisin, I'm sure you're capable of a great many things, but this—this doesn't sound safe. Look at what she has done to you."
"It will be different," Taisin insisted, keeping her eyes on Kaede. Kaede grounded her. "If we are together; if you are willing; it will be different."
Kaede asked, "But if she can't use me because I'm so... self-contained, why can you do it?
Taisin's cheeks burned. "Because you have already opened yourself to me." There was an upwelling emotion in Taisin's face that reached straight into Kaede's belly and tugged at her. Her own face colored. Taisin said hurriedly, "I tried it very quickly last night, when you were asleep. I can do it."
"All right," Kaede said, feeling awkward. She took a breath. "So, let's say your theory holds: She can't use me the way she might use you."
"Then you will go to the fortress," Taisin said, "and I will stay here with Con. And when you need my help, I will be there with you."
"How will you know when I need your help?"
"She has put so much energy into this place that it's practically glowing with it. It magnifies everything that's alive. I think I'll be able to feel when you need me."
"What if you can't?"
"I know I can. I can already sense your feelings, even now." Kaede's stomach gave a little lurch, and Taisin had the grace to look embarrassed. She continued, "And when the time comes, I'll help you."
Kaede said, "You'll help me kill her."
The words hung heavily in the air.
Taisin said, "Yes."
They decided that Kaede would leave that very morning. There was no reason to wait any longer.
She decided to bring nothing but the clothes on her back and the iron dagger that Fin had given her. She unsheathed it and looked at it again. Its blade was dark, inelegant; the textured skin that covered the hilt was nearly black, as though many hands had held it over the decades. It was cold and heavy and sharp, and it had been made for killing. Though she had carried it at her side ever since she had left the Academy, it seemed oddly unfamiliar to her, as if she had never truly looked at it before. She thought she could smell the tang of iron in the air. She wanted for this to be finished.
She moved to resheathe the dagger, but Con said, "Wait." He was sitting by the fire, his broken leg covered with a blanket. "You shouldn't wear it at your waist."
"Why?"
He held out his hand. "Let me see it." She gave it to him and then squatted down nearby. Taisin watched them both curiously. Con ran his hand over the edge of the blade, turning the dagger around. "It's a solid knife," he said. "This is what the Fairy Queen was talking about? Your weapon?"
"I think so. It is made of iron."
"The Xi can't tolerate iron," Taisin said.
He was silent for a few minutes, thinking. Finally he looked at Kaede seriously and said, "I am not a guard, but I have spent my life in the company of them, and I hope you'll take my advice."
"Please," Kaede said, "tell me."
"You should conceal this dagger. If you wear it openly, she'll see it; from what Taisin has said of this woman's power, I believe she could easily disarm you. Your only advantage—besides Taisin—will be surprise. And you've seen how open the land is here. We can't surprise her with our approach—surely she knows we're here already—but you can keep this weapon a secret until you need to use it."
"Where should I conceal it?"
She was dressed in the clothing the Fairy Hunt had given them all: fur-lined boots, warm woolen leggings beneath supple leather leg guards, tunic and fur vest and cloak. Con tapped at her boots. "You can slide it in here. Give me your scabbard and I can fit it into your boot." She took it off, and while he worked out a way to tie it to her leg, he said, "Don't forget your goal. You're not there to negotiate; you're there to kill. Take every advantage you can, Kaede. I don't think it's going to be a fair fight."
After he had lashed the scabbard onto her shin, she fitted her boot over it. The dagger was like a hard splint against her leg, but the boot concealed it neatly, and she could reach in and pull it out without much effort. When she was ready to go, Taisin offered to help with the boat and began to walk toward the dock, leaving Kaede with Con as he inspected the boot and the dagger one last time.
"I wish I could go with you," he muttered.
"You have to watch over Taisin," she told him. "She does things in her sleep sometimes, when she is being visited. She'll talk, or start shaking. You have to make sure she's all right."
"I will." He smiled faintly. "You watch out for yourself. I mean to bring you back to Cathair after this, you know, and make sure you don't have to marry that Lord Win."
She surprised herself by laughing. "I can't wait to have that conversation with my father. Thanks for giving me something to live for, Con."
The corners of his mouth lifted, but his eyes were sad.
At the dock, Kaede surveyed the rowboat. It was small; it looked as though it had never been used before. Elowen had made it especially for them.
Taisin stood beside her. "Are you ready?" she asked.
"As ready as I'm going to be."
"I will be with you." Taisin bit her lip and then asked hesitantly, "Do you trust me?"
"Trust you," Kaede repeated, as if it were an odd thought. "I love you."
Taisin's face twisted with sorrow and fear. This was the moment she had seen in that vision, and she felt it anew, and it was so much worse than she had ever anticipated. Yet she was the one who was sending Kaede to do this terrible thing. Had she always known it? Had part of the dread always been because she knew, somehow, that she was the reason Kaede left?
She cupped Kaede's face in her hands and pressed a hard kiss to her mouth. She whispered: "And I love you."
Kaede wanted to put her arms around Taisin, but she forced herself to step away. It would be easier, she told herself, if she didn't linger.
Her boots scratched against the wooden dock, and she lowered herself into the boat.
# Chapter XXXVI
he tried to not look back as she rowed. She didn't know if she would have the courage to keep going if she saw Taisin and Con on the beach behind her. So she lifted and lowered the oar, watching the icy water fall in clear droplets from the blade, and soon the fortress loomed large ahead of her.
When the bottom of the boat scraped onto the icy beach, she jumped out, her boots splashing into the shallow water as she dragged the boat onto the shore. There was no dock on this side, only the fortress. It was like an iceberg—if an iceberg could form in such a way that towers erupted from it. All around the island the ocean was a deep azure blue, and the colors here were so bright and crisp that Kaede had to squint. There was a causeway leading from the shore into the fortress, and at the end of it she could see doors. The island seemed deserted; the snowy ground was scrubbed clean by the wind. There was no sign of activity, human or fay. She moved toward the causeway, her feet scarring the snow for the first time.
The doors to the fortress were made of some kind of white stone, and in the center of each was a round silver ring hanging from a gleaming hinge. Kaede reached out and wrapped her fingers around one of the rings—it was as thick as her own wrist—and when she lifted it, the door swung open. Inside, sunlight spilled through windows set high in walls so tall that Kaede could barely make out the ceiling far above. The hall she stood in was bare of ornamentation but for a pattern inlaid in the floor. Giant diamonds of glass marked out an impressive star. Opposite the doors, a flight of stairs that seemed to be built of blocks of ice curved up out of sight. There was no other exit from the hall, so Kaede crossed the cold floor and began to climb the stairs. With each step she felt the dagger nestled hard against her leg, nudging the muscles of her calf, reminding her of her purpose.
The stairs ended in a long chamber lined with uncurtained windows. Everywhere she looked, the fortress had the faint blue tinge of ice; even the sunlight seemed less golden than white. She stepped into a slanting square of light coming through one of the windows, and though she felt its warmth on her face, it had no effect on the ice all around her. She went to look out the window and saw the sloping shoulder of the fortress, dusted with snow. Far below was the beach, and there was the boat she had rowed, a dark mark against the white. There was certainly no chance she had arrived unnoticed. Where was Elowen?
She heard a faint sound behind her—like the flapping of delicate wings—but when she spun around, her heartbeat quickening, there was nothing there, only a faint shadow disappearing through a doorway she had not noticed before. She forced herself to walk toward it, even though every nerve in her body was telling her to run away from this place. A cold sweat broke out on her forehead.
The corridor she entered curved upward. At first the walls were square with the floor, but as she continued on, they began to curve, too, until the corridor was more like a tunnel carved out of the interior of a mountain. There were still windows in the thick walls, but now they were irregularly cut in the ceiling or at floor level. Tunnels branched off to the sides; some of them slanted down; others had steps carved into them leading up. Once she passed a huge archway, and the sight beyond it caused her to stop and look again. There was a crystal cradle there, and a rocking chair, and on the floor a smear of what looked like blood. It was a nursery. She was drawn inside almost against her will, her curiosity vying against the desire to flee. The hairs on the back of her neck rose as she approached the cradle, but it was empty, and the blood was long dried.
Somewhat relieved—for the memory of the Ento creature had reared up fresh in her mind—she went back out into the corridor, and the shadow fluttered in the distance again. She followed it with renewed determination, but she only ever saw the shadow out of the corner of her eye. The tunnel was so interminable that she was unprepared when it abruptly ended in a vast chamber as large as a cavern. Far above, icicles hung from the rough ceiling. Round windows scattered high in the walls revealed the blue sky, and sunlight streamed in over a sight that caused Kaede to catch her breath. The cavernous room was filled with golden cages, round and square and rectangular, some stacked on top of each other, others standing alone. Inside the cages were the fay she had seen in Mona's book. Some of them looked at her, and their eyes were pinpoints of light: gold and silver and emerald green. The ones closest to her crept to the bars of their cages, and a few extended their arms, reaching for her. One, an excited creature with wings, began to throw itself against the bars, creating a ringing noise. That sound attracted the attention of its neighbors, and a whisper began to spread throughout the chamber, a moving wave of voices that Kaede realized, with a sinking feeling, she had heard before. These were the sounds that Taisin had made at night in her dreams: the eerie, half-senseless murmurings of beings trapped behind bars.
On the far side of the cavern was a door, and Kaede knew, as soon as she glimpsed it, that this was her destination. Her stomach heaved, for this meant that she had to walk through the cavern, past all the cages and all those strange creatures with their sad, brilliant eyes. She took a deep breath and stepped into the prison.
As she walked, she saw that some of the cages were empty, and some of the fay looked almost human. Some were very small—barely the size of her hand, tiny humanoid beings with butterfly-like wings in riotous shades of gold and orange. Several were hunched over in their cages, paying no attention to her as she passed. There were some who looked like human women, but had skin the color of moss and lips like bark; they moved with a lissome grace, treading circles in their cages. One of them reached out to her, and her fingers resembled roots twisting up from the ground. There were cages large enough to contain pools built into the floor, and beings with silvery scales instead of skin swam beneath the surface. Some of the imprisoned fay looked like harmless children, and these horrified her the most, for she wondered if any of them had ever been sheltered in that nursery.
By the time she reached the other side of the cavern, the whispering words had ceased. She glanced back, and the fay in her vicinity were watching her with expectant eyes. In one motion, as if pulled by a greater force, they looked behind her, and a shiver ran down her spine. She turned around slowly, half expecting a monster to rise up and consume her—but there was nothing but the door. An ordinary, human-sized door, with an ordinary, human-sized handle. She walked to it, and when she put her hand on the doorknob, a sigh ran through all the creatures in the hall. She squared her shoulders, nervous sweat dampening her skin, and opened the door.
The first thing she saw was a long expanse of shining ice—the floor was like a frozen lake in midwinter—and at the far end was a dais and a throne that looked just like the Fairy Queen's. But on this throne, Elowen waited. She had golden hair and eyes, high cheekbones, and her mouth was a red slash across white skin. She was clothed from head to toe in white fur, and at her right hand a fairy no more than a foot tall hovered in midair, her wings fluttering like a hummingbird's. A sprite, Kaede remembered.
"Welcome," Elowen said. "Please come closer; it is so rare that I have visitors." She spoke in Kaede's language with the same accent the Fairy Queen had.
Kaede was moving before she knew what she was doing. The floor was slick and cold; she could feel it seeping through the soles of her boots as she walked toward the throne. She also felt the unexpected, dizzying sensation of someone pushing into her mind. Everything suddenly tipped off-balance; the icy floor and walls and windows spun around her; she fell to her knees.
Her vision went black.
There was a deep, insistent tugging, as though someone were trying to pull the very core of her out through her mouth. She moaned, her fingernails scraping against the ice.
Just as suddenly, the pressure eased, and the blackness exploded into blinding white light. She blinked and blinked; the light became white walls and floor and windows—and a throne.
She was twenty feet away from Elowen, and the dagger was pressing against her calf. Her breath steamed out of her.
"That's a surprise," Elowen said. "You're not the one I expected. Who are you?"
"My name is Kaede," she said before she could stop herself.
" _Kaede_ ," Elowen said, her tongue caressing the sounds as though they were made of the sweetest honey. Kaede felt her entire body quiver, and for a moment she thought she might do anything at all for Elowen—anything. Still on her knees, she gazed up at Elowen, who seemed to glow with a radiant light.
"What brings you to my fortress?" Elowen asked.
"I have come to kill you," Kaede said, the words pouring out of her, and Elowen laughed.
"Is that so? Wonderful. I hope you will allow me to offer you some refreshment before you undertake your task." From nowhere, a chair appeared in the middle of the floor, and when Elowen said, "Sit down," Kaede obeyed her.
A little round table was drawn up nearby, and on that table stood a crystal goblet filled with golden liquid. "Drink," Elowen said. The word was freighted with such seductiveness that Kaede picked up the goblet without hesitation. She could smell the fragrance wafting up from the wine: honey, peaches, flowers in midsummer, as intoxicating as first love. Kaede's eyelids fluttered as the scent of it wrapped around her.
She raised it to her lips, and just as she was about to take a sip, Taisin flooded into her as though a dam had broken. Kaede couldn't breathe; Taisin was breathing for her. She felt oddly doubled, as if she could see everything twice as clearly. The goblet—the wine—she knew instantly that she must not drink it. With shaking hands, she set it roughly back down on the table. Some of the wine splashed over the rim, spilling onto her hand. She rubbed the sticky liquid onto the edge of her cloak. She could feel Taisin's heart beating in time with her own, and it made her light-headed. To have Taisin so close to her—inside her—and yet not physically present—it was an extraordinarily strange experience. She looked at her hands; they were her own hands, and yet it was like seeing them for the first time. The palms were torn up from the descent down the glacier wall, the skin scabbed over where the ice had cut her. She felt as though Taisin were sliding her own hands into hers, like gloves—but Kaede was the glove. She was the armor that Taisin had put on, here, to face Elowen.
Elowen looked at Kaede with narrowed eyes, unable to discern exactly what had happened, but certain that something had changed. Earlier, Kaede's mind had been a closed box; that was not unexpected for an ordinary human, but no ordinary human should be able to resist the wine. The girl should have drunk it and fallen into a delirium; that was what happened when Elowen issued a command: It was obeyed. Who was this girl? Elowen decided to change her strategy.
She said, "I see my mother has sent someone to challenge me." She twisted the word _mother_ in her mouth as if it tasted bitter. She saw the shock on Kaede's face, and a smile pulled at her lips. "Does that come as a surprise to you? No wonder—my mother was always so ashamed of her own weakness for _humans_. She tried to make sure that no one knew I was her true daughter. Not even, it seems, the human she sent to kill me." The sprite floated down to alight on the armrest of the throne, and Elowen stroked her yellow hair, making her shiver. "I suppose she thinks it's some kind of poetic justice: sending a human to do the job. But I think it's more like cowardice. She didn't have the nerve to do it herself. What do you think?"
"I—I don't know," Kaede said. Taisin was fully within her; Kaede couldn't discern which of them was speaking.
Elowen pulled a disappointed face. "Oh, come now. I have so few visitors. You must indulge me with a little conversation. Tell me: What did my mother do to convince you to become a murderer?"
Kaede felt Taisin tense with fear inside her, and the fear spread into her own body as she faced Elowen's catlike golden eyes. Neither of them knew what to say.
Elowen was impatient. "I suppose she told you that I am selfish; that I hunger for power that should never be mine. Did she tell you that? She is wrong, Kaede. She knows nothing of what I want—she has never known. But she can be very convincing, it is true. I believe she has convinced you, even though she did it with lies."
Taisin rejected Elowen's words, but Kaede wanted to know: "What lies?"
"Ah," Elowen said, as though pleased to be asked. "Did she tell you that she raised me with every luxury? That I had everything a girl could wish for? She lied. A thousand baubles are nothing when you are raised to know that you were a mistake—the result of a tragic accident. She told me that my human half meant that I would never be as powerful as an ordinary Xi; that I would be doomed to live a short life and die decades before she would need to name her heir." Elowen's face filled with anger. "I was such a disappointment to her. Do you know what it is like to grow up under that shadow? To have your only parent look at you with disgust?"
Even though Kaede recoiled from the golden-eyed woman in front of her, part of her recognized that Elowen's bitterness disguised a deeper hurt, and Kaede's sympathy showed on her face.
"You understand," Elowen said, her voice turning soft and gentle. "How hard it is, to be rejected by one's own flesh and blood. I see that you have experienced this, too."
Kaede wanted to object, but she felt Taisin pulling her back. Taisin's thoughts came through as clearly as if she had spoken them out loud: _She is trying to manipulate you_. Kaede stayed silent, and Elowen went on.
"How could I endure it? I couldn't. I had to leave. I traveled to your kingdom, though I kept myself cloaked and concealed. I knew that I would never be able to find my father—my mother would never even tell me his name—but I wanted to see what sort of people he came from. I soon learned that my mother, for all her secret weakness for humans, knows nothing about them. She couldn't see, as I did, that the shortness of your life makes you work so much harder than any Xi. It's the fear of death that does it, I think. Don't you agree?"
Taisin and Kaede said together: "Yes."
Elowen smiled. "Yes. And when I learned this, I came north to this place. It called to me; the meridians seemed to speak my name. I knew what I had to do. I raised this fortress, and I called the fay here, to help me. They feed me willingly; they have made me so strong." Her face was suffused with pleasure in her own power, and she leaned forward, asking in a coquettish tone, "Can you guess what I'm doing, Kaede?"
Kaede swallowed. "No."
"I am creating a new race of beings—one that has all the relentless determination of a human and all the power of the fay." Her smile faltered a bit. "It isn't easy, but I've learned from my human side. I'm close to success. And when my people are ready, my mother will have no choice but to submit to me, for I will be so much more powerful than her. She will give up her throne to me. I will rule all the Xi and all the fay, and one day, perhaps, I will go to your kingdom and rule that, too. Who could be a better choice than me? I am both fay and human; I understand both worlds."
Elowen sat back in her throne, a serene look on her face as she folded her ringed hands in her lap. "Now," she continued pleasantly, "you said that you came here to kill me. But I am willing to forget that, Kaede, because I see that my mother has lied to you. And because I do not reject my human half the way that she does, I will extend an invitation to you. It is quite admirable that you have come all this way to me. Of course, I thought it would be someone else—your companion, perhaps?—but you are the one who took the last few steps. And to reward you, I will offer you the chance to serve me. You will live a long life, and your parents will see how wrong they were about you, just as my mother was wrong about me. They will have to bow down to you, as my representative. So, I ask you: Will you join me?"
Elowen's words had been spoken in such a calm, measured tone of voice that it seemed almost irrational to disagree with her. Taisin was frantic, fearing that Kaede would give in to Elowen. And Kaede did feel a certain amount of compassion for the Fairy Queen's daughter, but she could never say yes. She thought of her father, who had his own expectations for her. She had chafed under his demands before, but he had never treated her in the way that Elowen assumed. Kaede knew that he loved her. Perhaps the Fairy Queen loved her daughter, too, but Elowen had never been able to see it.
Kaede said: "I'm sorry. I can't join you."
Elowen's face flushed; her mouth twisted. "That was an unwise decision," she said, and she stood up. "You know that I can't allow you to leave this place alive."
She stretched her right hand toward Kaede, her fingers curling. It was as if she was drawing the air toward her; Kaede could feel the currents in the room bending to her will. And then, to her horror, the air turned and rushed at her; it swirled around her throat like a thousand scarves, tightening until she had lost all her breath. Elowen was regarding her coolly, as if she were merely an unpleasant task to take care of, little larger than an insect she could crush beneath her shoe. Kaede reached her hands up to her throat, her eyes blinking as she began to faint. She could not breathe; her fingers scrabbled at her skin, but there was nothing there to grab onto.
_Taisin_ , she thought dimly. But she felt no response, and everything began to shatter into spots of white upon black.
# Chapter XXXVII
iny sparks danced before her eyes; they were as beautiful as fireflies in a purple twilight. And then the sparks multiplied until they were all she could see, and she wondered if she was flying up into the night sky, coming closer and closer to that giant cloud of stars she had seen above the ice field.
She was no longer in her body; she felt free. She was as small as a drop of dew quivering on a spider's web; she was a minute in an hour in a day in a million years. So much had passed to bring her to this moment: births, deaths, countless insignificant decisions that made her who she had become. All of that—all of her—could end now. She could return to the limitless state that every living creature once was in and will be again.
But she was not ready. Not yet.
And not without regret, she turned away from the pull of the starry sky, and far below her, she saw the fortress, a mountain of white snow. She saw the azure sea broken with ice floes. She saw the beach. She saw Con kneeling on the cold ground gripping Taisin's hands in his. She saw Taisin, her eyes wide open and looking directly at her. Her gaze was magnetic; it pulled her down, down, until she was plummeting toward the earth, toward Taisin and through her. Now, with a stunning clarity, she could feel every fiber of Taisin's being. She could feel her pain, her excitement, her fear. There was the clenching and release of the muscle of her heart. And there was the love between them: a revelation. A way in.
In those brief moments when she was floating free, Kaede had almost forgotten what it was like to be corporeal. Then, she was being channeled through Taisin back into her own flesh and bones again, as if she were being squeezed into clothes that were much too small. Her body was so limited, so attached to the ground. She couldn't, at first, remember how to move, but Taisin did, and she was still within her. Kaede watched her own hand fly up; it grasped the currents of air that Elowen had wrapped around her throat and tore through them. It was like ripping a great bolt of silk, and the air fell in ragged ribbons away from her.
Elowen stood in front of her throne with her arm still outstretched. She looked as shocked as Kaede felt. In that heartbeat, they were equals, and Kaede knew she had to act before Elowen regained her wits. She reached down to her boot, feeling her blood rushing into her fingertips, and drew out the dagger and threw it at her.
But there was no time to even hope it would reach its mark, for Elowen flung it aside with a fistful of energy. The dagger clattered to the floor and slid until it lodged itself in the wall beneath the windows, and then Elowen began to advance on her.
Kaede ran for the dagger, but her boots slipped. The icy floor came rushing up to slam into her hands and knees. She slid; she scrambled on all fours toward the wall. Taisin was gathering up the energy she would need for one more assault, and Kaede felt Taisin's strength rising inside her like a fever.
Elowen came after her, vowing that she would put her own hands around this human's throat. But at the last moment, Kaede's fingers found the dagger, and as she whirled around, Taisin spoke through her.
"Elowen!"
The woman stopped, startled by the sound of her name on someone else's lips.
Kaede swung her hand and slashed through Elowen's gown, cutting into her leg. Elowen let out a scream; she looked down at the blood that dripped onto the floor. A curious steam rose from the wound, and the fabric around it curled back as if it were burning away.
"What have you done?" Elowen shrieked. The skin of her face was nearly translucent; her veins were black rivers beneath her temples.
Kaede pushed herself to her feet. The handle of the dagger fitted into her palm like an old friend. She felt Taisin readying herself. "Elowen," they said together, and Kaede charged at the Fairy Queen's daughter and plunged the dagger into her heart.
Elowen's eyes widened; her mouth parted. Her blood streamed over Kaede's hand. She fell, looking as frightened as a child facing the dark.
Kaede stared at Elowen's body, stunned. The moment the blade made contact with Elowen's heart, all the power that had surged between her and Taisin drained away, and now she felt emptied, unsteady. Her hands were shaking; they were wet with blood. Without thinking, she smeared them over her thighs. When she looked back, the same scene awaited her: Elowen lay there with her eyes half-open, the dagger fixed in her chest, blood pooling down on the floor. It was indeed made of ice, and it was melting.
She forced herself to kneel down and pull the dagger out. The wound itself was burned black as if the iron had scorched Elowen's flesh, and Kaede had to swallow her nausea as she wiped the blade on the very edge of Elowen's ermine cloak.
As she resheathed the dagger in her boot and stood up, the sprite who had fluttered near Elowen's throne bobbed into sight. She was a girl, or she looked like one, except she had little wings growing from her shoulder blades. Her skin was as golden as her hair, and she looked up at Kaede with wide blue eyes that were both sad and triumphant. Then she fluttered down to Elowen's waist, where she pushed aside the folds of the fur robe to reveal a silver key ring. She picked up the ring in her little hands and struggled to fly up to Kaede's eye level, where she said something that Kaede did not understand.
Frustrated, the girl gestured to the open door at the end of the throne room. Kaede heard a rising cacophony coming from the cavern beyond. The girl was shaking the keys, causing them to clink together like bells, and Kaede realized they were the keys to the cages. The fay wanted to be set free.
"Of course," Kaede said out loud. "You should free them." When the girl gave her a puzzled look, Kaede pointed to the door, gesturing the act of turning a key in its lock. The girl understood, and a brilliant smile spread over her delicate features. She even bounced a little in the air before flying speedily down the length of the throne room toward the door.
Kaede looked back at Elowen. The weight of what she had done settled over her again. She took a ragged breath.
She could not leave the body there. It felt wrong.
She glanced around the room for something to use as a shroud, but there was nothing. Finally she settled for folding Elowen's cloak more securely around her. Her flesh was still warm, and it seemed unreal that she was truly dead. Taking a deep breath, Kaede dragged Elowen up and over her shoulder. Her body was surprisingly light, and though it was not a comfortable position, Kaede thought she could manage to carry her some distance this way. She trudged down the length of the throne room and through the door to the prison.
Every last one of the fay came to watch her pass this time. Some appeared sad; others eager; but none seemed interested in avenging Elowen's death. The sprite had already begun to unlock some of the cages, and those who had been set free started to follow Kaede and her burden out of the cavern.
It was a long, hard walk through the many tunnels of the fortress, and several times Kaede thought she might have lost her way. Elowen's body, which had once seemed light, soon felt so heavy that Kaede wanted to weep with the strain of it, but she would not let herself stop, and she would not accept the help of the fay who followed her. She had killed Elowen, and she had a superstitious feeling that it was her task to bring this to its proper conclusion.
At last she arrived at the entry hall, and she went through the great doors and outside into the sunlit afternoon. She was almost surprised that the sun had not already set, for it felt as though she had been inside that fortress for a lifetime. And then she wondered if carrying Elowen outside had been pointless, for she had been intending to build a funeral pyre, but there was no wood on the beach—not even a single spare piece of driftwood. She laid Elowen's body on a stretch of icy sand and sat near Elowen's head, her eyes squinted against the setting sun. She wanted to give up.
The sprite emerged from the fortress first, followed by one of the lithe, willowy nymphs with fingers like small branches. More and more of them came outside, blinking up at the blue sky, and many of them were carrying torches as though they had known what Kaede was preparing to do. They came toward her, and the first one set her torch down upon Elowen's body, the flames flaring up as they touched the fur cloak that served as her shroud. One by one, they set her afire, and in this way, Elowen's prisoners built her funeral pyre.
Kaede sat still on the beach, watching the flames grow, and she felt a thick, ashen despair settle over her. She had come to this island in the far north with the goal of murder, and she had done her job, but now she only felt like a killer. There was no glory in this. She had seen Elowen's face as she died, and she knew the memory of it would haunt her for the rest of her life. Kaede put her head in her hands and wanted to weep, but tears would not come. She felt split apart, broken, as frozen as the island that bore the weight of Elowen's ambition.
Kaede looked into the flames late into the night, and forced herself to watch as the cloth curled back from Elowen's face, as it ate through her furred mantle and burned away her flesh, until all that was left to see was an empty skull, blackened and charred.
# Chapter XXXVIII
aisin heard the voice from very far off, dim and faint. It was comfortable where she was: Everything was dark and soft. Her mind was empty, quiet. She felt free for the first time in weeks, and she just wanted to linger there. A cushion of nothing at all. Blankness.
But the voice would not stop.
Gradually the sounds formed syllables. The syllables formed a word. Her name.
_"Taisin."_
She recognized that voice.
"Taisin! _Come back._ " It was a demand. There was dust in her mouth, the taste of ashes, gritty and dry. Her tongue was thick and swollen. Her head throbbed. Her shoulder ached—and that was what pulled her back into her body at last. The stabbing, twisting pain in her muscles, where she had wrenched her arm climbing down the glacier wall.
She gasped, her eyes opening to a star-strewn sky.
"Taisin," said the voice again. It was Con. He was holding her head in his lap, and she looked at his face upside down above her, filling with relief as she blinked. "Taisin, what happened?"
The air was freezing, and it carried the smell of burning. The waxing moon was a sliver in the east. She said: "Elowen is dead."
When dawn broke, Kaede rowed the little boat back to the mainland. A small wind had risen with the sun, blowing drifting snow over the smoking ashes. Elowen would never leave her island.
Taisin and Con had the camp half-packed by the time Kaede set foot on the dock. The dogs came running to greet her, barking loudly in the early morning stillness. Taisin met her halfway and put her arms around her, holding her tight. Kaede wanted to stay there forever, with her face buried in Taisin's hair, but she could still smell the scent of Elowen's funeral pyre, and she wondered if it would always be with her.
When they parted at last, she saw Con hobbling toward them. She embraced him, and he said gruffly, "Welcome back."
She gave him a weak smile, then glanced at their camp. The provisions were already packed up; they only had to strip down the tent, and they could go. She said: "We must leave this place."
Con nodded. "We're almost ready."
They reached the point where they had descended from the glacier by early afternoon, and though they were all exhausted, they had no intention of waiting another minute. It took several hours to make the climb back up. Con was wet with sweat by the time he reached the top, and for long minutes he simply lay there on the snow, looking up at the sky, his breath misting out above him as his leg throbbed.
The sledge was where they had left it, perched alone in a vast white landscape. There was no sign of storm clouds in the sky. The weather, in fact, had been still all day, as though it were waiting, testing out the new balance of power in the world. It put Kaede on edge. It felt like something was unfinished. Elowen was dead, but nothing had been made right.
Their journey across the ice field took less time than their journey out to the fortress, for the weather remained calm and the sledge was lighter now. They left the broken tent behind, and their supplies were mostly gone. Both Kaede and Taisin walked with a kind of dull determination across the snow. Taisin was so exhausted from their battle with Elowen that it was all she could do to put one foot in front of the other. Con watched them with an alert eye, for he was worried about them. At night he gave them more than their fair share of the rations, but they did not notice. They only ate what he handed over and slept so deeply he was afraid, in the morning, that they might never awaken.
They did not know that in the distance behind them, the fay had begun their own journeys home. The knockers—hardy mountain dwellers accustomed to the cold—carried those who would have otherwise frozen: some of the dryads, or the winged sylphs, whose bodies were limp in the wintry air. The asrai and the undines had slipped into the icy northern sea to head south for the mouth of the Kell, where they would swim upstream to their cool lakes and rocky rivers. The sprite who had attended Elowen that last day remembered the name of the one who had saved them, and she repeated it to every fairy she set free with those keys: _Kaede._ So the story of the girl who had defeated their tormentor was passed from one to another in languages that had gone generations without once uttering the word _human_.
Had Kaede known this, she would have told them that she had not acted alone, that both Taisin and Con had helped her. But she did not know the fay were speaking her name, so she was spared the burden of becoming their hero, when in fact she still felt like a murderer.
When they saw the ragged line of the Wood in the distance, Con felt like a sailor long at sea, finally sighting land. Relief surged through him; he hadn't realized how much he had feared that they would never leave that frozen wasteland behind. They quickened their pace that afternoon, the dogs running faster as though they, too, were eager to seek the shelter of the trees. Waiting at the edge of the Wood was the Fairy Hunt: the same riders who had sent them off across the ice field so many days before.
The Huntsman took stock of their bedraggled appearance and ordered someone to care for Con's leg and Taisin's shoulder, and then he came to Kaede and regarded her gravely. "You have done a good deed for us all."
She said dispiritedly, "Have I?"
"You have," he said, but she was not convinced.
The journey back to Taninli took several days. The farther they rode into the Wood, the warmer it became, until at last it was summer again, and they could strip off their furs and pack them away. But despite the warmth, a pall hung over them, and the sun remained hidden behind clouds. Kaede remembered how the Xi had seemed to glow the first time she had entered Taninli, but this time the whole world was muted. She wondered if there was something wrong with herself, for ever since leaving the fortress of ice, she saw everything through a film of ashes.
But as they rode through the streets of the Xi city, it became clear that the same miasma was affecting everyone. Few of the Xi came out to watch them pass, and the ones who did looked haunted. At the palace, a thin layer of dust drifted over the white stone. Their horses kicked it up when they rode into the courtyard, and it floated into Kaede's nose and throat and made her cough.
The Huntsman did not allow them to rest. He took them directly through the quiet, dim halls to the Fairy Queen's throne room. Kaede was shocked to see the Fairy Queen slumped over in her throne, her face as gray as the dust that drifted in ashy piles around their feet. The Huntsman seemed terribly affected by this; he went to her side and knelt down to take her hand, and Kaede realized by the way he touched her that he loved the Queen. When he turned back to them, his face was drawn with grief.
"What is wrong?" Kaede asked, stepping forward. She put one foot on the first step at the bottom of the dais but hesitated to go farther.
"She is not well," the Huntsman said.
"Should we return at a later time?" Kaede asked.
The Queen stirred. "No." She pushed herself upright and looked at the three humans. "Which one of you killed Elowen?"
The question sent a chill through Kaede. Before she could speak, Con answered, "We acted together, Your Majesty."
"Which of you held the knife?" the Queen demanded, and Kaede flinched, for she sounded like Elowen. "Which one of you?"
Kaede bowed her head. "It was me, Your Majesty. I held the knife."
The Queen sighed. "Come here."
Dread filling her, Kaede climbed the low steps of the dais. The Queen extended her hand, and when Kaede took it, the skin was dry as paper. The Queen pulled her closer so that she had to kneel before the throne. The edge of the seat cut into her belly, and the hard stone floor bit into her knees. The Queen's cheeks were marked with unnaturally bright red spots; her burning golden eyes had the same fierceness Kaede had seen in Elowen. Her hair was white and brittle. She looked defeated; she looked ancient.
"This is what has become of me," the Queen whispered, "for ordering the murder of my own child."
Kaede heard the anguish in the Queen's voice, and guilt burned through her. She was the Queen's accomplice in this murder.
"You are not surprised," the Queen murmured. "Did she tell you that I was her mother?"
Kaede lowered her eyes to where their hands were clasped together, remembering the curl of Elowen's lip as she said the word _mother_. "Yes. She told me."
"I thought that removing her from this world would set things right, but I find that I was wrong. Her death has killed part of me, as well."
A droplet of liquid splashed down on their hands, and Kaede realized that the Queen was crying. Every drop was cold as ice: hard little shards pricking at her skin. Kaede watched numbly as tiny red marks erupted on her hands where the Queen's tears struck. She did not know how long the two of them remained there, the floor bruising her knees as the Queen wept. But at last the Queen drew her hand away and lifted Kaede's chin so that she had to look into the Queen's golden eyes.
She saw the world in them. The Wood around Taninli, the trees bowed down with the weight of the Queen's sorrow. The wind sighing over brown, broken grasses. The glacier, dry and frigid, spread all over with funeral ashes. She couldn't look away, even though the sight of it made her wither inside. Had she done this to the Queen? Was it all her doing—because she had killed Elowen? Kaede drew in a shaking breath. She deserved to feel all the misery the Queen was feeling. She wanted to taste the dust that coated the palace. She wanted to drown in the deepness of the Northern Sea, feel its gelid water seeping into her.
The Queen's fingers pressed against her cheeks. Her nails scraped against Kaede's skin. "Listen to me," the Queen whispered, her voice rough with pain. "You can save me. You can save all of us."
The words floated into Kaede's mind as if from a great distance. She heard them, but she did not understand. She was engulfed in the enormity of the Queen's grief.
Taisin's voice was thin and sharp behind them. "How?" she asked. She took three quick steps toward Kaede and put her hand on Kaede's shoulder.
Kaede twitched. She felt Taisin's fingers, firm and warm; she drew another uneven breath. The Queen's face wavered before her, coalesced into the image of an old woman, lines cracking from the corners of her eyes and spreading down her cheeks.
"How?" Taisin asked again, her fingers digging into Kaede's shoulder bone, prodding her back to the reality of the throne room. The Queen's hands fell away from her face, and Kaede swayed. Taisin held her arm; helped her to her feet.
"There is only one cure for me," said the Queen.
"What is it?" Taisin put her arm around Kaede, steadying her.
The Queen ached with regret. She felt her energy leaking out of her. Her heart was punctured; she would become a hollow shell. "The water of life," she answered. "I must drink it."
"Where is it found?" Taisin asked.
"It is far from here. Through the darkest Wood and across the three rivers; beyond the red hills and within the trees of gold."
Con had been standing silent nearby, watching Kaede kneeling before the Fairy Queen as if entranced, and a sense of disquiet filled him. "What will happen if you don't drink this water of life?" he asked.
The Queen closed her eyes. "I will die," she said, her voice light as a dry wind. "And my land will die with me."
"Your land," Con said. "What do you mean?"
Kaede understood, now, what the Queen had wanted her to see in her bright yellow eyes. "She means that Taninli will crumble," Kaede said. "She means that the fay will die. And she means that the Wood itself will perish. The trees will fall; the rivers will dry up; the earth will become nothing but ash." As she spoke, the words uncoiling through her, she felt her heartbeat quickening. What would the world come to? It would surely spread to the Kingdom. The border between their lands was porous; the Queen's death would hover over their cities and villages, too. She had a terrifying vision of Cathair drenched in ash-gray rain, covering the red roofs of her parents' home in a choking sludge.
Taisin put a hand on Kaede's cheek. "Kaede," Taisin said. "Open your eyes."
Kaede blinked them open. She hadn't realized they were closed. She saw Taisin's worry-filled face.
"Are you all right?" Taisin asked.
Kaede rubbed at her forehead. She felt unbalanced, disoriented. "I don't know. I saw—I saw Cathair. It was dying, too."
Taisin looked the Fairy Queen. "Are you putting these visions in her mind?"
"She must see what will happen if I die," the Queen said.
"Why?" Kaede and Taisin asked together.
"You, Kaede, are the only one who can save me," the Queen said. "So you must know what will happen if you choose not to."
"Why only Kaede?" Taisin demanded.
The Huntsman said, "The hand that took Elowen's life is the only hand that can bring life to our queen."
Kaede was hot and cold at the same time. Visions, apparently, disagreed with her. "What do I have to do?" she asked. "How do I find the spring where this water comes from?"
"It is not a spring," the Queen said.
Taisin stiffened. She remembered, suddenly, Mona and that little sharp knife drawn along her skin.
"The water of life is the blood of the unicorn," the Huntsman explained.
Kaede stared at him. "The unicorn?"
He nodded. "You must seek out the unicorn and submit to its judgment. If it finds you innocent, then it will sacrifice itself to you and give you its lifeblood. You will bring it back to the Queen."
Kaede remembered the stories, of course. Everyone told them. But this was akin to asking her to hunt down a dragon, and though she had seen enough wonders for an entire lifetime in the short period she had been in Elowen's fortress, this was too much to take in. Besides, in those tales, no one ever survived the judgment of a unicorn. "What if it finds that I'm... not innocent?" she asked, and once again she felt the weight of guilt pulling her down. Her hand had been smeared with Elowen's blood. She had done it, had taken the Fairy Queen's daughter's life. She had seen it pouring out of her onto the ice.
The Huntsman said somberly, "If it judges you guilty, then it will kill you."
A thick silence blanketed the throne room. Kaede felt feverish. Everything seemed unreal. She wiped her hand across her brow, leaving a streak of dust over her skin.
Con's voice cut through everything. "This is mad," he objected. "Kaede, you can't go alone."
"We were there with her in the fortress," Taisin insisted. "Your Majesty, I helped Kaede kill Elowen. I share the burden with her."
The Huntsman looked terribly sad. "Your friends do you much honor, but in the end, it is your choice alone."
Kaede looked at the Queen, frail and aged. She looked at Taisin and Con, whom she might never see again if she did as the Queen asked. But the Queen's grief—and her own guilt—pulled her in the only direction she could go. She turned to the Huntsman and said, "I will do it."
He bowed deeply to her in thanks. "We will leave as soon as possible."
# PART V
Those who love are clouds floating side by side:
Dewdrops bending blades of grass at sunrise.
Yet love is the rhythm of nature;
Love is oneness with beauty;
Love is the joyful revelation of the way.
—The Thirty Blessings
# Chapter XXXIX
aede rode with the Huntsman out of Taninli later that day. He would not allow anyone else to accompany them. They traveled so quickly that the Wood became a blur of green and brown, moss and bark, but their horses did not tire. She ate the food that the Huntsman gave her, and she drank from the water skin he handed to her without question. The liquid burned down her throat, making her eyes open wide in momentary shock, and then they were riding again.
When they stopped to sleep, she dreamed of ashes, drifts upon drifts of them, covering the Wood in a stale scent of burning. She heard the Queen's voice: _Please hurry_. All around them, the trees were dying. She could feel it so clearly, though she did not understand how or why. Something had changed within her when she looked into the Queen's eyes; now there was a bond between them, Fairy Queen and human girl. Sometimes she would reach out along the length of that bond, and at the very end, she could just sense the quiver of the Queen's heartbeat. She still waited in her throne room.
Kaede and the Huntsman passed through a forest of giant trees, their trunks black with age, the sun obscured by thick, tangled vines. They crossed a narrow wooden bridge over a rushing river, and a bridge that swayed over a gorge carved out of a granite mountainside. Kaede held her breath as her horse picked his way across, seemingly oblivious to the precipitous drop beneath them. Far below another river churned, and above them birds with vast wingspans shrieked, their calls echoing down the rocky canyon.
On the other side, the trees were so densely packed together that their horses had to slow to a walk. From time to time sunlight shone in tall shafts through the foliage, and then there were stretches of shadow, or brief squalls of rain and mist. She saw deer in flight, white tails like flags. She saw crows with their darting black eyes, perched on branches above. Eventually they came to a river that ran sweetly over rounded boulders, and the Huntsman told her it flowed south to meet the Nir. There was no bridge here, and they waded across, for the water was barely higher than her knees. On the opposite bank, the trees began to thin out, and the next time they camped, the earth was the color of ocher and smelled of metal.
They climbed one hill, and then another, and the red soil covered everything until even her hands were tinged a rusty brown. At last they came to a spring that bubbled out of a tiny little cleft in the rocky red hillside, and the Huntsman dismounted and knelt down to it, cupping up a handful of water. When he had tasted it, he said, "We are near. We'll camp here tonight, and tomorrow you'll continue on your own."
"You're staying here?"
He nodded. "The rest of the journey is for you alone."
"But... how will I know where to go?"
He pointed up the hillside. In the distance she saw trees, their leaves as gold as the Queen's eyes. "You'll go that way. Through the trees."
She dismounted and watched as her horse drank from the spring. Her head felt fuzzy. The Queen's presence was much more distant now, and she felt almost unmoored. She wondered how far they were from Taninli. "The unicorn—will it be waiting for me?"
The Huntsman shook his head. "You must seek it out. It does not show itself to everyone."
"Is there only one?"
"I don't know. Once, there were many. But those days are gone."
"How do I seek it out?"
He bent down to unbuckle the saddle from his horse. "That is for you to discover."
"What if I can't?" she asked, and a bubble of panic rose in her stomach. "What if I fail?"
He set the saddle down on the ground and looked at her with a grave expression. "I hope that you won't."
That night she slept poorly. She fell in and out of the same dream she always had: ashes falling over the land, settling into the crevices between tree roots, dusting over every unfurled bud, smothering each hint of life. She allowed herself to get up as soon as dawn broke, and she knelt beside the spring and splashed the freezing cold water on her face, gasping at the chill.
The Huntsman brewed a bitter, dark tea that morning that she had never tasted before. "It will give you strength," he said, noticing her grimace. "You should drink it all."
As the sun rose, she sipped the tea, feeling her body slowly coming to life. The daze that had cloaked her during their journey was lifting, like cobwebs being brushed aside. She looked over the red hillside, at the rocks and the soil and the scrub grass, and then at the arch of the sky, pink and gold in the east. A question that had been forming in her ever since they left Taninli finally found its way to her tongue: "Why is the Queen so tied to these lands? Why does the land fall sick when she does?"
The Huntsman considered her question for some time before he answered. "Our queen is the embodiment of our land. It has been this way since the dawn of time, and it will be so until our last queen dies."
"There have been many queens?"
"Yes."
"Then when one queen dies, why does the land not die with her?"
"She is not like your king. She is not born into her station. Each queen chooses her successor, and each chosen successor must undergo many rituals to prepare for her duties. It may take decades. When the chosen one is ready, her predecessor goes willingly to her death."
"But this queen is not ready to die."
"No. She is not ready. She has not yet chosen a successor, and without one..." He could not finish the sentence. His heart constricted at the thought of his queen being taken before her time.
Kaede dug her fingers into the ground, trapping the soil beneath her nails. It was already turning to dust.
The Huntsman gave her a horn cup with a leather strap affixed to it. The cup had an ingenious cap, carved also of horn, and it latched into place with silver hinges. It was made from the horn of a unicorn.
"After the judgment," he told her, "you must fill this cup with blood, and bring it back." He did not mention the possibility that the judgment might render her incapable of returning. "I will be waiting for you here."
She took the horn from him, feeling oddly calm. She thought she ought to be afraid—terrified, even, for she might be riding to her death. But instead she only felt ready. She had come so far, and in a way she felt as though she had been preparing for this her whole life. She buckled the iron dagger onto her belt and mounted her horse.
She rode toward the golden trees as quickly as she could, but it was noon before she felt the shade of the first tree on her back, and she paused beneath its limbs to eat a dry biscuit and get her bearings. She had never seen trees like this before: white bark and branches so delicate she could not understand how they supported the weight of those leaves. They looked like gold coins, and when the wind blew through them, she heard a thousand tiny chimes. The trees sang.
She continued on, and the trees began to grow more thickly, until all around her were slim white trunks. Sunlight dappled the ground; afternoon slid into dusk; and shadows spread purple and blue across the golden forest. The wind grew cooler. As far as she could see were these golden trees. There was no end to this forest, and she did not know which direction to go. She dismounted from her horse and decided to make camp for the night.
Her horse was unusually skittish. She felt his muscles trembling as she unsaddled him, and he pranced as if he wanted to leave. "What is it?" she asked, her voice sounding strange in this wilderness. She tried to calm him down, but he continued to be nervous, and at last she had to tie him to a tree, afraid that he would bolt.
She tried to sleep, but the horse's anxiety and the keening of the trees kept her awake. She finally dozed off a little before dawn, only to wake up when she heard the horse whinny loudly. She scrambled to her feet, still half asleep, and saw the tail end of her horse disappearing through the trees.
"Stop!" she yelled, but the horse did not halt. She looked at the tree where she had tied it, and the rope was still knotted around the trunk. The end that had been tied to her horse's halter flapped loose in a slight breeze.
Cold slid down her spine, and her heart pounded. She bent over, hands on her knees, trying to calm herself. She was suddenly aware of how alone she was in this queer place, and she had the uncanny sensation that the singing trees had been singing about _her_. It was a chilly morning, but she felt perspiration rise on her skin. The direction of the wind abruptly shifted, and the melody that had been running through the leaves changed.
Something—or someone—was nearby.
She could not sense people's energies the way that a sage could, but this spirit or consciousness was so focused, so brilliant, that anyone would know it was there.
She straightened, glancing around, but she saw only trees. She tried to swallow her fear; tried to ignore the prickles of panic that raced along her skin. She told herself she was there for a reason, and it was an honorable reason. She clenched her hands into fists and turned into the wind, letting it stream over her head, loosening her hair. The sun was rising, shedding gray light over the golden forest, and in the shadows she thought she saw something moving in the distance.
"I am here for your judgment," she whispered. The shadows moved again, but they did not come closer. She raised her voice, bracing herself. "I am here for your judgment!"
She felt suspended in the wind. The music of the trees rang in her ears. She wondered how long she would have to stand there, waiting. The leaves shook like tambourines.
The unicorn seemed to step out of nowhere. It was a male. His head was small and perfectly formed, shaped like that of a deer, but with a gray beard growing from his chin. The horn, a speckled, ivory spiral, protruded from between black eyes that were undeniably intelligent. He was about the size of a mature buck, with fur that contained all the colors of the rainbow. From one angle, he might look like lichen or moss; but from another, he was as stunning as a phoenix, his coat sliding from gold to silver to fire.
She knelt down before him, her whole body tense, and asked for the judgment.
Though she had felt Taisin enter her mind in Elowen's fortress, this was entirely different. As his consciousness filled her, there was a sensation of perfect openness. All of her, heart and soul, was spread out before this creature, and he examined every last detail of her life.
He saw her memories of childhood—roughhousing with her brothers, running around their courtyard home, begging their mother for rock sugar. There was her first trip to the Academy; the time she had upset Fin by leaving the workshop a mess; the warm saltiness of the sea on a summer day. The moment, that morning in the Council chambers, when she truly noticed Taisin for the first time.
She felt the sway of the King's ship as she left the Academy behind. Shock as she watched the King's guards execute the bandit on the highway.
In Ento: the black eyes of the monstrous child as she plunged the knife into its belly. The horror that gripped her as she watched its funeral pyre.
The split second of sheer panic as the wolves came at her. The stretch of the bowstring as she shot arrow after arrow into their bodies, her stomach tight as a fist.
Taisin: the warmth and the smell of her skin; the pleasure of her kisses. Love, new and fierce.
And then there was Elowen, reaching for her throat. Blackness; everything snuffed out. She floated free, like a seed on the wind. Kaede wondered: Had she died? There had been a moment—she was sure now—when she had ceased to exist as a living human being.
She remembered opening her eyes to see Elowen's snarling face. Her knees skidding across the floor, her hand reaching for her weapon. The iron dagger, buried in Elowen's heart. Blood on her hands.
If she had killed someone who already killed her, did that still make her a murderer?
Her eyes flew open. The unicorn lowered his head. She looked into his black eyes, and though he did not speak in words, she understood him.
Harmony: This was the heart of nature. Every living being—plant, animal, human, fay—had its place in the cycle of life and death. In this cycle, countless creatures worked in tandem as well as against one another. All of these beings formed a complicated whole that shifted and changed in order to maintain that harmony.
Elowen had taken many lives in order to extend her own. Her stockpiling of power had wreaked havoc on nature. Her death was justified. But that did not mean that harmony was restored, for harmony is never achieved through murder.
And Kaede had to accept her part in that. Tears slid down her face. The experience of killing Elowen—of death on her hands—would be imprinted on her always. She had been given an extraordinary gift in Elowen's fortress: a second life. She understood that now, and she knew she had a responsibility to live up to it—if the unicorn allowed her to.
He lowered his horn until the point came to rest lightly against her chest. The touch of it sent a shock through her. All he had to do was push forward, and she would be dead. But he remained still. He was not finished with her.
He showed her that although she may have held the knife, it was the Fairy Queen who put it there, and the Queen had acted out of desperation and self-hatred. She did not want to accept her own responsibility for the tragedy of Elowen's life. Now the Queen was paying her own price: She was dying, and so were her land and her people.
If the Queen died without an heir, the ash that had blanketed Taninli would spread, sifting into the cracks and corners of the Wood, sinking into the Nir until the river became thick and slow. There would be no summer; there would be no autumn or winter or spring—only this never-ending grayness, as if all the color had been leached from the world.
This could not be allowed to pass. The Fairy Queen must live, so that her land could heal. Kaede knew that the Queen would never be the same again. Her time to die would come soon. But she needed to live—for now.
The unicorn lifted his head and gave Kaede permission to draw his blood with her knife, the same one that had killed Elowen.
With shaking hands, she slid the blade across his throat, holding the horn cup beneath it, and drop by drop, his life fell into her hands.
The Huntsman looked as if he had aged a decade when she returned to his camp. Her horse had found his way back on his own, looking none the worse for his experience in the unicorn's grove.
"Is it done?" the Huntsman asked.
She held up the horn. "Yes." She was drained, exhausted.
Relief flooded into the Huntsman's face, making him look almost human. "Then we must return," he said, and called their horses.
He pushed them hard on the journey back to Taninli. Every day that passed brought the Queen one step closer to her premature death, and he could sense the Wood already beginning to wither. The sun, now, was always covered by cloud.
When they returned to Taninli, they found the city much changed. The layer of dust that had fallen over the palace had spread to the streets. The scent of burning hung heavily in the air.
At the palace courtyard, they dismounted quickly. Kaede had slung the horn over her shoulder, and the knife slapped against her hip as she hurried after the Huntsman. In the throne room, the Queen still lay in her crystal chair, and Taisin and Con paced near the windows as if they had never left. But Kaede could not spare more than a glance for them, for the Queen was on the verge of death.
Kaede climbed the steps to the dais and knelt before the Queen as she had knelt before the unicorn. She unlatched the cap and dipped her fingers into the blood, which was as warm as it had been when it dripped from the creature's throat. She smeared it in long strokes over the Fairy Queen's sunken cheeks, and words came to her mouth as though the unicorn were speaking through her: "As life is in the blood, so you shall receive it, for it is blood that brings life." She lifted the horn cup to the Queen's mouth, and a great shudder ran through the Queen's body.
As the blood spilled over the Queen's tongue, Kaede's world lurched. The floor seemed to shake beneath her, and she clutched the horn cup, feeling dizzy. The Queen leaned toward her, and she was so close now that Kaede could see the Queen's pupils dilating. The Queen's mouth opened in a gasp. Kaede saw the smear of blood on her lips, and somehow Kaede, too, could taste it, metallic and bitter. She felt it traveling through her body as if she had drunk from the cup herself. She realized that iron was burning through the Queen—iron from the unicorn's blood—and it would kill her just like Kaede's dagger had killed Elowen.
The Queen's eyes were almost entirely black now; only a thin rim of gold encircled her pupils, and a chill was spreading over her skin like frost. She was dying. Kaede wanted to sob: This was not what she had intended. The Queen was supposed to live!
She closed her eyes; she did not want to see the Queen die. A memory rose like a ghost between them, and Kaede could see it just as the Queen did: a birth. A night of pain, horrible pain, followed by the sweetest dawn of the Queen's life. A baby girl with eyes of gold and hair the color of sunlight. Elowen.
Another ghost of a memory appeared: A hot summer afternoon in the Great Wood. A man alone, lost. There was something beautiful about him: the openness of his face, the strength of his hands. The Queen had no intention of keeping him for long, but he was so different from her many courtiers, with their elegant clothes and cool, appraising blue eyes. This man's eyes were the color of the earth, and his mouth was warm.
Kaede felt the Queen's heart pounding. Moments before she had felt the chill of death on the Queen's skin, but now there was a rising heat. Kaede opened her eyes and saw the Queen's face glowing as if she were lit by a fire within. The light grew until the Queen was bright as a star; she was the brightest, strongest star in a constellation, and every living creature was in orbit around her. But even the Fairy Queen was not invulnerable, for even she could be wholly changed by the smile of a handsome young man on a hot summer day.
The Queen was alive; she was reborn. Joy and relief swept through Kaede, and she took the Queen's hands in her own, discovering that the Queen was clutching Elowen's medallion in her fingers. The chain rustled as it slid between their hands; the stone warmed as the Queen's papery skin became strong and smooth, and her cheeks bloomed pink as a rose.
She smiled at Kaede, a smile that sloughed off Kaede's lingering doubts and sadnesses, and she said, "My huntress: You shall have your reward for what you have given me." She leaned close to her so that she spoke in Kaede's ear, and no one but she could hear.
"My name," she whispered, "is Ealasaid."
When she drew back, Kaede saw her for who she truly was, and she wept to see the Queen's love for her dead daughter, and what difference there was between fay and human was erased, for both understood the sorrow of loss.
# Chapter XL
fterward there was a great celebration, and Kaede, Taisin, and Con were granted free reign to go where they pleased within all of Taninli. Con spent many hours with the Fairy Queen, discussing the terms of a new treaty between their lands, for they both agreed that the time of isolation should end. He planned to present the treaty to his father as soon as he was back in Cathair, and if possible, he would bring the King himself to Taninli the next year.
Kaede and Taisin spent their last night in Taninli in the rooms they had been given during their first visit. Though they could have joined the revelry in the streets below, they were content to simply be near each other, for they both sensed that something precious was coming to an end.
It was Kaede who finally said the words, for she could not bear to pretend. "You're going back to the Academy, aren't you?"
Taisin looked away, but she could not deny it.
"I understand, you know," Kaede said resolutely, though it felt like her heart might break.
Tears trickled from Taisin's eyes. She covered her mouth with her hands as if that would hold the emotion inside.
Kaede got up and walked the few steps to where Taisin was seated nearby, and pulled her close. Taisin's shoulders shook as she cried, her face pressed against Kaede's stomach, her arms wrapped around her waist. It was a long time before she could speak, and Kaede knelt down and held her hands while she listened to her.
"It's the only thing I've ever wanted my entire life," Taisin said, her voice breaking. "I've dreamed of becoming a sage since I knew what a sage was, and I've always known what sacrifices it would require. There is still so much for me to learn, and I have so many questions to ask my teachers. But I love you so much. How can I give you up?"
"You're not giving me up," Kaede said, and she kissed her hands. "You'll always have me."
Taisin's eyes welled up with tears again. She dragged one hand free and wiped them away, drawing a ragged breath. "Kaede," she said, and she had never before realized how much she loved the sound of her name, the way it felt to say it, the look on Kaede's face when she heard Taisin call her. "Kaede, if I become a sage, you know what that means. I have to take a vow of celibacy. I will be with no one."
Kaede had planned to tell her that she should not give up her lifelong dream for her; that she had proven herself too gifted in her power to not continue her training at the Academy. But she also ached deeply to think that she might never hold her again. It was like someone was digging a hole in her and dragging out her heart, and she didn't know if she could bear the pain. "It's a ridiculous rule," she said bitterly, startling a laugh out of Taisin.
"There is a reason for it," Taisin said gently.
"What reason?" Kaede demanded.
Taisin stroked Kaede's hair back from her face, her fingers tangling in the black strands. "Every time I look at you, Kaede, I—" She stopped, breathless, her cheeks reddening.
"What?" Kaede said, the core of her quickening.
"Every time I—I—you know I can't think, Kaede. You make me stop thinking." She gave a brief laugh, and when Kaede's hand ran over her thigh, she shivered.
"You think too much," Kaede murmured, and she pulled Taisin's hand from her hair and kissed her bare wrist, pushing back the sleeve of her tunic. Her skin was warm and golden and unmarked.
Taisin sighed, her whole body coming alive. "I'm not a sage yet," she whispered, and they kissed, and kissed, and a few minutes later, they left the sitting room and went to the round chamber overlooking all the city lights, and they closed the door.
It was easier to say some things in the dark.
"When we leave here—"
"—things will change."
"It's better this way," Taisin said. "We'll have to get used to—to the way things are going to be." She felt as though she were kicking herself in the gut.
"You should change the rule."
Taisin smiled. "No matter what happens, I'll always love you."
"Taisin—"
"Wait," Taisin said, putting her finger over Kaede's lips. "Let me say this. I'll always love you, but I make no claim on you. You aren't bound the way I'll be. I know that. There's no reason for you to be alone—"
"Taisin," Kaede said, raising herself up on her elbows and looking down at her. "Stop it. I love you, and right now, that's all there is."
# Chapter XLI
he Huntsman and several of his riders escorted them through the Wood as far south as the river Kell.
One morning, Kaede emerged from her tent to find a wreath woven from new leaves and perfect pink and white flowers. She stared at it, confused, until the Huntsman told her it was a gift from the wood nymphs, who had visited during the night.
"A gift? Why?"
"Because you saved them, and you saved their queen."
She blinked at the wreath; it was so lovely, a crown fit for a woodland princess. She gave it to Taisin, who blushed to receive it, and thanked her with words so formal that Kaede's heart ached. They did not know how to tread this new path they had chosen, and sometimes it hurt so much that Kaede had to turn her back on Taisin. When she stared out at the Wood, at the trees and the sunlight and the pattern of oak leaves against the sky, it helped, if only a little.
One night, Con asked her why things had changed between her and Taisin, and when she told him, he was saddened. "Are you sure?" he asked softly. Taisin had already gone to sleep, burying herself in her blankets so that she might not have to stay awake beside the person she had decided to be parted from.
"No," Kaede said, "and yes. How can I ask her to give up what she wants most?"
"She wants you."
"Not only me, and that's as it should be." Though it pained her to say it, she was beginning to discover that she believed it. "Her path is different from mine."
"And what do you think your path is?" he asked.
She looked at the Huntsman, who was standing with his riders some distance away. "I think... I think my path lies with them."
Con glanced over his shoulder at the Xi. "With the Fairy Hunt?" He was surprised.
"With the Xi. And with you." She looked at Con. "When you bring that treaty to your father, I want to be there."
He nodded. "The Queen asked me to bring you next year, when I come back with my father."
"Did she?" Kaede said, and she found she was pleased to hear it.
"Yes. So: Will you come back with me?"
"I will," she said immediately.
"We'll have to give you some sort of title," he mused. "We can't keep calling you the Chancellor's daughter."
She smiled. "A title. I'll think about it."
When they came to the river Kell, Kaede could hardly believe her eyes, for there was a bridge. It was obviously old, and barely wide enough for one rider, but it seemed sturdy enough.
The Huntsman walked to her side and said, amused, "Did you think there was no crossing?"
She glared at him. "You saw us that day—of course we had no idea! Where are we? Are we south of where you found us?"
He glanced up at the blue sky. "South, yes, I think a little bit. If only you had gone a bit farther."
"How would we know?" she cried, exasperated. "All the maps are inaccurate."
"Then it's certainly time to correct them," he said, and gave her a warm smile.
She was overcome with bittersweet emotion. "Thank you," she said, "for everything."
He bowed his head to her. "We are grateful to you. And you—and Con and Taisin, too—will always be welcome in our lands. Perhaps your kingdom has a need for a huntress, to tend the Wood south of this river. You might ride with us one day, and we could teach you."
"You are very generous," she said, and tears came to her eyes.
He seemed to struggle with some emotion of his own, and Kaede wondered if he had ever had a daughter, for she thought he would make a good father.
South of the Kell, the Wood was awakening from its long slumber. Sunlight streamed through the branches overhead, each one heavy with green buds. Flowers bloomed along the edges of the trail, pink and purple and white, and birdsong filled the air every morning. It was like an entirely different forest than the one they had traveled through on their way north. There seemed to be no sign of the malignant Wood that had taken their friends Tali and Pol, and nearly taken Shae, as well.
Con intended to stop first at Mona's cottage, in case she was still waiting for them, and the closer they came to it, the more quickly he wanted to ride. Kaede and Taisin understood his eagerness, and the three of them pushed their horses hard on the first day without the Xi. On the third day, they were startled when Con left them behind in a cloud of dust, galloping down the trail toward a horse they could not quite make out in the distance. As they drew nearer, Kaede recognized it, and she said to Taisin, "It's Shae." She and Taisin halted their horses some distance back, not wanting to intrude on their reunion.
Con pulled his horse to a stop and slid out of the saddle, but when his feet touched the ground he felt unexpectedly shy. Shae dismounted from her horse, but she left one hand on the saddle to steady her, for her leg was still not entirely healed. Her hair had grown so that it fell softly around her face, and though she was thinner than she had been before the journey, Con was glad to see that she had color in her cheeks, and some of that color, he hoped, was due to seeing him.
"Con," she said, and gave him a tentative smile. "Well met."
"Shae," he said, and before he could lose his nerve, he went to her and kissed her, cupping her face in his hands. She let out a little sob, reaching up to put her arms around his neck.
Kaede turned slightly away, not wanting to stare. She had worried that the sight of them might make her mourn what she couldn't have with Taisin, but instead, it awakened something warm and alive inside herself. She was only happy for them, and when she glanced at Taisin, she was glad to see that Taisin felt the same way.
"Do you think it will make a good story?" Taisin asked. "The prince and the guard, who fell in love on a journey to the Fairy Queen's city." The sun seemed to shine especially brightly on this part of the trail. It gave Taisin's hair a halo of deep, dark red; it made her face glow.
Kaede smiled, and though her heart still ached, the love she felt was stronger than the pain. "It will make an excellent story," she agreed. And after they had given the prince and the guard another few moments to themselves, Kaede and Taisin rode down the trail to meet them.
# ACKNOWLEDGMENTS
Even though a writer sits at her desk alone, there are many people who stand behind her. Thanks to my wonderful agent, Laura Langlie. Thanks to my awesome editor, Kate Sullivan, who shares my storytelling vision. Thanks to my early readers, Sarah Pecora, Lesly Blanton, and Cindy Pon, for your feedback. Thanks to the whole team at Little, Brown Books for Young Readers who helped to bring _Huntress_ into the world: Barbara Bakowski, Kristin Dulaney, Alison Impey, Zoe Luderitz, Stephanie O'Cain, Ames O'Neill, Jen Ruggiero, Victoria Stapleton, and Amy Verardo. And last but not least, thanks to my partner, Amy Lovell, who witnesses good writing days and bad, and loves me anyway. This book is for you.
# [INTRODUCTION TO
"THE FOX"](toc.html#toc-appendix001)
By Malinda Lo
The world of _Huntress_ is inspired, in many aspects, by Chinese and Japanese traditions. The magic that Taisin practices is based on Taoism and qigong; the archery that Kaede learns is based on kyudo. I also intended to include magical creatures from Asian cultures in the novel, but during the writing process I realized there simply wasn't room to go into detail about them. One chapter that I wrote but ultimately discarded involved Kaede encountering a fox spirit, which is a supernatural being known in Chinese folktales as _huli jing_ , and in Japanese stories as _kitsune_. The fox spirit is a shapeshifter, and in many tales it transforms into a beautiful woman who can trick or seduce a human victim.
After I finished _Huntress_ , I found that I missed the characters terribly—something that I think a lot of authors experience when they connect deeply with their fictional creations! And I kept remembering the abandoned chapter about the fox spirit. When I was invited to submit a story to the online edition of _Subterranean_ magazine for their special young adult issue, I knew instantly that I wanted to turn that chapter into a short story about Kaede. "The Fox" is that story, and it was originally published online in April 2011. It is set about two years after the end of _Huntress_ , when Kaede is already working as the King's Huntress. I hope you enjoy it.
# "THE FOX"
THE WAY THE WIND BLEW, KAEDE KNEW IT was going to rain soon. The grasses were laid flat to the hillside; the trees shook in the gusting air.
She was five days northeast of the village of Anshu, forty-six days into her first circuit as King's Huntress of the northernmost province in the Kingdom. Forty-eight days since she had last seen her: the person she had traveled so far to forget. Now she was scarcely a week's ride from the mountains marking the Kingdom's border, but she was no closer to forgetting.
For several days, she had been following a dry streambed through the foothills, but today she urged her horse uphill. If the storm was bad, the stream would flood. She headed for a rocky outcropping partially hidden behind two giant oak trees. As she approached, she saw the skeleton of a fallen oak on the ground, its bark encrusted with white lichen. A narrow but well-worn trail led around the tree, where the rocky hillside opened up in a narrow, dark crack just wide enough for a horse to pass through. She dismounted, looping her horse's reins over one of the branches jutting from the oak, and went inside.
The light from the entrance did not shine far; darkness pooled only a few feet from where she stood. But in the distance, she saw the faint glow of daylight. "Is anyone there?" she called out. Her voice echoed slightly.
There was no answer; the cave felt empty.
She went back outside as thunder rumbled. Her horse stamped, and Kaede put her hand briefly on the mare's neck. "We'll be under cover soon," she said. She untied the bedroll from her saddle and unhooked the lantern, then unbuckled the saddlebags, carrying everything into the cave. She knelt down in the entrance and lit the lantern, and when she shone the light into the cave, she saw a wide open space with a hard-packed dirt floor. The rock walls arched overhead in a ceiling two or three times her height, then sloped down to a lower opening, shaped like a narrow little door, about twenty feet away. This was the source of that dim light.
Holding the lantern, she crossed to the opening and crouched down to peer through. On the other side was a roughly oval space, and on the far side the ceiling went up and up until it abruptly narrowed into a tunnel that ended in a small opening. She saw the sky there like a blue-gray eye. A breath of cool air twisted down from the opening, and below were the ashes of a fire pit.
Someone had stayed here before.
Of course, she should have expected it. She recalled the trail leading around the fallen oak to the entrance of the cave. She shook off the whisper of apprehension that slid down her spine and ducked through the opening into the interior chamber. As she straightened, lifting the lantern in her left hand, black shapes shivered over the walls.
She started, and the hand that held the lantern jerked. The light jumped, and the shapes seemed to jump as well. Her right hand moved automatically to the dagger on her belt, and just as her fingers closed over the hilt she realized what she was seeing. Pictures were painted on the walls: dozens, perhaps hundreds, of sinuous, curving animals, some moving among trees, others running together in packs. She recognized some of the shapes: a deer with branching antlers, a hawk, a wolf, many foxes. As she shone the light over the paintings, the lines seemed to move. She could have sworn that the foxes twisted their ink-black heads to look at her. But when she blinked and looked back, they were only dark strokes on the stone.
She took a step closer to the wall and reached out to touch the nearest image: a fox with its brushlike tail held high as it ran on elegant, delicately rendered paws. It looked like it might leap off the wall straight at her, but the black ink was dry and cool beneath her fingers. She wondered who had known these creatures well enough to paint them with such liveliness.
Thunder cracked again, so loud this time that it felt as though the earth itself had rumbled in response. A gust of wind sang over the chimney hole, sounding a deep, ringing note, as if the hill itself were an instrument. She looked up to see purple clouds scudding over the opening. The rain was coming.
It took some coaxing to convince the mare to enter the outer cave, but once inside, she settled down fairly quickly. Kaede unpacked her hatchet and went back out to the dead tree, hacking off firewood as fast as she could, racing against the coming storm. Just as she carried the last armful of wood into the cave, the first raindrops fell, heavy and cold.
She built a fire over the ashes in the interior chamber. She boiled water for tea. She cooked rice and ate it with some dried pork. She could hear the rain pounding on the hill above, and from time to time, drops hissed into the fire from the chimney hole, but mostly the cave was warm and dry, and she was glad she had found it.
The firelight sent leaping shadows over the painted walls, making the foxes seem to dance, nose to tail, in one long, sweeping motion across the stone. Leaning against her bedroll, Kaede watched the movement of the light, her eyelids growing heavy, her stomach full. Sometimes, in the evenings, after too many days of riding alone, she allowed herself to remember her: the one she could not forget. The one she tried to leave behind. The one she loved.
Tonight, she drifted on threads of memory until one drew tight: midnight in the palace in Cathair, two days before she was due to depart on her northern circuit. She stood before the moon-shaped gates to the little courtyard guesthouse, her hand on the polished iron knocker.
When the door opened, Kaede saw a woman holding an oil lamp in one hand, her eyes cast into shadow as the light illuminated the tense line of her jaw, her lips parting to say, "Kaede."
"I am leaving," Kaede said, her voice so low it was almost a whisper. "I will be gone for several months."
A pause. "I know."
Kaede looked at her, hoping to find some trace of regret, some shred of sadness. But her face was obscured, and the only sign Kaede saw was the slightest quiver of her mouth. If this had been a dream, perhaps what happened would be different—if Kaede could change it, she would—but it was a memory, and in her memory, she stepped back from the door, turning her face away to hide her own sorrow.
"I only came to say good-bye," Kaede said.
A log crashed in the fire, and Kaede blinked her eyes open. The shapes on the walls twisted as the flames flared, and she rubbed a hand over her face, drawing in a shaking breath.
She wanted to blot out this memory and forget it forever, but it rose up again and again until all she heard was the word _good-bye_ , echoing like a curse inside her.
She hated the word. She hated the way it made her feel: desolate, lost.
Angry with herself for sliding into those feelings again, she sat up and yanked at one of the saddlebags, jerking it open and pulling out a battered, leather-bound book. Her pen and ink rolled out, the little black bottle spinning across the ground until she lunged after it and clapped her hand down, striking the dirt with a sound like a slap. She set the bottle upright and uncorked it, her hand shaking only slightly as she dipped the quill into the black ink.
She had begun to keep a record of her journey because she realized soon after she left Cathair that she would never be able to remember everything she encountered, and the King would want a report upon her return. It had become a nightly ritual that soothed her: an accounting of the day's events, carefully trimmed to the barest facts, devoid of emotion.
> _Day 46: No settlement. The foothills continue, and I can see the red mountains coming. A storm, the first_ _I have encountered in a fortnight, has broken. I am sheltering in a cave behind a stand of oak trees, uphill from the dry streambed. The walls are painted with numerous animals, and the cave has clearly been_ _occupied before. The Kingdom's border is approximately one week distant from here. Then I will enter the Fairy Queen's lands._
Kaede's official title, now, was King's Huntress, but she felt less loyalty to the human King than to the Fairy Queen. On her left hand, she still wore the ring the Queen had given her: a moonstone, simple and round, set flat in a band of hammered silver. In the light of the fire, the stone looked almost pink. Like a sweet spring bud. While she wore the ring, she was under the Queen's protection, but she had never had to call on that privilege. Wherever she went, the fay knew her. There was only one human who went where she did with impunity. But she tried to respect fairy lands and to leave the fay to their own business. Her duties, if not her loyalties, were clear: survey the border and its inhabitants; return to Cathair; report to the King.
By then, two entire seasons would have passed. After so long in the wilderness, the city would be a new thing to her. And her memories, she told herself, would be like dust—easily swept away.
She finished her notes for the day and unrolled her blankets. She was tired, and the cave was as warm and secure as a womb. She fell asleep moments after she lay down.
When she opened her eyes, she knew she must be dreaming, for she saw a woman leaning over her. She had russet-colored hair and a pale face with angular green eyes and a thin nose. Foxlike and lithe, she bent down, and when her lips parted Kaede saw the pointed teeth of a predator.
A sliver of fear ran through her, but she reminded herself that this was a dream—this was not real.
The woman's breath was warm on Kaede's face, and it smelled of something she could not quite place. She had smelled it before. What was it? This little mystery consumed her; it was all she could think of as the woman came closer. It reminded her of an afternoon in the Wood in early winter. A memory of autumn leaves packed on the damp ground, the air carrying the threat of snow—
The woman kissed her, and Kaede felt the prick of sharp teeth on her lips. Her skin parted; blood seeped up to the surface. And like a fist stuffed down her throat, the kiss reached deep into her and pulled at the knot of longing buried there. Her back arched; her mouth opened in a gasp as all those tightly wound emotions came loose. Anguish, dragging roughly through her; suffocating heartache; absence, deep and vast. Yet beneath it all was a thin but strong hum of pleasure, as if she had been born to nurture this grief, and now she was finally free to drink from this bittersweet well until she was intoxicated by it.
She wanted to stop. She was desperate to stop—but she was afraid of what would happen if she did. Would she be hollow afterward? Like a shell discarded on the sand, filled only briefly by the restless lick of the salty sea, and then emptied again.
Kaede felt weighted down by despair, as if someone or something was pinning her down, pressing against her lungs so that she could barely breathe. Hot tears blurred her eyes, and they felt so real running down her cheeks that she began to wonder if she was still dreaming or if in fact she was awake. She blinked slowly, heavily, and as her vision cleared, she did not see the same woman above her. She saw a girl. A girl she knew.
She knew those eyes, the brown irises flecked with shards of black. She knew the smooth curve of those cheekbones. She knew the shape of that mouth and the way it smiled. The way it was smiling now. Kaede could not quite believe it. She thought the face above her must be a mirage. She reached up to touch the girl's long black hair and whispered, "Is that you?"
The girl did not answer, but she tilted her head slightly and shifted her body until she was pressed close to Kaede. She was naked. Kaede could feel the heat emanating from her pale skin, and her own body flushed in response. Her disbelief melted into desire. She wanted to believe it was her.
Kaede ran her fingers along the girl's cheek, traced the line of her jaw. She caressed the girl's throat, her thumb resting on the pulse that beat there. Everything about her was just as Kaede remembered. Her warm skin, the muscles of her back, the weight of her breasts. When Kaede kissed her, she tasted her own longing: a memory of sunlight shining through glass, the fall of her hair in a black fan across the pillow. She wanted to fold all of her into her arms and never let her go again.
But the scent that clung to her was unusual. It was not the same scent of flushed skin and sweat, just slightly metallic—the scent that made Kaede's heart leap. This was different. She remembered, again, that early winter afternoon in the Wood, the scent of fallen leaves crushed underfoot as she ran after the buck. She remembered him stumbling, the arrow lodged in his chest, his antlers dripping with velvet as his head sank to the ground. The smell of blood as she slit his throat. The smell of blood.
This girl smelled, subtly but surely, of blood.
This girl was not who she seemed.
The instant that Kaede realized this, she tasted her own blood on her tongue, hot and bitter. The girl's face wavered; her hair was red again, and then black. Kaede reached up with her left hand and clutched at the girl's bare arm. The moonstone ring glowed white with fairy light when it touched her skin, bright as a beacon. As it spread over them both, the girl let out a sharp, inhuman cry. Kaede stared, transfixed, as the girl's body changed in the light, morphing before her eyes. Her shining black hair thickened into a coarse red; her brown eyes narrowed into sharp emeralds; her face lengthened, developing a pointed chin. She opened her mouth in a snarl, and blood stained the tips of her pointed teeth.
The woman tried to twist out of Kaede's grasp, and the startling quickness of her movements finally shook Kaede fully awake. She realized she was pinned on the ground beneath a woman whose skin was covered with a fine, ruddy down, whose body was taut with muscle. The face she had been wearing was nothing more than a glamour. Kaede had heard stories about this woman—this creature—in many of the northern villages she had visited during her circuit. None of the tales were clear on whether the woman came first, or the fox did, but they all agreed that she could take on the face of any woman, and anyone who succumbed to her charms was sure to die, for she drank all of a person's spirit, leaving only a shattered husk behind.
Now, feeling the lithe weight of this woman-who-was-not-a-woman pressing down upon her, Kaede had no doubt she was real. Her sharp green eyes were heavy with hunger, giving her a kind of rough, bloodthirsty beauty.
Kaede braced herself, sliding her feet up so that her knees were bent, and in one swift motion she flipped her onto her back. Kaede yanked the woman's wrists up with her left hand, pinning her arms on the ground above her head, and with one knee on the woman's belly, she unsheathed her iron dagger with her right hand and pressed it to the woman's throat. She was strong but light, and without her glamour to dull Kaede's senses, she was easily overpowered.
"You are _not_ her," Kaede said in a harsh voice. A droplet of blood fell from her own mouth, striking the woman's cheek.
The woman opened her bloodstained lips and said, "I could be her." She had the accent of the fay—a kind of lilting tone, as if she were singing.
"No," Kaede said. "You could never be her."
The woman gave her a frightening smile and said, "If you desire it, I could be."
"No," Kaede said again. She pushed away the weakness in her that made her yearn to give in. "No." She pressed her dagger against the woman's throat until the skin broke, and the scent of burning rippled up from the cut: iron against fay skin.
Pain lit the woman's green eyes. Pain and fury. Her whole body rippled, stretched, as lithe as a snake, as quick as a fox. The downy red hairs on her skin became fur; the joints of her limbs turned. Her nose and mouth became a snout that snapped at Kaede's arm. Kaede recoiled, stunned. A heartbeat later the woman was gone, and the fox she had become had fled from the cave.
The air seemed to reverberate in her wake.
Driven by something she did not understand, Kaede scrambled to her feet. She stumbled through the outer cave and plunged outside into the storm. The rain pounded like a drum on the hollow hill behind her, soaking through her clothes. Rain slid down length of her black braid, pouring like tears over her face. She could barely see five feet in front of her, but she thought she saw a shape rising up just beyond the remains of the fallen tree.
"Stop," she gasped.
The shape lengthened, became a female form again, and looked back.
"Stop," Kaede cried. She could not resist. She wanted to see her again.
The woman stayed where she was, drawing back when Kaede approached so that she remained shrouded by the dark, just out of reach of the glow from the Fairy Queen's ring. But Kaede knew the woman had put on the other face again. The one that Kaede wanted more than anything else in the world to see.
"If you want to see her again," the woman said, "then you must take off your ring."
"If I take it off, you'll kill me. I won't give up my life so easily," Kaede said, though her hand twitched. Would it be worth it? The thought chilled her more than the rain.
"You are already giving up your life, with every day that you long for her."
Kaede flinched at the easy condemnation in the woman's words—and at the uncomfortable truth of them. "You're wrong," she said, but even she heard the lack of conviction in her voice.
The woman came one step closer. The light of the ring, which had faded somewhat, flared up again and exposed the delicate, sharp points of her nails. "Why do you deny yourself?"
"I don't—"
"You could have me," the woman said simply.
The rain slid in cold rivulets down Kaede's back. She said, "But I would still not have her."
The woman asked, "Will you ever have her?"
Without waiting for Kaede to answer, she turned away, her body shifting again, and in the blink of an eye the fox was gone and Kaede was standing alone in the dark, in the rain, with the Fairy Queen's ring cold on her hand.
She was packed up and ready to go well before dawn. When the first light brightened the sky, she smothered the fire and pulled on her oil-slicked cloak, preparing to go out into the dull gray drizzle. She had changed into dry clothes and tied her wet ones into a knot, which she hung from her saddle. She had not slept at all.
At first she had been afraid that the fox-woman would return, but as the night slowly passed with no sign of her, that fear subsided and was replaced by a persistent, familiar ache. All she could see, in her mind's eye, was that face looming over her. She had thought she was long finished with crying over this, but as she sat slumped by the fire, tears coursed down her cheeks until her body began to shake, and then she was rocking back and forth, clutching her knees to her chest like a little girl. When no more tears came, she sat in silence, drained of her sorrow. A peace seemed to steal over her, quiet and unassuming.
When she went outside, the morning light was soft on her face, and the rain was gentle, too, like a fine mist that cloaked the world in an ethereal tracery of tiny droplets. She inhaled the damp, late summer air, and she was suddenly buoyed by it. All the earth around her was drinking it in—a wash of water, slicking down the blades of grass, clinging to the oak leaves and softening the bark. The ground was wet, too, but she saw no footprints from the night before. There were only the marks she made this morning as she led her mare down the hill toward the newly swollen stream to drink. When she reached the bank and her horse lowered her head to the rushing water, Kaede looked back toward the oak grove and the black crease in the hillside where she had spent the night.
Sitting there on the ground beside the fallen tree was a fox. Its red tail waved briefly, then wrapped around its delicate paws.
Startled, Kaede let go of her horse's reins. She took a step, two steps, back up the hill before she stopped, her eyes fixed on the fox looking back at her.
"Good-bye," she said, tasting the misty air on her tongue, delicate and new.
Turn the page for
an exclusive peek at
the first book in Malinda Lo's
new sci-fi duology.
coming September 2012
#
The birds plummeted to the tarmac, wings loose and limp. They struck the ground with such force that their bodies smashed into dark slicks on the concrete.
"What the—" Reese Holloway pushed herself out of the hard plastic seat facing the floor-to-ceiling windows. Outside, heat waves rippled over the oil-stained runway. She glanced back at David, her forehead wrinkled. "Did you see that?"
David Li looked up from his book. "See what?" His dark brown eyes reflected the hard, bright daylight in tiny dots of white.
Reese tried to swallow the flutter of self-consciousness that rose within her as David met her gaze. She pointed at the windows. "These birds just fell dead from the sky."
David's eyebrows rose. "No way."
"Yeah."
David closed the book over his right index finger and stood. "Where?"
His shoulder brushed against her as he joined her at the windows. She took a tiny step away and said, "Over there—by those two workers." A man in a blue jumpsuit pulled up in a baggage cart while another man, in an orange vest, ran toward him.
"You mean that dark stuff on the ground? Those are birds?"
" _Were_ birds."
"Damn."
Blue Jumpsuit was gesticulating at the sky and the remains on the ground, apparently explaining the birds' fatal descent to Orange Vest.
"That was bizarre," Reese said. The unforgiving glare of the sun on the neon-orange vest and the glistening lumps on the concrete gave the scene a surreal cast—like overexposed film. "Have you ever seen birds just crash to the ground like that?"
"No," David said.
Reese watched Blue Jumpsuit pull a plastic bag from a container on the baggage cart. He stuck his hand in the bag and squatted down to pick up the remains as if he were cleaning up after a dog. David went back to his seat, but Reese remained standing until the birds were removed, leaving only a smudge on the pavement: the stamp of their final moments. When she sat down again she felt unsettled, as if the ordinary world had been knocked off-balance and everything was now listing slightly to one side.
Beside her, David had returned to his book, and she saw the title angling across the cover in a retro-futuristic font: The Left Hand of Darkness. She glanced at her watch. Their plane to San Francisco had been delayed, but it was due to take off, finally, in an hour. The waiting had made her twitchy, and her leg bounced with nervous energy. She bent down to pull out her iPod from her backpack, and as she fitted the headphones into her ears she surreptitiously watched David turn a page. He was wearing a short-sleeved shirt, and the skin of his arm had a golden tone like sunlight during Indian summer. She took a shallow breath and forced herself to look at her iPod, scrolling through her music. But as the song titles rolled past, she wasn't paying attention.
David was her debate partner. They had both joined the debate team at Kennedy High School their freshman year, but it wasn't until junior year last fall that their coach, Joe Chapman, suggested they might work well together. And they did. They worked so well together that they qualified for nationals. When Reese's mom found out, she was ecstatic. She even wanted to fly to Phoenix with them for the tournament, but her case ended up going to court during nationals—she was an assistant district attorney in San Francisco—so only Mr. Chapman had come with them.
Now, in the airport as she sat beside David, the memory of that day—was it only yesterday?—and all its disappointments surged up again, slamming into the off-kilter tension that gripped her after witnessing the demise of those birds. Get a grip on yourself, she thought.
"I'm going to walk around," Reese said abruptly to David. "Will you watch my stuff?"
David nodded, and she stood, dropping her iPod back into her backpack on the floor. She saw Mr. Chapman threading his way through the seats toward them, carrying two bottles of water. He waved at her, and she waved back as she walked toward the center of the concourse. This trip could not be over soon enough. There were only a few weeks before school ended for the year, and thankfully no more debate practice. All of this weird crap with David would be done with, and she doubted they would be partners again next fall. That'll be a relief, she thought, ignoring the twinge in her chest that told her she was lying to herself.
Reese passed the podium, where a blue-and-white-uniformed flight attendant was dealing with a line of five or six travelers. A harassed-looking mother herded two toddlers forward while dragging a suitcase and pushing a stroller. Reese was trying to avoid the stroller, her sneakers squeaking across the glossy floor, when she heard someone scream, "Oh my God!"
She turned to see a woman standing up, hands over her mouth and staring at the flat-screen TV hanging from the ceiling. The news was on as usual, and the Asian American anchorwoman had a hand pressed to her ear as if she were listening to a feed. Her face was grim. Reese took a few steps closer until she could read the headline at the bottom of the screen: _PLANE CRASH IN NEW JERSEY KILLS ALL PASSENGERS_.
Reese gasped.
The anchorwoman lowered her hand from her ear and said: "We have confirmed reports that an Airbus A320 has crashed outside Newark Airport. The cause of the crash has not yet been determined, but eyewitnesses have reported that the plane collided with a flock of Canada geese during takeoff. While airplanes are designed to withstand isolated bird strikes, apparently this was an entire flock—more than a dozen birds in all."
A jolt went through Reese. Birds? In her mind's eye she saw the birds plunge to the tarmac again.
Other travelers began to gather beneath the TV screen while the anchorwoman repeated the bare facts. The plane had burst into flames when its fuel tanks exploded upon impact. One hundred forty-six passengers were presumed dead. Emergency crew on the scene were hoping to salvage some clues from the burning mess.
"This is crazy," said a middle-aged woman standing near Reese. "Those poor people!"
"What is this about birds?" said a man in a Red Sox cap. "How could birds do this?"
The anchorwoman interrupted her own report, saying, "We have news of a second crash, this time in the Pacific Northwest. A Boeing 747 has crashed onto the coast near Seattle." The anchorwoman pressed her hand to her ear again. "Information is still coming in. We do not know if there are any survivors of this second plane crash." Her face stiffened, and she stopped speaking for a moment. Finally she lowered her hand and looked into the camera. "Early reports indicate that this plane was struck by birds."
Reese gaped at the television as a collective gasp arose from the travelers around her.
"We have Lamont Bell on the line from the Federal Aviation Administration," the anchorwoman said. "Mr. Bell, what is the chance of two planes being downed by bird strikes within an hour?"
The man's voice sounded scratchy over the audio transmission, but it was clear that he was unnerved. "It's not—it's very unusual. I've never in my entire career encountered two plane crashes of such magnitude due to bird strikes."
"Are you saying that you believe the planes crashed due to a different, unnatural cause?"
"I—no, I'm not saying that. I don't know what caused the crashes. We shouldn't speculate."
"Eyewitness accounts indicate the presence of large flocks of birds. Is it impossible that the plane crashes were due to bird strikes?"
"No, it's not impossible, but it's unlikely."
"Then you do think something else is part of the equation?"
"I don't know," Bell said, sounding exasperated. "Look, I don't want to speculate."
"Mr. Bell, I'm afraid I have to interrupt you again," the anchorwoman said. "I've just received news that there has been a third crash, this time in Texas. Once again, reports do indicate that bird strikes may have been the cause of the crash. And—" She stopped speaking, turning to look off camera. Someone offscreen handed her a sheet of paper, and when she faced the camera again, she read directly from it. "I've been informed that the FAA has grounded all aircraft in the United States while officials assess the threat level posed by these accidents." She looked into the camera. "I'm afraid we have some bad news for travelers today. I repeat: The Federal Aviation Administration has grounded all aircraft in the United States."
Reese's stomach dropped, and the crowd around the TV monitor erupted with questions.
"What do you mean? Is my flight canceled?"
"This is bullshit!"
"What is going on? How could birds possibly do this?"
"It can't be birds—it must be terrorists."
"That's insane. Terrorists can control birds now?"
As the questions piled one on top of another, louder and louder, Reese's heart began to race. The birds that had smashed onto the runway. Three plane crashes. Three. One is unusual; two is a coincidence; but three... how could it be an accident?
People were bumping into her, craning their necks at the TV, talking over the anchorwoman. Reese shoved her way out of the crowd, her skin crawling as disbelief warred with growing panic inside her. What is going on? She halted in front of a bank of monitors displaying the flight departure times. One by one, those times blinked out and were replaced by a single word, repeated over and over: _CANCELED_.
Reese couldn't get through to her mom; the call went straight to voice mail. She checked her watch; it was 3:38 in San Francisco. She knew her mom was probably still in court, but Reese was stiff with anxiety. If terrorists were behind these plane crashes, how safe was her mom in a courthouse? David paced nearby, talking to his parents on his phone in Chinese.
Mr. Chapman lowered himself into the seat beside Reese, frowning, and pushed up his black-framed glasses. "This is a mess," he said. Behind them, dozens of travelers were clustered around the podium, trying to rebook their plane tickets. CNN was still droning in the background, but Reese had stopped watching after the fourth plane crash in Colorado. She was filled with a kind of paranoid helplessness, and she kept glancing out the windows as if she were waiting for more birds to plunge from the sky.
"What are we going to do?" she asked, sounding more frightened than she intended.
Mr. Chapman gave her a thin smile. She thought he was trying to be reassuring, but he didn't quite succeed. "We just have to wait. You're too young to remember 9/11, but at first it was just a bunch of waiting. Waiting to hear from the president, waiting to find out who was behind it." He shook his head and pushed up his glasses again, a nervous tick that betrayed his own tension. "Hopefully, there will be some news soon."
The line at the Wendy's counter snaked back and forth unevenly across the polished concrete floor of the concourse. Reese guessed there were about twenty-five people ahead of her, which put her right at the edge of the seating area next to the overflowing trash bin. An abandoned Frosty was perched on its side and dripping onto the floor, forming a pool of beige liquid. Reese looked away from the mess, her gaze sweeping up toward the windows set high against the ceiling. The sky outside was dusky blue. She had been stuck in this airport since eleven o'clock that morning—almost nine hours.
Earlier, she had called her best friend, Julian Arens, to tell him she was stuck in Phoenix. He told her that all major airports in the United States were full of stranded passengers, and already some people were concerned the airports might run out of food. If the planes couldn't fly, they couldn't bring in supplies either.
"You're freaking me out," Reese said, only half joking. "Are you saying I should start hoarding those disgusting airport sandwiches?"
"They're probably gone by now," he answered. By the time she went to search out dinner, Julian was right. The deli cases that had once been full of sandwiches and salads were picked clean, and the only food left was the square-shaped burgers at Wendy's.
Her phone buzzed as she was scrolling through the feeds on the Hub; Julian had just texted her.
> > Stuff is getting crazy out there.
>
> U have 2 check this out:
>
> www.short.349sy
She clicked on the link, which took her to a blog post on a website called Bin 42. The headline made her eyebrows rise: Government cover-up of plane crashes continues with media blackout.
> If you've been on the Hub today, you probably noticed that everyone around the world is freaked out about one thing: these bizarre plane crashes. But you might also have noticed that your feeds about them keep mysteriously disappearing. We've uncovered evidence that every 15 minutes, feeds relating to plane crashes, bird strikes, and the causes of such are routinely wiped.
>
> Who has the power to do this? Only one entity: the US government.
# PRAISE FOR _H UNTRESS_
"Lo's storytelling and prose are masterful, and her protagonists will fascinate, particularly Taisin and her relationship to death and its accompanying rituals, her visions, and the way she can occupy another's mind."
— _Publishers Weekly_ (starred review)
"Most notably, the inclusion of gay characters in a young adult fantasy, and the natural unfolding of their relationship, comes as a refreshing change."
— _The Horn Book_
"Heartbreaking sensuality... blossoms between the female leads. Beyond romance, however, stunning action sequences abound, including one literal cliffhanger and a breathtaking confrontation with the villain. Fans who found themselves entranced by Lo's previous work will be pleased to know that the magic has returned to the Wood."
— _Bulletin of the Center for Children's Books_
"The lovely thing about this fantasy... is the completely natural sweetness of the attraction between Kaede and Taisin, which is unremarkable in their culture."
— _Kirkus Reviews_
"Lo has created a wonderfully detailed world, and this dynamic and moving story of love that must find a way against nearly insurmountable odds will be as well received as _Ash_."
— _School Library Journal_
# Contents
Welcome
Dedication
Map
Author's Note
Pronunciation Guide
Part I
Chapter I
Chapter II
Chapter III
Chapter IV
Chapter V
Part II
Chapter VI
Chapter VII
Chapter VIII
Chapter IX
Chapter X
Chapter XI
Chapter XII
Chapter XIII
Chapter XIV
Part III
Chapter XV
Chapter XVI
Chapter XVII
Chapter XVIII
Chapter XIX
Chapter XX
Chapter XXI
Chapter XXII
Chapter XXIII
Chapter XXIV
Chapter XXV
Chapter XXVI
Part IV
Chapter XXVII
Chapter XXVIII
Chapter XXIX
Chapter XXX
Chapter XXXI
Chapter XXXII
Chapter XXXIII
Chapter XXXIV
Chapter XXXV
Chapter XXXVI
Chapter XXXVII
Chapter XXXVIII
Part V
Chapter XXXIX
Chapter XL
Chapter XLI
Acknowledgments
Introduction to "The Fox"
"The Fox"
A Preview of _Adaptation_
Praise for Huntress
Copyright
# Copyright
This book is a work of fiction. Names, characters, places, and incidents are the product of the author's imagination or are used fictitiously. Any resemblance to actual events, locales, or persons, living or dead, is coincidental.
Copyright © 2011 by Malinda Lo
Map illustration copyright © 2011 Dave Stevenson
"The Fox" © 2011 by Malinda Lo
Excerpt of _ADAPTATION_ © 2012 by Malinda Lo
All rights reserved. In accordance with the U.S. Copyright Act of 1976, the scanning, uploading, and electronic sharing of any part of this book without the permission of the publisher constitute unlawful piracy and theft of the author's intellectual property. If you would like to use material from the book (other than for review purposes), prior written permission must be obtained by contacting the publisher at permissions@hbgusa.com. Thank you for your support of the author's rights.
Little, Brown and Company
Hachette Book Group
237 Park Avenue, New York, NY 10017
www.hachettebookgroup.com
www.twitter.com/littlebrown
Second e-book edition: June 2012
Little, Brown and Company is a division of Hachette Book Group, Inc.
The Little, Brown name and logo are trademarks of Hachette Book Group, Inc.
The publisher is not responsible for websites (or their content) that are not owned by the publisher.
The Hachette Speakers Bureau provides a wide range of authors for speaking events. To find out more, go to www.hachettespeakersbureau.com or call (866) 376-6591.
ISBN 978-0-316-17520-3
|
{
"redpajama_set_name": "RedPajamaBook"
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| 1,741
|
{"url":"https:\/\/dro.dur.ac.uk\/22538\/","text":"We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.\n\nDurham Research Online\nYou are in:\n\u2022 Home\n\u2022 Research\n\u2022 Durham Research Online\n\u2022 Galaxy-scale bars in late-type Sloan Digital Sky Survey galaxies do not influence the average accretion rates of supermassive black holes.\n\n# Galaxy-scale bars in late-type Sloan Digital Sky Survey galaxies do not influence the average accretion rates of supermassive black holes.\n\nGoulding, A. D. and Matthaey, E. and Greene, J. E. and Hickox, R. C. and Alexander, D. M. and Forman, W. R. and Jones, C. and Lehmer, B. D. and Griffis, S. and Kanek, S. and Oulmakki, M. (2017) 'Galaxy-scale bars in late-type Sloan Digital Sky Survey galaxies do not influence the average accretion rates of supermassive black holes.', Astrophysical journal., 843 (2). p. 135.\n\n## Abstract\n\nGalaxy-scale bars are expected to provide an effective means for driving material toward the central region in spiral galaxies, and possibly feeding supermassive black holes (BHs). Here we present a statistically complete study of the effect of bars on average BH accretion. From a well-selected sample of 50,794 spiral galaxies (with ${M}_{* }\\sim 0.2\\mbox{--}30\\times {10}^{10}\\,{M}_{\\odot }$) extracted from the Sloan Digital Sky Survey Galaxy Zoo 2 project, we separate those sources considered to contain galaxy-scale bars from those that do not. Using archival data taken by the Chandra X-ray Observatory, we identify X-ray luminous (${L}_{{\\rm{X}}}\\gtrsim {10}^{41}\\,\\mathrm{erg}\\,{{\\rm{s}}}^{-1}$) active galactic nuclei and perform an X-ray stacking analysis on the remaining X-ray undetected sources. Through X-ray stacking, we derive a time-averaged look at accretion for galaxies at fixed stellar mass and star-formation rate, finding that the average nuclear accretion rates of galaxies with bar structures are fully consistent with those lacking bars (${\\dot{M}}_{\\mathrm{acc}}\\approx 3\\times {10}^{-5}$ ${M}_{\\odot }$ yr\u22121). Hence, we robustly conclude that large-scale bars have little or no effect on the average growth of BHs in nearby ($z\\lt 0.15$) galaxies over gigayear timescales.","date":"2022-05-29 08:55:52","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.4880480468273163, \"perplexity\": 3514.8127530125294}, \"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\/1652663048462.97\/warc\/CC-MAIN-20220529072915-20220529102915-00780.warc.gz\"}"}
| null | null |
Q: Can CSS render text twice, in two different fonts or colors? In this jsfiddle the same text is drawn twice:
*
*first in white, in a solid font
*then in black, in an outline font
The two fonts, Londrina Solid and Londrina Shadow, are designed to have exactly the same metrics and to be used together in this way.
Is there a way to use CSS to achieve this effect without putting two copies of the text into the HTML? (Of course, I don't want to put a copy of the text into the CSS, either.)
A: Five text-shadows is almost identical1:
text-shadow: 0.03em 0.03em 0 black, -1.25px 0 0 black, 1.25px 0 0 black, 0 -1.25px 0 black, 0 1.25px 0 black;
Here's a demo!
1 Yes, I know this is an oxymoron.
A: You could try using :after and use the content attribute:
h1:after, h1 > span.shadow:after {
content: "Nashville hack day is November 11";
font-size: 700%;
}
And the html could be:
<body>
<h1><span class="shadow"></span></h1>
</body>
I realize this could be cumbersome, but at least you'd only have to write the content once.
See jsfiddle.
A: If you're trying to create text shadows, then check out W3C: Css: text shadows.
These are not compatible with non-compliant IE<10 though.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,318
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Karl Ludwig von Bruck, född 8 oktober 1798 och död 23 april 1860, var en österrikisk-ungersk friherre och statsman.
von Bruck deltog som officer i preussiska armén i kriget 1814-15. Han grundade efter vidsträckta resor i det kända rederiet Österrikiska Lloyd i Triest 1833. 1848 valdes von Bruck in i tyska nationalförsamlingen i Frankfurt am Main som representant för Triest, varvid han även fungerade som ombud för Österrike-Ungern. 1849-1851 var han handelsminister, och var som sådan medarbetare till författningen av 4 mars 1849. Han användes 1853 som diplomatisk underhandlare med Preussen och Turkiet och gjorde härvid sitt land stora tjänster. 1855 blev han finansminister, och fortsatte på den posten de storslagna reformer på det ekonomiska området, som han under sin tidigare ministertid påbörjat. 1860 blev han dock med orätt anklagad för delaktighet i den stora finansskandalen Eynatten, och avskedade 27 april samma år under onådiga former, och tog i förtvivlan häröver sitt liv. Hans oskuld blev senare konstaterad.
Källor
Svensk uppslagsbok, Lund 1930
Österrikiska diplomater
Österrikes finansministrar
Födda 1798
Avlidna 1860
Män
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,993
|
import mimetypes
import os
import smtplib
from email import encoders
from email.mime.audio import MIMEAudio
from email.mime.base import MIMEBase
from email.mime.image import MIMEImage
from email.mime.multipart import MIMEMultipart
from email.mime.text import MIMEText
def adiciona_anexo(msg, filename):
if not os.path.isfile(filename):
return
ctype, encoding = mimetypes.guess_type(filename)
if ctype is None or encoding is not None:
ctype = 'application/octet-stream'
maintype, subtype = ctype.split('/', 1)
if maintype == 'text':
with open(filename) as f:
mime = MIMEText(f.read(), _subtype=subtype)
elif maintype == 'image':
with open(filename, 'rb') as f:
mime = MIMEImage(f.read(), _subtype=subtype)
elif maintype == 'audio':
with open(filename, 'rb') as f:
mime = MIMEAudio(f.read(), _subtype=subtype)
else:
with open(filename, 'rb') as f:
mime = MIMEBase(maintype, subtype)
mime.set_payload(f.read())
encoders.encode_base64(mime)
mime.add_header('Content-Disposition', 'attachment', filename=filename)
msg.attach(mime)
de = 'seumail@gmail.com'
para = ['outroemail@gmail.com']
msg = MIMEMultipart()
msg['From'] = de
msg['To'] = ', '.join(para)
msg['Subject'] = 'Buteco Open Source'
# Corpo da mensagem
msg.attach(MIMEText('Exemplo de email HTML com anexo do <b>Buteco Open Source<b/>.', 'html', 'utf-8'))
# Arquivos anexos.
adiciona_anexo(msg, 'texto.txt')
adiciona_anexo(msg, 'imagem.jpg')
raw = msg.as_string()
smtp = smtplib.SMTP_SSL('smtp.gmail.com', 465)
smtp.login('seumail@gmail.com', 'suasenha')
smtp.sendmail(de, para, raw)
smtp.quit()
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 439
|
package com.cyosp.mpa.api.rest.homebank.v1dot2.response;
import com.cyosp.mpa.api.rest.homebank.v1dot2.model.Currency;
import lombok.Getter;
import lombok.Setter;
/**
* Created by CYOSP on 2017-07-26.
*/
@Getter
@Setter
public class CategoryResponse extends RootResponse {
private String name;
private String balance;
private Currency currency;
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,760
|
{"url":"https:\/\/mailman.ntg.nl\/pipermail\/ntg-context\/2005\/011110.html","text":"John R. Culleton john at wexfordpress.com\nMon May 30 13:04:13 CEST 2005\n\n```For a particular section I wish to substitute a graphic for the\nsection header, but have the TOC entry named as usual. Is there\na way to say e.g.,\n\\section{foo}\nand have foo show up in the TOC but not as a section header?\n\n--\n\nJohn Culleton","date":"2019-05-19 10:41:17","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\": 0.9713422656059265, \"perplexity\": 5545.007897380085}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-22\/segments\/1558232254751.58\/warc\/CC-MAIN-20190519101512-20190519123512-00550.warc.gz\"}"}
| null | null |
/*
* To change this license header, choose License Headers in Project Properties.
* To change this template file, choose Tools | Templates
* and open the template in the editor.
*/
package interviews.ceb;
/**
*
* @author Bharat
*/
public class TestObject {
public static void main(String args[]) {
Super s = new Sub();
Super s1 = s.add();
System.out.print(s1==s);
}
}
class Super {
public Super add() {
System.out.print("Super ");
return this;
}
}
class Sub extends Super {
@Override
public Sub add() {
System.out.print("Sub ");
return this;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,568
|
Chemical Weapons Probes Can Expose Western Plots against Syria
Islam Times - The UN and its sunsets that for a decade along with the Western-Arab-Israeli triangle backed the Syrian opposition and terrorists fighting the Syrian government now admitted they found documents that show the ISIS terrorist group was the party that used chemical weapons in the past years.
UN experts said they have cited digital evidence and witness evidence that all confirm the use of chemical weapons by the terrorist group in Iraq between 2014 and 2019. The UN investigation team confirmed that ISIS had produced and used rockets, chemical mortars, chemical ammunition for rockets, chemical warheads, and homemade chemical bombs. The report specifically mentions the ISIS attack on Tuz Khurma town in Kirkuk province on March 8, 2016.
This report is while the Iraqi government in July 2014, when ISIS occupied many western regions of the country, confirmed in a report that a center related to the country's former chemical weapons program had fallen into the hands of terrorists and expressed concern about this issue.
In the past years, the issue of using banned weapons, especially chemical weapons, has been very controversial and at times it became a tool for the propaganda campaigns and the political pressure of the Westerners on the Syrian government. The UN has not submitted a report on the use of unconventional weapons by the terrorists so far, but now that the crimes of ISIS have been exposed to everyone, it had to disclose some realities.
Scenario of chemical weapons use in Syria
The UN has confirmed the use of chemical weapons by ISIS in Iraq while it refuses to prepare such reports in Syria. This is while ISIS was present in Syria before it rose in Iraq and occupied the border areas of the two countries and could easily move such weapons between the two countries and there are reports published by Moscow and Damascus that disclosed the use of chemical weapons by terrorists. A number of chemical attacks in Syria may have been carried out by ISIS, but since dozens of terrorist groups were present in the Syrian provinces at the same time, it is difficult to confirm which one was behind the attacks and this requires a comprehensive investigation.
The use of chemical weapons is not limited to ISIS, and other Takfiri groups have also committed these crimes many times. Terrorist groups based in Syria have committed such crimes in different regions in the past years, but the UN has always accused the Syrian government of using chemical weapons instead of the Takfiris under the pressure of the Americans and Europeans. Even when all Syrian chemical weapons were removed from the country under the UN supervision in 2013, accusations against the Syrian government continued.
In October 2013, a year after outbreak of conflict, the UN inspectors reported that from the seven areas they inspected, in five areas, chemical weapons were used. Ghouta, Khan Ersal, Juber, Sargheb, and Ashrafia were areas in which these weapons were used, but the UN report did not specify which party, the government or the terrorists, used them. The ambiguity of reports paved the way for backers of terrorists to point the fingers at the Syrian government. Even former US President Barack Obama planned to attack Syria with the help of NATO in September 2013 under the pretext that the Syrian government was attacking terrorists and civilians with chemical weapons, but he eventually abandoned this plan as Damascus agreed to hand over its chemical weapons.
In another report, the UN claimed that the Syrian government used chlorine gas chemical weapons in the attacks on Idlib city in March 2016, and this substance was embedded in barrel bombs. In 2017, the UN claimed that the Syrian government used chemical weapons against armed groups in Khan Sheikhoun. In April 2018, when the use of chemical weapons in the Duma city in the Damascus suburbs was raised by the Western powers, Bashar al-Jaafari, the permanent representative of Syria to the UN, stressed that his country would not accept any results published by the investigation team of the Organization for the Prohibition of Chemical Weapons regarding the incident in Duma, adding: "Some countries are trying to repeat what happened in Iraq and find excuses with the aim of starting an aggression against Syria, but we do not allow the falsification of reality."
In Syrian crisis, the UN has always tried to take the Western-backed terrorists' side, and this is why it does not admit crimes by the terrorist groups— a behavior drawing strong-toned reaction from Damascus. Syria's deputy UN envoy during a meeting of the Security Council on Monday, in a speech lashed out at the body's "politically-motivated" approach to the Syrian chemical weapons case. Al-Hakam Dandi expressed strong Syrian opposition to use of chemical weapons by any side at any time and place, adding that Damascus joined the Organization of Prohibition of Chemical Weapons voluntarily and adhered to its commitments to destroy all its chemical stockpiles and facilities and continues to work with the UN on the case.
Although many terrorist groups have been destroyed by the Syrian government, there are still thousands of fighters from these groups in Idlib, who can still repeat scenarios and attract the world community's attention. The Russian Center for the Reconciliation in Syria warned last month in a report about the scenario of the Al-Nusra Front terrorist group against the Syrian army and asserted that the terrorist group is planning to use toxic substances against civilians and accuse the Syrian army in a false flag attack. This is while the West and the UN, which in the past supported the foreign and moderate opponents, tried to form a government in which the opponents of Assad have a role, but now there is no news of these groups amid Arab normalization with Damascus and severance of Arab aids to them. Even Turkey as their biggest backer closed down their offices on its soil to show a good will for normalization with the Syrian government.
The recent UN report comes as during the war, whenever the terrorists could not make advances against the government forces on the battlegrounds, they resorted to the threadbare scenario of false flag chemical attacks to provoke the international community against Damascus. Then it was disclosed that the videos showing the alleged attacks were shot based on a pre-planned scenario in association with the White Helmets, who claimed to be rescue workers of an international mission but were actually intelligence agents and militants fighting the government.
Now, if the Syrian government and its allies launch an operation to retake Idlib as the last stronghold of the foreign-backed terrorists, a similar scenario may be on the Western table to block recapture of the province.
A decade after terrorist groups ran unchecked in Syria and Iraq, the UN report was a belated admission that accusations against Syria for chemical weapons use were false and all the crimes were committed by the Western-backed terrorists seeking to conclude a scenario aimed at toppling President Bashar al-Assad. But all their moves met their failure and from now on, if they return to this trick, no country would believe them.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 259
|
719-392-1234 We travel coast-to-coast every 1 1/2-2 weeks.
Call 800-451-7696 for current trip dates.
Natural Horse Magazine is a publication FOR the horse, and applies to every breed, discipline, and geographical area.
EHorseEquipment is a full service provider of horse equipment including a complete line of equestrian gift items, sportswear and jewelry. We have been meeting the needs of horse lovers for over 25 years. Our primary goal is to provide you with superior quality, reliable merchandise at a reasonable price. Our staff is composed of horse people like yourself who are ready and willing to assist you with any questions or concerns you may have.
US Department of Transportation: The Federal Motor Carrier Safety Administration (FMCSA) is focused on reducing crashes, injuries, and fatalities involving large trucks and buses.
Horse Racing: Australian Horse racing tips, selections and information. Service for Australian and International punters.
All State Horse Express has joined with Nation-Wide Horse Transportation to better server our customers.
All State Horse Express is a proud sponsor of the Colorado Shaketails, the oldest cowboy action shooting society in the Colorado Territory.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,601
|
VinFast es un fabricante de automóviles y motocicletas vietnamita, entidad subordinada del conglomerado privado vietnamita Vingroup. El nombre VinFast es el acrónimo de:
"Việt Nam (Vietnam)
Phong cách (Elegante, Ph=F)
An toàn (Seguridad)
Sáng tạo (Creatividad)
Tiên phong (Pionero)."
VinFast y es el único fabricante nacional de origen vietnamita. Fue fundada en 2017 bajo la dirección del Pham Nhat Vuong, propietario de VinGroup, un conglomerado inmobiliario privado.
VinFast inauguró su filial en la ciudad alemana de Frankfurt y completó los últimos trámites para abrir otras dos en Shanghái (China) y Seúl (Corea del Sur).
La casa de diseño Pininfarina ayudará a diseñar los primeros modelos, después de haber concurrido dos decenas de ideas por la atención de VinFast. Alemania concedió la licencia para el establecimiento de la sociedad con responsabilidad limitada VinFast GmbH, especializada en la compraventa, distribución de piezas de repuestos, accesorios y otros materiales para el sector automovilístico.
En diciembre de 2018, vingroup, una empresa de VinFast compró el 51% de BQ, una empresa electrónica de España, y la ha sumado a su sede de empresas convirtiéndola en otra fábrica más de automóviles VinFast.
Ya se encuentra en construcción una planta en Hai Phong que costará de 1.000 a 1.500 millones de dólares, podrá estar produciendo coches en septiembre de 2019 o a las puertas de 2020.
VinFast ha cooperado con socios alemanes como BMW, Siemens, Bosch y Eisenmann para completar las líneas de fabricación y su presencia en Alemania, China y Corea del Sur le permitirá estudiar las necesidades de los consumidores para elevar las exportaciones.
Esta empresa exhibirá sus primeros modelos de Sedán y SUV en la Exposición de Automóviles de París en octubre próximo, antes de presentarlos oficialmente a los clientes domésticos.
Vinfast anunció la inversión de 2,000 millones de dólares para la construcción de hasta 150 mil autos por año y la creación de miles de puestos de trabajo en 800 hectáreas del llamado Triángulo de la Innovación en Raleigh, Carolina del Norte. La marca vietnamita construirá baterías, coches y autobuses además de atraer proveedores.
Referencias
Enlaces externos
Fabricantes de automóviles de Vietnam
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,537
|
What to See in Lima
Despite the name,… @ S2RD2
The Plaza Mayor or Plaza de Armas of Lima, is the birthplace of the city of Lima, as well as the core of the city.
Circuito Mágico del Agua… @ Miguel A. Vera León
Magic Water Circuit
The largest fountain complex in the world. Awe-inspiring show you have never seen before - a must do not only if you have kids.
Convent of San Fransisco @ Sygic Travel User
Monastery of San Francisco
Basílica y Convento de San Francisco is the Spanish name for Saint Francis Monastery located in Lima, Peru, south of Parque la Muralla and…
Night shot of the Lima… @ S23678
Cathedral of Lima
The Basilica Cathedral of Lima, otherwise Lima Cathedral, is a Roman Catholic cathedral located in the Plaza Mayor of downtown Lima, Peru.
The beautiful… @ McKay Savage
St. Martin Square
The Plaza San Martín is one of the most representative public spaces of the city of Lima, Peru.
Pucllana Archaeological… @ AgainErick
Pucllana
Huaca Pucllana or Huaca Juliana is a great adobe and clay pyramid located in the Miraflores district of central Lima, Peru, built from…
Miraflores, Lima Peru. @ saddlesaw2
Love Park
Quite touristy but still well worth your attention if in the vicinity. Its walls are inscribed with love-related quotes.
Peru, Lima, the great… @ Marie Thérèse Hébert & Jean Robert Thibault
Convent of Santo Domingo
The three-nave church and monastery with rich facade embellishments and a huge dome is simply unmissable. Note the typical Sevillian tiles.
A cat in Parque Kennedy,… @ Stvabod
A park which is famous not for its name which honors the late President Kennedy, but mainly for the numerous cats that roam this lush green…
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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What is an EMP and why should You and I be concerned?
11 March, 2016 By Patrick Mikell Leave a Comment
EMP stands for Electromagnetic pulse. It is a burst of electromagnetic radiation that results from suddenly fluctuating magnetic fields that can be caused by solar activity, nuclear explosions, lightening, and other sources. These EMP's are known to produce damaging current and voltage surges that destroy electronic circuits, microprocessors and computer chips. Basically everything from delicate electronics to the power company's transformers is at risk. In other words life as we know it in America would be changed drastically and thousands of people will die.
There are naturally occurring EMPs that come from our sun and lightning. One devastating source of EMPs radiation is our own sun. The Earth has been burned more than once by EMPs from geomagnetic storms caused by Solar Coronal Mass Ejections or CMEs. They are solar storms that originate at the surface of the sun. These Coronal Mass Ejections often occur along with high solar flare activity. When material from a CME reaches the Earth, widespread effects can result from the EMP effect. One of the best known and documented was the solar super storm of 1859 that is called "The Carrington Event". It is named after the 19th century astronomer who observed the solar flare associated with this incident.
You can see a more in depth story at this link.
http://www.history.com/news/a-perfect-solar-superstorm-the-1859-carrington-event
Another source of EMPs is the lightning seen during thunderstorms but its effect is largely localized.
The big threat in our life time are Man Made EMPs or High Altitude Electromagnetic Pulse (HEMP) Devices. These Nuclear Explosions are the most powerful man made EMP sources developed to date. Their power poses one of the greatest threats to our modern electronic based infrastructure that our society depends. These EMP effects are lessened when a low-level ground strike happens. It's the high-altitude nuclear explosion that produces the powerful and widespread EMP radiation effects. Using a bomb used to create EMP effects is referred to by the military as a HEMP (high-altitude electromagnetic pulse) device. Historical examples of testing these devices has shown that they can be used as a effective weapon to neutralize an enemy's infrastructure while creating minimum damage to buildings, structures and people.
Some Quotes from people in the know.
I have believed for a long time that EMP or electromagnetic pulse may be the greatest strategic threat we face, because without adequate preparation its impact would be so horrifying that we would, in fact, basically lose our civilization in a matter of seconds.
-Newt Gingrich, Former Speaker of the House of Representatives
The idea that this is some science fiction that has no basis in reality denies and defies what a bipartisan EMP commission agreed that it did represent – and that is a serious threat to the safety and security of every single American.
-Mike Huckabee, former Governor of Arkansas
It's not a secret. You can't do anything about something that's this broad in impact and still secret. So in order to get anything done you actually have to acknowledge we have a weakness. And, we worried about the fact that if we acknowledged that we had a weakness, how damaging will that be since we will inform our adversaries. We came to the conclusion that our adversaries are really quite well informed already.
-Robert Hermann, Commissioner, Congressional EMP Commission
So, what can you or I do to prepare for life after an EMP? We will follow that up in the next post.
Filed Under: News of The Day, Self Reliance Tagged With: EMP, EMP Facts, preparedness, Threats from an EMP, Weakness of the Grid
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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\section{Introduction}\label{intro}
\setcounter{equation}{0}
The aim of this paper is to study the higher order approximation
in the class of elliptic boundary value problems, where the heterogeneous
media is governed by the well known generalized Hashin-Shtrikman
micro-structures \cite{JKO}, \cite[page no. 281]{T}. To first order, we approximate
the medium by the associated homogenized medium ``$q$''.
First of all, while the macro tensor ``$q$'' has been introduced for arbitrary
micro-structures, the next order macro tensor, in particular, the fourth order
dispersion tensor ``$d$'' is introduced so far only for periodic structures
\cite{COVB,CMSV2,CMSV,CMSV3}. Thanks to the spectral approach to the homogenization
problem using Bloch waves \cite{CV} which naturally leads to other
macroscopic quantities apart from the ``$q$''.
Following our previous work \cite{TV1}, here we introduce the idea of higher
order approximation among Hashin-Shtrikman structures, in particular, we define
the dispersion tensor and denote it by ``$d_{HS}$''.
Note that, following by the its construction, Hashin-Shtrikman structures
provide examples of non-periodic structures. More precisely, the inhomogeneous
coefficients are invariant in a certain way of both translation and dilation of
the medium with incorporating a family of small scales $\{\varepsilon_p>0\}$.
Periodic micro-structure incorporates uniform translation and uniform dilation
with respect to only one scale $\varepsilon$, whereas Hashin-Shtrikman
micro-structures incorporates non-uniform translation and dilation with a family
of scales $\{\varepsilon_p\}$. It is an open problem to introduce ``$d$'' for more
general non-periodic structures. One general result concerning ``$d$'' is that it
has a sign irrespective of the underlying micro-structure and it is negative in
contrast to ``$q$'' which is positive (see \cite{COVB}).\\
\begin{figure}
\begin{center}
\includegraphics[width=14cm]{H-S.pdf}
\vspace*{-12ex}\hspace*{-26ex}
\caption{Murat--Tartar Bounds.}
\end{center}
\end{figure}
Let us mention the significance of studying of such dispersion tensor in
Hashin-Shtrikman structures. Motivated by Optimal Design Problems (ODP) (see \cite{A}),
one wishes to characterize the first macro tensor ``$q$'' for $2$-phase
mixtures taken in a known proportion. As we know in the problem of characterizing
conductivities, the crucial dependence comes from the way they are getting mixed
(micro-structures). Above task is carried out in a
well-known theorem in Homogenization Theory \cite{MT2,MT1}.
Geometrically, conductivities of all possible mixtures lie in a convex
lens-shaped region bounded by an upper hyperbola and a lower hyperbola.
Analytically, conductivities of mixtures satisfy certain inequalities.
There are two aspects in the theorem: first one is to
find ``$q$'' corresponding to a given class of micro-structures and the second
one is to construct underlying micro-structures associated to a given
conductivity. Both laminates ($(A,B)$ in Figure 1) and Hashin-Shtrikman
structures ($(M,N)$ in Figure 1) appear among others as
extremal structures in this characterization in the sense that they are on
the boundary of the above region. No wonder therefore that these structures have
played important role in the construction of the above set.
The goal is to be able to carry out a similar programme for the second
macro tensor ``$d$'' which is known as Bloch dispersion tensor. The name is due
to the fact that it appears in well-posed macro dispersive models
approximating the acoustic equation in periodic media \cite{ABM}. Thus, bounds on
``$d$'' will be useful in ODP in which one wishes to manipulate
micro-structures to have a desired dispersion coefficient. One is far away
from realizing such a goal.\\
First attempt in this endeavor is to see the
modification that ``$d$'' brings to the phase diagram of ``$q$''.
A current activity in this attempt is to study the variation of ``$d$''
on extremal structures of ``$q$'' and to characterize the range of its values
on them. Recall that ``$q$'' remains constant when
restricted to such structures, whereas ``$d$'' varies on them. In such a
situation, it is particularly interesting to know its range of values on
them and to know the extremal structure chosen by ``$d$'' to realize its
maximum and minimum values. Such a study was completed in the case of
laminates in \cite{CMSV3}. Some surprises were found in our experience
with one dimension case \cite{CMSV} and laminates. For instance, ``$d$''
picks up a unique element from such laminates at its maximum and minimum.
Its maximum value is zero and the maximizer is
a unique relaxed/generalized laminate. However, at its minimum value, the
minimizer is unique, but it is a classical structure and not a relaxed one.\\
Having studied periodic laminates, the next natural step is to treat
periodic Hashin-Shtrikman structures (PHS) and this is what we plan to do in our
present study. Just like molecules are made out of interacting atoms
inside, PHS consist of Hashin-Shtrikman structures inside the periodic cell $Y$.
Our idea is to study these ``atoms'' first. Of course, the major difficulty in this is
that they do not form a periodic structure in the usual sense. However,
there is still the invariance by the action of translation and dilation
groups but the action is now different.
One of the advantages of this work is that it enables us resolve one of
the conjectures (Section \ref{conj} below) regarding the optimal micro-structure,
when we consider the macro dispersion coefficient on the class periodic
Hashin-Shtrikman structures.
\section{Preliminaries}
\setcounter{equation}{0}
In the beginning, we remark that the
summation with respect to the repeated indices is understood throughout this paper. Let us start with the known periodic case.
\subsection{Dispersion tensor and periodic structures}
We consider the operator
\begin{equation*}
\mathcal{A}_Y \equiv -\frac{\partial}{\partial y_k}\left( a^Y_{kl}(y)\frac{\partial}{\partial y_l} \right) ,\quad y\in\mathbb{R}^N,
\end{equation*}
where the coefficient matrix $A_Y(y) = [a^Y_{kl}(y)]$ defined on $Y$ a.e. with $Y =[0,1]^N$ is known as the periodic cell
and $A_Y\in\mathcal{M}(\alpha,\beta;Y)$ for some $0<\alpha <\beta$, i.e.
\begin{equation*}a^Y_{kl}=a^Y_{lk}\hspace{5pt}\forall k,l \mbox{ and }\ (A_Y(y)\xi,\xi) \geq \alpha|\xi|^2,\ \ |A_Y(y)\xi|\leq \beta|\xi|\mbox{ for any } \xi \in \mathbb{R}^N,\mbox{ a.e. on }Y.\end{equation*}
For each $\varepsilon >0 $, we consider the $\varepsilon$-periodic elliptic operator
\begin{equation*}
\mathcal{A}^{\varepsilon}_Y \equiv -\frac{\partial}{\partial x_k}\Big( a^Y_{kl}\Big(\frac{x}{\varepsilon}\Big)\frac{\partial}{\partial x_l} \Big) ,\quad x\in\mathbb{R}^N,
\end{equation*}
where $x$ (slow variable) and $y$ (fast variable) are related by $y = \frac{x}{\varepsilon}$.\\
We now define the Bloch waves $\psi_Y$ associated with the operator $\mathcal{A}_Y$.
Let us consider the following spectral problem parametrized by $\eta\in\mathbb{R}^N$:
Find $\lambda_Y=\lambda_Y(\eta)\in \mathbb{R}$ and $\psi_Y=\psi_Y(y;\eta)$ (not zero) such that
\begin{align*}
\mathcal{A}_Y\psi_Y(\cdot;\eta)&= \lambda_Y(\eta)\psi_Y(\cdot;\eta) \quad\mbox{in }\mathbb{R}^N,
\ \ \psi_Y(\cdot;\eta) \mbox{ is }(\eta;Y)\mbox{--periodic, i.e. }\\
\psi_Y(y+2\pi m;\eta) &= e^{2\pi i m\cdot\eta}\psi_Y(y;\eta) \quad \forall m \in \mathbb{Z}^N, \, y \in \mathbb{R}^N.
\end{align*}
Next, by Floquet theory, we define $\varphi_Y(y;\eta)=e^{iy\cdot\eta}\psi_Y(y;\eta)$
to rewrite the above spectral problem as follows:
\begin{equation}\label{s1}
\mathcal{A}_Y(\eta)\varphi_Y= \lambda_Y(\eta)\varphi_Y \quad\mbox{in }\mathbb{R}^N,\ \ \ \varphi_Y \mbox{ is }Y\mbox{--periodic.}
\end{equation}
Here the operator $\mathcal{A}_Y(\eta)$ is called the translated operator and is defined by
$$\mathcal{A}_Y(\eta)= e^{-iy\cdot\eta}\mathcal{A}_Ye^{iy\cdot\eta} = -\Big(\frac{\partial}{\partial y_k} + i\eta_k\Big)\Big[a^Y_{kl}(y)\Big(\frac{\partial}{\partial y_l} + i\eta_l\Big)\Big].$$
It is well known that for $\eta\in Y^{\prime}= [-\frac{1}{2},\frac{1}{2}[^N$ the dual torus, the above spectral
problem \eqref{s1} admits a discrete sequence of eigenvalues and their eigenfunctions
referred to as Bloch waves introduced above enable us to describe the spectral resolution
of $\mathcal{A}_Y$ an unbounded self-adjoint operator in $L^2(\mathbb{R}^N)$ in the
orthogonal basis ͕$\{e^{iy\cdot\eta}\varphi_{Y,m}(y;\eta)| m\geq 1, \eta\in Y^{\prime}\}$.\\
To obtain the spectral resolution of $\mathcal{A}^{\varepsilon}_Y$,
we introduce Bloch waves at the $\varepsilon$-scale as
$$\lambda_{Y,m}^{\varepsilon}(\xi)= \varepsilon^{-2}\lambda_{Y,m}(\eta),\quad \psi_{Y,m}^{\varepsilon}(x;\xi)=\psi_{Y,m}(y;\eta),\quad \varphi_{Y,m}^{\varepsilon}(x;\xi)=\varphi_{Y,m}(y;\eta),$$
where the variables $(x, \xi)$ and $(y, \eta)$ are related by $y = \frac{x}{\varepsilon}$ and $\eta =\varepsilon\xi$.
Observe that $\varphi^{\varepsilon}_{Y,m}(x;\xi)$ is $\varepsilon Y$--periodic (in $x$) and $\varepsilon^{-1}Y^{\prime}$--periodic
with respect to $\xi$. In the same manner, $\psi^{\varepsilon}_{Y,m}(\cdot; \xi)$ is $(\varepsilon\xi; \varepsilon Y )$--periodic.
The dual cell at $\varepsilon$-scale, where
$\xi$ varies, is $\varepsilon^{-1}Y^{\prime}$.\\
We consider a sequence $u^{\varepsilon} \in H^1(\mathbb{R}^N)$ satisfying
\begin{equation}\label{ed1}
\mathcal{A}^{\varepsilon}_Yu^{\varepsilon} = f \quad\mbox{ in }\mathbb{R}^N,
\end{equation}
with the fact $u^{\varepsilon}\rightharpoonup u$ in $H^{1}(\mathbb{R}^N)$
weak and $u^{\varepsilon}\rightarrow u $ in $L^{2}(\mathbb{R}^N)$ strong.\\
The homogenization problem consists of passing to the limit in \eqref{ed1},
as $\varepsilon \rightarrow 0$ and we get the homogenized equation
satisfied by $u$, namely
\begin{equation*} \mathcal{A}^{*}_Yu =\ -\frac{\partial}{\partial x_k}\Big( q_{kl}\frac{\partial u}{\partial x_l} \Big) = f \quad\mbox{in }\mathbb{R}^N, \end{equation*}
where $A^{*}_Y=[q_{kl}]$ is the constant homogenized matrix (see \cite{A}).\\
Simple relation linking $A^{*}_Y$ with Bloch waves is the following: $q_{kl}=\frac{1}{2}D^2_{kl}\lambda_{Y,1}(0)$ (see \cite{CV}).
At this point, it is appropriate to recall that derivatives of the first eigenvalue
and eigenfunction at $\eta=0$ exist, thanks to the regularity property established in \cite{COV,CV}.
\begin{proposition}[Regularity of the ground state \cite{COV,CV}]\label{based}
Under the periodic assumption on the matrix $A_Y\in \mathcal{M}(\alpha,\beta; Y)$, there exists $\delta > 0$
such that the first eigenvalue $\lambda_{Y,1}(\eta)$ is an analytic function on
$B_{\delta}(0) = \{\eta\in\mathbb{R}^N \ |\ |\eta| < \delta\}$ and
there is a choice of the first eigenvector $\varphi_{Y,1}(y;\eta)$ satisfying
\begin{equation*}
\eta \mapsto \varphi_{Y,1}(\cdot;\eta) \in H^1_{\#}(Y)\mbox{ is analytic on } B_{\delta}\mbox{ and }\ \varphi_{Y,1}(y;0)= |Y|^{-1/2}.
\end{equation*}
Moreover, we have the following relations:
\begin{equation*}\begin{aligned}
& \lambda_{Y,1}(0) = 0,\quad D_k \lambda_{Y,1}(0) = \frac{\partial\lambda_{Y,1}}{\partial \eta_k}(0) = 0 \quad\forall k = 1,..,N.\\
& \varphi_{Y,1}(\cdot,0)= |Y|^{-1/2},\quad D_k\varphi_{Y,1}(\cdot,0) = i|Y|^{-1/2}\chi_k(y),\\
&\frac{1}{2}D^2_{kl}\lambda_{Y,1}(0) = \frac{1}{2}\frac{\partial^2\lambda_{Y,1}}{\partial \eta_k\partial\eta_l}(0) = q_{kl} \quad\forall k,l =1,\ldots,N,
\end{aligned}
\end{equation*}
where the last expression is considered as the Bloch spectral representation of the homogenized tensor,
which are essentially defined as
\begin{equation}\label{ed2}
\frac{1}{2}D^2_{kl}\lambda_{Y,1}(0) = q_{kl}=\ \frac{1}{|Y|}\int_{Y} A_Y(\nabla \chi_k + e_k)\cdot(\nabla \chi_l + e_l) dy,
\end{equation}
for each unit vector $e_{k}$ and the functions $\chi_k\in H^1_{\#}(Y)$ solving the following conductivity problem in the periodic unit cell:
\begin{equation*}
-div_y\left( A_Y(y)(\nabla_y\chi_k(y)+e_k)\right) = 0 \quad\mbox{in }Y,\quad y \longmapsto\chi_k(y) \quad\mbox{is $Y-$periodic.}
\end{equation*}
Moreover, all odd order derivatives of $\lambda_{Y,1} $ at $\eta=0$ are zero, i.e.
\begin{equation*}D^{q}\lambda_{Y,1}(0)=0 \quad\forall q\in \mathbb{Z}^N_{+}, \, |q|\mbox{ odd.}
\end{equation*}
Additionally, all even order derivatives need not to be zero and can be calculated in a systematic way.\\
The fourth order derivative of $\lambda_{Y,1}$ at $\eta=0$ is non-zero and
known as the \textbf{Burnett coefficient} or the \textbf{dispersion tensor} $d_{Y}$ of the medium,
\begin{equation}\label{dl22}
\frac{1}{4!}\frac{\partial^4\lambda_{Y,1}(0)}{\partial\eta_k\partial\eta_l\partial\eta_m\eta_n}\eta_k\eta_l\eta_m\eta_n = d_{klmn}\eta_k\eta_l\eta_m\eta_n =\ d_{Y}\eta^4,
\end{equation}
which is essentially a non-positive definite fourth order tensor and can be expressed as follows:
let us call $D^2_{kl}\varphi_{Y,1}(\cdot;0) = |Y|^{-1/2}\chi_{kl}$ and define
\begin{equation}\begin{aligned}\label{dl19}
C_Y &=\eta_n C^Y_n \quad\mbox{ with }\quad C^Y_n(\varphi) = - a^Y_{nj}(y)\frac{\partial \varphi}{\partial y_j} - \frac{\partial}{\partial y_j}(a^Y_{nj}(y)\varphi), \\
X^{(1)}_Y &= \eta_n\chi_{n},\quad X^{(2)}_Y= \eta_k\eta_n\chi_{kn},\quad \widetilde{A_Y}= \eta_k\eta_n a^Y_{kn},\quad \widetilde{A^{*}_Y}=\eta_k\eta_n q_{kn}
\end{aligned}\end{equation}
satisfying
\begin{equation*}
-div(A_Y\nabla X^{(1)}_Y) = \eta_k\frac{\partial a^Y_{kl}}{\partial y_l} \mbox{ in }Y, \quad X^{(1)}_Y\in H^1_{\#}(Y) \mbox{ with }\int_Y X^{(1)}_Y dy = 0
\end{equation*}
and
\begin{equation}\label{ll9}
-div(A_Y\nabla X^{(2)}_Y) = (\widetilde{A_Y}-\widetilde{A^{*}_Y}) - C_Y X^{(1)}_Y \mbox{ in }Y, \quad X^{(2)}_Y\in H^1_{\#}(Y) \mbox{ with }\int_{Y} X^{(2)}_Ydy =0.
\end{equation}
Then, by summation, one has the following expression of the dispersion tensor:
\begin{equation}\label{dy}
d_{Y}\eta^4 = \ -\frac{1}{|Y|}\int_{Y} \mathcal{A}_Y\Big( X^{(2)}_Y -\frac{(X^{(1)}_Y)^2}{2}\Big)\cdot\Big( X^{(2)}_Y -\frac{(X^{(1)}_Y)^2}{2}\Big)\leq 0.
\end{equation}
\end{proposition}
\begin{remark}
In order to see the role of the dispersion tensor $d_Y$ arises in wave propagation problems, let us consider the wave propagation problem in periodic
structure governed by the operator $\partial_{tt} + \mathcal{A}^{\varepsilon}_Y$
with appropriate initial conditions. As we see,
we have\begin{align*}
\lambda_{Y,1}^{\varepsilon}(\xi) &\approx\ \frac{1}{2!} \lambda_{Y,1}^{(2)}(0)\xi^2 \quad\mbox{if }\varepsilon^2|\xi|^4 \mbox{ is small,}\\
\lambda_{Y,1}^{\varepsilon}(\xi) &\approx\ \frac{1}{2!}\lambda_{Y,1}^{(2)}(0)\xi^2 + \frac{1}{4!}\varepsilon^2\lambda_{Y,1}^{(4)}(0)\xi^4 \quad\mbox{if }\varepsilon^4|\xi|^6 \mbox{ is small}.
\end{align*}
Thus, if we consider short waves of low energy with wave number satisfying
$\varepsilon^2|\xi|^4 = \mathcal{O}(1)$ and $\varepsilon^4|\xi|^6 = o(1)$,
then a simplified description is obtained with the operator
$\partial_{tt} + \mathcal{A}^{*}_Y + \varepsilon^2D_Y$,
where $D_Y$ is the fourth-order operator whose symbol is
$\frac{1}{4!}\frac{\partial^4\lambda_{Y,1}(0)}{\partial\eta_k\partial\eta_l\partial\eta_m\eta_n}\xi_k\xi_l\xi_m\xi_n$.
\end{remark}
\subsection{Survey of Bloch waves, Bloch eigenvalues and eigenvector
in Hashin-Shtrikman structure}
In this part, we recall our recent work \cite{TV1} of introducing Bloch waves and associated
Bloch spectral analysis in the class of generalized Hashin-Shtrikman micro-structures concerning the homogenization result.
\subsection*{Hashin-Shtrikman micro-structures}
We follow \cite[page no. 281]{T} in this sequel.
Let $\omega \subset \mathbb{R}^N$ be a bounded open subset with Lipschitz boundary.
Let $A_\omega(y)=[a^{\omega}_{kl}(y)]_{1\leq k,l\leq N} \in \mathcal{M}(\alpha,\beta;\omega)$
be such that after extending $A_\omega$ by $A_\omega(y) = M$ for $x \in \mathbb{R}^N\smallsetminus \omega$, where $M \in L_{+}(\mathbb{R}^N ; \mathbb{R}^N)$
(i.e. $M = [m_{kl}]_{1\leq k,l \leq N}$ is a constant positive definite $N\times N$ matrix),
if for each $\lambda \in \mathbb{R}^N$ there exists $w_{\lambda}\in H^{1}_{loc}(\mathbb{R}^N)$ satisfying
\begin{equation}\label{hsw}
- div (A_{\omega}(y)\nabla w_{\lambda}(y)) = 0 \quad\mbox{in }\mathbb{R}^N,\quad w_{\lambda}(y) = (\lambda, y) \quad\mbox{in }\mathbb{R}^N \smallsetminus \omega,
\end{equation}
then $A$ is said to be \textit{equivalent} to $M$.\\
\\
Then one uses a sequence of Vitali coverings of $\Omega$ by reduced copies of $\omega,$
\begin{equation}\label{ll1} meas\big(\Omega \smallsetminus \underset{p\in K}{\cup} (\varepsilon_{p,n}\omega + y^{p,n})\big) = 0, \mbox{ with } \kappa_n = \underset{p\in K}{sup}\hspace{2pt} \varepsilon_{p,n}\rightarrow 0,
\end{equation}
for a finite or countable $K$. These define the micro-structures in $A^{n}_\omega$. One defines for almost everywhere $x\in \Omega$,
\begin{equation}\label{hs}
A^{n}_\omega(x) = A_\omega\Big(\frac{x - y^{p,n}}{\varepsilon_{p,n}}\Big)\ \ \mbox{ in } \varepsilon_{p,n}\omega + y^{p,n},\quad p\in K,
\end{equation}
which makes sense since, for each $n$, the sets $\varepsilon_{p,n}\omega + y^{p,n}, p\in K$ are disjoint.
The above construction \eqref{hs} represents the so called \textbf{Hashin-Shtrikman} micro-structures.\\
\\
Following that, one defines $v^{n} \in H^1(\Omega)$ by
\begin{equation}\label{uB}
v^{n}(x) = \varepsilon_{p,n}w_{\lambda}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\Big)+ (\lambda, y^{p,n})\quad\mbox{ in }\varepsilon_{p,n}\omega + y^{p,n}.
\end{equation}
Then one has the following properties (see \cite[Page no. 283]{T}):
\begin{equation}\begin{aligned}\label{uC}
v^{n}(x) &\rightharpoonup (\lambda,x) \mbox{ weakly in }H^1(\Omega;\mathbb{R}^N),\\
A^{n}_\omega\nabla v^{n}(x) &\rightharpoonup M\lambda \mbox{ weakly in } L^2(\Omega;\mathbb{R}^N),\\
- div( A^{n}_\omega(x)\nabla v^{n}(x)) &=\ 0 \ \mbox{ in }\Omega.
\end{aligned}\end{equation}
So, by the definition of $H$-convergence (see \cite[Page no. 82]{T}), one has the following convergence of the entire sequence
\begin{equation} A^{n}_\omega \xrightarrow{H-\mbox{converges }} M,
\end{equation}
where $M\in L_{+}(\mathbb{R}^N,\mathbb{R}^N)$ is a positive definite matrix equivalent to $A$.\\
\\
We have the following integral representation similar to \eqref{ed2}:
\begin{equation}\begin{aligned}\label{dl12}
Me_k\cdot e_l=\ m_{kl} &=\ \frac{1}{|\omega|}\int_{\omega} A_\omega(y)\nabla w_{e_k}(y)\cdot\nabla w_{e_l}(y)\ dy \\
&=\ \frac{1}{|\omega|}\int_{\omega} A_\omega(y)\nabla w_{e_k}(y)\cdot e_l\ dy,
\end{aligned}\end{equation}
where $w_{e_k}, w_{e_l}$ are the solution of \eqref{hsw} for $\lambda= e_k$ and $\lambda=e_l$, respectively.
\hfill\qed
\begin{example}
[Spherical Inclusions in two-phase medium] \label{si}
If $\omega= B(0,1)=\{ y\ | \ |y|\leq 1\} $ and
\begin{equation*}
A_\omega(y)=a_B(r)I=
\left\{
\begin{array}{ll}
\alpha I \quad\mbox{if } |y| \leq R,\\[1ex]
\beta I \quad\mbox{if } R < |y| \leq 1,
\end{array}
\right.
\end{equation*}
$\alpha$ and $\beta$ are known as core and coating, respectively. Then $A_\omega$ is equivalent to $\gamma I$, where $\gamma$ satisfies
\begin{equation*}
\frac{\gamma - \beta}{\gamma + (N-1)\beta} = \theta \frac{\alpha - \beta}{\alpha + (N-1)\beta},\ \mbox{ with }\theta= R^N .
\end{equation*}
\end{example}
\begin{example}[Elliptical Inclusions in two-phase medium]\label{ei}
For $m_1,\ldots,m_N\in \mathbb{R}$ and $\rho + m_j >0 $ for $j=1,\ldots,N$, the
family of confocal ellipsoids $S_\rho$ of equation
$$ \sum_{j=1}^N \frac{y^2_j}{\rho + m_j} = 1$$ defines implicitly a
real function $\rho$, outside a possibly degenerate ellipsoid in
a subspace of dimension $<$ $N$.\\
Now, if we consider $\omega=E_{\rho_2+m_1,\ldots,\rho_2+m_N}= \Big\{ y\ | \ \sum\limits_{j=1}^N \frac{y^2_j}{\rho_2 + m_j} \leq 1\Big\},$
with $\rho_2 + \underset{j}{min}\ m_j >0 $ and
\begin{equation*}
A_\omega(y)= a_E(\rho)I =
\left\{
\begin{array}{ll}
\alpha I \quad\mbox{if } \rho \leq \rho_1,\\[1ex]
\beta I \quad\mbox{if } \rho_1 < \rho \leq \rho_2,
\end{array}
\right.
\end{equation*}
then $A_\omega$ is equivalent to a constant diagonal matrix $\Gamma= [\gamma_{jj}]_{1\leq j\leq N}$ satisfying
$$ \sum_{j=1}^N \frac{1}{\beta - \gamma_{jj}} =\ \frac{(1-\theta)\alpha + (N+\theta-1)\beta}{\theta \beta(\beta-\alpha)},\ \mbox{ with }\theta = \underset{j}{\Pi}\ \sqrt{\frac{\rho_1 + m_j}{\rho_2 + m_j}}.$$
\end{example}
\hfill\qed
\subsection*{Bloch waves, Bloch eigenvalues and eigenvectors associated with the Hashin-Shtrikman structures}
Let $\omega \subset \mathbb{R}^N$ be a bounded open domain with Lipschitz boundary and $A_\omega(y)=[a^\omega_{kl}(y)]_{1\leq k,l\leq N}\in \mathcal{M}(\alpha,\beta,\omega)$.
We consider the following spectral problem parameterized by $\eta \in \mathbb{R}^N$:
Find $\lambda_\omega := \lambda_\omega(\eta) \in \mathbb{C}$ and $\varphi_\omega := \varphi_\omega(y; \eta)$ (not identically zero) such that
\begin{equation}\begin{aligned}\label{NE1}
\mathcal{A}_\omega(\eta)\varphi_\omega(y;\eta)=\ -\Big(\frac{\partial}{\partial y_k} + i\eta_k\Big)&\Big[a^\omega_{kl}(y)\Big(\frac{\partial}{\partial y_l} + i\eta_l\Big)\Big]\varphi_\omega(y;\eta) = \lambda_\omega(\eta)\varphi_\omega(y;\eta) \mbox{ in }\omega, \\
\varphi_\omega(y;\eta)\mbox{ is constant on }\partial\omega &\mbox{ and }
\int_{\partial\omega} a^\omega_{kl}(y)\Big(\frac{\partial}{\partial y_l} + i\eta_l\Big)\varphi_\omega(y;\eta)\nu_k\ d\sigma = 0,
\end{aligned}\end{equation}
where $\nu$ is the outer normal vector on the boundary and $d\sigma$ is the surface measure on $\partial\omega$.
\\
\noindent
We introduce the state spaces of this above spectral problem:
\begin{align*}
L^2_c(\omega) &= \ \{\varphi\in L^2_{loc}(\mathbb{R}^N) \ | \ \varphi \mbox{ is constant in } \mathbb{R}^N \smallsetminus\omega\},\\
H^1_c(\omega) &=\ \{\varphi\in H^1_{loc}(\mathbb{R}^N) \ | \ \varphi \mbox{ is constant in } \mathbb{R}^N \smallsetminus\omega\}\\
&= \ \{\varphi\in H^1(\omega) \ | \ \varphi|_{\partial\omega} = \mbox{ constant}\}.
\end{align*}
Here, "$c$" is a floating constant depending on the element under consideration.
$L^2_c(\omega)$ and $H^1_c(\omega)$ are proper subspace of $L^2(\omega)$ and $H^1(\omega)$ respectively, and they inherit
the subspace norm-topology of the parent space.
Prior to that, we have this following result establishing the existence of the Bloch eigenelements.
\begin{proposition}[Existence result \cite{TV1}]\label{dl1}
Fix $\eta \in \mathbb{R}^N$. Then, there exist a sequence of eigenvalues $\{ \lambda_{\omega,m}(\eta); m \in \mathbb{N} \}$
and its corresponding eigenvectors $\{ \varphi_{\omega,m} (y; \eta)\in H^1_c(\omega), m \in \mathbb{N} \}$ such that
\begin{align*}
&(i) \ \mathcal{A}_\omega(\eta)\varphi_{\omega,m}(y;\eta) = \lambda_{\omega,m}(\eta)\varphi_{\omega,m}(y;\eta) \quad \forall m \in \mathbb{N}.\\
&(ii) \ 0 \leq \lambda_{\omega,1}(\eta) \leq \lambda_{\omega,2} (\eta) \leq \ldots \rightarrow \infty; \ \mbox{each eigenvalue is of finite multiplicity. }\\
&(iii)\ \{\varphi_{\omega,m}(\cdot;\eta);\ m \in \mathbb{N} \}\ \mbox{ is an orthonormal basis for }L^2_c(\omega).\\
&(iv)\ \mbox{ For }\phi \mbox{ in the domain of } \mathcal{A}_\omega(\eta), \mbox{ we have }\\
&\hspace{3cm}\mathcal{A}_\omega(\eta)\phi(y) = \sum_{m=1}^{\infty} \lambda_{\omega,m} (\eta)\big(\phi, \varphi_{\omega,m} (\cdot;\eta)\big)\varphi_{\omega,m} (y;\eta).
\end{align*}
\end{proposition}
\noindent
As the eigen-branch emanating from the first eigenvalue plays the key role,
we concentrate only for $m=1$ to have the following regularity properties.
\begin{proposition}[Regularity of the ground state \cite{TV1}]
Let $\lambda_{\omega,1}(\eta),\varphi_{\omega,1}(\cdot;\eta)$ be the first eigenvalue and the first eigenvector of the spectral problem defined in \eqref{NE1}.
Then, there exists a neighborhood $\omega^{\prime}$ around zero such that
\begin{equation*}
\eta \longmapsto \left( \lambda_{\omega,1}(\eta), \varphi_{\omega,1}(\cdot;\eta)\right) \in \mathbb{C}\times H^1_c(\omega)\mbox{ is analytic on }\omega^{\prime}.
\end{equation*}
At $\eta=0$, $\lambda_{\omega,1}(0)$ is simple. There is a choice of the first eigenvector $\varphi_{\omega,1}(y;\eta)$ satisfying
\begin{equation*}
\varphi_{\omega,1}(y;\eta) =\ \frac{1}{|\omega|^{1/2}} \ \forall y\in\partial\omega\mbox{ and }\forall\eta\in \omega^{\prime} .
\end{equation*}
Moreover, we have the following relations:\begin{equation}\begin{aligned}\label{lZ}
& \lambda_{\omega,1}(0) = 0,\quad D_k \lambda_{\omega,1}(0)=\frac{\partial\lambda_{\omega,1}}{\partial \eta_k}(0)= 0 \quad\forall k = 1,\ldots,N,\\
& \varphi_{\omega,1}(\cdot;0)= |\omega|^{-1/2},\quad D_k\varphi_{\omega,1}(y,0) = i|\omega|^{-1/2}(w_{e_k}(y)-y_k),\\
&\frac{1}{2}D^2_{kl}\lambda_{\omega,1}(0) = \frac{1}{2}\frac{\partial^2\lambda_{\omega,1}}{\partial \eta_k\partial\eta_l}(0) = m_{kl} \quad\forall k,l =1,\ldots,N,
\end{aligned}\end{equation}
where the last expression is considered as a Bloch spectral representation of the homogenized tensor.
\hfill\qed\end{proposition}
\noindent
Moreover, all odd order derivatives of $\lambda_{\omega,1} $ at $\eta=0$ are zero, i.e.
\begin{equation}D^{q}\lambda_{\omega,1}(0)=0 \quad\forall q\in \mathbb{Z}^N_{+},\ |q| \mbox{ odd}. \end{equation}
In particular, the third order derivative is zero. However, we are interested in the further next order approximation
by calculating the fourth order derivatives of $\lambda_{\omega,1}(0)$, i.e.
$D^4_{klmn}\lambda_{\omega,1}(0)$, which is in general a non-positive definite tensor and can be defined as follows:
the second order derivative of the eigenvector $D^2_{kl}\varphi_{\omega,1}(\cdot;0)\in H^1_0(\omega)$ solves
\begin{equation}\begin{aligned}\label{dl17}
&\mathcal{A}D^2_{kl}\varphi_{\omega,1}(y;0)= -( a^\omega_{kl}(y) - m_{kl} )\varphi_{\omega,1}(y;0) - iC_k(D_l(\varphi_{\omega,1}(y;0)) - iC_l(D_k\varphi_{\omega,1}(y;0))\mbox{ in }\omega,\\
&D^2_{kl}\varphi_{\omega,1}(y;0) = 0 \mbox{ on }\partial\omega \mbox{ and} \int_{\partial\omega} A_\omega(y)\nabla_y D^2_{kl}\varphi_{\omega,1}(y;0)\cdot\nu \ d\sigma= 0 .
\end{aligned}\end{equation}
We call $D^2_{kl}\varphi_{\omega,1}(y;0) = |\omega|^{-1/2}w_{kl}(y)$ and let us define
\begin{center}$X^{(1)}_{\omega} =\ \eta_k(w_{e_k}(y)-y_k)\mbox{ and }\ X^{(2)}_{\omega}=\ \eta_k\eta_lw_{kl}\ $ likewise in \eqref{dl19}.\end{center}
Then, by summation, following \cite[Proposition 3.2]{COVB} it can be shown
that the following expression defines the fourth order derivative of $\lambda_{\omega,1}(\eta)$ at $\eta=0$:
\begin{equation}\begin{aligned}\label{dl20}
\frac{1}{4!}D^4_{klmn}\lambda_{\omega,1}(0)\eta_k\eta_l\eta_m\eta_n &= -\frac{1}{|\omega|}\int_{\omega} \mathcal{A}\Big( X^{(2)}_{\omega} - \frac{1}{2}(X^{(1)}_{\omega})^2\Big)\cdot \Big( X^{(2)}_{\omega} - \frac{1}{2}(X^{(1)}_{\omega})^2\Big) dy\\
&\leq 0\ .
\end{aligned}\end{equation}
This tells us that $\lambda_{\omega,1}^{(4)}(\eta)$ at $\eta=0$ is a non-positive definite tensor.
\hfill\qed
\\
\\
Next, we consider a medium in $\Omega$ with Hashin-Shtrikman micro-structures.
Let us introduce the operator $\mathcal{A}^{n}_\omega$ governed with the Hashin-Shtrikman construction:
\begin{equation}\label{dl5}\mathcal{A}^{n}_\omega = -\frac{\partial}{\partial x_k}\Big(a^{n}_{kl}(x)\frac{\partial}{\partial x_l}\Big)
\ \mbox{ with }\ a_{kl}^{n}(x) =\ a^\omega_{kl}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\Big)\ \mbox{ in } \varepsilon_{p,n}\omega + y^{p,n} \mbox{ a.e. on } \Omega, \end{equation}
where $ meas\big(\Omega \smallsetminus \cup_{p\in K} (\varepsilon_{p,n}\omega + y^{p,n})\big) = 0,$ with
$\kappa_n = \underset{p\in K}{sup}\hspace{2pt} \varepsilon_{p,n}\rightarrow 0$
for a finite or countable $K$ and, for each $n$, the sets
$\varepsilon_{p,n}\omega + y^{p,n},\ p\in K$ are disjoint.\\
\\
We obtain the spectral resolution of $\mathcal{A}^{n}_\omega$ for fixed $n$, in each $\{\varepsilon_{p,n}\omega +y^{p,n}\}_{p\in K}$ domain, in an analogous manner.
We introduce the following shifted operator
\begin{equation}\label{dl2}
(\mathcal{A}^{n,p}_\omega)(\xi)=\ -\Big(\frac{\partial}{\partial x_k} + i\xi_k\Big)\Big( a^\omega_{kl}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\Big)\Big(\frac{\partial}{\partial x_l} +i\xi_l\Big) \Big),\quad x\in \varepsilon_{p,n}\omega +y^{p,n}.
\end{equation}
By homothecy, for a fixed $n$ and for each $p$, we define the first Bloch eigenvalue $\lambda_{\omega,1}^{n,p}(\xi)$
and the corresponding Bloch mode $\varphi_{\omega,1}^{n,p}(\cdot;\xi)$ for the operator $(\mathcal{A}^{n,p}_\omega)(\xi)$ for $\xi \in \kappa_n^{-1}\omega^{\prime}$ as follows:
\begin{equation}\label{dl3}
\lambda_{\omega,1}^{n,p}(\xi) := \varepsilon_{p,n}^{-2}\lambda_{\omega,1}(\varepsilon_{p,n} \xi),\quad
\varphi^{n,p}_{\omega,1}(x;\xi):= \varphi_{\omega,1}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}; \varepsilon_{p,n}\xi\Big), \quad x\in\varepsilon_{p,n}\omega + y^{p,n},
\end{equation}
where $\lambda_{\omega,1}(\eta)$ and $\varphi_{\omega,1}(y;\eta)$ are the eigenelements defined in Proposition \ref{dl1}. \\
\\
This leads to define the Bloch transformation in $L^2(\mathbb{R}^N)$ in the following manner:
\begin{proposition}[Bloch transformation \cite{TV1}]
\noindent
\begin{enumerate}
\item For $g \in L^2(\mathbb{R}^N)$, for each $n$, the following limit in $L^2(\kappa_n^{-1}\omega^{\prime})$ space exists:
\begin{equation}\label{btype}
B^{n}_1 g(\xi): = B^{(\varepsilon_{p,n},\ y^{p,n})}_1 g(\xi) := \sum_p\int_{\varepsilon_{p,n}\omega + y^{p,n}} g(x)e^{-ix\cdot\xi}\overline{\varphi_{\omega,1}}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}};\varepsilon_{p,n}\xi\Big)dx,
\end{equation}
where, for each $n$, $ meas\big( \mathbb{R}^N \smallsetminus \underset{p\in K}{\cup} (\varepsilon_{p,n}\omega + y^{p,n})\big) = 0,$
with $\kappa_n = \underset{p\in K}{sup}\hspace{2pt} \varepsilon_{p,n}\rightarrow 0$
for a finite or countable $K$ and the sets $\varepsilon_{p,n}\omega + y^{p,n},\ p\in K$ are disjoint.\\
\\
The above definition \eqref{btype} is the corresponding first Bloch transformation governed with
Hashin-Shtrikman micro-structures.
\item We have the following Bessel inequality for elements of $L^2(\mathbb{R}^N)$:
\begin{equation}\label{basel}
\int_{\kappa_n^{-1}\omega^{\prime}} |B^{n}_1 g(\xi)|^2 d\xi \leq \mathcal{O}(1) ||g||^2_{L^2(\mathbb{R}^N)}.
\end{equation}
\item For $g\in H^1(\mathbb{R}^N)$, we have
\begin{equation}\label{rln}
B^{n}_1 \left(\mathcal{A}^{n}_{\omega}g(\xi)\right) := \sum_p\int_{\varepsilon_{p,n}\omega + y^{p,n}}\lambda_{\omega,1}^{n,p} g(x)e^{-ix\cdot\xi}\overline{\varphi_{\omega,1}}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}};\varepsilon_{p,n}\xi\Big)dx.
\end{equation}
\end{enumerate}
\end{proposition}
\noindent
One has the first Bloch transform is an approximation to the Fourier transform.
\begin{proposition}[First Bloch transform tends to Fourier transform \cite{TV1}]
\noindent
\begin{enumerate}
\item If $g_{n} \rightharpoonup g$ in $L^2(\mathbb{R}^N)$ weak, then
$\chi_{\kappa_n^{-1}\omega^{\prime}}(\xi)B_1^{n}g^{n}(\xi) \rightharpoonup \widehat{g}(\xi)$
in $L^2(\mathbb{R}^N)$ weak, provided there is a fixed compact $R$
such that support of $ g^n\subseteq R\quad\forall n.$
\item If $g_{n} \rightarrow g$ in $L^2(\mathbb{R}^N)$ strong, then for the subsequence $\varepsilon_{p,n}$,
$\chi_{\kappa_n^{-1}\omega^{\prime}}(\xi)B_1^{n}g^n \rightarrow \widehat{g}(\xi)$
in $L^2_{loc}(\mathbb{R}^N).$
\end{enumerate}
\end{proposition}
\noindent
Using these above tools the following homogenization theorem has been deduced in \cite{TV1}.
\begin{theorem}[Homogenization result \cite{TV1}]
Let us consider $\Omega$ be an open subset of $\mathbb{R}^N$
and consider the operator $\mathcal{A}^{n}_\omega$ introduced in \eqref{dl5} governed with the Hashin-Shtrikman construction, where
the matrix $A_\omega\in \mathcal{M}(\alpha,\beta;\omega)$ is equivalent to $M$ in the sense of \eqref{hsw}.
Let $f \in L^2(\Omega)$ and consider $u^{n} \in H^1_0(\Omega)$ being the unique solution of the boundary value problem
\begin{equation*} \mathcal{A}^{n}_\omega u^{n} = f \quad\mbox{in }\Omega.\end{equation*}
Then, there exists $u\in H^1_{0}(\Omega)$ such that the sequence $u^{n}$ converges to $u$ in $H^1_{0}(\Omega)$ weak,
with the following convergence of the flux:
\begin{equation*}
\sigma^{n}_{\omega}= A^{n}_{\omega}\nabla u^{n} \rightharpoonup M\nabla u =\sigma_{\omega} \quad\mbox{in } L^2(\Omega)\mbox{ weak. }
\end{equation*}
In particular, the limit $u$ satisfies homogenized equation:
\begin{equation*}\mathcal{A}^{*}_{\omega}u = -\frac{\partial}{\partial x_l}\Big(m_{kl}\frac{\partial}{\partial x_k}u\Big) = f \quad\mbox{in }\Omega.\end{equation*}
\end{theorem}
\hfill
\qed
\\
We end our discussion here concerning with the homogenized matrix. In the next section we will move into defining the dispersion tensor for the Hashin-Shtrikman micro-structures.
\section{Dispersion tensor and Hashin-Shtrikman structures}\label{conj}
\setcounter{equation}{0}
Here we are going to define the dispersion tensor or the \textit{Burnett coefficient,} more precisely,
the fourth order approximation of the medium governed by the Hashin-Shtrikman micro-structures, while in the previous section we have studied the
homogenized coefficient as a second order approximation of the medium. \\
\\
Let us consider $\Omega$ be an open subset of $\mathbb{R}^N$. We recall \eqref{dl5} where we have introduced the operator $\mathcal{A}^{n}_\omega$ governed with the Hashin-Shtrikman construction:
$$\mathcal{A}^{n}_\omega = -\frac{\partial}{\partial x_k}\Big(a^{n}_{kl}(x)\frac{\partial}{\partial x_l}\Big),$$
with $A^{n}_\omega(x)=\ [a_{kl}^{n}(x)] =\Big[a^\omega_{kl}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\Big)\Big]\ \mbox{ in } \varepsilon_{p,n}\omega + y^{p,n}, \mbox{ a.e. on } \Omega$,
where $ meas\big(\Omega \smallsetminus \cup_{p\in K} (\varepsilon_{p,n}\omega + y^{p,n})\big) = 0,$ with
$\kappa_n = \underset{p\in K}{sup}\hspace{2pt} \varepsilon_{p,n}\rightarrow 0$
for a finite or countable $K$ and, for each $n$, the sets
$\varepsilon_{p,n}\omega + y^{p,n},\ p\in K$ are disjoint.\\
\\
Previously, for each $n$, we restricted the operator $\mathcal{A}^{n}_\omega$ in each $\{\varepsilon_{p,n}\omega +y^{p,n}\}_{p\in K}$ to define $\mathcal{A}^{n,p}_\omega$. Then,
by homothecy, we obtained its first Bloch spectral data $(\lambda_{\omega,1}^{n,p},\ \varphi_{\omega,1}^{n,p})$ in \eqref{dl3}. We have
the following Taylor expansion around zero:\begin{align*}
\lambda_{\omega,1}^{n,p}(\xi) &=\ \frac{1}{2!}\frac{\partial^2\lambda_{\omega,1}}{\partial\eta_k\partial\eta_l}(0)\xi_k\xi_l + \varepsilon_{p,n}^2\frac{1}{4!}\frac{\partial^4\lambda_{\omega,1}}{\partial\eta_k\partial\eta_l\partial\eta_m\partial\eta_n}(0)\xi_k\xi_l\xi_m\xi_n + o(\varepsilon_{p,n}^2)\\
&=\ m_{kl} \xi_k\xi_l + \varepsilon_{p,n}^2\frac{1}{4!}\frac{\partial^4\lambda_{\omega,1}}{\partial\eta_k\partial\eta_l\partial\eta_m\partial\eta_n}(0) \xi_k\xi_l\xi_m\xi_n + o(\varepsilon_{p,n}^2),\ \ \xi\in \kappa_n^{-1}\omega^{\prime}.
\end{align*}
The first term in the above expression is providing the homogenized medium as the second order approximation.
The second term provides the next order that is the fourth order approximation of the medium
by considering the last term to be sufficiently small enough. As we know, for each $n$ depending
upon the parameter $p$, the scales $\varepsilon_{p,n}$ could vary in plenty of ways with remaining inside
the class of sequences of Vitali coverings of $\Omega$. The second order approximation or the homogenized
tensor $m_{kl}\xi_k\xi_l$ is universal among all possible Vitali coverings, whereas the fourth order
approximation is not so. There is a more vibrant dependence on the scales $\varepsilon_{p,n}$, and it varies
over the Vitali coverings.
Taking into account this fact, in order to define the \textit{Burnett coefficient} or the dispersion tensor $d_{HS}$
in the class of generalized Hashin-Shtrikman structures,
we will introduce an approximating quantity $d^{n}_{HS}$ by taking
an average over the various scales $\varepsilon_{p,n}^2$ and then, quotient it out by the highest
scale factor $\kappa_n^2$ $(\kappa_n = \underset{p\in K}{sup}\ \varepsilon_{p,n})$. For that, we will consider the first Bloch eigenvalue
associated with the shifted operator $\mathcal{A}^{n}_{\omega}(\xi)$ ($\xi\in\mathbb{R}^N$) in $\Omega$.
Finally, by passing to the limit as $n\rightarrow \infty$, we will characterize the dispersion tensor $d_{HS}$ for the medium.\\
\\
We begin by introducing the following spectral problem in $\Omega$
associated with the shifted operator $\mathcal{A}^{n}(\xi)$ ($\xi\in\mathbb{R}^N$) likewise in \eqref{NE1}: for each fixed $n\in\mathbb{N}$,
\begin{equation}\begin{aligned}\label{dl4}
\mathcal{A}^{n}_\omega(\xi)\varphi^{n}_{\Omega}(x;\xi)=\ -\Big(\frac{\partial}{\partial x_k} + i\xi_k\Big)&\Big[a_{kl}^{n}(x)\Big(\frac{\partial}{\partial x_l} + i\xi_l\Big)\Big]\varphi^{n}_{\Omega}(x;\xi) = \lambda^{n}_{\Omega}(\xi)\varphi^{n}_{\Omega}(x;\xi) \mbox{ in }\Omega, \\
\varphi^{n}_{\Omega}(x;\xi)\mbox{ is constant on }\partial\Omega&\mbox{ and } \int_{\partial\Omega} a_{kl}^{n}(x)\Big(\frac{\partial}{\partial x_l} + i\xi_l\Big)\varphi^{n}_{\Omega}(x;\xi)\nu_k\ d\sigma = 0,
\end{aligned}\end{equation}
where $\nu$ is the outer normal vector on the boundary and $d\sigma$ is the surface measure on $\partial\Omega$.
\paragraph{Weak formulation:}
Here first we introduce the function spaces
\begin{align*}
L^2_{c}(\Omega) = \ \{\varphi\in L^2_{loc}(\mathbb{R}^N) \ | \ &\varphi \mbox{ is constant in }\mathbb{R}^N \smallsetminus \Omega \},\\
H^1_{c}(\Omega)=\ \{\varphi\in H^1_{loc}(\mathbb{R}^N) \ | \ &\varphi \mbox{ is constant in }\mathbb{R}^N \smallsetminus \Omega \}.
\end{align*}
Here "$c$" is a floating constant depending on the element under consideration. \\
\\
As a next step we give the weak formulation of the problem in these function spaces.
We are interested in proving the existence of the eigenvalue and the corresponding eigenvector
$(\lambda^{n}_{\Omega}(\eta), \varphi^{n}_{\Omega}(x;\xi))\in \mathbb{C}\times H^1_{c}(\Omega)$ of
the following weak formulation of \eqref{dl4}: for each fixed $n$,
\begin{multline}\label{dl8}
\int_\Omega a^{n}_{kl}(x)\Big(\frac{\partial \varphi^{n}_{\Omega}(x;\xi)}{\partial x_l} +i\xi_l \varphi^{n}_{\Omega}(x;\xi) \Big) \overline{ \Big( \frac{\partial \psi}{\partial x_k} + i\xi_k \psi \Big) }dx
\\= \lambda^{n}_{\Omega}(\xi)\int_{\Omega}\varphi^{n}_{\Omega}(x;\xi)\overline{\psi}dx \quad \forall \psi\in H^1_{c}(\Omega).
\end{multline}
\paragraph{Existence Result:}
By following the same analysis presented in \cite{TV1}, we state the corresponding existence result for the problem \eqref{dl8}.
\begin{proposition}
Fix $\xi \in \mathbb{R}^N$. For each fixed $n$, there exist a sequence of eigenvalues $\{ \lambda^{n}_{\Omega,m}(\xi) \geq 0; m \in \mathbb{N} \}$
and its corresponding eigenvectors $\{ \varphi^{n}_{\Omega,m} (x; \xi)\in H^1_{c}(\Omega); m \in \mathbb{N} \}$ satisfying \eqref{dl8}.
\end{proposition}
\paragraph{Regularity of the ground state:}
In the next proposition, we announce the regularity result of ground state based on the Kato-Rellich analysis which has been done in \cite{TV1}.
\begin{proposition}
For each fixed $n\in\mathbb{N}$, we have
\begin{enumerate}
\item Zero is the first eigenvalue of \eqref{dl8} at $\xi=0$ and it is an isolated point of the spectrum
with its algebraic multiplicity equal to one.
\item There exists an open neighborhood $\Omega^{\prime}_{n}$ around zero such that the
first eigenvalue $\lambda^{n}_{\Omega,1}(\xi)$ is an analytic function on $\Omega^{\prime}_{n}$ and
there is a choice of the first eigenvector $\varphi^{n}_{\Omega,1}(x;\xi)$ satisfying
$$\xi \longmapsto \varphi^{n}_{\Omega,1}(\cdot;\xi) \in H^1_{c}(\Omega)\mbox{ is analytic on }\Omega^{\prime}_{n}\mbox{ and }\ \varphi^{n}_{\Omega,1}(x;0)= |\Omega|^{-1/2},$$
with the boundary normalization condition
\begin{equation*}
\varphi_{\omega,1}(y;\eta) =\ \frac{1}{|\omega|^{1/2}} \quad \forall y\in\partial\omega \mbox{ and }\forall\eta\in \omega^{\prime}.
\end{equation*}
\end{enumerate}
\end{proposition}
\paragraph{Derivatives of $\lambda^{n}_{\Omega,1}(\xi)$ and $\varphi^{n}_{\Omega,1}(\xi)$ at $\xi=0$:}
The procedure consists of differentiating the eigenvalue equation \eqref{dl4}
for $\lambda^{n}_{\omega}(\xi)=\lambda^{n}_{\omega,1}(\xi)$ and $\varphi^{n}_{\Omega}(\cdot;\xi)=\varphi^{n}_{\Omega;1}(\cdot;\xi)$.
\paragraph{Step 1.\hspace{2pt} Zeroth order derivatives:}
We simply recall that $\varphi^{n}_{\Omega,1}(x;0) = |\Omega|^{-1/2}$ by our choice and $\lambda^{n}_{\Omega,1}(0) = 0.$
\paragraph{Step 2.\hspace{2pt} First order derivatives of $\lambda^{n}_{\Omega,1}(\xi)$ at $\xi =0$:}
Differentiating the equation \eqref{dl4} once with respect to $\xi_k$ and then
taking scalar product with $\varphi^{n}_{\Omega,1}(\cdot;\xi)$ in $L^2(\Omega)$ at $\xi=0$, we get
\begin{equation*}\big\langle D_k (\mathcal{A}^{n}_\omega(0) - \lambda^{n}_{\Omega,1}(0))\varphi^{n}_{\Omega,1}(\cdot;0),\varphi^{n}_{\Omega,1} (\cdot;0)\big\rangle = 0.\end{equation*}
Then, using the fact that
\begin{align*}
D_k \mathcal{A}^{n}_\omega(0)\varphi^{n}_{\Omega,1}(\cdot;0) =\ iC^{n}_k(\varphi^{n}_{\Omega,1}(\cdot;0))&=\ - a^{n}_{kj}(x)\frac{\partial}{\partial x_j}(\varphi^{n}_{\Omega,1}(\cdot;0)) - \frac{\partial}{\partial x_j}(a^{n}_{kj}(y)\varphi^{n}_{\Omega,1}(\cdot;0))\\
&=\ -\frac{\partial}{\partial x_j}(a^{n}_{kj}(x)\varphi^{n}_{\Omega,1}(\cdot;0)),
\end{align*}
whose integral over $\Omega$ vanishes through integration by parts together with using the boundary conditions in \eqref{dl4}, it follows that
\begin{equation}D_k \lambda^{n}_{\Omega,1}(0) = 0 \quad \forall\hspace{2pt} k = 1,\ldots,N. \end{equation}
\paragraph{Step 3. \hspace{2pt} First order derivatives of $\varphi^{n}_{\Omega,1}(\cdot;\xi)$ at $\xi=0$:}
By differentiating \eqref{dl4} once with respect to $\xi_k$ at zero, one has
\begin{align}
&\mathcal{A}^{n}_\omega(D_k\varphi^{n}_{\Omega,1}(\cdot;0)) =\ -\frac{\partial}{\partial x_j}(a^{n}_{kj}(x)\varphi^{n}_{\Omega,1}(\cdot;0)) \quad\mbox{in }\Omega, \label{dl6} \\
&D_k\varphi^{n}_{\Omega,1}(\cdot;0) =\ 0 \quad\mbox{ on }\ \partial\Omega \label{dl7}\\
\mbox{and}\quad \int_{\partial\Omega}& A^{n}_\omega(x)\left( \nabla_x D_k\varphi^{n}_{\Omega,1}(\cdot;0) + i\varphi^{n}_{\Omega,1}(\cdot;0)e_k\right)\cdot\nu \ d\sigma =\ 0 . \label{dl9}
\end{align}
As we can see along with boundary condition \eqref{dl7} for the elliptic equation \eqref{dl6},
the solution $D_k\varphi^{n}_{\Omega,1}(\cdot;0)$ gets uniquely determined. And the condition \eqref{dl9} is consistent as it comes
via integrating the equation \eqref{dl6}.
By comparing with \eqref{uB}, let us define
\begin{equation}\begin{aligned}\label{dl10}
D_k\varphi^{n}_{\Omega,1}(x;0)=
\left\{
\begin{array}{ll}
i|\Omega|^{-1/2}\ \varepsilon_{p,n}\big( w_{e_k}(\frac{x-y^{p,n}}{\varepsilon_{p,n}}) - (e_k,\frac{x-y^{p,n}}{\varepsilon_{p,n}})\big)\quad\mbox{ in }\varepsilon_{p,n}\omega + y^{p,n},\\[1ex]
0 \quad\mbox{ otherwise. }
\end{array}
\right.
\end{aligned}\end{equation}
Then, clearly $D_k\varphi^{n}_{\Omega,1}(\cdot;0) \in H^1(\Omega)$ satisfies \eqref{dl7}. We also notice that
\eqref{dl10} solves the equation \eqref{dl6} in each $\{\varepsilon_{p,n}\omega + y^{p,n}\}_{p\in K}$.
In order to show it solves \eqref{dl6} in entire $\Omega$, we need to prove that
\begin{equation}\label{ll5} \int_{\Omega} A^{n}_\omega(x)\left( \nabla_x D_k\varphi^{n}_{\Omega,1}(x;0) +i\varphi^{n}_{\Omega,1}(x;0) e_k \right)\cdot \nabla_x \varphi(x) dx =\ 0 \quad\forall\varphi\in\mathcal{D}(\Omega).\end{equation}
We have that
\begin{multline}\label{dl11}
\int_{\Omega} A^{n}_\omega(x)\left( \nabla_x D_k\varphi^{n}_{\Omega,1}(x;0) + i\varphi^{n}_{\Omega,1}(x;0)e_k \right)\cdot \nabla_x \varphi(x) dx\\
=\ \frac{i}{|\Omega|^{1/2}}\sum_p \varepsilon_{p,n}^{N-1}\int_{\omega} A_\omega(y)\nabla_y w_{e_k}(y)\cdot \nabla_y\varphi_p(y) dy,
\end{multline}
where $y=\ \frac{x-y^{p,n}}{\varepsilon_{p,n}} \in \omega$ whenever $ x\in \varepsilon_{p,n}\omega + y^{p,n}$
and $\varphi_p(y) =\ \varphi(\varepsilon_{p,n}y+y^{p,n})$ with $\nabla_y\varphi_p(y)=\ \varepsilon_{p,n}\nabla_x \varphi(x)$.
Then, doing integration by parts on the right hand side of \eqref{dl11} together with using \eqref{hsw}, we get
\begin{align*}
\int_{\Omega} A^{n}_\omega(x)\left( \nabla_x D_k\varphi^{n}_{\Omega,1}(x;0) + i\varphi^{n}_{\Omega,1}(x;0)e_k \right)\cdot \nabla_x \varphi(x) dx &=\ \frac{i}{|\Omega|^{1/2}}\sum_p \varepsilon_{p,n}^{N-1} \int_{\partial\omega} Me_k\cdot \nu \varphi_p(y) d\sigma\\
&=\ \frac{i}{|\Omega|^{1/2}}Me_k \cdot \sum_p \varepsilon_{p,n}^{N-1}\int_{\omega} \nabla_z \varphi_p(y) dy \\
&=\ \frac{i}{|\Omega|^{1/2}}Me_k\cdot \int_{\Omega}\nabla_x \varphi(x) dx\\
&=\ 0 \quad\quad\forall \varphi\in \mathcal{D}(\Omega).
\end{align*}
Thus $D_k\varphi^{n}_{\Omega,1}(x;0)$ is rightly defined in \eqref{dl10} to satisfy \eqref{dl6}, \eqref{dl7}, \eqref{dl9} uniquely.
\paragraph{Step 4.\hspace{2pt} Second derivatives of $\lambda^{n}_{\Omega,1}(\xi)$ at $\xi=0$:}
By differentiating \eqref{dl4} twice with respect to $\xi_k$ and $\xi_l$, respectively
and then taking scalar product with $\varphi^{n}_{\Omega,1}(\cdot;\xi)$ in $L^2(\Omega)$ at $\xi=0$, we get
\begin{multline*}
\big\langle D^2_{kl}(\mathcal{A}^{n}_\omega(0) - \lambda^{n}_{\Omega,1}(0))\varphi^{n}_{\Omega,1}(\cdot;0), \varphi^{n}_{\Omega,1}(\cdot;0)\big\rangle \\
+ \big\langle [D_k(\mathcal{A}^{n}_\omega(0) - \lambda^{n}_{\Omega,1}(0))]D_l\varphi^{n}_{\Omega,1}(\cdot;0), \varphi^{n}_{\Omega,1}(\cdot;0)\big\rangle\\
+ \big\langle [D_l(\mathcal{A}^{n}_\omega(0)- \lambda^{n}_{\Omega,1}(0))]D_k \varphi^{n}_{\Omega,1}(\cdot;0), \varphi^{n}_{\Omega,1}(\cdot;0)\big\rangle = 0.
\end{multline*}
By using the information obtained in the previous steps, we get
\begin{equation*}\begin{aligned}
\frac{1}{2}&D^2_{kl}\lambda^{n}_{\Omega,1}(0) =\ \frac{1}{|\Omega|}\int_{\Omega} a^{n}_{kl}(x)dx -
\frac{1}{2|\Omega|}\int_{\Omega}\Big[C^{n}_k(D_l\varphi^{n}_{\Omega,1}(x;0)) + C_l(D_k\varphi^{n}_{\Omega,1}(x;0))\Big]dx\\
&=\ \frac{1}{2|\Omega|}\sum_p \int_{\varepsilon_{p,n}\omega +y^{p,n}}A_\omega\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\Big)\Big( \nabla w_{e_k}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\Big)\cdot e_l + \nabla w_{e_l}\Big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\Big)\cdot e_k \Big) dx\\
&=\ \frac{1}{2} \int_{\omega} A_\omega(y)\big( \nabla_y w_{e_k}(y)\cdot e_l\ + \nabla_y w_{e_l}(y)\cdot e_k\big) dy\\
&=\ m_{kl} \quad\forall k,l=1,\ldots,N,
\end{aligned}
\end{equation*}
due to the integral identity \eqref{dl12},
which are indeed the homogenized coefficients governed with the Hashin-Shtrikman constructions.
We see that $\frac{1}{2}D^2_{kl}\lambda^{n}_{\Omega,1}(0)$ is independent of $n$. Thus, it
does not depend on the choice of translations $y^{p,n}$ and the scales $\varepsilon_{p,n}$
as long as they are bound to satisfy the Vitali covering criteria \eqref{ll1}.
\paragraph{Step 5. Higher order derivatives:}
In general, the process can be continued indefinitely to compute all derivatives of
$\lambda^{n}_{\Omega,1}(\xi)$ and $\varphi^{n}_{\Omega,1}(\cdot;\xi)$ at $\xi = 0$.
In particular, the third order derivative is zero, i.e. $D^{q}\lambda^{n}_{\Omega,1}(0)=0, \,|q|=3$.
However, we are interested in the fourth order derivatives of $\lambda^{n}_{\Omega,1}(0)$, i.e.
$D^4_{klmn}\lambda^{n}_{\Omega,1}(0)$, which is in general a non-positive definite tensor and can be defined as follows: the second order derivative of the eigenvector $D^2_{kl}\varphi^{n}_{\Omega,1}(\cdot;0)\in H^1_0(\Omega)$ solves
\begin{equation}\begin{aligned}\label{dl15}
&\mathcal{A}^{n}_\omega D^2_{kl}\varphi^{n}_{\Omega,1}(x;0)= -( a^{n}_{kl}(x) - m_{kl} )\varphi^{n}_{\Omega,1}(x;0) - iC^{n}_k(D_l(\varphi^{n}_{\Omega,1}(x;0)) - iC_l(D_k\varphi^{n}_{\Omega,1}(x;0))\mbox{ in }\Omega,\\
&D^2_{kl}\varphi^{n}_{\Omega,1}(x;0) = 0 \mbox{ on }\partial\Omega \mbox{ and } \int_{\partial\Omega} A^{n}_\omega(x)\nabla_x D^2_{kl}\varphi^{n}_{\omega,1}(x;0)\cdot\nu \ d\sigma= 0 .
\end{aligned}\end{equation}
The above equation \eqref{dl15} has an unique solution and we would like to define as
\begin{equation}\begin{aligned}\label{dl16}
D^2_{kl}\varphi^{n}_{\Omega,1}(x;0) =
\left\{
\begin{array}{ll}
|\Omega|^{-1/2}\ \varepsilon^2_{p,n} \widetilde{w}_{kl}\big(\frac{x-y^{p,n}}{\varepsilon_{p,n}}\big)\quad\mbox{ in }\varepsilon_{p,n}\omega + y^{p,n},\\[1ex]
0 \quad\mbox{ otherwise,}
\end{array}
\right.
\end{aligned}\end{equation}
where $\widetilde{w}_{kl}$ is defined likewise by \eqref{hsw} as follows: after extending $A_\omega\in\mathcal{M}(\alpha,\beta;\omega)$ by $A_\omega(x) = M$ for $x \in \mathbb{R}^N\smallsetminus \omega$, $\widetilde{w}_{kl}\in H^1(\mathbb{R}^N)$ satisfies
\begin{equation}\begin{aligned}\label{dl14}
- div (A_\omega\nabla \widetilde{w}_{kl}(x)) &= -( a^\omega_{kl}(x) - m_{kl} ) - iC^{\omega}_k(w_{e_l}(x)-x_l) - iC^{\omega}_l(w_{e_k}(x)-x_k)\quad\mbox{ in }\mathbb{R}^N,\\
\widetilde{w}_{kl}(x) &=\ 0 \quad\mbox{ in }\mathbb{R}^N \smallsetminus \omega,
\end{aligned}\end{equation}
where $C^{\omega}_k(\varphi) = - a^{\omega}_{kj}(x)\frac{\partial \varphi}{\partial x_j} - \frac{\partial}{\partial x_j}(a^{\omega}_{kj}(x)\varphi)$.\\
\\
If such $\widetilde{w}_{kl}\in H^1(\mathbb{R}^N)$ exists $\forall k,l=1,\ldots,N$, then following the same arguments
presented in Step 3, $D^2_{kl}\varphi^{n}_{\Omega,1}(\cdot;0)$ defined in \eqref{dl16} belongs to $ H^1_0(\Omega)$ and solves \eqref{dl15} in $\Omega$.\\
\\
Notice that $w_{kl}\in H^1_0(\omega)$ defined in \eqref{dl17} and $\widetilde{w}_{kl}\in H^1_0(\omega)$ solves the same equation \eqref{dl14}.
The only difference occurs in the co-normal derivative of $\widetilde{w}$ on $\partial\omega$, because we have
\begin{center}$\nabla \widetilde{w}_{kl}(x)\cdot \nu =\ 0 \ \mbox{ on }\partial\omega.$\end{center}
In the next section (cf. Proposition \ref{ll2} below), we show that in the case of two-phase spherical
inclusions (see Example \ref{si}) such $\widetilde{w}_{kl}$ exists and is equal to $w_{kl}$ for each $k,l=1,\ldots,N.$ \\
\\
We further define
\begin{center}$ X^{n}_{\Omega,1}= -i|\Omega|^{1/2}\ \xi_kD_k\varphi^{n}_{\Omega,1}(\cdot;0)$ and $X^{n}_{\Omega,2}= |\Omega|^{1/2}\ \xi_k\xi_l D^2_{kl}\varphi^{n}_{\Omega,1}(\cdot;0).$\end{center}
Then, following \cite[Proposition 3.2]{COVB}, the fourth order derivative of $\lambda^{n}_{\Omega,1}(\xi)$ at $\xi=0$ defines as
\begin{equation}\begin{aligned}\label{dl18}
\frac{1}{4!}D^4_{klmn}\lambda^{n}_{\Omega,1}(0)\xi_k\xi_l\xi_m\xi_n&= -\frac{1}{|\Omega|}\int_{\Omega} \mathcal{A}^{n}\Big( X^{n}_{\Omega,2} - \frac{1}{2}(X^{n}_{\Omega,1})^2\Big)\cdot\Big( X^{n}_{\Omega,2} - \frac{1}{2}(X^{n}_{\Omega,1})^2\Big) dx \\
&\leq 0.
\end{aligned}\end{equation}
Moreover, using \eqref{dl10} and \eqref{dl16}, the above expression \eqref{dl18} becomes
\begin{equation}\begin{aligned}\label{ll3}
\frac{1}{4!}D^4_{klmn}\lambda^{n}_{\Omega,1}(0)\xi^4 &=\ -\frac{1}{|\Omega|}\sum_p \varepsilon_{p,n}^{N+2} \int_{\omega} \mathcal{A}\Big( X^{(2)}_{\omega} - \frac{1}{2}(X^{(1)}_{\omega})^2\Big)\cdot\Big( X^{(2)}_{\omega} - \frac{1}{2}(X^{(1)}_{\omega})^2\Big) dy \\
&=\ \frac{|\omega|}{|\Omega|}\sum_p \varepsilon_{p,n}^{N+2}\cdot \frac{1}{4!}D^4_{klmn}\lambda_{\omega,1}(0)\xi^4,
\end{aligned}\end{equation}
where the last equality follows from \eqref{dl20}.
\begin{remark}
The above equality \eqref{ll3} establishes the relation between the fourth order derivatives of $\lambda_{\omega,1}$ and $\lambda_{\Omega,1}$.
Remember that the first and second order derivatives of them are equal.
\end{remark}
Here we define an approximating dispersion tensor $d^{n}_{HS}$ for the medium with respect to the highest scale factor $\kappa_n^2$ as follows:
$$ \frac{1}{4!}D^4_{klmn}\lambda^{n}_{\Omega,1}(0) =\ \kappa_n^2 d^{n}_{HS}.$$
Then, as $n\rightarrow \infty$, we define the \textit{Burnett coefficient} or the dispersion tensor for the medium:
\begin{equation}\label{dl21} d_{HS}=\ \underset{n \rightarrow \infty}{limsup\ }d^{n}_{HS} =\ \frac{|\omega|}{|\Omega|}\left(\underset{n\rightarrow \infty}{limsup\ }\kappa_n^{-2}\sum_p \varepsilon_{p,n}^{N+2}\right)\cdot \frac{1}{4!}D^4_{klmn}\lambda_{\omega,1}(0).\end{equation}
The above limit always exists finitely. It can be seen through the following simple estimate:\begin{align*}
\sum_p\varepsilon_{p,n}^{N+2} \leq \kappa_n^2 \sum_p \varepsilon_{p,n}^N = \kappa_n^2 \frac{|\Omega|}{|\omega|}\quad\mbox{ or } \quad\kappa_n^{-2}\sum_p \varepsilon_{p,n}^{N+2} \ \mbox{ is uniformly bounded. }
\end{align*}
The identity \eqref{dl21} reads as $d_{HS}$ is a purely locally defined macro quantity incorporating only various scales associated with the structure. For each $n$, we have the following approximation:
$$ \lambda^{n}_{\Omega,1}(\xi)=\ M\xi^2 + \kappa_n^2\ d_{HS}\ \xi^4 + o(\kappa_n^2), \quad \xi\in\Omega^{\prime}_{n}.$$
\begin{remark}
Remember that the above expression \eqref{dl21} is valid only when $A$ is equivalent to $M$ through the existence of
$w_{e_k}\in H^1_{loc}(\mathbb{R}^N)$ satisfying \eqref{hsw} and with the existence of $\widetilde{w}_{kl}\in H^1(\mathbb{R}^N)$ satisfying \eqref{dl14}, for each $k,l=1,\ldots,N$.
In the next section, as an example of ``Spherical inclusions in two-phase medium'', we establish their existence.
\end{remark}
\begin{remark}
For the periodic micro-structures with the uniform $\varepsilon$-scaling
and translation, the above definition \eqref{dl21} of the dispersion tensor coincides with the coefficient $d_{Y}$ defined in
\eqref{dl22}.\hfill\qed
\end{remark}
Motivated from the optimal design and so on,
the interesting question can be taken into account in
this matter that which Vitali coverings are responsible
for the minimum or maximum value for $d_{HS}$. Regarding that, we prove
the following conjecture stated below.
\paragraph{Conjecture:}\textit{Minimizer of the dispersion tensor is unique among $2$-phase periodic Hashin-Shtrikman micro-structures of a given proportion and it is given by the
Apollonian-Hashin-Shtrikman micro-structure.}\\
\\
This conjecture was arrived at by a previous study of the same problem in
one-space dimension \cite{CMSV}. Roughly speaking, the result in one dimension says
that the value of ``$d$'' increases when we increase the number of interfaces between
the two phases in the micro-structure. At the maximum value of ``$d$'', we have a
continuum of interfaces and at the minimum value, there is an unique
minimizer with a single interface. We prove it in the following section.
\section{Spherical inclusions in 2-phase periodic Hashin- Shtrikman micro-structures}
\setcounter{equation}{0}
In the class of periodic spherical Hashin-Shtrikman micro-structures,
we consider the unit cell $Y=[0,1]^N$ in $\mathbb{R}^N$ and identify with $\mathbb{R}^N$
through $\mathbb{Z}^N-$translation invariance. We first find a
Hashin-Shtrikman construction to cover the whole space $\mathbb{R}^N$ and if it is invariant
under $\mathbb{Z}^N-$translations, then we will consider it as a Hashin-Shtrikman structure
for $Y$ and conversely. So, let us start with a cover for $\mathbb{R}^N$ by a sequence
of reduced copy of disjoint balls $B(y^p,\varepsilon_p)= \varepsilon_{p}B(0,1) + y^{p}$ with center $y^{p}$ and radius $\varepsilon_p$ such that
\begin{equation}\label{ll7}
\begin{aligned}
& meas\big(\mathbb{R}^N \smallsetminus \underset{p\in \mathbb{K}}{\cup} B(y^p,\varepsilon_p)\big) = 0,\mbox{ where }K \mbox{ is some infinite countable set}\\
\mbox{and }\ & m\in\mathbb{Z}^N,\ \forall p\in {K}, \ m+ B(y^p,\varepsilon_p) = B(y^p+m,\varepsilon_p) \in \underset{p\in K}{\cup} B(y^p,\varepsilon_p).\\
\mbox{Moreover, }\ &\forall m\in \mathbb{Z}^N, \ meas(\mathbb{R}^N \smallsetminus \underset{p\in \mathbb{K}}{\cup} (m+ B(y^p,\varepsilon_p)) ) = 0.
\end{aligned}
\end{equation}
Consequently, the unit periodic cell $Y$ is understood as $Y= \underset{p\in K}{\cup}\big( [0,1]^N\cap B (y^p,\varepsilon_p)\big)$.\\
\\
Let us now consider $a_B(y)$ be the two-phase conductivity profile in $B(0,1)$, defined as
follows:\begin{equation*}\begin{aligned}
a_B(y)=\ a(r) =
\left\{
\begin{array}{ll}
\alpha \quad\mbox{if } |y| < R,\\
\beta \quad\mbox{if } R < |y| < 1,
\end{array}
\right.
\end{aligned}\end{equation*}
with $0<\alpha\leq \beta < \infty$. We define $\theta = R^N$ as the volume proportion of the two-phase profile.\\
\\
Then $a_B(y)$ is \textit{equivalent} to some $m$ ($\alpha \leq m\leq \beta$) (see \cite[Page no. 282]{T}), i.e., after extending $a_B(y)$ by $a_B(y)=m$ in $\mathbb{R}^N\smallsetminus B(0,1)$,
for each unit vector $e_l \in \mathbb{R}^N$ ($l=1,\ldots,N$), there exists $w_{e_l}\in H^{1}_{loc}(\mathbb{R}^N)$ satisfying\begin{equation}\label{ED1}
- div(a_B(y)\nabla w_{e_l}(y))= 0 \quad\mbox{in }\mathbb{R}^N,\quad w_{e_l}(y) = y\cdot e_l \quad\mbox{in }\mathbb{R}^N \smallsetminus B(0,1).
\end{equation}
The co-normal flux satisfies
\begin{equation*}a_B(y)\nabla w_{e_l}(y)\cdot \nu =m \quad\mbox{on }\partial B(0,1),\end{equation*}
where $m$ satisfies the relation
\begin{equation}\label{ED9}\frac{m - \beta}{m + (N-1)\beta} = \theta \frac{\alpha - \beta}{\alpha + (N-1)\beta}.\end{equation}
Now, by homothecy, we extend $a_B$ to the entire $\mathbb{R}^N$ defining
$$a_{\mathbb{R}^N}(y)= a_B\Big(\frac{y-y^p}{\varepsilon_p}\Big)\quad\mbox{in }B(y^p,\varepsilon_p)\ \mbox{ a.e. in }\mathbb{R}^N$$
and reveal that $a_{\mathbb{R}^N}(y)$ is a $Y-$periodic function due to \eqref{ll7}, i.e. $a_{\mathbb{R}^N}\in L^{\infty}_{\#}(Y)$.
We define
\begin{center}$a_Y(y) =\ a_{\mathbb{R}^N}(y),\ \ $ $y\in Y=[0,1]^N$.\end{center}
Next, we set
\begin{center}$ a^{\varepsilon}(x) = a_{Y}\big(\frac{x}{\varepsilon}\big),\ x\in\mathbb{R}^N\ \mbox{and } \frac{x}{\varepsilon}= y\in Y$\end{center}
and extend it to the whole $\mathbb{R}^N$ by $\varepsilon$-periodicity with a small period of scale $\varepsilon$,
which is considered as two-phase periodic Hashin-Shtrikman micro-structures with spherical inclusions.
\paragraph{(i) Homogenized coefficients:}
\noindent
The sequence $a^{\varepsilon} \xrightarrow{ H-\mbox{converges }} m$.
One defines $\chi_{l}\in H^1_{\#}(Y)$ (see \cite[page no. 195]{JKO}) solving the cell--problem in the periodic cell $Y$:
\begin{equation}\label{PN1}
-div(a_{Y}(y)(\nabla{\chi_l}(y) + e_l)) = 0 \ \mbox{ in }Y,\ \mbox{ where } \chi_l\in H^1_{\#}(Y)\ \mbox{ with }\ \int_Y \chi_l dy = 0.
\end{equation}
And then, one need to show that the homogenized coefficient $a^{*}$, defined below, is equal to $m$, i.e.
\begin{equation}\label{ED3}
a^{*}= \frac{1}{|Y|}\int_{Y} a_{Y}(y)(\nabla\chi_l(y) + e_l)\cdot(\nabla\chi_l(y) + e_l)dy\ =\ m.
\end{equation}
Let us first look for a solution of the following extended equation in the entire space $\mathbb{R}^N$:
\begin{equation}\label{ll4}
-div (a_{\mathbb{R}^N}(y)(\nabla \chi_{\mathbb{R}^N} + e )) = 0 \ \mbox{ in }\mathbb{R}^N,\ \chi_{\mathbb{R}^N}\in H^1_{loc}(\mathbb{R}^N),
\end{equation}
where $e$ is some canonical basis vector in $\mathbb{R}^N$.\\
\\
Prior to that, we define
\begin{equation}\label{ll6}
\chi_{\mathbb{R}^N}(y) =\ \varepsilon_{p}\Big( w_{e}\Big(\frac{y-y^{p}}{\varepsilon_{p}}\Big) - \Big(e\cdot\frac{y-y^{p}}{\varepsilon_{p}}\Big) \Big)\ \ \mbox{ if }y\in B(y^p,\varepsilon_p).
\end{equation}
Then, we see that $\chi_{\mathbb{R}^N}$ is a $H^1_{loc}(\mathbb{R}^N)-$function and it solves the problem \eqref{ll4} restricted into each balls $\{B(y^p,\varepsilon_p)\}_{p\in K}$.
Moreover, for any $\varphi \in \mathcal{D}(\mathbb{R}^N)$, we have
$$ \int_{\mathbb{R}^N} a_{\mathbb{R}^N}(y)(\nabla\chi_{\mathbb{R}^N}(y) + e)\cdot \nabla \varphi (y)\ dy =0.$$
The above equality follows in a similar manner that we did before for \eqref{ll5}. It establishes that \eqref{ll6} solves \eqref{ll4} locally in $\mathbb{R}^N$.\\
Now, we claim that, $\chi_{\mathbb{R}^N}(y)$ is a $Y-$periodic function, i.e. $\chi_{\mathbb{R}^N}\in H^1_{\#}(Y)$.
It simply follows by using \eqref{ll7}, i.e. for $y\in \mathbb{R}^N$ and $m\in \mathbb{Z}^N$, we have
\begin{align*}
\chi_{\mathbb{R}^N}(y-m) &=\ \varepsilon_p\Big( w_{e}\Big(\frac{y-m-y^{p}}{\varepsilon_{p}}\Big) - \Big(e\cdot\frac{y-m-y^{p}}{\varepsilon_{p}}\Big) \Big)\ \mbox{ if } y-m \in B(y^p,\varepsilon_p)\\
&=\ \varepsilon_{p}\Big( w_{e}\Big(\frac{y-y^{p^{\prime}}}{\varepsilon_{p}}\Big) - \Big(e\cdot\frac{y-y^{p^{\prime}}}{\varepsilon_{p}}\Big) \Big)\ \mbox{ if } y \in B(y^{p^{\prime}},\varepsilon_{p})= B(m+y^p,\varepsilon_p)\\
&=\ \chi_{\mathbb{R}^N}(y) \quad\mbox{ (due to }\eqref{ll7} ).
\end{align*}
We define
\begin{center}$ \widetilde{\chi_{Y}}(y)= \chi_{\mathbb{R}^N}(y) ,\ \ $ $y\in Y=[0,1]^N$.\end{center}
Then $\widetilde{\chi_{Y}}(y)\in H^1_{\#}(Y)$ and by simply considering $\chi_{Y}(y)= \widetilde{\chi_{Y}}(y)- \frac{1}{|Y|}\int_Y\widetilde{\chi_{Y}}(y)dy$, it
solves \eqref{PN1} for each $e= e_l$. Finally, by taking $\chi_Y(y)$ in the integral identity \eqref{ED3} and using \eqref{ED1}, it follows the homogenized coefficient $m$. Precisely, we have
\begin{align*}
\frac{1}{|Y|}\int_{Y} a_Y(y)(\nabla \chi_Y(y) + e)&\cdot(\nabla \chi_Y(y) + e) dy \\
=& \ \frac{1}{|Y|}\sum_p \int_{B(y^p,\varepsilon_p)\cap Y} a\Big(\frac{y-y^{p}}{\varepsilon_{p}}\Big)\Big|\nabla w_{e}\Big(\frac{y-y^{p}}{\varepsilon_{p}}\Big)\Big|^2 dy\\
=&\ \frac{1}{|B(0,1)|} \int_{B(0,1)} a(z) |\nabla w_{e_l}(z)|^2 dz\ =\ m.
\end{align*}
It is now remaining to establish the relation \eqref{ED9}. We seek the solution of the above equation \eqref{ED1} in the following form
\begin{equation}\label{ED7}w_{e_l}(y) =\ y_lf(r),\ y\in B(0,1),\end{equation}
where $f(r)$ is given by
\begin{equation}\begin{aligned}\label{ED5}
f(r) =
\left\{
\begin{array}{ll}
\widetilde{b_1} \ &\mbox{ if }r< R,\\[1ex]
\widetilde{b_2} + \frac{\widetilde{c}}{r^N} \ &\mbox{ if }R < r < 1,\\[1ex]
1 \ &\mbox{ if }1 < r.
\end{array}
\right.
\end{aligned}\end{equation}
In order to keep the solution $w_{e_l}(y)$ and flux $a(r)(f(r)+rf^{\prime}(r))$ to be continuous across
the inner boundary $(r=R)$ and the outer boundary $(r=1)$,
we need to impose the following conditions: \begin{equation}\begin{aligned}\label{b1b2}
\widetilde{b_1} =\ \widetilde{b_2} + \frac{\widetilde{c}}{r_1^N}, &\ \mbox{ }\ \alpha\widetilde{b_1} =\ \beta\Big(\widetilde{b_2} + \frac{(1-N)\widetilde{c}}{r_1^N} \Big),\\
\widetilde{b_2} + \widetilde{c} =\ 1 &\ \mbox{ and }\ \beta(\widetilde{b_2} + (1-N)\widetilde{c}) =\ m. \\
\end{aligned}\end{equation}
Then, solving $(\widetilde{b_1},\widetilde{b_2},\widetilde{c})$ in terms of $(\alpha,\ \beta,\ \theta)$ from the first three equation of \eqref{b1b2}, we have
\begin{equation}\label{PN2}
\widetilde{b_1} = \ \frac{N\beta}{(1-\theta)\alpha + (N+\theta -1)\beta},\quad \widetilde{b_2} = \ \frac{(1-\widetilde{b_1}\theta)}{(1-\theta)} \quad\mbox{and}\quad \widetilde{c} = \frac{(\widetilde{b_1} -1)\theta}{(1-\theta)}
\end{equation}
and finally putting it into the fourth equation of \eqref{b1b2}, $m$ can be written as in \eqref{ED9}.
\paragraph{(ii) Dispersion coefficient:}
In the periodic Hashin-Shtrikman structures we denote the dispersion tensor by $d_{PHS}$.
Concerning to our case, we recall the integral expression \eqref{dy} to write $d_{PHS}$ as follows:
\begin{equation}\label{dphs}
d_{PHS}\eta^4 = -\frac{1}{|Y|}\int_{Y} \mathcal{A}_Y\Big( X^{(2)}_Y -\frac{(X^{(1)}_Y)^2}{2}\Big)\cdot\Big( X^{(2)}_Y -\frac{(X^{(1)}_Y)^2}{2}\Big) dy,
\end{equation}
where $\mathcal{A}_Y$, $X^{(1)}_Y$, $X^{(2)}_Y$ are defined in \eqref{dl19}.\\
\\
Let us denote $X_{B(0,1)}^{(1)}(y) = \eta_k ( w_{e_k}(y) - y_k )$, where $w_{e_k}$ is the solution of \eqref{ED1}
and $X_{B(0,1)}^{(2)}= \eta_k\eta_l w_{kl}$, where $w_{kl}$ is the solution of the following auxiliary cell-equation in $B(0,1)$:
\begin{equation}\begin{aligned}\label{auxN}
-div(a_B(y)\nabla w_{kl}(y)) &=\ a_B(y)\delta_{kl} - m\delta_{kl} - \frac{1}{2}\left( C^B_{l}(w_{e_k}(y)-y_k) + C^B_{k}(w_{e_l}(y) -y_l)\right) \mbox{ in }B(0,1),\\
w_{kl}(y) &=\ 0 \ \mbox{ on }\partial B(0,1),
\end{aligned}\end{equation}
where $C^{B}_k(\varphi) = - a_B(y)\frac{\partial \varphi}{\partial x_k} - \frac{\partial}{\partial x_k}(a_B(y)\varphi)$.\\
\\
We observe that \eqref{auxN} is an elliptic partial differential equation with
Dirichlet boundary condition which possess an unique solution $w_{kl} \in H^1_0(B(0,1))$.
Having that, we claim that the co-normal derivative of $w_{kl}$ on $\partial B(0,1)$ is
zero, i.e.
\begin{equation}\label{fed12}
\nabla w_{kl} (y)\cdot \nu = 0 \quad\mbox{on } \partial B(0,1).
\end{equation}
\begin{remark}
If we extend $a_{B}(y)$ by $m$ in $\mathbb{R}^N\smallsetminus B(0,1)$ and $w_{e_k}(y)$ by $y_k$ in $\mathbb{R}^N\smallsetminus B(0,1)$, then \eqref{auxN} becomes
\begin{equation}\label{ED6}-div(m\nabla \widetilde{w_{kl}}(y)) = 0 \quad\mbox{in }\ \mathbb{R}^N\smallsetminus B(0,1)\quad\mbox{with }\ \ \widetilde{w_{kl}}(y) = 0 \ \mbox{on }\partial B(0,1).\end{equation}
If $ \widetilde{w_{kl}} \in H^1(\mathbb{R}^N\smallsetminus B(0,1))$, then simply using the maximum principle (see \cite[Page no. 164, (3.10)]{KS}), we
get $\widetilde{w_{kl}}(y) = 0 $ in $\mathbb{R}^N\smallsetminus B(0,1)$, which says that $0$ is the natural extension. \\
\\
Let us define
\begin{equation}\begin{aligned}\label{ll8}
\widetilde{w_{kl}} =
\left\{
\begin{array}{ll}
w_{kl} \ \mbox{ in } B(0,1),\\[1ex]
0 \ \mbox{ in }\mathbb{R}^N\smallsetminus B(0,1).
\end{array}
\right.
\end{aligned}\end{equation}
Now, if \eqref{ll8} solves both \eqref{auxN} and \eqref{ED6} as a $H^1(\mathbb{R}^N)-$function,
then from the continuity of the boundary normal flux, we have
$$ a_B(y)\nabla w_{kl} (y)\cdot \nu = 0 \quad\mbox{on } \partial B(0,1)\quad\mbox{or }\ \nabla w_{kl} (y)\cdot \nu = 0 \quad\mbox{on } \partial B(0,1).$$
However, at this moment we don't know whether $\widetilde{w_{kl}}$ is a $H^1(\mathbb{R}^N)-$function or not.\\
Secondly, as we have experienced from the previous case, it is required to have such extension property in order to get
$\chi_{kl}\in H^1_{\#}(Y)$ from $w_{kl}\in H^1_0(B)$, which solves the cell-problem \eqref{ll9}.
\end{remark}
\begin{proposition}\label{ll2}
The unique solution $w_{kl}$ of \eqref{auxN} satisfies the additional boundary condition \eqref{fed12}.
\end{proposition}
\begin{proof}
The proof is divided into several steps.
We begin with calculating the right hand side of the equation \eqref{auxN}.
\paragraph{Step 1)} \textbf{RHS of \eqref{auxN}: }
Following the definition of the 1st order operator $C^B_l$ and $w_{e_k}(y) = y_kf(r)$, we get
\begin{align*}
- C^B_l(w_{e_k}(y)-y_k) &=\ a(r)\frac{\partial}{\partial y_l} (w_{e_k}(y)-y_k) + \frac{\partial}{\partial y_l}(a(r)(w_{e_k}(y)-y_k))\\
&=\ 2a(r)(f(r)-1)\delta_{kl} + y_ky_l \Big( a(r)\frac{f^{\prime}(r)}{r} + \frac{(a(r)(f(r)-1))^{\prime}}{r} \Big).
\end{align*}
Or,
\begin{multline}\label{fed2}
a(r)\delta_{kl} - m\delta_{kl} -\frac{1}{2}\big( C^B_l(w_{e_k}(y)-y_k) + C^B_k(w_{e_l}(y)-y_l) \big) \\
= a(r)\delta_{kl} - m\delta_{kl} + 2a(r)(f(r)-1)\delta_{kl} + y_ky_l \Big( a(r)\frac{f^{\prime}(r)}{r} + \frac{(a(r)(f(r)-1))^{\prime}}{r} \Big).
\end{multline}
The structure of RHS suggests the following ansatz for the solution of \eqref{auxN}:
\begin{equation*}
w_{kl}(y) = y_ky_l g(r) + h(r).
\end{equation*}
\textbf{LHS of \eqref{auxN}:} We have
\begin{align*}
\frac{\partial w_{kl}}{\partial y_m}(y) = y_ky_l g^{\prime}(r)\frac{y_m}{r} + y_kg(r)\delta_{lm} + y_lg(r)\delta_{km} + h^{\prime}(r)\frac{y_m}{r}.
\end{align*}
Consequently,
\begin{align*}
\frac{\partial}{\partial y_m} \Big( a(r)\frac{\partial w_{kl}}{\partial y_m}(y)\Big) =&\ y_ky_ly_m \Big(\frac{a(r)g^{\prime}(r)}{r}\Big)^{\prime}\ \frac{y_m}{r} + y_ky_l \frac{a(r)g^{\prime}(r)}{r}
+ y_k\delta_{lm}y_m\frac{a(r)g^{\prime}(r)}{r}\\
& +y_l\delta_{km}y_m\frac{a(r)g^{\prime}(r)}{r} +
2\delta_{km}\delta_{lm}a(r)g(r)
+ y_ky_m\delta_{lm}\frac{(a(r)g(r))^{\prime}}{r}\\
& + y_ly_m\delta_{km}\frac{(a(r)g(r))^{\prime}}{r}
+ \frac{a(r)h^{\prime}(r)}{r} + y_m\Big(\frac{a(r)h^{\prime}(r)}{r}\Big)^{\prime}\ \frac{y_m}{r},
\end{align*}
or\begin{equation}\label{fed3}\begin{aligned}
div (a(r)\nabla w_{kl}(y)) =&\ y_ky_l \Big( r \Big(\frac{a(r)g^{\prime}(r)}{r}\Big)^{\prime} + (N+2)\frac{a(r)g^{\prime}(r)}{r} + 2\frac{(a(r)g(r))^{\prime}}{r} \Big)\\ &+ 2a(r)g(r)\delta_{kl}
+ N \frac{a(r)h^{\prime}(r)}{r} + r\Big(\frac{a(r)h^{\prime}(r)}{r}\Big)^{\prime}.
\end{aligned}\end{equation}
\textbf{Step 2)}
Both LHS \eqref{fed3} and RHS \eqref{fed2} contain the quadratic term $y_ky_l$ and the constant term in $y$. Equating the corresponding coefficients, we get
\begin{equation}\label{fed4}
r \Big(\frac{a(r)g^{\prime}(r)}{r}\Big)^{\prime} + (N+2)\frac{a(r)f^{\prime}(r)}{r} + 2 \frac{(a(r)g(r))^{\prime}}{r} = - \Big[ a(r)\frac{f^{\prime}(r)}{r} + \frac{(a(r)(f(r)-1))^{\prime}}{r} \Big]
\end{equation}
and
\begin{equation}\label{fed5}
2a(r)g(r)\delta_{kl} + N \frac{a(r)h^{\prime}(r)}{r} + r\Big(\frac{a(r)h^{\prime}(r)}{r}\Big)^{\prime} = - \Big[ a(r)\delta_{kl} - m\delta_{kl} + 2a(r)(f(r)-1)\delta_{kl}\Big].
\end{equation}
We have
\begin{equation*}
a(r) =
\alpha \quad\mbox{and }\ \ f(r) =\ \widetilde{b_1} \quad\mbox{when } r < R \quad
\end{equation*}
and
\begin{equation*}
a(r) =\beta \quad\mbox{and }\ \ f(r)=\ \widetilde{b_2} + \frac{\widetilde{c}}{r^N} \quad\mbox{when } R< r <1,
\end{equation*}
where ($\widetilde{b_1},\widetilde{b_2},\widetilde{c}$) are known in terms of $\alpha,\beta, N $ and $ \theta$ (see \eqref{PN2}).\\
\\
We further seek $h(r)$ and $g(r)$ in the general form of
\begin{align}\label{fed6}
g(r) =\ b + \frac{c}{r^N} + \frac{d}{r^{N+2}} \quad\mbox{and }\ h(r) =\Big (\frac{p}{r^N} + q r^2 + t\Big)\delta_{kl}.
\end{align}
The set of constants $(b,c,d)$ and $(p,q,t)$ can take different values in
the ranges $r < R $ and $ R< r<1$. We denote them
by $(b_1,c_1,d_1)$, $(p_1,q_1,t_1)$ and $(b_2,c_2,d_2)$, $(p_2,q_2,t_2),$ respectively.\\
Now, by using \eqref{fed6} in \eqref{fed4}, we get the following cases:\\
{\it Case 1.} When $r < R$, we have
\begin{multline*}
-N(N+2)\frac{c_1}{r^{N+2}} - (N+2)^2\frac{d_1}{r^{N+4}} + N(N+2)\frac{c_1}{r^{N+2}} \\+ (N+4)(N+2)\frac{d_1}{r^{N+4}}+ 2 \Big(- N\frac{c_1}{r^{N+2}} - (N+2)\frac{d_1}{r^{N+4}} \Big) = 0,
\end{multline*}
or
\begin{multline*}
\frac{c_1}{r^{N+2}} ( -N(N+2) + N(N+2) -2N )
\\
+ \frac{d_1}{r^{N+4}} ( -(N+2)^2 +(N+4)(N+2)- 2(N+2)) = 0,
\end{multline*}
or
\begin{equation*}
-2N\frac{c_1}{r^{N+2}} = 0,
\end{equation*}
which implies $c_1 = 0$.
{\it Case 2.} When $ R < r <1,$ we have
\begin{align*}
-2N\frac{c_2}{r^{N+2}} = -2N\frac{\widetilde{c}}{r^{N+2}},
\end{align*}
which implies $c_2 = - \widetilde{c}$.
\\
Moreover, using \eqref{fed6} in \eqref{fed5}, we get\\
{\it Case 1.} When $ r < R$, we have
\begin{align*}
\alpha &\Big[ 2\Big(b_1 + \frac{d_1}{r^{N+2}}\Big)\delta_{kl} - N^2\frac{p_1}{r^{N+2}} + N(N+2)\frac{p_1}{r^{N+2}} + 2Nq_1 \Big] = - [\alpha - m + 2\alpha (\widetilde{b_1} -1)]\delta_{kl},\\
\mbox{or }\\
& \alpha ( 2 d_1\delta_{kl} - N^2p_1 + N(N+2)p_1 )\frac{1}{r^{N+2}} + \alpha( 2b_1\delta_{kl} + 2N q_1 ) = - [ \alpha - m + 2\alpha (\widetilde{b_1} -1) ]\delta_{kl},
\end{align*}
which implies that
\begin{align}\label{fed71}
d_1\delta_{kl} + Np_1 &= 0 \\
\mbox{and}\ \ \ \alpha( 2b_1\delta_{kl} + 2N q_1 ) &= - [\alpha - m + 2\alpha (\widetilde{b_1} -1) ]\delta_{kl}.\label{fed72}
\end{align}
{\it Case 2.} When $R < r < 1$, we have
\begin{align*}
\beta \Big[ 2\big(b_2 + \frac{c_2}{r^N} + \frac{d_2}{r^{N+2}}\big)\delta_{kl} + 2N\frac{p_2}{r^{N+2}} + 2Nq_2 \Big] = - \Big[ \beta - m + 2\beta \big( \widetilde{b_2} -1 + \frac{\widetilde{c}}{r^N}\big) \Big]\delta_{kl},
\end{align*}
then, by using $c_2 = - \widetilde{c}$, it gives
\begin{align}\label{fed81}
d_2\delta_{kl} + Np_2 &= 0 \\
\mbox{and}\ \ \beta( 2b_2\delta_{kl} + 2N q_2 ) &= - [ \beta - m + 2\beta (\widetilde{b_2} -1) ]\delta_{kl}.\label{fed82}
\end{align}
\textbf{Step 3) Boundary Conditions: \\
i) Transmission conditions: }\\
\textit{a) Continuity of the $w_{kl}$ over the inner boundary at $r=R$:}
\begin{align}\label{fed91}
b_1 + \frac{d_1}{R^{N+2}} &=\ b_2 + \frac{-\widetilde{c}}{R^N} + \frac{d_2}{R^{N+2}}, \\
\Big(\frac{p_1}{R^N} + q_1R^2 + t_1\Big)\delta_{kl} &=\Big(\frac{p_2}{R^N} + q_2R^2 + t_2\Big)\delta_{kl}.\label{fed92}
\end{align}
\textit{b) Continuity of the flux over the inner boundary at $r=R$:}
We must rewrite the equation \eqref{auxN} in the following divergence form of
\begin{align*}
-\frac{\partial}{\partial y_m}a(r)&\Big( \frac{\partial}{\partial y_m}w_{kl}(y) + \frac{1}{2}\big((w_{e_k}(y)-y_k)\delta_{lm} + (w_{e_l}(y) - y_l)\delta_{km}\big)\Big) \\
&=\ a(r)\delta_{kl} - m\delta_{kl} + \frac{1}{2}a(r)\Big( \frac{\partial}{\partial y_k} (w_{e_l}(y)-y_l) + \frac{\partial}{\partial y_l}(w_{e_k}(y)-y_k)\Big).
\end{align*}
So, the boundary normal flux term, which we are concerned with, becomes\begin{align*}
&a(r)\Big( \frac{\partial}{\partial y_m}( w_{kl}(y) ) + \frac{1}{2}\big((w_{e_k}(y) - y_k)\delta_{km} + (w_{e_l}(y) - y_l)\delta_{km}\big)\Big)\cdot \nu \\
&= \ a(r)\Big( \frac{\partial}{\partial y_m}( y_ky_lg(r) +h(r) ) + \frac{1}{2}\big(y_k(f(r) - 1)\delta_{km} + y_l(f(r) - 1)\delta_{km}\big)\Big)\frac{y_m}{r} \\
&=\ y_ky_l\Big( a(r)\Big( g^{\prime}(r)+ 2\frac{g(r)}{r} + \frac{f(r)-1}{r} \Big) \Big) + a(r)h^{\prime}(r).
\end{align*}
Thus, from the required continuity of the boundary normal flux over the inner boundary at $r=R$, we get
\begin{equation}\begin{aligned}\label{fed111}
\alpha \Big[ (b_1 + \frac{d_1}{r^{N+2}} )^{\prime} &+ 2\frac{(b_1 + \frac{d_1}{r^{N+2}})}{r} + \frac{(\widetilde{b_1}-1)}{r} \Big]|_{r=R} \\
&=\ \beta \Big[ \Big(b_2 + \frac{-\widetilde{c}}{r^N} + \frac{d_2}{r^{N+2}} \Big)^{\prime} + 2\frac{b_2 + \frac{-\widetilde{c}}{r^N} + \frac{d_2}{r^{N+2}}}{r} + \frac{\widetilde{b_2}+ \widetilde{-\widetilde{c}}{r^N} -1}{r} \Big]|_{r=R}\\
\end{aligned}\end{equation}
and
\begin{align}\label{fed112}
\alpha \Big( \frac{p_1}{r^N} + q_1r^2 +t_1 \Big)^{\prime}|_{r=R} \,\delta_{kl} =\ \beta \Big( \frac{p_2}{r^N} + q_2r^2 + t_2 \Big)^{\prime}|_{r=R}\, \delta_{kl}.
\end{align}
\textbf{ii) Dirichlet boundary condition:}
From the Dirichlet boundary condition of $w_{kl}$ on $\partial B(0,1),$ we get
\begin{align}\label{fed101}
b_2 - \widetilde{c} + d_2 &= 0, \\
(p_2+ q_2 + t_2)\delta_{kl} &= 0. \label{fed102}
\end{align}
\textbf{Step 4)}
The unknown constants $(b_1,d_1),(p_1,q_1,r_1)$ and $(b_2,d_2),(p_2,q_2,t_2)$ can be found uniquely by solving equations \eqref{fed71} to \eqref{fed102}. There are $10$ unknown constants, $10$ linearly independent equations. Here, $10$ coefficients
are uniquely determined, this confirms the already known fact, namely, unique solution to \eqref{auxN}.
Now, we claim that the co-normal derivative of $w_{kl}$ on $\partial B(0,1)$ is zero, i.e.
\begin{equation}
\nabla w_{kl} (y)\cdot \nu = 0 \quad\mbox{on } \partial B(0,1).
\end{equation}
Above equation \eqref{fed12} is equivalent to two linear equations involving the coefficients $(b_2,d_2)$ and $(p_2,q_2,t_2)$
\begin{align}\label{fed131}
\Big[ (b_2 + \frac{-\widetilde{c}}{r^N} + \frac{d_2}{r^{N+2}} )^{\prime} + 2\frac{b_2 + \frac{-\widetilde{c}}{r^N} + \frac{d_2}{r^{N+2}}}{r}\Big]|_{r=1} &=0 \\
\mbox{and}
\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad \Big( \frac{p_2}{r^N} + q_2r^2 + t_2 \Big)^{\prime}\ |_{r=1}\ \delta_{kl} &=0.\label{fed132}
\end{align}
In order to establish our claim we have to show with the addition of these two new linear equations \eqref{fed131}, \eqref{fed132},
totally all these $12$ linear equations \eqref{fed71} to \eqref{fed132}
form a consistent system of $10$ unknown coefficients.
To this end, (for case of computation), we replace \eqref{fed82}, \eqref{fed112} by
\eqref{fed131}, \eqref{fed132} and we solve the resulting system of $10$ equations. Their solution
is then shown to satisfy \eqref{fed82}, \eqref{fed112} as well.\\
\\
First, we determine $d_2$ from \eqref{fed131} and consequently $p_2$ and $q_2$ from \eqref{fed81} and \eqref{fed132}, respectively, to get
\begin{align}\label{fed141}
(N+2)d_2 - N\widetilde{c} =\ 0, &\quad\mbox{or}\ \ \ d_2 = \frac{N}{(N+2)}\widetilde{c},\\
d_2\delta_{kl} + Np_2 =\ 0, &\quad\mbox{or}\ \ \ p_2 = - \frac{1}{(N+2)}\widetilde{c}\ \delta_{kl},\\
(-Np_2+ 2q_2) = 0, &\quad\mbox{or}\ \ q_2= -\frac{N}{2(N+2)}\widetilde{c}\ \delta_{kl}.
\end{align}
Using them, we determine $b_2$ and $t_2$ from \eqref{fed101}, \eqref{fed102} respectively, to get
\begin{align}\label{fed15}
b_2 = \frac{2}{(N+2)}\widetilde{c},\quad t_2 = \frac{1}{2}\widetilde{c}\ \delta_{kl} .
\end{align}
Next, we consider \eqref{fed91} and \eqref{fed111} to determine $(b_1, d_1)$ and we get
\begin{equation*}\begin{aligned}
\alpha(N+2) b_1 =& \ ( \beta( \widetilde{b_2} + \frac{\widetilde{c}}{R^N} -1 ) - \alpha (\widetilde{b_1} -1 ) ) + \alpha\Big(\frac{2}{(N+2)} - \frac{1}{R^N} + \frac{N}{(N+2)}\frac{1}{R^{N+2}} \Big)\widetilde{c}\\
& + \beta \Big( \frac{4}{(N+2)} + \frac{(N-2)}{R^N} - \frac{N^2}{(N+2)}\frac{1}{R^{N+2}} \Big)\widetilde{c}
\end{aligned}\end{equation*}
and
\begin{equation*}\begin{aligned}
\alpha(N+2)\frac{d_1}{R^{N+2}} =& -( \beta( \widetilde{b_2} + \frac{\widetilde{c}}{R^N} -1 ) - \alpha (\widetilde{b_1} -1 ) ) + 2\alpha\Big(\frac{2}{(N+2)} - \frac{1}{R^N} + \frac{N}{(N+2)}\frac{1}{R^{N+2}} \Big)\widetilde{c}\\
&- \beta \Big( \frac{4}{(N+2)} + \frac{(N-2)}{R^N} - \frac{N^2}{(N+2)}\frac{1}{R^{N+2}} \Big)\widetilde{c}.
\end{aligned}\end{equation*}
Successively, we can find $p_1$, $q_1 $ and $t_1$ from \eqref{fed71}, \eqref{fed72}
and \eqref{fed92}, respectively. \\
\\
Thus we have determined all $10$ coefficients and it is remained to check that the solutions obtained
above satisfies \eqref{fed82} and \eqref{fed112}. We recall \eqref{PN2} to write as
\begin{align*}
\widetilde{b_2} -1 &=\ -\widetilde{c} \quad\mbox{and }\ \widetilde{b_1} -1 =\ \frac{(1-\theta)}{\theta}\widetilde{c}, \quad\mbox{where } \theta= R^N,\\
\ m -\beta &=\ -N\beta\widetilde{c} \quad\mbox{and } \ m-\alpha = \ \frac{(1-\theta)((N-1)\beta +\alpha)}{\theta}\widetilde{c}.
\end{align*}
Now, let us see that LHS of \eqref{fed82} is equal to
\begin{equation*}
\beta( 2b_2\delta_{kl} + 2N q_2 ) =\ \beta ( 2\frac{2}{(N+2)}\widetilde{c}\delta_{kl} - 2N\frac{N}{2(N+2)}\widetilde{c} ) = \beta (2-N)\widetilde{c}\delta_{kl}
\end{equation*}
and RHS of \eqref{fed82} is equal to
\begin{equation*}
-(\beta-m)\delta_{kl} - 2\beta(\widetilde{b_2} -1 )\delta_{kl} =\ -N\beta \widetilde{c}\delta_{kl} + 2\beta\widetilde{c}\delta_{kl}=\ \beta (2-N)\widetilde{c}\delta_{kl},
\end{equation*}
which is exactly equal to the LHS of \eqref{fed82}.
Next, we consider \eqref{fed112} and we have that:
\begin{align*}
\mbox{LHS of }&\eqref{fed112}:=\ \alpha\Big(\frac{p_1}{r^N} + q_1r^2 +t_1 \Big)^{\prime}\ |_{r=R}\ \delta_{kl} =\ \alpha\Big( -\frac{Np_1}{R^{N+1}} + 2q_1R \Big)\ =\ R\alpha\Big(\frac{d_1}{R^{N+2}} + 2q_1 \Big)\\
&=\ R\Big( \alpha\frac{d_1}{R^{N+2}} + \frac{-2\alpha b_1 - (\alpha -m) -2\alpha(\widetilde{b_1}-1)}{N}\delta_{kl} \Big)\ =\ R \beta \frac{N}{N+2} \Big(\frac{1}{R^{N+2}} -1 \Big)\widetilde{c}.\\
\mbox{RHS of }&\eqref{fed112}:=\ \beta \Big(\frac{p_2}{r^N} + q_2r^2 +t_2 \Big)^{\prime}\ |_{r=R}= \ \beta\Big( -\frac{Np_2}{R^{N+1}} + 2q_2R \Big)=\ R\beta \frac{N}{N+2} \Big(\frac{1}{R^{N+2}} -1 \Big)\widetilde{c}\\
&\quad\quad\quad= \ \mbox{LHS of }\eqref{fed112}.
\end{align*}
Therefore, all these $12$ linear equations \eqref{fed71} to \eqref{fed112} form a consistent
system for $10$ variables and which establishes our claim of
having zero Neumann data together with zero Dirichlet data on the boundary of the unit ball.
\hfill
\end{proof}
\paragraph{Resolution of \eqref{dl19}:}
Then, as we did before (see \eqref{ll6}), using $w_{kl}\in H^1_0(B(0,1))$ with $\nabla w_{kl}\cdot\nu = 0 $ on $\partial B(0,1)$,
we will define $\chi_{kl}\in H^1_{\#}(Y)$ in order to solve \eqref{dl19}. First, we define
$\widetilde{\chi_{kl} }\in H^1_{loc}(\mathbb{R}^N)$ by
\begin{align*}
\widetilde{\chi_{kl}}(y) = \varepsilon_{p}^2\ w_{kl}\Big(\frac{y-y^{p}}{\varepsilon_{p}}\Big)\ \ \mbox{ in }\ B(y^p,\varepsilon_p)\ \mbox{ a.e. in }\ \mathbb{R}^N,
\end{align*}
solving
\begin{equation}\label{auxN2} -div(a_{\mathbb{R}^N}(y)\nabla \widetilde{\chi_{kl}}(y)) = a_{\mathbb{R}^N}(y)\delta_{kl} - m\delta_{kl} - \frac{1}{2}\left( C_{l}(\chi_k) + C_{k}(\chi_l)\right) \ \mbox{ in }\mathbb{R}^N. \end{equation}
Then, we conclude that $\widetilde{\chi_{kl}}$ is a $Y$-periodic function and in order to get $\chi_{kl} \in H^1_{\#}(Y)$ with $\int_Y \chi_{kl} dy = 0 $ solving \eqref{auxN2} in $Y$,
we simply define $ \chi_{kl}(y) = \widetilde{\chi_{kl}}(y) - \frac{1}{|Y|}\int_Y \widetilde{\chi_{kl}} dy $, by restricting it in $Y$.
Subsequently, one has $X^{(2)}_Y= \eta_k\eta_l\chi_{kl}$, which solves the cell-problem \eqref{dl19}.
\paragraph{Expression for $d_{PHS}$:}
Hence, the integral identity \eqref{dphs}
of $d_{PHS}$ becomes
\begin{equation*}\begin{aligned}
-|Y|\cdot d_{PHS}\ \eta^4 &=\ \int_{Y} \mathcal{A}_Y\Big( X^{(2)}_Y -\frac{(X^{(1)}_Y)^2}{2}\Big)\cdot\Big( X^{(2)}_Y -\frac{(X^{(1)}_Y)^2}{2}\Big) dy\\
&= \sum_p \varepsilon_p^{N+2}\cdot \int_{B(0,1)} \mathcal{A}_{B(0,1)} \Big( X_{B(0,1)}^{(2)} - \frac{(X_{B(0,1)}^{(1)})^2}{2}\Big) \cdot\Big( X_{B(0,1)}^{(2)} - \frac{(X_{B(0,1)}^{(1)})^2}{2}\Big) dy.
\end{aligned}\end{equation*}
\textbf{Elimination of }$X_{B(0,1)}^{(2)}$:
We simplify the above expression to express it solely depending on $X^{(1)}_{B(0,1)}$ by eliminating $X^{(2)}_{B(0,1)}$.
Let us define
$\widetilde{X}_{B(0,1)} = X^{(2)}_{B(0,1)} -\frac{(X^{(1)}_{B(0,1)})^2}{2}$, then
using \eqref{ED7} and \eqref{auxN}, we write
\begin{equation}\label{phs3}
-div(a_B(y)\nabla \widetilde{X}_{B(0,1)}(y) )= div \Big( a_B(y) \nabla \frac{(X_{B(0,1)}^{(1)}(y) +\eta\cdot y)^2}{2} \Big) - \widetilde{m}\quad\mbox{ in }\ B.
\end{equation}
It simply follows that
\begin{equation*}\begin{aligned}
div\Big( a_B(y)\nabla\frac{(w_{e_k})^2}{2}\Big) &= \ div\big(a_B(y)\nabla(w_{e_k} - y_k)\big)\cdot(w_{e_k} - y_k) + a_B(y)\nabla(w_{e_k} - y_k)\cdot\nabla(w_{e_k} - y_k)\\
&= \ -div (a_B(y)e_k)\cdot(w_{e_k} - y_k) + a_B(y)\nabla(w_{e_k} - y_k)\cdot\nabla(w_{e_k} - y_k)\\
&=\ a_B(y)(\nabla(w_{e_k} - y_k) + e_k)\cdot(\nabla(w_{e_k} - y_k) + e_k) - a_B(y) + C^B_k(w_{e_k} - y_k) \\
&= \ div \Big( a_B(y) \nabla \frac{((w_{e_k} - y_k) + y_k)^2}{2} \Big) - a_B(y) + C^B_k(w_{e_k} - y_k).
\end{aligned}\end{equation*}
Now, multiplying \eqref{phs3} by $\widetilde{X}_{B(0,1)}$, doing integration
by parts and using the fact that $X^{(1)}_{B(0,1)}= X^{(2)}_{B(0,1)}=0$ on $\partial B(0,1)$, we get
\begin{equation*}\begin{aligned}
|Y|\cdot d_{PHS}\ \eta^4 = \ \sum_p \varepsilon_p^{N+2}\Bigg[\int_{B(0,1)} a_B(y)\nabla \frac{(X^{(1)}_{B(0,1)}+\eta\cdot y)^2}{2}&\cdot\nabla\Big( X^{(2)}_{B(0,1)} -\frac{(X^{(1)}_{B(0,1)})^2}{2}\Big) \\ - &\widetilde{m}\int_{B(0,1)} \frac{(X^{(1)}_{B(0,1)})^2}{2} dy\Bigg].
\end{aligned}\end{equation*}
Then, multiplying \eqref{phs3} by $\frac{(X^{(1)}_{B(0,1)}+\eta\cdot y)^2}{2}$, doing the integration by parts and using the fact that
$X^{(1)}_{B(0,1)}=0$ and $\nabla X^{(2)}_{B(0,1)}\cdot\nu=0$ on $\partial B(0,1)$, we finally get
\begin{equation}\label{phsd}\begin{aligned}
-d_{PHS}\ \eta^4\cdot|Y| = \ \sum_p \varepsilon_p^{N+2}\Bigg[\int_{B(0,1)} a_B(y)&\nabla \frac{(X^{(1)}_{B(0,1)}+\eta\cdot y)^2}{2}\cdot \nabla \frac{(X^{(1)}_{B(0,1)}+\eta\cdot y)^2}{2} dy\\
+ &\widetilde{m}\int_{B(0,1)}\frac{(X^{(1)}_{B(0,1)})^2}{2} dy\Bigg].
\end{aligned}\end{equation}
\textbf{Final expression for $d_{PHS}$:}
Moreover, due to explicit formula of the solution $X^{(1)}_{B(0,1)}= \eta_k(w_{e_k}(y)-y_k)\ $ (see \eqref{ED5}) and taking $\eta = e_k$, we express \eqref{phsd} as follows:
\begin{equation}\begin{aligned}\label{frN}
-2|Y|\cdot d_{PHS}=\ \sum_p &\varepsilon_p^{N+2} \cdot \ \Bigg[ \int_{B(0,R)}{\widetilde{b_1}}^2(m-\alpha {\widetilde{b_1}}^2) y_k^2\ dy \\
& + \int_{B(0,1)\smallsetminus B(0,R)} \Big( m-\beta\big( \widetilde{b_2} + \frac{\widetilde{c}}{r^N}\big)^2 \Big|\nabla \Big(y_k\big(\widetilde{b_2} +\frac{\widetilde{c}}{r^N}\big)\Big) \Big|^2 \Big) y_k^2\ dy \Bigg],
\end{aligned}\end{equation}
where $\widetilde{b_1}$, $\widetilde{b_2}$, $\widetilde{c}$ are known in terms of given data $\alpha, \beta, \theta$ and $N$ found in \eqref{PN2}.
\noindent
\begin{remark}
It is already known from the expression \eqref{dphs} (or \eqref{phsd})
that the dispersion tensor $d_{PHS}$ is a non-positive definite tensor.
Moreover, the expression \eqref{phsd} tells us that $d_{PHS}$ depends upon only
on the scales $\{ \varepsilon_p \}_{p\in K}$, not on the translations $\{ y^p \}_{p\in K}$.
The last aspect
signifies the following property of $d_{PHS}$: position of balls in a
micro-structure is not important; what matters is only their radii. Thus, two
Hashin-Shtrikman micro-structures consisting of different arrangements of
core-coating balls, but having the same set of radii, have the same value of
the Bloch dispersion coefficient $d_{PHS}$. This aspect of Hashin-Shtrikman micro-structure
is not obvious to start with. Thus, even though $d_{PHS}$ varies among Hashin-Shtrikman
structures, its variation is somewhat
special: it does not depend on position of centers of balls in the micro-structure;
it depends only on radii. Recall that the homogenized coefficient $m$ depends only on $\{\alpha,\beta,\theta,N\}$,
but independent of radii $\{\varepsilon_p\}_{p\in K}$ and centers $\{y^p\}_{p\in K}$.
\end{remark}
The above computation reduced the original problem which was posed on micro-structures, to space
of sequences $l^1$ (cf. `Conjecture' at the end of the Section 3). As long as the macro quantity $(\widetilde{b_1}, \widetilde{b_2},\widetilde{c})$
are getting fixed through \eqref{PN2}, from the expression \eqref{frN} we can compute
$d_{PHS}$ explicitly and moreover, due to the negativity of the dispersion tensor, it
will be maximized or minimized whenever $\underset{p}{\sum} \varepsilon_p^{N+2}$ is
got minimized or maximized, respectively under the constraint
$\underset{p}{\sum} \varepsilon_p^N = c_N$ (a dimension constant).
As a next step, we exploit the properties of $l^1$ to prove existence of minimizers.
\section{Proof of the Conjecture}
\setcounter{equation}{0}
Let us consider a Vitali covering of $Y=[0,1]^N$ with a countable infinite union
of disjoint balls with center $y^p$ and radius $\varepsilon_p$, where
$p\in K$, i.e. $meas\big(Y\smallsetminus \underset{p\in K}{\cup} (B(y^p,\varepsilon_p)\cap Y)\big)=0$.
We first rearrange the sequence $\{\varepsilon_{p}\}_{p\in K}$ to make it as a decreasing sequence,
i.e., $\varepsilon_1 \geq \varepsilon_2 \geq \ldots \geq \varepsilon_p \geq \ldots $ Let us define $d_p = \frac{\varepsilon_p^N}{c_N} $, with $d_1 \geq d_2 \geq \ldots \geq d_p \geq \ldots $.
Then, we want to minimize $I = -c_N^{\frac{N+2}{N}}\underset{p}{\sum} d_p^{\frac{N+2}{N}} $,
under the constraint $\underset{p}{\sum} d_p = 1$:
\begin{center}
\textit{Minimization of $I = -c_N^{\frac{N+2}{N}}\underset{p}{\sum} d_p^{\frac{N+2}{N}} $ under the constraint $\underset{p}{\sum}d_p = 1$. }
\end{center}
\noindent
\textbf{Difficulties with the minimization problem:}\\
The peculiarity of our problem is that it is concerned with a (constrained) minimization of a strictly
concave functional over the unit sphere of $l^1$ (the unit sphere
representing the constraint set). From the point of view of Functional
Analysis, difficulties with the existence of a minimizer are
well-known, owing to the non-reflexivity of $l^1$. In general, working in such
spaces, a bounded sequence may not have any weakly converging subsequence
and even if it has one, we cannot conclude it satisfies the
constraint.\\
\\
\textbf{Existence of Minimizers:}\\
Fortunately, in our case, the criterion of de la Vallee Pousin \cite[Page no. 19]{MP}
is applicable and it guarantees $l^1$-weak compactness of a
minimizing sequence. It is also known that weak and norm convergences are
equivalent in the case of $l^1$. These arguments establish that any
minimizing sequence has a converging subsequence in $l^1$ and, so, a minimizer
satisfying the constraint exists.\\
\\
\textbf{Uniqueness Issue:}\\
However, uniqueness is an issue since we have a strictly
concave functional to minimize. Uniqueness of the minimizer can however be
proved using other arguments below. Combining both results, we
obtain that the entire minimizing sequence is $l^1$ strongly convergent.
It is not clear how uniqueness can be proved by analytical method.
However, with a geometric point of view, we can settle both existence and
uniqueness of minimizer. This is done in the sequel:\begin{figure}
\begin{center}
\includegraphics[width = 6cm]{ball_cover.pdf}
\caption{Apollonian-Hashin-Shtrikman structures in $Y$.}
\end{center}
\end{figure}
\paragraph{Existence and Uniqueness via Geometrical Method:}
\noindent
For a geometrical picture, we ask the reader to imagine the flat torus
obtained by identifying the opposite sides of the cell $Y=[0,1]^N$.
We have already seen that the dispersion coefficient $d_{PHS}$ is
invariant under translation, and as $Y$ is identified with $\mathbb{R}^N$ through $\mathbb{Z}^N-$translation invariance.
Then, we first find a Hashin-Shtrikman construction to cover the whole space $\mathbb{R}^N$ and if it is invariant
under $\mathbb{Z}^N-$translations, then we will consider it as a Hashin-Shtrikman structure for $Y$ and conversely.
Note that it is enough to consider decreasing sequences of
non-negative numbers in the minimization process. These numbers represent
the radii of balls in the Hashin-Shtrikman micro-structure.
Finding the first element of the minimizer, being the
highest, amounts to putting a ball with maximum radius $\big(\varepsilon_1^{*} = \frac{1}{2}\big)$
inside the torus. It is geometrically clear that this ball (and hence its radius) is uniquely
determined. In the second step, the same pattern is repeated: the second
element of the minimizer, being the next highest, represents the radius $\big(\varepsilon_2^{*} = \frac{\sqrt{2}-1}{2}\big)$
of the biggest ball embedded in the complement of the previous
ball. Again, this is unique. In the third step, we observe that there
is no uniqueness and in fact there are four balls of maximum radii
$\big(\varepsilon_3^{*} = \frac{(\sqrt{2}-1)(2\sqrt{2}-1)}{14}\big)$,
which can be placed in the complement of the union of the first and the second
balls. The radii of these four balls are however equal. This amount to
saying that the third, fourth, fifth, sixth elements of the minimizer are
equal. The above argument can be repeated at every subsequent step and this
procedure identifies the \textit{Apollonian-Hashin-Shtrikman} micro-structures (Figure 2)
as the unique solution of our geometric problem. The radii $\{\varepsilon_p^{*}\}_{p\in K}$ of the balls thus
obtained provide the minimizer for our constrained minimization problem.
Hence, we denote the minimum value as $I_{min}= -c_N^{\frac{N+2}{N}} \underset{p}{\sum} (\varepsilon_p^{*})^{N+2}$.
\paragraph{Optimal bounds on $I$:}
We have found the minimum value of $I$ with its unique minimizer, next we find its maximum value under the constraint $\sum_p d_p =1$. We simply see that
\begin{center}
$I = -\ c_N^{\frac{N+2}{N}}\underset{p}{\sum} d_p^{\frac{N+2}{N}} \leq -c_N^{\frac{N+2}{N}}d_1^{\frac{2}{N}}. $
\end{center}
Clearly, $d_1>0$ can be chosen arbitrarily small. Thus, $0$ is the supremum value of $I$
and it is not the maximum value of $I$. So, unlike to the previous case of minimization, here the maximizer doesn't
exist in the classical micro-structures. In particular, we have a bound for $I$, that is, $I \in [I_{min},0)$.
\hfill
\qed
\subsection*{Acknowledgments} The authors thank support from ECOS-CONICYT Grant~C13E05.
The second author is partially supported by PFBasal-001 and PFBasal-003 projects and by Fondecyt Grant~N$^\circ$1140773. PFBasal-001 also partially supports the fourth author.
\bibliographystyle{plain}
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Cari Champion [ESPN] Age, Height, Net Worth & Dating Info
Cari Champion made a name for herself as an ESPN sportscaster...joined the ESPN team in 2012...covered some of the biggest sports and entertainment news...her career in ESPN...left ESPN in...her net worth...her bio reveals her age and height...details about her dating life...was dating a fellow ESPN personality named...mentioned her boyfriend in...more about her...
Profession Journalist
Boyfriend/Dating Not Known
Ethnicity Afro-American
Height 6 Feet 1 Inch (185 cm)
Education University of California, Los Angeles
Parents Dylan Champion (Father), Mariah Champion (Mother)
American journalist, Cari Champion, made a name for herself as an ESPN sportscaster. Since joining the ESPN team, she has covered some of the biggest sports and entertainment news. Also, she served as a host of the show named Sports Nation.
Besides, she has also stepped her foot in the entertainment industry. Some of her TV series credits include Dirty Sexy Money (2008), The Young and the Restless (2009), CSI: Miami (2012), and Grown-ish (2018).
Bio (Age) Plus Parents
Cari Champion was born in California on 1 June 1975 as Cari Racquel Brooks. Her birth sign is Gemini.
Also An ESPN's Employee: ESPN's Eduardo Perez Bio: Age, Wife, College, Height & Facts
Her father, Dylan Champion, and mother Mariah Champion raised her in Pasadena. Her ethnicity is African-American. For her education, she attended the University of California, Los Angeles (UCLA), and graduated with a degree in English and a minor in Mass Communications.
Who Is Cari Champion Dating? Her Personal Life
On the Twitter post on 26 May 2014, Cari Champion officially mentioned the fellow ESPN news personality, Ryen Russillo, as her significant other.
Furthermore on a Twitter post of 23 April 2015, while referencing to Ryen, she said that:
he's my boyfriend so he says nice things. I paid him to say that.
Cari Champion with her partner, Ryen Russillo on 26 May 2014 (Photo: Cari Champion's Twitter)
Cari and Ryen had even worked together for a few shows while working at ESPN.
However, the duo hasn't been giving any sorts of hints regarding their relationship lately.
Career At ESPN
After initiating her broadcasting career, Cari Champion worked for different channels like Starz Network, The Insider, and Hollywood 411. During that time, she moved to various places such as West Virginia, California, and Florida.
Later, her career at ESPN began in October 2012, as a host plus moderator of First Take. After seeing her dedication towards work, she was promoted as an anchor of SportsCenter in July 2015. Seven months later, in February 2016, she was again appointed as a SportsCenter Coast to Coast's Anchor—there she co-hosted with David Lloyd.
A Talented Actor: Paul Marcarelli Wiki: Age, Net Worth & Sexuality
After serving for more than two years, Cari was finally hired as the host of Sports Nation in March 2018. Afterward, she continued to showcase her skills plus talent and continued to take ESPN into the higher limits.
However, on 10 January 2020, Cari tweeted heartbreaking news for her fans. In the tweet, she revealed that she would be leaving ESPN.
As per Celebrity Net Worth, the American journalist plus TV personality, Cari Champion has managed to make a healthy net worth of $2 million. She reportedly receives an annual salary of $1 million from her career.
Five Interesting Facts About Cari Champion
Cari shares a good bond with her parents. On 14 May 2018, she shared an old picture of her mother on the occasion of mother's day.
She has garnished more than 247.9 thousand followers in her Twitter account only.
She has also covered news for ABC, CBS, and NBC.
In 2016, she had signed a multi-year contract with ESPN.
She stands at a towering height of 6 feet 1 inch (1.85 meters).
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\section{Introduction}\label{sec:intro}
Federated learning (FL) is a privacy-preserved distributed learning paradigm. Throughout, we focus on the specific notion of FL proposed by by \citep{aopfl},
\begin{quote}
\emph{\textbf{Federated learning} is a machine learning setting where multiple entities (clients) collaborate in solving a machine learning problem, under the coordination of a central server or service provider. Each client's raw data is stored locally and not exchanged or transferred; instead, focused updates intended for immediate aggregation are used to achieve the learning objective.}
\end{quote}
FL enables learning effective models across wide populations and varied data sources, while still preserving the privacy of each individual client. In comparison to other distributed learning frameworks, some challenges become much more prominent in federated learning, including constraints on communication, client memory usage, and privacy~\citep{aopfl}. Another key facet of federated learning is \emph{data heterogeneity}. Clients typically have different distributions and quantities of local data, and learning across these diverse datasets under the aforementioned constraints can be challenging. In this work, we will focus primarily on \emph{cross-device} FL, in which clients are typically edge devices with limits on download bandwidth, storage, compute, and upload bandwidth~\citep[Table 1]{aopfl}.
One notable method for performing federated learning is \emph{federated averaging} (FedAvg)~\citep{mcmahan2017aistats}. While many other optimization methods for FL have since been proposed~\citep{reddi2021adaptive, karimireddy2020mime, li2018federated}, many of these can be parameterized in a thematically similar manner. In general, these methods perform multiple rounds of training, which can roughly be broken down into broadcast, client training, aggregation, and server update stages. In short, the server possesses a global model that is broadcast to the clients, which then update the model according to their own data. The resulting local models are aggregated by the server, and the result of this is used to update its global model.
We now arrive at an important challenge for cross-device FL: While machine learning has moved towards larger and larger models, especially in natural language processing domains~\citep{dai2019transformer, devlin2018bert, yang2019xlnet, kaplan2020scaling, irie2019language}, this movement is predicated on the availability of hardware with sufficient storage and compute capacity. By contrast, clients in cross-device FL systems often have limited compute and storage, as well as constraints on the amount of data they can download and upload. Thus, without any extra modifications, algorithms like FedAvg may require using smaller models than if we were simply training in a data-center~\citep{ro2022scaling}.
While compression techniques can help reduce communication costs in cross-device settings~\citep{sattler2019robust, haddadpour2020fedsketch, reisizadeh2020fedpaq, rothchild2020fetchsgd, mitchell2022optimizing}, they often do not provide mechanisms for training in more memory-efficient ways. While approaches like knowledge distillation and student-teacher models have shown great promise in reducing client model sizes~\citep{li2019fedmd}, such approaches often require artifacts like public data that may not be present in many tasks. Similarly, a number of works have validated that partial model training approaches can often allow clients to only train a much smaller portion of the server model~\citep{ro2022scaling, liang2020think, yang2022partial}. However, such approaches still require transmitting the entire server model in full, and as such may simply not fit in memory on some clients. In general, the approaches above may often communicate the full model to a client, \emph{even parts of the model that are not needed by a given client}. For example, a client with sparse features may only require the portion of the model relevant to those features.
In this work, we explore an algorithmic framework for FL that allows us to train large server models while enforcing limits on client communication, computation, and storage. Our approach allows the server to train models far larger than the clients are able to download, train, or upload. We propose a novel primitive we refer to as \emph{federated select}. This primitive allows each client to select a sub-model of the server model that will be used for local training. Notably, these sub-models can be significantly smaller, and therefore are more amenable to cross-device FL. Moreover, federated select allows clients to select different sub-models, which can be crucial due to the aforementioned data heterogeneity. This framework is fully compatible with existing optimization frameworks for FL, as well as communication compression methods.
\section{Background}\label{sec:background}
\subsection{Federated Computations}
\newcommand{\texttt{@S}\xspace}{\texttt{@S}\xspace}
\newcommand{\texttt{@C}\xspace}{\texttt{@C}\xspace}
In order to formalize the notion of data location in a federated system, we define the concept of \textbf{federated values}. Our framing and exposition here is building on analogous notions defined first in the TensorFlow Federated framework~\citep{tff}. Federated values are data hosted across a group of devices in a distributed system. For our purposes, we will only consider two possible placements of a value:
\begin{enumerate}
\item A value located at the (conceptually) singleton server (server-placed). We will use the shorthand $x\texttt{@S}\xspace$ to denote a value $x$ placed at the server.
\item A value located at all clients participating in a computation (client-placed). We model the collection of values across all available clients as a \emph{single} federated value. We use the shorthand $\{x_1, \dots, x_N\}\texttt{@C}\xspace$ to denote a a client-placed federated value as where $x_i$ is the value held by client $i$.
\end{enumerate}
Given the above, a \textbf{federated computation} is a function whose inputs and outputs are federated values. Note that unlike federated values, federated computations do not have an inherent placement. By contrast, non-federated computations can only modify the value, not the placement. When writing non-federated computations, we will omit the \texttt{@S}\xspace and \texttt{@C}\xspace designations.
For example, suppose our client devices are all temperature sensors, each with some temperature reading $t_n$. Then the corresponding federated value is the set $\{t_1, \dots, t_N\}\texttt{@C}\xspace$. The definition of federated learning suggests that the server cannot access individual values in this set, but can compute aggregates such as the average temperature across clients. Thus, we may be interested in the federated computation which maps client-placed temperatures to their server-placed average, that is
\[
\{t_1, \dots, t_N\}\texttt{@C}\xspace \mapsto \left(\dfrac{1}{N}\sum_{n=1}^N t_n \right)\texttt{@S}\xspace.
\]
However, clients could first compute some local function $f(t_n)$ of their temperature value (for example, rounding to the nearest integer) and then take a ``federated mean'', which we would denote
\[
\{t_1, \dots, t_N\}\texttt{@C}\xspace \mapsto \left(\dfrac{1}{N}\sum_{n=1}^N f(t_n) \right)\texttt{@S}\xspace.
\]
Note that in this context, $f$ is a non-federated computation, only changing the value of the temperature readings locally.
This abstraction helps encode the data restrictions in federated learning and understand possible implementations. For example, a federated computation whose inputs and outputs are all placed at the server would have no need for communication between clients and server, while functions with mixed placement usually incur some form of communication between clients and server.
In order to describe algorithms that involve clients and a server, we will formalize two standard FL primitives: \textsc{Broadcast}\xspace and \textsc{Aggregate}\xspace. \textsc{Broadcast}\xspace is simply a federated computation that takes $x\texttt{@S}\xspace$ and returns $\{x, x, \dots, x\}\texttt{@C}\xspace$. Notably, each client receives the same value under this function. \textsc{Aggregate}\xspace effectively does the reverse. It takes as input $\{x_1, \dots, x_N\}\texttt{@C}\xspace$, and produces some aggregate $y\texttt{@S}\xspace$. For simplicity, we focus on the specialization of \textsc{Aggregate}\xspace that computes the mean over the client values, which we denote \ensuremath{\textsc{Aggregate}_{\textsc{mean}}}\xspace, but the discussion is valid for many other types of operations. Formally, we define \textsc{Broadcast}\xspace and \ensuremath{\textsc{Aggregate}_{\textsc{mean}}}\xspace via
\begin{equation}\label{eq:broadcast_and_aggregate}
\textsc{Broadcast}\xspace(x\texttt{@S}\xspace) = \{x, x, \dots, x\}\texttt{@C}\xspace,~~~\ensuremath{\textsc{Aggregate}_{\textsc{mean}}}\xspace(\{x_1,\dots, x_N \}\texttt{@C}\xspace) = \left(\dfrac{1}{N}\sum_{n=1}^N x_n\right)\texttt{@S}\xspace.
\end{equation}
While we assume a fixed number of clients $N$ for notational simplicity, in general the server will not know how many clients actually successfully contributed to a round until after the rounds execution completes, due to client failures and dropouts, etc.
In general, other reduce-like operations could be used for \textsc{Aggregate}\xspace, as could non-linear operations such as applying some robust estimator.
\subsection{Federated Model Training}\label{sec:federated_model_training}
Federated learning methods often aim to learn a global "server model" that minimizes the expected loss of a function across some (generally unknown) distribution $\mathcal{P}$ of clients:
\[
\min_{x \in \mathbb{R}^s} f(x)~~~~\text{where}~~~~f(x) := \mathbb{E}_{n \sim\mathcal{P}} [f_n(x)]
\]
where $\mathbb{R}^s$ is the model space and $f_n: \mathbb{R}^s \to \mathbb{R}$ is the loss function for client $n$. Due to data restrictions, clients cannot directly share their loss functions $f_n$. Instead, most methods (including the de facto standard, FedAvg~\citep{mcmahan2017aistats}) operate in the following general manner: The server has a global model $x$, which at each round uses \textsc{Broadcast}\xspace to send $x$ to some set of available clients (referred to as a \emph{cohort}~\citep{charles2021large}). The clients in the cohort use their local loss function $f_n$ to compute some \emph{model update} $u_n = \textsc{ClientUpdate}\xspace(x, f_n)$.
The server then receives the result of \ensuremath{\textsc{Aggregate}_{\textsc{mean}}}\xspace applied to these client updates, which we refer to as the \emph{server update} $u$. Finally, the server uses some subroutine $\textsc{ServerUpdate}\xspace(x, u)$ to update its own global model. Pseudo-code for this procedure is given in \cref{alg:model_train}.
\begin{algorithm}[t]
\begin{algorithmic}
\caption{Federated Model Training}
\label{alg:model_train}
\STATE {\bf Input:} \textsc{ClientUpdate}\xspace, \textsc{ServerUpdate}\xspace, $T \in \mathbb{Z}_{\geq 1}, x^0 \in \mathbb{R}^s$
\FOR {$t = 1, \dots, T$}
\STATE Sample a set $S^t$ of available clients
\FOR{each client $n \in S^t$ \textbf{in parallel}}
\STATE Receive $x^t$ via \textsc{Broadcast}\xspace
\STATE $u_n^{t} = \textsc{ClientUpdate}\xspace(x^t, f_n)$
\ENDFOR
\STATE Server receives $u^t\texttt{@S}\xspace = \ensuremath{\textsc{Aggregate}_{\textsc{mean}}}\xspace(\{u_n^t : n \in S^t\}\texttt{@C}\xspace)$
\STATE $x^{t+1} = \textsc{ServerUpdate}\xspace(x^t, u^t)$
\ENDFOR
\end{algorithmic}
\end{algorithm}
For example, in FedAvg, $\textsc{ClientUpdate}\xspace(x, f_n)$ is a model produced via $E$ epochs of mini-batch SGD on the loss function $f_n$, starting from $x$. The server updates its model to be the average of these locally updated models, so $\textsc{ServerUpdate}\xspace(x, u) = u$. Note that in realistic settings, clients may drop out during the computation~\citep{bonawitz2017practical}, so that the aggregation step may involve a system-dependent set of clients. We omit this in our discussion for simplicity of notation, but the same training algorithm applies in this setting.
Generalizations of FedAvg often use a ``model-delta'' approach. In this, $\textsc{ClientUpdate}\xspace(x, f_n)$ is the difference between $x$ and a model learned by performing $E$ epochs of mini-batch SGD on $f_n$ starting from $x$. Note that when clients do a single gradient descent step, $\textsc{ClientUpdate}\xspace(x, f_n) = \gamma\nabla f_n(x)$ where $\gamma$ is the learning rate. Thus, the average client update $u$ is a kind of approximation to $\nabla f$, and so we can let $\textsc{ServerUpdate}\xspace(x, u)$ be a first-order optimization method, treating $u$ as the gradient~\citep{reddi2021adaptive}. This allows the incorporation of techniques like adaptivity and momentum into the server update.
While often empirically effective~\citep{reddi2021adaptive}, \cref{alg:model_train} may not work in settings where the model $x$ is large. Clients may not be able to receive the model, compute $\textsc{ClientUpdate}\xspace$, or send the corresponding model update to the server. However, in certain settings, there are natural ways to use a smaller model $y$ in this training procedure, as we detail below.
\subsection{Motivating Example 1 - Logistic Regression with Sparse Features}\label{sec:sparse_log_reg}
Suppose that we wish to use \cref{alg:model_train} to perform federated logistic regression where \textsc{ClientUpdate}\xspace is the ``model-delta'' update discussed above. For simplicity, suppose that each client has a single example $v_n \in \mathbb{R}^s$, and that their loss function is $f_n(x) = \sigma(\langle x, v_n\rangle)$ where $\sigma(a)$ is the logistic loss. In order to perform \cref{alg:model_train}, each client would need to download, store, and compute inner products of $s$-dimensional vectors.
Let us now assume that for each client $n$, the example $v_n$ is supported on some smaller set of indices $A_n$. Letting $\pi_{A}(x)$ denote the restriction of a vector $x$ to the coordinates in $A$, we have
\begin{equation}\label{eq:sparse_log_reg}
\langle x, v_n\rangle = \langle \pi_{A_n}(x), \pi_{A_n}(v_n)\rangle.
\end{equation}
By linearity, we see that to compute $\nabla f_n(x)$, the client need only know $A_n$ and $\pi_{A_n}(x)$. Moreover, $\nabla f_n(x)$ can be computed in time $|A_n|$ which could be significantly smaller than $s$. Note that in applications like click-through-rate prediction, it is common to have $s \approx 10^9$ or more, with $|A_n|$ only a small constant like 100~\citep{mcmahan13ctr}.
For the sake of exposition, let us assume that the server and client both know $A_n$, and that \textsc{ClientUpdate}\xspace is some number of SGD steps. To execute \cref{alg:model_train}, the server need only send client $n$ the vector $\pi_{A_n}(x)$. By \eqref{eq:sparse_log_reg}, the client can compute $\pi_{A_n}(\textsc{ClientUpdate}\xspace(x, f_n))$, which it can then send back to the server. By assumption, gradient descent does not change the coordinates outside of $A_n$, so $\textsc{ClientUpdate}\xspace(x, f_n)$ is 0 at coordinates in the complement of $A_n$ (as we are using the model-delta \textsc{ClientUpdate}\xspace). Thus, the server can take the received $\pi_{A_n}(\textsc{ClientUpdate}\xspace(x, f_n))$, fill in zeros in all other coordinates. Thus, we can exactly recover \cref{alg:model_train}, but with a reduction in the download, storage, compute, and upload costs of each client.
In general, we say that this example exhibits \emph{fine-grained} sparsity; Clients need only operate on a moderately-sized subset of a high-dimensional vector.
\subsection{Motivating Example 2 - Conditional and Multi-modal Models}\label{sec:multi_model}
Suppose that we wish to use \cref{alg:model_train} to train models with layers that trigger conditionally depending on the input, such as ``mixture-of-experts'' models~\citep{eigen2013learning, shazeer2017outrageously}. We may also want to train multi-modal models, which perform different tasks but with shared representations. For example, \citet{zhu2022diurnal} propose the use of multi-modal models in the context of federated learning by \citet{zhu2022diurnal} in order to incorporate temporal modality among clients.
When using such models, a client may only need a small fraction of the model during training, either because its dataset only triggers a subset of the conditional layers~\citep{zhu2022diurnal}, or because it has data relevant to only a subset of the tasks performed by a multi-modal model~\citep{shazeer2017outrageously}. However, in \cref{alg:model_train}, the entire model would need to be broadcast to each client.
In order to avoid this, we would like clients to select which part of the model is relevant to them. Under this viewpoint, we say that this example exhibits \emph{coarse-grained} sparsity; The number of components to a given conditional or multi-modal model are generally much smaller than the number model parameters (eg. on the order of tens, hundreds, or thousands~\citep{eigen2013learning, shazeer2017outrageously}, not millions or billions), and clients may only need to operate on a small number of them.
\section{Federated Select}\label{sec:select}
Generalizing the examples above, we are interested in the following scenario: Suppose we have a cohort of $N$ available clients (indexed by the set $[N] = \{1, 2, \dots, N\})$. Further suppose there is $x\texttt{@S}\xspace$ (with $x \in \mathcal{X})$, and $\{z_1, \dots, z_N\}\texttt{@C}\xspace$ where $z_n \in \mathcal{Z}$. There is a function $\rho: \mathcal{X} \times \mathcal{Z} \to \mathcal{Y}$, and we would like to compute the federated computation
\begin{equation}\label{eq:generalized_select}
(x\texttt{@S}\xspace, \{z_1, \dots, z_N\}\texttt{@C}\xspace) \mapsto \{\rho(x, z_1), \dots, \rho(x, z_N)\}\texttt{@C}\xspace.
\end{equation}
In the context of \cref{sec:sparse_log_reg} and \cref{sec:multi_model}, $x$ is the server model, $z_n$ is some information that allows client $n$ to determine which part of $x$ is relevant to its data, and $\rho(x, z_n)$ is some smaller model for client $n$. However, the operation in \eqref{eq:generalized_select} is much more general than in these examples, especially as we impose no restrictions on the space $\mathcal{Z}$.
For example, one operation that fits under \eqref{eq:generalized_select} would be some operation that takes a server model $x$ and client datasets $z_1, \dots, z_N$, and fine-tunes the model on each client's dataset, sending the result back to the client. This ambiguity in the space $\mathcal{Z}$ being operated on in turn means that implementing \eqref{eq:generalized_select} in full-generality, while preserving data privacy of clients, can be challenging for any practical FL system.
In order to discuss realistic and privacy-preserving FL systems, we will consider a special-case of \eqref{eq:generalized_select} where the set $\mathcal{Z}$ of client values is \textbf{finite}, which we call \emph{federated select}.
Let $K \in \mathbb{N}$, and recall that $[K] := \{1, 2, \dots, K\}$. Let $\psi: \mathcal{X} \times [K] \to \mathcal{Y}$ be some (non-federated) function, which we will call the \emph{select function}. Intuitively, it should be thought of as selecting the $k$-th component of $x$. The server has some value $x \in \mathcal{X}$ and each client $n$ has a sequence $z_n = [z_{n, 1}, \dots, z_{n, m}] \in [K]^m$. These $z_{n, i}$ are referred to as the client's \emph{select keys}.
Federated select is the federated computation that takes $x\texttt{@S}\xspace$, $\{z_1, \dots, z_N\}\texttt{@C}\xspace$, and a selection function $\psi$, and whose output is
\begin{equation}\label{eq:federated_select}
\textsc{FedSelect}\xspace(x\texttt{@S}\xspace, \{z_1, \dots, z_N\}\texttt{@C}\xspace, \psi) = \{[\psi(x, z_{n, 1}), \dots, \psi(x, z_{n, m})] : n \in [N]\}\texttt{@C}\xspace.
\end{equation}
\begin{figure}[t]
\centering
\includegraphics[width=0.8\linewidth]{figures/federated_select.pdf}
\caption{A graphical representation of federated select. In this setting, the clients' select keys correspond to rows of the server model, which are then sent to the clients. Note that 1) clients can have overlapping keys, 2) the order of the client keys is respected by \textsc{FedSelect}\xspace, and 3) the select function $\psi(x, z)$ simply picks out the $z$-th row of $x$. More sophisticated usages of \textsc{FedSelect}\xspace could also transform the items being selected.}
\label{fig:fed_select}
\end{figure}
A graphical representation of \textsc{FedSelect}\xspace is given in \cref{fig:fed_select}. Note that \eqref{eq:federated_select} is the special-case of \eqref{eq:generalized_select} where $\rho(x, z_n) = [\psi(x, z_{n, 1}), \dots, \psi(x, z_{n, m})]$. Notably, this limits the scope of possible $\rho$ to functions that have this key-structure as in $\psi$. By restricting this scope, we are able to better ensure that $\textsc{FedSelect}\xspace$ can be computed in realistic FL systems. In fact, as we will see below, \eqref{eq:federated_select} has a number of possible implementations, each with different levels of privacy and communication.
While we suppose that all clients have $m$ keys for notational simplicity, in reality clients could have varying numbers of keys. This is in fact another benefit of \textsc{FedSelect}\xspace. In settings where devices have heterogeneous memory and computation power (eg. high-end and low-end mobile phones), we can use \textsc{FedSelect}\xspace to send models of different sizes to different clients.
Conceptually, \textsc{FedSelect}\xspace is a federated analog of gather-type primitives in machine learning (such as \texttt{tf.gather} in TensorFlow and \texttt{torch.index\_select} in PyTorch). These operations are often used by models with sparse structure, such as in looking up values in an embedding layer. However, \textsc{FedSelect}\xspace allows more generality, by allowing transformations of the gathered data (rather than just restricting to sparse access).
\subsection{Motivating Examples, Revisited}
We now discuss how \textsc{FedSelect}\xspace can be applied in the examples of Sections \cref{sec:sparse_log_reg} and \cref{sec:multi_model}.
\paragraph{Sparse logistic regression. }
Recall that in this example, the server has a logistic regression model $x \in \mathbb{R}^{s}$, and each client has a single example $v_n$ supported on a set $A_n \subseteq [s]$. For simplicity, we will assume $|A_n| = m$, but this is not strictly necessary. In this case, the client's select keys $z_n$ are simply the set $A_n$ in order as a sequence, and the function $\psi(x, i) := x_i$. In this case, $\textsc{FedSelect}\xspace(x\texttt{@S}\xspace, \{z_1, \dots, z_N\}\texttt{@C}\xspace, \psi)$ computes $\{\pi_{A_1}(x), \dots, \pi_{A_n}(x)\}\texttt{@C}\xspace$, that is, the restriction of $x$ onto the coordinates in $z_n$ for each client. In other words, \textsc{FedSelect}\xspace specializes to projecting $x$ onto each client's coordinate subspace.
\paragraph{Conditional and multi-modal models. }
In this setting, we assume that we have a server model $x$ with a shared component, and $C$ conditional components (eg. components for each possible task of a multi-task model). Let $x = (a_1, \dots, a_C, b)$ where $a_1, \dots, a_C$ are the conditional components and $b$ is the shared component. The selection key space will be $[C+1]$, and the selection function $\psi$ is defined as $\psi(x, i) = a_i$ if $i \in [C]$ and $\psi(x, C + 1) = a$. A client's select keys are the elements of $[C]$ indexing the conditional components relevant to the client, plus an extra key of $C + 1$. Note that this key is used by all clients since it corresponds to the shared component. Under this setup, \textsc{FedSelect}\xspace will exactly send to each client the conditional components relevant to the client, along with the shared component.
We note that this implicitly assumed that the client could determine the relevant conditional components of a model, without access to the global model. While this may not be true in general, for many models, especially multi-modal models, the conditional components correspond to what types of data are present in a client's dataset. For example, a language model with different components for different languages could apply in this setting, as the client can reasonably know which languages are present in its local data.
\subsection{Possible Implementation of Federated Select}\label{sec:select_impl}
We now discuss possible ways to compute \eqref{eq:federated_select} in an actual federated system. Here we will outline their various trade-offs, especially trade-offs between communication-efficiency and privacy. For more detail and a greater focus on systems challenges of these implementations, see \cref{sec:trust_models}. While each implementation has a variety of pros and cons, we will specifically focus on the communication and computation costs of each method. While we briefly mention the privacy trade-offs of each implementation, we discuss this in greater detail in \cref{sec:trust_models}.
\paragraph{Option 1: Broadcast and compute on clients.} In this implementation, the server would simply broadcast $x$ in full to the clients. Each client $n$ then computes $[\psi(x, z_{n, 1}), \dots, \psi(x, z_{n, m})]$ locally. This method fully preserves the privacy of the clients' select keys (as they never leave the device), but can incur high communication costs. In particular, there is no reduction in communication costs compared to $\textsc{Broadcast}\xspace(x\texttt{@S}\xspace)$.
\paragraph{Option 2: On-demand slice generation.} In this implementation the clients would first upload their select keys to the server. The server can then directly compute \eqref{eq:federated_select}, and send each client their resulting values. Effectively, the server would function as an on-demand service for computing \textsc{FedSelect}\xspace according to inputs uploaded by the clients. This can reduce communication costs (as the server need not send its model in full), but on-demand computation may lead to wasted computation effort if many clients are selecting the same key (e.g. if $K$ is comparable to the number of clients), or else may require a more complicated distributed caching system to avoid such re-computation. Additionally, increased care must be given to privacy risks in this implementation, as the slice computation server will have access to the client selection keys. For greater discussion of this, see \cref{sec:trust_models}.
Notably, both of the implementation options above could also be used to compute \eqref{eq:generalized_select}. However, they both come with significant downsides, both in terms of systems constraints and privacy constraints. Thus, we consider a third implementation that relies on the space of possible select keys being of moderate size (and notably, finite, as in \cref{eq:federated_select}).
\paragraph{Option 3: Pre-generation of slices.} In this implementation, the server would, before a given round of training, compute all $\psi(x, k)$ for all $k \in [K]$. It would send the values to some high-capacity content delivery network (CDN). In order to compute \eqref{eq:federated_select}, each client would simply query the content delivery network with their own select keys. In the case where most keys are selected by multiple clients, this implementation will minimize the computation cost (without need for a distributed cache or similar technique). However, if the space of keys is much larger than the number of clients, this implementation will waste significant compute resources computing unnecessary values of $\psi(x, k)$. As in Option 2, the CDN will be able to see each client's key, and so care must be given to the privacy implications. Again, see \cref{sec:trust_models} for more details.
\subsection{Relationship to Other Primitives}\label{sec:reductions}
Up to this point, we have introduced two general primitives for server-to-client communication in FL systems: \textsc{Broadcast}\xspace \eqref{eq:broadcast_and_aggregate} and \textsc{FedSelect}\xspace \eqref{eq:federated_select}. In this section we briefly discuss the relation between these and other possible operations.
First, we note that \textsc{FedSelect}\xspace is strictly more general than \textsc{Broadcast}\xspace. To see this, suppose that we wished to compute $\textsc{Broadcast}\xspace(x)$. This can be done via \textsc{FedSelect}\xspace simply by letting the select function be $\psi(x, k) = x$ and having each client select any single key, for example, $0$. Then \eqref{eq:federated_select} simply becomes
\[
\textsc{FedSelect}\xspace(x\texttt{@S}\xspace, \{0, \dots, 0\}\texttt{@C}\xspace, \psi) = \{\psi(x, 0), \dots, \psi(x, 0)\}\texttt{@C}\xspace = \{x, x, \dots, x\}\texttt{@C}\xspace.
\]
Next, we note that in many examples, there are components that we would like to apply \textsc{FedSelect}\xspace to, and others that we would like to apply \textsc{Broadcast}\xspace to; for example, we may simultaneously want to compute $\textsc{FedSelect}\xspace(x\texttt{@S}\xspace, \{k_1, \dots, k_N\}\texttt{@C}\xspace, \psi)$ and $\textsc{Broadcast}\xspace(y\texttt{@S}\xspace)$. In this case, we can combine the two operations into a single \textsc{FedSelect}\xspace, using the tuple $(x, y)$ as the model. That is, we could execute a single $\textsc{FedSelect}\xspace((x, y)\texttt{@S}\xspace, \{k_1, \dots, k_N\}\texttt{@C}\xspace, \psi')$ operation, defining
\[
\psi'((x, y), k) = (\psi(x, k), y)
\]
Similarly, we note that two applications of \textsc{FedSelect}\xspace can be merged, even if they operate on different key spaces. Suppose we wish to compute
\[
m^{(1)} = \textsc{FedSelect}\xspace(x^{(1)}\texttt{@S}\xspace, \{k^{(1)}_1, \dots, k^{(1)}_N\}\texttt{@C}\xspace, \psi^{(1)});~~~k^{(1)}_n \in [K^{(1)}]
\]
\[
m^{(2)} = \textsc{FedSelect}\xspace(x^{(2)}\texttt{@S}\xspace, \{k^{(2)}_1, \dots, k^{(2)}_N\}\texttt{@C}\xspace, \psi^{(2)});~~~k^{(2)}_n \in [K^{(2)}]
\]
We can replace these two instances of \textsc{FedSelect}\xspace with a single \textsc{FedSelect}\xspace operating on a keyspace $[K^{(1)}] \times [K^{(2)}]$:
\[
(m^{(1)},m^{(2)}) = \textsc{FedSelect}\xspace(
(x^{(1)}, x^{(2)})\texttt{@S}\xspace,
\{(k^{(1)}_1,k^{(2)}_1), \dots, (k^{(1)}_N,k^{(2)}_N) \}\texttt{@C}\xspace, \psi')
\]
defining\footnote{In order to maintain an integer keyspace, we can interpret $(k^{(1)}, k^{(2)})$ as an integer in mixed-radix notation, in $[K^{(1)} \cdot K^{(2)}]$}:
\[
\psi'((x^{(1)}, x^{(2)}), (k^{(1)}, k^{(2)})) = (\psi^{(1)}(x^{(1)}, k^{(1)}), \psi^{(2)}(x^{(2)}, k^{(2)}))
\]
Finally, we note that applying $\textsc{FedSelect}\xspace$ with multiple keys can be subsumed by a select call where each client has a single key. To see this, suppose that each client has $m$ keys $z_n = [z_{n, 1}, \dots, z_{n, m}]$ that it would like to use in \textsc{FedSelect}\xspace (with select function $\psi$), with each key in $[K]$. We can simply order all possible sets of this form, so that client $n$ has a single key $z_n' \in [K^m]$ representing this ordered sequence. By defining $\psi'(x, z_n')$ accordingly, then we have
\[
\textsc{FedSelect}\xspace(x\texttt{@S}\xspace, \{z_1, \dots, z_N\}\texttt{@C}\xspace, \psi) = \textsc{FedSelect}\xspace(x\texttt{@S}\xspace, \{z_1', \dots, z_N'\}\texttt{@C}\xspace, \psi')
\]
where each $z_n'$ is a single key instead of $m$ keys. While conceptually useful, this may be inefficient from a systems standpoint, particularly with respect to pre-generation of slices where it might require $K^m$ slices instead of $K$.
\section{Model Training with Federated Select}\label{sec:select_training}
We now re-focus our attention on federated model training. In particular, we would like to incorporate \textsc{FedSelect}\xspace into \cref{alg:model_train}, in order to improve communication-efficiency and client memory usage. Recall that in \cref{alg:model_train}, we assume that given a model $x \in \mathbb{R}^s$ and some loss function $f_n: \mathbb{R}^s \to \mathbb{R}$, each client can compute $\textsc{ClientUpdate}\xspace(x, f_n) \in \mathbb{R}^s$.
We now assume that $s$ is sufficiently large such that $x \in \mathbb{R}^s$ does not fit on client devices. Instead, let us assume that we have some select function $\psi$ such that given select keys $[z_{n, 1}, \dots, z_{n, m}]$ for client $n$, the vector $y_n = [\psi(x, z_{n, 1}), \dots, \psi(x, z_{n, m})]$ is an element of $\mathbb{R}^c$ where $c \ll s$. In other words, the result of \textsc{FedSelect}\xspace produces a smaller $c$-dimensional vector. Note that in full generality, there could also be components of the model $x$ that are broadcast to the client without the use of \textsc{FedSelect}\xspace.
Analogous with \cref{alg:model_train}, we will assume that each client also has a loss function $g_n: \mathbb{R}^c \to R$, and can compute a local update $u_n = \textsc{ClientUpdate}\xspace(y_n, g_n) \in \mathbb{R}^c$. However, we must now take pause. Recall that in \cref{alg:model_train}, the server receives the average of all the client updates. With \textsc{FedSelect}\xspace, averaging the client model updates may no longer be meaningful, as they can correspond to updates to different parts of the model.
In order to actually update the server's model, we will need a kind of inverse to \textsc{FedSelect}\xspace in \eqref{eq:federated_select}. Motivated by the aggregation step in \cref{alg:model_train}, we assume that there is a ``deselection'' function $\phi: \mathbb{R}^c \times [K]^m \to \mathbb{R}^s$ mapping a ``small'' model and some selection keys to a large model. We can then extend \ensuremath{\textsc{Aggregate}_{\textsc{mean}}}\xspace to take the deselection function $\phi$ as an argument, computing:
\begin{equation}\label{eq:deselect}
\ensuremath{\textsc{Aggregate}_{\textsc{mean}}^{\star}}\xspace(\{u_1, \dots, u_N\}\texttt{@C}\xspace, \{z_1, \dots, z_N\}\texttt{@C}\xspace, \phi) = \left(\dfrac{1}{N}\sum_{n=1}^N \phi(u_n, z_n)\right)\texttt{@S}\xspace.
\end{equation}
Just as with the specialization of \textsc{Aggregate}\xspace in \eqref{eq:broadcast_and_aggregate}, the use of averaging here is not strictly necessary; any \textsc{Aggregate}\xspace function can be similarly extended. Once the server receives the $s$-dimensional update to its own model from \ensuremath{\textsc{Aggregate}_{\textsc{mean}}^{\star}}\xspace, it can use then use with \textsc{ServerUpdate}\xspace (as in \cref{alg:model_train}). Putting this all together, we can perform model training with federated select. Pseudo-code for this is given in \cref{alg:select_model_train}. We note a few immediate advantages to this framework:
\begin{itemize}
\item When $c \ll s$, this can reduce memory and computational costs on clients substantially.
\item The reduction in communication can be used in tandem with compression methods in order to further reduce communication. For example, we could use a select function $\psi$ in \cref{eq:federated_select} that extracts some index from $x$ and then applies quantization.
\item This approach can be immediately integrated with other existing \textsc{ClientUpdate}\xspace (which uses SGD with an extra proximal term) or first-order optimization in \textsc{ServerUpdate}\xspace (as in methods like FedAdam).
\end{itemize}
\begin{algorithm}[t]
\begin{algorithmic}
\caption{Federated Model Training with Federated Select}
\label{alg:select_model_train}
\STATE {\bf Input:} \textsc{ClientUpdate}\xspace, \textsc{ServerUpdate}\xspace, $T \in \mathbb{Z}_{\geq 1}, x^0 \in \mathbb{R}^s$
\FOR {$t = 1, \dots, T$}
\STATE Sample a subset $S^t$ of available clients
\FOR{each client $n \in S^t$ \textbf{in parallel}}
\STATE Choose select keys $z_n^t = [z_{n, 1}^t, \dots, z_{n, m}^t] \in [K]^m$
\STATE Receive $y_n^t = [\psi(x^t, z_{n, 1}^t), \dots, \psi(x^t, z_{n, m}^t)]$ via \textsc{FedSelect}\xspace
\STATE $u_n^{t} = \textsc{ClientUpdate}\xspace(y_n^t, g_n)$
\ENDFOR
\STATE Server receives $u^t\texttt{@S}\xspace = \ensuremath{\textsc{Aggregate}_{\textsc{mean}}^{\star}}\xspace(\{u_n^t : n \in S^t\}\texttt{@C}\xspace, \{z_n^t: n \in S^t\}\texttt{@C}\xspace, \phi)$.
\STATE $x^{t+1} = \textsc{ServerUpdate}\xspace(x^t, u^t)$
\ENDFOR
\end{algorithmic}
\end{algorithm}
\subsection{Applying \cref{alg:select_model_train}}\label{sec:select_training_examples}
While \cref{alg:select_model_train} gives a general framework for applying \textsc{FedSelect}\xspace for model training, it is not immediately clear how best to apply it to specific machine learning models of interest. In this section, we detail a few possible approaches. These are corroborated by empirical evaluation in \cref{sec:experiments}.
For expository purposes, we assume that each client has some finite set of examples $D_n$, and their loss function $g_n$ is of the form
\begin{equation}\label{eq:g_loss}
g_n(y) = \dfrac{1}{|D_n|}\sum_{q \in D_n} \ell(y ; q)
\end{equation}
where $\ell(y ; q)$ is the loss of the local model $y$ on the example $q$. We will also let $\textsc{ClientUpdate}\xspace(y, g_n) = y - y'$, per the ``model-delta'' approach discussed in \cref{sec:federated_model_training}. In particular, for the remainder of this work, we will let $\textsc{ServerUpdate}\xspace(x, u)$ be a first-order optimization step treating $u$ as a gradient estimate, with some server learning rate $\eta$.
Given the above, we will discuss how to use \textsc{FedSelect}\xspace to give clients small sub-models of a server model. Typically, we do this by applying \textsc{FedSelect}\xspace to some of the largest layers of a model, while broadcasting the other layers in full. For example, when training a logistic regression model, we typically only apply \textsc{FedSelect}\xspace to the dense weight matrix, not the bias vector (as it is comparatively small).
With this in mind, there are two primary ways to apply \textsc{FedSelect}\xspace to a model. In the first, which utilizes \textbf{structured select keys}, clients choose their select keys based on their local datasets $D_n$. In the second, which utilizes \textbf{random select keys}, clients select their keys randomly from the set $[K]$ of all possible keys. We discuss the motivation and examples of these two paradigms below, as well as a paradigm that uses both.
\subsubsection{Structured Select Keys}\label{sec:structured_key_selection}
First, we revisit the example in \cref{sec:sparse_log_reg}. In that example, $D_n$ contains a single vector $v_n$ that is supported on some set of indices $A_n$. Thus, one natural approach to \textsc{FedSelect}\xspace would be to have each client use these support indices as their set of select keys, and select the weight sub-matrix corresponding to this index set. More generally, if $D_n$ has sparse feature vectors, then clients could total the frequency of each feature and use the most frequently occurring feature indices as their set of select keys. We will explore this empirically in \cref{sec:so_tag}.
From a modeling perspective, this approach is relevant to any model whose first layer is a fully-connected layer (which of course includes logistic and linear regression models). It is also relevant to models with sparse embedding layers, such as the kind often employed by language models. In such models, the inputs are often sequences of integer tokens, each of which is mapped into some higher-dimensional space. If $D_n$ only contains a subset of all possible words in the embedding layer's vocabulary, then this same approach can be used to select the portion of the embedding layer relevant to the client's dataset.
We note that structured select keys may also be relevant to a model's output layer. For example, if a model's output layer has a discrete set of possible outcomes (such as when applying softmax) and a client can discern that its possible outputs are only a small subset of this, then \textsc{FedSelect}\xspace could also be used to select the relevant component of the output layer. For example, if we are performing next-word prediction with a model whose input layer is an embedding layer, then the set $A_n$ of words in a client's dataset $D_n$ can be used for applying \textsc{FedSelect}\xspace to the input and output layers. Notably, unlike the input selection, sub-sampling outputs in a softmax layer actually changes the behavior of the network, though this can potentially be alleviated via softmax subsampling~\citep{waghmare2022efficient}.
\subsubsection{Random Select Keys}\label{sec:random_key_selection}
Unfortunately, in many modeling settings there is no sparse structure to harness for \textsc{FedSelect}\xspace. For example, in computer vision tasks the inputs typically do not have native sparse structure. When using a CNN for instance, we may wish to apply \textsc{FedSelect}\xspace to the filters in a convolutional layer. Unlike in \cref{sec:structured_key_selection}, it is not clear \textit{a priori} how a client could choose which filters are relevant to them without accessing the model. In such settings, we can instead have clients select their keys randomly from the set $[K]$ of all possible keys. In effect, clients use \textsc{FedSelect}\xspace to obtain a random sub-model of $x$. This approach is analogous to that of Federated Dropout~\citep{caldas2018expanding}, though differs in that the modeler can pick how the select keys correspond to sub-models.
Notably, we have not specified how clients choose keys in relation to one another. While clients could select keys independently, we may also want to choose one set of random keys per round and have all clients in that round use that same set. We explore random key selection, and whether clients choose keys independently or not, empirically in \cref{sec:emnist_image}.
\subsubsection{Combining Structured and Random Keys}\label{sec:mixed_key_selection}
While the discussion above appears to delineate structured and random keys, in many cases we may wish to apply both to a model. While structured keys can be more useful than random keys when they can be applied (as we have no extra variance incurred), many models have components not amenable to structured keys (such as internal layers with no sparse structure in their input and output). Thus, \textsc{FedSelect}\xspace with structured keys may not be enough by itself to reduce the server model size sufficiently. In many realistic models we would like to apply both. We will explore this in the context of training a transformer model for next-word prediction in \cref{sec:so_word}.
\subsection{Sparse Aggregation and Privacy Considerations}\label{sec:select_aggregation}
Aggregations in federated systems typically represent the most privacy-sensitive flow of information from client devices towards the server, and thus are crucial privacy-preservation opportunities. Federated systems typically ensure that the updates from clients are held only ephemerally~\citep{bonawitz2019towards}, but significant effort has gone into enhancing the formal privacy properties of aggregations, both through the use of cryptography (in the form of secure multiparty computation, e.g. the Secure Aggregation protocol~\citep{bonawitz2017practical, bell2020secure}) and through the use of secure enclaves~\citep{mo2019efficient, huba2022papaya}.
Existing FL systems have typically focused their privacy-preserving aggregation efforts on the computation of sums of dense vectors\footnote{Notably, the same is not true of federated analytics (FA). Many recent FA works have focused on privacy-preserving mechanisms for non-linear or sparse aggregates of user data. This includes work on private heavy hitters~\citep{zhu2020federated}, which involves estimating the most frequent items across users, and data queries with inherently sparse structure, such as location heatmaps~\citep{bagdasaryan2021towards}.}. However, when aggregating in the context of a deselection function (e.g., when using \ensuremath{\textsc{Aggregate}_{\textsc{mean}}^{\star}}\xspace as defined in \cref{sec:select_training}) the operation looks much more like a sparse aggregation: each key selects a sub-model of the full model to which to apply the model update. In some settings, especially when clients have structured select keys (see \cref{sec:structured_key_selection}), we would like to perform this sparse aggregation while ensuring that both the model updates and the selection keys are not visible to the server.
Similarly to the options for \textsc{FedSelect}\xspace implementations presented in \cref{sec:select_impl}, a variety of options present themselves for aggregation with deselect. One could simply apply the deselection function at the client, then use standard dense aggregation function; this would directly inherit the privacy properties of the the system's dense aggregation function, and would protect the privacy of the selection keys (up to the limit of what could be learned from the aggregate value itself). However, this strategy is typically communication-inefficient as it entails sending an update the size of the full (pre-selection) model.
Instead, it should be possible to extend the implementations of the cryptographic and/or enclave-based private aggregation protocols (such as secure aggregation~\citep{bonawitz2019towards}) to directly accept (key, update) pairs and incorporate the application of the deselection function inside the security boundary (i.e. computing it as part of the cryptographic protocol or inside the secure enclave). While such strategies holds the promise of improving the communication-efficiency of \ensuremath{\textsc{Aggregate}_{\textsc{mean}}^{\star}}\xspace to match that of \textsc{FedSelect}\xspace while maintaining their security properties, we leave the specifics of their implementation as a topic for future works. Notably, recent work has already proposed the use of invertible Bloom lookup table for secure aggregation in order to deal with inherently sparse structure~\citep{bell2020secure}, as could occur in federated select settings.
\section{Experiments}\label{sec:experiments}
We wish to understand whether (and by how much) training with federated select can actually reduce client model sizes, while still learning a global model with good accuracy. In order to study this, we perform an evaluation of federated select across 4 tasks, using 2 distinct datasets. In this section, we focus on the Stack Overflow dataset. Along the way, we will discuss how selection occurs in each example.
\subsection{Experimental Setup}\label{sec:experimental_setup}
\begin{table}[t]
\caption{Dataset statistics.}
\label{table:datasets}
\begin{center}
\begin{small}
\begin{sc}
\begin{tabular}[t]{ccccccc}
\toprule
Dataset & \begin{tabular}{@{}c@{}}Train \\ Clients\end{tabular} & \begin{tabular}{@{}c@{}}Train \\ Examples\end{tabular} & \begin{tabular}{@{}c@{}}Validation \\ Clients\end{tabular} & \begin{tabular}{@{}c@{}}Validation \\ Examples\end{tabular} & \begin{tabular}{@{}c@{}}Test \\ Clients\end{tabular} & \begin{tabular}{@{}c@{}}Test \\ Examples\end{tabular} \\
\midrule
EMNIST & 3,400 & 671,585 & N/A & N/A & 3,400 & 77,483 \\
\hline
\begin{tabular}{@{}c@{}}Stack \\ Overflow\end{tabular} & 342,477 & 135,818,730 & 38,758 & 16,491,230 & 204,088 & 16,586,035 \\
\bottomrule
\end{tabular}
\end{sc}
\end{small}
\end{center}
\end{table}
\paragraph{Datasets.} We use two datasets: Stack Overflow~\citep{stackoverflow} and EMNIST~\citep{cohen2017emnist}. In the former, clients are users on the Stack Overflow forum, and their examples consist of their posts. In the latter, clients are authors of hand-written digits. The number of train, validation, and test clients (along with the total number of examples in each split) is given in \cref{table:datasets}.
\paragraph{Implementation and tuning.} We use \cref{alg:select_model_train} to do the training. We let $\textsc{ClientUpdate}\xspace(y, g) = y' - y$ where $y'$ is the model learned by doing one epoch of training via SGD with learning rate $\gamma$ using the client's local dataset (assuming $g$ is of the form \eqref{eq:g_loss}). We let $\textsc{ServerUpdate}\xspace(x, u)$ be a first-order optimization step using either SGD, Adagrad, or Adam with learning rate $\eta$. We refer to the combination of SGD at the clients and SGD, Adagrad, or Adam at the server as FedAvg, FedAdagrad, and FedAdam respectively, as proposed by \citet{reddi2021adaptive} (though our training is more general due to the use of \textsc{FedSelect}\xspace).
In each round of \cref{alg:select_model_train}, we sample we sample $50$ clients uniformly at random without replacement from the set of training clients. When running multiple trials of two different algorithms, we use different random model initializations, and vary which clients are sampled in each round in a pseudo-random manner (so that across the same trial, both algorithms see the same sequence of clients), as this helps control for variance across algorithms.
We tune client and server learning rates $\gamma, \eta$ over $\{10^i | -3 \leq i \leq 1\}$. This tuning is done without using \textsc{FedSelect}\xspace, and we pick the parameters that maximize the average validation performance over 5 random trials. Since EMNIST does not have a built-in validation split, we reserve 20\% of the training clients for held-out validation when tuning. For Stack Overflow, we use the built-in split provided by TensorFlow Federated~\citep{tff}.
\paragraph{Presentation of results.} We run 5 random trials for each experiment discussed below, using the learning rates tuned without \textsc{FedSelect}\xspace. These trials vary the model initialization and which clients are sampled per round. In all figures, dark lines indicate the mean across the 5 trials, and shaded regions indicate the standard deviation across trials.
\subsection{Structured Select Keys}\label{sec:so_tag}
In this section, we will use structured select keys to train a logistic regression model whose inputs are sparse feature vectors. Specifically, we will apply multi-class logistic regression models (with one-versus rest classification) to the task of predicting tags in the Stack Overflow datasets. The input data are binary indicator bag-of-words vectors for each example in a client's dataset. We restrict the server's model to the $n$ most frequently occurring words across the entire dataset, and the $t = 500$ most frequent tags. We use FedAdagrad as the server optimizer.
As outlined in \cref{sec:structured_key_selection}, clients can use \textsc{FedSelect}\xspace to select a sub-matrix of the logistic regression weight matrix corresponding to some subset of size $m$ of the total vocabulary set of size $n$. Clients choose their select keys to be the $m$ most frequently occurring words in their local dataset. The validation recall across communication rounds for varying $m$ is given in \cref{fig:so_tag_validation_recall}, while the final test recall is given in Figure \ref{fig:so_tag_test_recall} along with the ratio of the client model size to the server model size. Note that when $m = n$, we recover model training without the use of \textsc{FedSelect}\xspace.
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{figures/tag_prediction_select_val_recall.pdf}
\caption{Validation recall@5 for Stack Overflow tag prediction with federated select. We use FedAdagrad and vary the server vocabulary size $n$ and the number of select keys per client $(m)$. Clients pick the $m$ most frequently occurring words in their local datasets.}
\label{fig:so_tag_validation_recall}
\end{figure}
\begin{figure}[t]
\centering
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[width=1\linewidth]{figures/tag_prediction_select_model_sizes.pdf}
\caption{Relative model size of client and server.}
\end{subfigure}%
\hfill
\begin{subfigure}{0.48\linewidth}
\includegraphics[width=\linewidth]{figures/tag_prediction_select_heatmap.pdf}
\caption{Test recall.}
\end{subfigure}
\caption{Relative model size and test recall tag prediction using \textsc{FedSelect}\xspace. We vary the server's vocabulary size $n$ as well as the number of select keys per client $m$. Clients pick the $m$ most frequently occurring words in their local datasets.}
\label{fig:so_tag_test_recall}
\end{figure}
While $m = 100$ select keys leads to reduced accuracy, we see little to no gain by increasing $m$ from $10^3$ to $10^4$. In particular, using \textsc{FedSelect}\xspace can lead to a $10\times$ reduction in client model size without adversely affecting accuracy. Particularly notable is the case where $n = 10^4$, as setting $m = 10^4$ recovers training without \textsc{FedSelect}\xspace. Analyzing \cref{fig:so_tag_test_recall}, we see another important observation: If we fix the number of select keys $m$, we can generally increase the server's vocabulary size $n$ to increase accuracy, without affecting client compute costs.
\paragraph{Ablation: Key selection strategies. }One natural question that arises is whether we can improve the client key selection method over selecting the most frequent words (which we refer to as ``Top''). To that end, we try two other simple approaches. In the first (Random), clients randomly choose $m$ select keys from the set of words in their own vocabulary. In the second (Random Top), clients identify the $2m$ most frequently occurring words in their vocabulary, and randomly use $m$ keys from this set. Note that in contrast to selecting the $m$ most frequent, these other two methods allow clients to use different keys at different rounds of training. We compare these methods in \cref{fig:so_tag_choosing_keys}.
While all three methods eventually reach comparable accuracy levels, we note that Top $k$ strictly dominates the other two in performance across rounds. Moreover, we find that while all methods have a significant amount of variance, the variance in the Random $k$ method persists throughout training, and is generally larger than the variance of the other two methods. Finally, we note that Random Top $k$ offers little to no benefit over Random $k$, suggesting that the importance of a word to a client is somewhat strongly correlated with its frequency.
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{figures/tag_prediction_sampling_val_recall.pdf}
\caption{Validation recall for Stack Overflow tag prediction with federated select. We use FedAdagrad and vary the server's vocabulary size $(n)$ and set the number of select keys per client $(m)$ to 1000. Clients use different methods for choosing their select keys.}
\label{fig:so_tag_choosing_keys}
\end{figure}
\subsection{Random Select Keys}\label{sec:emnist_image}
In this section, clients use random keys to apply \cref{alg:model_train} to image classification on the EMNIST dataset. We try two different models, both extracted from the original work on FedAvg~\citep{mcmahan2017aistats}: A convolutional model (CNN) with two convolutional layers, and a densely-connected network with two hidden layers (2NN). For the CNN model, the model size is dominated by the \emph{second} convolutional layer, which has 64 filters. We apply \textsc{FedSelect}\xspace to these filters, having each client select $m$ of these filters randomly (without replacement). For the 2NN model, the model size is dominated by the \emph{first} dense layer, which has 200 neurons. We apply \textsc{FedSelect}\xspace to these neurons, where each client selects $m$ neurons randomly (also without replacement).
\begin{figure}[t]
\centering
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=1\linewidth]{figures/emnist_cnn.pdf}
\end{subfigure}%
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=1\linewidth]{figures/emnist_2nn.pdf}
\end{subfigure}%
\caption{Test accuracy of the CNN model (left) and 2NN model (right) on EMNIST when training with \textsc{FedSelect}\xspace, using $m$ randomly chosen select keys per client.}
\label{fig:emnist_select}
\end{figure}
\begin{table}[t]
\begin{varwidth}[b]{.47\linewidth}
\caption{Final test accuracy and relative model size when applying \textsc{FedSelect}\xspace to the CNN model. Clients select $m$ filters randomly (out of 64 total) from the second convolutional layer.}
\label{table:emnist_test_cnn}
\begin{center}
\begin{sc}
\begin{tabular}{lcc}
\toprule
$m$ & Test Accuracy & Rel. Model Size \\
\midrule
$4$ & $75.02 \pm 0.92$ & $0.08$ \\
$8$ & $81.92 \pm 0.10$ & $0.14$ \\
$16$ & $84.15 \pm 0.12$ & $0.26$ \\
$32$ & $85.66 \pm 0.15$ & $0.51$ \\
$64$ & $86.71 \pm 0.06$ & $1.00$ \\
\bottomrule
\end{tabular}
\end{sc}
\end{center}
\end{varwidth}%
\hfill
\begin{varwidth}[b]{.47\linewidth}
\caption{Final test accuracy and relative model size when applying \textsc{FedSelect}\xspace to the 2NN model. Clients select $m$ neurons randomly (out of 200 total) from the first hidden layer.}
\label{table:emnist_test_2nn}
\begin{center}
\begin{sc}
\begin{tabular}{lcc}
\toprule
$m$ & Test Accuracy & Rel. Model Size \\
\midrule
$10$ & $14.17 \pm 0.78$ & $0.11$ \\
$50$ & $50.61 \pm 0.93$ & $0.30$ \\
$100$ & $63.97 \pm 0.32$ & $0.53$ \\
$200$ & $74.93 \pm 0.13$ & $1.00$ \\
\bottomrule
\end{tabular}
\end{sc}
\end{center}
\end{varwidth}
\end{table}
For both of these models, we vary $m$ and plot the test accuracy throughout the course of training in \cref{fig:emnist_select}, and the final test accuracy along with relative client-to-server model size in Tables \ref{table:emnist_test_cnn} and Table \ref{table:emnist_test_2nn}. We see that the impact of \textsc{FedSelect}\xspace varies significantly across the two model architectures. While many settings of $m$ obtain relatively good accuracy for the CNN model, accuracy drops precipitously with $m$ for the 2NN model.
\paragraph{Ablation: Independent key selection. } We also wish to see whether clients need to sample their keys independently. If we were to randomly select a single set of selection keys each round, and have all clients in the round use that same key set, then there would be no need to actually use \textsc{FedSelect}\xspace. Rather, the server could randomly choose the keys, compute the appropriate sub-model, and simply apply \textsc{Broadcast}\xspace. In \cref{fig:emnist_select_fix}, we compare the test accuracy of model training with \textsc{FedSelect}\xspace when we clients use the same keys per round (ie. they use some ``fixed'' set of keys per round) or clients use different keys per round. We find that the difference in performance between these two approaches depends on the model architecture. While fixing the set of keys yields no real loss of accuracy on the CNN model, it further drops accuracy on the 2NN model.
\begin{figure}[ht]
\centering
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=1\linewidth]{figures/emnist_cnn_sample_methods.pdf}
\end{subfigure}%
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=1\linewidth]{figures/emnist_2nn_sample_methods.pdf}
\end{subfigure}%
\caption{Test accuracy of the CNN model (left) and 2NN model (right) on EMNIST when training with \textsc{FedSelect}\xspace, using $m$ randomly chosen select keys per client. Either all clients use the same select keys per round (True) or independently sample their own keys at each round (False).}
\label{fig:emnist_select_fix}
\end{figure}
\subsection{Structured and Random Select Keys}\label{sec:so_word}
In this section, we give a more complex example of using structured and random keys in \textsc{FedSelect}\xspace. We use a transformer model to perform next-word prediction on the Stack Overflow dataset. Specifically, we use the same transformer model architecture used in \cite{fieldguide}. The model takes sequences (of length $20$) of tokenized words, with a vocabulary size of $n = 10000$. The model uses an embedding layer followed by a transformer model, followed by a final dense layer with $n = 10000$ output units, followed by a softmax. We use FedAdam for our optimization throughout.
First, we can apply structured key selection to the input and output layers, based on the $m$ most frequently occurring words in a client's dataset (as we did in \cref{sec:so_tag}). In order to further reduce the model size, we can also apply \textsc{FedSelect}\xspace with $d$ random keys to the largest dense layer in the transformer, which has $h = 2048$ neurons.
We parameterize our experiments by a factor $\alpha$ determining the number of structured and random keys used, with three different types of selection mechanisms. In our \emph{structured} experiments, we use $m = \alpha n$ structured select keys per client (applied to the input/output layers), and do not use random keys. In our \emph{random} experiments, we use $d = \alpha h$ random keys per client (applied to the dense layer) and do not use structured keys. Finally, in the \emph{mixed} experiments, we use $m = \alpha n$ structured select keys and $d = \alpha h$ random keys simultaneously. Note that in all three cases, $\alpha = 1$ we recover model training without \textsc{FedSelect}\xspace. Moreover, for the same value of $\alpha$, all three approaches lead to a different model size.
In \cref{fig:so_word_model_sizes}, we plot the trade-off between test accuracy and client model size incurred by each method. Notably, purely random key selection drops off in accuracy very quickly, without incurring significant model size reduction benefits. While structured maintains accuracy better as model size shrinks, there is a limit to how much the model size can be reduced. Notably, by using the mixed approach, we are able to recover comparable accuracy to the structure selection for large $\alpha$, but extend the frontier of test accuracy versus model size for smaller $\alpha$.
\begin{figure}
\centering
\includegraphics[width=0.6\linewidth]{figures/transformer_mixed_model_sizes.pdf}
\caption{Test accuracy for Stack Overflow word prediction with \textsc{FedSelect}\xspace when training using FedAdam, under structured, random, and mixed selection schemes. We plot the test accuracy with respect to the model size used by the clients during training.}
\label{fig:so_word_model_sizes}
\end{figure}
\section{Trust Models and System Constraints}\label{sec:trust_models}
The actual benefits (and costs) incurred by using \textsc{FedSelect}\xspace will necessarily depend on the surrounding FL system. While some of these trade-offs were discussed briefly in \cref{sec:select_impl}, in this section we give a more detailed and systems-oriented viewpoint of implementing \textsc{FedSelect}\xspace. We focus on the relation between systems implementations and the \emph{trust model} between clients and server.
Privacy is a broad concept, and for this discussion it is useful to highlight two privacy principles in particular: \emph{data minimization} and \emph{data anonymization}~\citep{bonawitz22acm}. In the context of a federated computation, data anonymization involves ensuring that the final output of the computation revealed at the server does not itself reveal private information. For example, it can help ensure that a language model does not memorize one user's data, or that an analytics query does not reveal information about an individual. These concerns are often addressed by differential privacy~\citep{dwork2008differential}, but are generally out-of-scope for this work.
In contrast, data minimization involves the properties of the system that runs a federated computation. In particular, it suggests that such a system should minimize access to any intermediate state of the computation to all parties including the service provider. Thus, an implementation of federated select held to the highest standards of data minimization should not reveal the select keys of any client to the service provider, as these are internal to the computation and not a designated output (e.g., the model being trained).
Recall that \textsc{FedSelect}\xspace requires clients to specify their own select keys. Above, we saw examples where the select keys were purely random, as well as instances where the select keys contained information about the client's local dataset (such as which words frequently appear). This leads us to a core observation: \emph{Depending on how \textsc{FedSelect}\xspace is used, the select keys may be more or less private.} The sensitivity of a client's select key is not simply binary (public or fully private), even when using structured keys that reflect information about a client's dataset. For example, select keys codifying the most frequent languages used by a client, while still derivative of a client's sensitive data, may be less sensitive than, for example, keys indicative of the actual content written in a messaging application.
We now consider the problem of implementing \textsc{FedSelect}\xspace in a way that 1) allows reduced communication between clients and server, 2) scales to large-scale FL settings, and 3) allows some data minimization and privacy-preserving techniques to be applied. We note that Option 1 in \cref{sec:select_impl} does not fit criteria 1, as it still requires the server value to be broadcast in full. Thus, we will focus on Options 2 and 3 in \cref{sec:select_impl}, wherein clients are sent slices either via on-demand slice generation or pre-generation of slices.
\paragraph{On-Demand Slice Generation} In this system, clients upload their select keys directly to the server. As the clients upload their keys to the server, the server computes and packages up the relevant model slices, and sends them to each client. While this does allow reduced communication between the server and the clients, this approach can suffer from privacy and systems issues.
In particular, suppose that we want a system that can handle communication rounds with thousands of clients. Even if the clients use a modest number of select keys on average (ie. $m$ is small), this means that the server has to compute the selection function $\psi(x, i)$ thousands of times before being able to send all clients their models. Furthermore, synchronous cross-device FL systems typically have execution patterns where the clients are coordinated to start rounds at the same time and where the clients only have limited time-windows in which they participate, and are prone to dropping out of a round. That makes it likely for the clients to upload their keys and request slices all at nearly the same time, which puts a peak demand on throughput of the on-demand slice generation. If the server model is stored in only a single place, the slice generation is likely to become a bottleneck leading to clients running out of their time-window and dropping out. And while it is possible to distribute the model over multiple places and parallelize on-demand slice generation requests, that by itself has a cost of replicating a potentially large model. This is a challenging system task, and can lead to significant latency and throughput issues.
This approach also reveals the clients' select keys to the server in full, thus assuming that the keys are not entirely private. In order to remedy this, we could also utilize data minimization techniques, though these will not suffice for totally private keys. While one might consider using systems like \emph{private information retrieval} (PIR)~\citep{chor1995private}, these often require some finite database of possible values and are not directly compatible with on-demand slice generation. PIR may be more amenable to slice pre-generation approaches, as we detail below.
In short, on-demand slice generation are a natural method for computing \textsc{FedSelect}\xspace, but can suffer from systems-issues in cross-device settings, and does not directly permit the use of cryptographic primitives for keeping client keys private.
\paragraph{Pre-Generation of Slices} When the space of select keys (of size $K$) is not too large, pre-generation of slices can remedy some of the issues of on-demand slice generation. In particular, we consider scenarios where the server can compute all possible slices of a model in a reasonable amount of time in-between communication rounds. This allows the server to send these slices to a content delivery network (CDN), effectively a database that clients can query in order to get model slices in a distributed, scalable way.
Pre-generation amortizes the cost of slice generation when clients have overlapping select keys, as is often the case. This amortization is particularly important in settings with large numbers of clients, and therefore may represent a better solution for large-scale cross-device settings. Since the slice-generation happens before the communication with clients begin, this helps mitigate issues where clients can dropout of a round while waiting for their on-demand slices. The pre-generation of slices may also be easier to parallelize than on-demand slicing, as the set of keys to operate on is not too large and is known a priori. It is worth noting that in synchronous FL systems, the server must wait until pre-generation is complete before accepting client connections for the next round. In asynchronous systems, such as Papaya~\citep{huba2022papaya}, this may not be necessary (though a detailed understanding of how staleness of slices impacts training is beyond this work).
This pre-generation approach also allows data minimization barriers between the CDN and the server that prevent the server from seeing what queries are being made to the CDN. However, even if we assume that the server has access to the queries being made to the CDN, we can utilize PIR~\citep{chor1995private}. This allows a set of clients to download keys from the CDN such that the server owner gains no information (cryptographically speaking) about which keys each client has requested. Such guarantees are more difficult to make in on-demand settings, especially when there is little to no overlap between clients' key sets. However, PIR does incur a certain amount of communication overhead, and we leave a formal evaluation of the trade-off between communication savings gained by federated select and communication increases incurred by PIR to future work. Alternatively, if secure enclave hardware is available , we could implement either the CDN or the on-demand slice computation server inside a sufficiently powerful secure enclave, such that decrypted select keys are only available inside the enclave's trust boundary and the client can verify how these keys will be used (and their privacy maintained) via remote attestation
This approach comes at a cost. Notably, since the key space cannot be too large, we must be careful about how \textsc{FedSelect}\xspace can be applied to a given model. For example, throughout language model experiments in \cref{sec:experiments}, keys correspond to words in some vocabulary set of size $K$. If $K$ is too large, pre-generation of slices may not be computationally tractable and many of the generated slices may not even be downloaded by clients resulting in a significant overhead. Thus, one avenue for future work would be to investigate dividing up the vocabulary set into a moderate number of buckets, each of which correspond to a possible select keys. Similarly, to use pre-generation of slices with the random key selection in \cref{sec:emnist_image}, we may need to bucket neurons in a dense layer. More generally, future work could investigate how to design \textsc{FedSelect}\xspace usages that only require a moderately-sized key space, rather than one that scales with the size of the model.
\section{Open Questions}
While we believe that \textsc{FedSelect}\xspace is a useful primitive for training large-scale models in federated settings, there are a number of important open questions related to its usage, implementation, and privacy concerns.
\textbf{Model-specific selection techniques.} While federated select is a general primitive for reducing communication and computation costs in federated learning, much of its application is model-dependent. While we detail some ways to use it in \cref{sec:experiments} above, these techniques need not work well across all model architectures (and indeed, have disparate impacts on model architecture even in our experiments). Thus, future work may need to develop more methods for applying federated select depending on the underlying client data and model architecture. More generally, one could investigate which architectures are more compatible with federated select.
\textbf{Compatibility with privacy-preserving technologies.} As discussed in \cref{sec:trust_models}, different implementations of federated select can incorporate different data minimization techniques. However, many federated settings require data anonymization techniques, including secure aggregation and differential privacy. While these can be used with naive implementations of federated select (see the "Broadcast and compute" implementation in \cref{sec:select_impl}), it is unclear how to make other implementations (including those based on on-demand slice generation and pre-generation of slices, as in \cref{sec:trust_models}) compatible.
\textbf{Implementation in practical systems.} While we have attempted to motivate, examine, and discuss system benefits and constraints of federated select, future work may investigate how federated select impacts practical FL training. In particular, how it affects problems such as client dropout~\citep{bonawitz2017practical}, or its impact on synchronous versus asynchronous training~\citep{huba2022papaya}. The scalability of such a system is a particularly important future investigation, especially with respect to model sizes. For example, when applying federated select to sufficiently large models, it may need to operate over millions, or even billions, of possible keys held by clients, each of which may have thousands or even millions of local keys.
\section*{Acknowledgments}
First and foremost, we would like to thank Krzysztof Ostrowski, Taylor Cramer, and Zachary Garrett for their contributions to the original design of federated select. We would also like to thank Taylor Cramer, Hubert Eichner, Timon Van Overveldt, Zachary Garrett, Keith Rush, Hugo Song, and Daniel Ramage for their valuable insights and inputs on the paper. Finally, we note that the experiments contained in this work would not be possible without the support of Taylor Cramer, Zachary Garrett, and Keith Rush, and the rest of the TensorFlow Federated team.
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{"url":"http:\/\/codeforces.com\/problemset\/problem\/958\/D2","text":"D2. Hyperspace Jump (hard)\ntime limit per test\n3 seconds\nmemory limit per test\n256 megabytes\ninput\nstandard input\noutput\nstandard output\n\nIt is now 125 years later, but humanity is still on the run from a humanoid-cyborg race determined to destroy it. Or perhaps we are getting some stories mixed up here... In any case, the fleet is now smaller. However, in a recent upgrade, all the navigation systems have been outfitted with higher-dimensional, linear-algebraic jump processors.\n\nNow, in order to make a jump, a ship's captain needs to specify a subspace of the d-dimensional space in which the events are taking place. She does so by providing a generating set of vectors for that subspace.\n\nPrincess Heidi has received such a set from the captain of each of m ships. Again, she would like to group up those ships whose hyperspace jump subspaces are equal. To do so, she wants to assign a group number between 1 and m to each of the ships, so that two ships have the same group number if and only if their corresponding subspaces are equal (even though they might be given using different sets of vectors).\n\nHelp Heidi!\n\nInput\n\nThe first line of the input contains two space-separated integers m and d (2\u2009\u2264\u2009m\u2009\u2264\u200930\u2009000, 1\u2009\u2264\u2009d\u2009\u2264\u20095) \u2013 the number of ships and the dimension of the full underlying vector space, respectively. Next, the m subspaces are described, one after another. The i-th subspace, which corresponds to the i-th ship, is described as follows:\n\nThe first line contains one integer ki (1\u2009\u2264\u2009ki\u2009\u2264\u2009d). Then ki lines follow, the j-th of them describing the j-th vector sent by the i-th ship. Each of the j lines consists of d space-separated integers aj, j\u2009=\u20091,\u2009...,\u2009d, that describe the vector ; it holds that |aj|\u2009\u2264\u2009250. The i-th subspace is the linear span of these ki vectors.\n\nOutput\n\nOutput m space-separated integers g1,\u2009...,\u2009gm, where denotes the group number assigned to the i-th ship. That is, for any 1\u2009\u2264\u2009i\u2009<\u2009j\u2009\u2264\u2009m, the following should hold: gi\u2009=\u2009gj if and only if the i-th and the j-th subspaces are equal. In addition, the sequence (g1,\u2009g2,\u2009...,\u2009gm) should be lexicographically minimal among all sequences with that property.\n\nExample\nInput\n8 215 010 110 120 60 120 11 02-5 -54 321 10 121 01 0\nOutput\n1 2 2 2 3 3 3 1\nNote\n\nIn the sample testcase, the first and the last subspace are equal, subspaces 2 to 4 are equal, and subspaces 5 to 7 are equal.\n\nRecall that two subspaces, one given as the span of vectors and another given as the span of vectors , are equal if each vector vi can be written as a linear combination of vectors w1,\u2009...,\u2009wk (that is, there exist coefficients such that vi\u2009=\u2009\u03b11w1\u2009+\u2009...\u2009+\u2009\u03b1kwk) and, similarly, each vector wi can be written as a linear combination of vectors v1,\u2009...,\u2009vn.\n\nRecall that a sequence (g1,\u2009g2,\u2009...,\u2009gm) is lexicographically smaller than a sequence (h1,\u2009h2,\u2009...,\u2009hm) if there exists an index i, 1\u2009\u2264\u2009i\u2009\u2264\u2009m, such that gi\u2009<\u2009hi and gj\u2009=\u2009hj for all j\u2009<\u2009i.","date":"2018-06-25 03:57:52","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 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\": 0.7062906622886658, \"perplexity\": 483.6122583909069}, \"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-2018-26\/segments\/1529267867424.77\/warc\/CC-MAIN-20180625033646-20180625053646-00167.warc.gz\"}"}
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Q: Corporate Proxy Azure Devops with Git I've created a Project and Repo inside of Azure Dev-Ops.
We are sitting behind a corporate proxy and would like to clone from this project.
I have set the environment variables http_proxy,https_proxy, HTTP_PROXY,HTTPS_PROXY, git config --global https.proxy, git config --global http.proxy to the matching http or https version below
http://domain\username:password@ProxAddr:Proxy
or
https://domain\username:password@ProxAddr:Proxy
When I run git clone https://username:pwd@dev.azure.com/username/ProjectName/_git/RepoName, I receive the error below.
Cloning into 'ProjectName'...
* Couldn't find host dev.azure.com in the .netrc file; using defaults
* Trying {proxyip} ...
* Connected to {proxyip} ({proxyip}) port {proxyport} (#0)
* Establish HTTP proxy tunnel to dev.azure.com:443
> CONNECT dev.azure.com:443 HTTP/1.1
Host: dev.azure.com:443
User-Agent: git/2.7.4
Proxy-Connection: Keep-Alive
< HTTP/1.1 407 Proxy Authentication Required
< Proxy-Authenticate: NEGOTIATE
< Proxy-Authenticate: NTLM
< Proxy-Authenticate: BASIC realm="{CORPRELM}"
< Cache-Control: no-cache
< Pragma: no-cache
< Content-Type: text/html; charset=utf-8
< Proxy-Connection: close
< Connection: close
< Content-Length: 849
<
* Ignore 849 bytes of response-body
* Connect me again please
* found 148 certificates in /etc/ssl/certs/ca-certificates.crt
* found 592 certificates in /etc/ssl/certs
* ALPN, offering http/1.1
* gnutls_handshake() failed: Error in the push function.
* Closing connection 0
* Couldn't find host dev.azure.com in the .netrc file; using defaults
* Hostname {proxyip} was found in DNS cache
* Trying {proxyip}...
* Connected to {proxyip} ({proxyip}) port {proxyport}(#1)
* Establish HTTP proxy tunnel to dev.azure.com:443
> CONNECT dev.azure.com:443 HTTP/1.1
Host: dev.azure.com:443
User-Agent: git/2.7.4
Proxy-Connection: Keep-Alive
< HTTP/1.1 407 Proxy Authentication Required
< Proxy-Authenticate: NEGOTIATE
* gss_init_sec_context() failed: : SPNEGO cannot find mechanisms to negotiate
< Proxy-Authenticate: NTLM
< Proxy-Authenticate: BASIC realm="{CORPREALM}"
< Cache-Control: no-cache
< Pragma: no-cache
< Content-Type: text/html; charset=utf-8
< Proxy-Connection: close
< Connection: close
< Content-Length: 849
<
* Received HTTP code 407 from proxy after CONNECT
* Closing connection 1
fatal: unable to access 'https://username:devopspwdF@dev.azure.com/username/DevOpsProject/_git/DevOpsRepo/': gnutls_handshake() failed: Error in the push function.
The error appears to be this?
< Proxy-Authenticate: NEGOTIATE
* gss_init_sec_context() failed: : SPNEGO cannot find mechanisms to negotiate
Do I need to explicitly state something?
A: It looks like your proxy may be misconfigured, and is offering authentication mechanisms it can't support (in this case, Negotiate). You can work around this by setting the http.proxyAuthMethod option to something suitable. Based on the output, you'll probably want to use ntlm or basic.
In addition, you can set this on a per-url or pattern basis by using something like git config http.https://*.azure.com/.proxyAuthMethod ntlm for all HTTPS URLs with hostnames matching *.azure.com.
A: Updating to a newer version of git resolves this.
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Category: top law schools
Prime Legislation Faculties In Us
Choosing which colleges to apply for can be very difficult. Boston College – Legislation Faculty. The College of California at Berkeley Boalt Corridor Faculty of Regulation is situated within the San Francisco Bay area and has at all times been ranked among the top 14 law colleges within the United States.
Speaking of the OJ Simpson trial, Johnnie Cochran attended Loyola University College of Regulation in Los Angeles as did the fiery tv and radio commentator Gloria Allred. In the record, we've listed prime-ranked Texas legislation faculties which offer essentially the most glorious programs to your legislation profession.
Stanford Law Faculty offers a scholar-centered, future-dealing with and interdisciplinary method to authorized training. The Best Law Faculties For Environmental Law (2020) A ranking for a apply space that may turn out to be more and more necessary as the impacts of global local weather change have an effect on the world round us.
Texas Tech College School of Legislation. The remaining schools mostly held onto their spots, including Columbia, the University of Virginia and Michigan. High Value: Whereas law colleges typically charge more than $20,000 a year, private faculties can cost a tuition payment of $30,000 to $40,000 a year.
They have some less generally provided concentrations, reminiscent of leisure regulation, that might be of explicit curiosity to some students. See if College of Kentucky is ranked and get information on packages, admission, tuition, and more. #7: University of Pennsylvania Regulation School, College of Virginia Law College.…
The New 2008 Regulation School Rankings Are Out, What Do They Mean?
Choosing which faculties to apply for may be very difficult. At the beneath graduate level, college students can choose between African and African American Research, Anthropology, Chemistry, Economics, Engineering and Applied Sciences, History, Music, Psychology, Sociology and Ladies, Gender and Sexuality. Stanford College, one of many world's leading teaching and research establishments, is dedicated to discovering solutions to big challenges and to preparing students for leadership in a fancy world.
The top colleges supply a wider selection of programs and hence the student intake is also larger. Additionally it is necessary that you simply find out the overall variety of students being enrolled in the top colleges of your selection from year to year.
#2: Harvard Legislation Faculty, Stanford Law Faculty. Many legislation schools enable students to specialize in a particular area, equivalent to advocacy, public law, or enterprise regulation. Cavalho simply received into one of many prime legislation schools in the nation, engaging in a purpose she didn't dare admit to herself because she felt it was so impossibly out of reach.
Find out in case your dream regulation faculty made considered one of our 11 distinctive rating lists. Our goal is to help college students find greatest regulation colleges on the planet. On the opposite facet of the courtroom, Marcia Clark attended Southwestern University Faculty of Law and Christopher Darden attended the College of California, Hastings Faculty of The Law.
Founded in 1967, The Texas Tech College College of Law is an ABA-accredited regulation college. Sadly, if you are planning on making use of to legislation school this 12 months, or applying to legislation college anytime within the close to future, I know that you'll have a really arduous time ignoring the law faculty rankings.…
Legislation Faculties
So its another 12 months and we are faced with another round of law faculty rankings from the so-referred to as "specialists." The 2008 legislation school rankings are not any totally different from every other yr – they're virtually meaningless to the typical student and must be largely ignored by you. Top law faculties in the US & Canada Of the 300 establishments featured within the ranking, 50 are found within the US, together with 14 in the prime 50. Exterior of the highest 10 above, other wonderful regulation schools in the US embrace the College of Chicago (ranked 11 th ), Georgetown College (17 th ), University of California, Los Angeles (UCLA) (joint 23 rd ) and the College of Michigan (27 th ).
He has some of the prestigious shopper lists of any legal professional including such notables as Michael Milken, Leona Helmsley, Mike Tyson, Penthouse, Patricia Hearst, John Landis and even fellow attorneys F. Lee Bailey(Boston College Legislation Faculty 1960) and William Kunstler(Columbia Regulation Faculty).
The defining characteristic of this website is the TLS forums which traditionally has been targeted totally on law faculty candidates with discussion boards such because the law school admissions forum, the LSAT prep forum, the private statement discussion board, and the selecting a legislation school forum.
PG faculties are Annenburg Faculty of Communication, Graduate College of Education, Regulation School, Faculty of Arts and Sciences, Faculty of Dental Medicine, College of Design, School of Engineering and Applied Sciences, College of Drugs, Faculty of Nursing, School of Policy and Apply and College of Veterinary Medicine.
What you'll finally be taught, whether you go to Harvard Regulation College, or a night legislation college in your native metropolis, is that the authorized training you'll receive will be substantially the same – no matter which regulation faculty you attend. …
Stanford Legislation School
Choosing which faculties to use for will be very troublesome. As I discuss in one other article about legislation school rankings, you have got to view the popular revealed regulation faculty rankings skeptically. Harvard Law School, Yale Legislation School, and Stanford Legislation College have occupied the highest three rankings for over a decade.
The standard of training at the high-tier colleges just isn't necessarily higher than that in the lower tiers, but the names certainly carry a certain cache with employers. These rankings are untrustworthy and mislead students into pondering they should attend a extremely ranked college or they are going to be second charge attorneys due to their "substandard" law school schooling.
Enrolling into prime faculties will make all of the distinction between the place you might be in your career 10 years from hence. Is Mercer College (George) the most effective law faculty for you? #four: College of Chicago Regulation College, Columbia Legislation College. On the finish of the day, I wouldn't even contemplate applying to any regulation faculty below the second tier of the U.S. News and World Report regulation faculty rankings.
Top law schools in Africa & the Center East. Extra important concerns embody cost, attractiveness of the situation, weather, where you wish to stay after legislation faculty, the social scene, and the applications provided. Admissions, tuition, and financial aid knowledge on prime law faculties.
And finally, looking firstly at Africa, South Africa has 4 representatives within the regulation school ranking, with the University of Cape Town continuing to paved the way at one hundred and one-one hundred fifty (down from fifty one-one hundred last 12 months). Gallery: The Finest Law Colleges For Career Prospects In 2018.…
Top Legislation Colleges Forum
Think about yourself working at the Hague, combating for international human rights or defending immigrants going through deportation. Stanford Legislation College has an Superior Diploma Students Affiliation that hosts many packages all year long for your entire law school group, together with movie nights, with college students suggesting films from their residence international locations, and potluck dinners, with students bringing food from their residence international locations.
Unless you want to chase the top one % of jobs, although, the highest ten to fifteen regulation colleges may not be well worth the value of admission. No checklist would be complete without Professor Alan Dershowitz of Harvard Law College. Baylor University – College of Legislation.
PG faculties are Annenburg Faculty of Communication, Graduate College of Training, Law Faculty, Faculty of Arts and Sciences, School of Dental Drugs, College of Design, School of Engineering and Applied Sciences, Faculty of Medicine, Faculty of Nursing, Faculty of Policy and Observe and Faculty of Veterinary Medicine.
You'll positively get a top notch authorized training at this college though for those who manage to get accepted, as only the highest students do. It is the oldest regulation school in Canada and continually ranks among the many finest regulation colleges in the civil law degree is ranked as the best in Canada, and constantly outranks Europe, Asia, and Latin America's prime civil regulation schools.
The standard of training at the prime-tier colleges just isn't necessarily higher than that in the lower tiers, however the names certainly carry a certain cache with employers. These rankings are untrustworthy and mislead students into considering they need to attend a highly ranked school or they are going to be second charge attorneys attributable to their "substandard" regulation college schooling.…
Prime Ten Greatest Regulation Schools
Choosing a Legislation College can be a tough determination. Usually, entry into legislation programs in Canada is predicated primarily on a mixture of the scholar's previous grades in addition to, for English-language common-legislation programs, their rating on the Legislation College Admission Test (LSAT). The New York College College of Legislation (NYU Legislation) is the legislation school of New York University.
The 2019 rankings placed Yale Regulation College, Yale University in fourth forward of Stanford Regulation College, Stanford College into fifth; whereas NYU Faculty of Law, New York University ranked sixth, and UC Berkeley Faculty of Legislation, College of California, Berkeley seventh.
Students might create their very own semester research abroad preparations, authorized by the Regulation Faculty, and lately have performed so with the College of Copenhagen, ITAM in Mexico City, the College of Hong Kong, and ICADE, Comillas, in Madrid, Spain.
Tap a school to see their twenty fifth percentile, median, and 75th percentile GPA and LSAT scores for marticulating college students for that year. T14 refers back to the top 14 law schools. See the entire listing of our one hundred sixty five Best Regulation Faculties, or view the checklist by region.
Stanford Legislation School has an Superior Diploma College students Affiliation that hosts many applications all year long for the whole regulation faculty neighborhood, together with film nights, with students suggesting motion pictures from their residence international locations, and potluck dinners, with college students bringing food from their house countries.…
The College of Michigan Regulation College, located in Ann Arbor, is a unit of the College of Michigan. One of the best colleges are within the Tier One, followed by those in Tier Two and Tier three. Traditional knowledge states that one of the best jobs to go Tier One college students, whereas those in Tier 3 can have the most trouble finding employment.
American University – Washington School of Legislation. Columbia College was established in 1754 in New York Metropolis and is the oldest publish secondary college in NY. It is accredited by Middle States Fee on Larger Training. I looked on the LSAT scores, common undergraduate GPAs, and admissions rates of the top one hundred legislation schools in the United States that can assist you determine how your LSAT score stacks up in opposition to the competitors.
He has one of the most prestigious shopper lists of any attorney including such notables as Michael Milken, Leona Helmsley, Mike Tyson, Penthouse, Patricia Hearst, John Landis and even fellow attorneys F. Lee Bailey(Boston University Regulation College 1960) and William Kunstler(Columbia Legislation School).
Explore the most effective regulation faculties in New York and join with any number of high ranked regulation colleges along with their common monetary aid packages, published tuition rates, LSAT scores, well-liked on-line levels, enrollment tendencies, scholar to trainer ratios, and way more to search out the perfect college for you with our proprietary search technology platform.
Yale doesn't make this ranking as a result of a lot of its graduates take judicial clerkships, which pay much less, bringing down the varsity's median salary to $70,000. Hence, it's good to select programs the place your individual skills are usually not too totally different from these of the other college students.…
Assist For Yahoo Search
Stepping into prestigious law schools has by no means been straightforward, even when the demand for law school admission was a lot less than it's right this moment. Whereas they might not have the identify attraction of a Harvard or Stanford, most faculties within the second tier additionally cost only a fraction of these colleges' overall value. Also college students are to submit a brief essay on why they want to enroll to this university along with a solution essay to the query on the web site.
Many online regulation faculty applications require the completion of an on-site internship within the student's local community. Finest Universities, Schools and Faculties in Malang, Indonesia 2019 On this web page you possibly can search for Universities, Faculties and Business colleges in Malang.
#2: Harvard Regulation College, Stanford Law College. Many law colleges permit college students to concentrate on a specific area, akin to advocacy, public law, or business legislation. Cavalho simply got into one of the top legislation schools in the country, conducting a purpose she didn't dare admit to herself as a result of she felt it was so impossibly out of reach.
Regulation Schools. One of the best online law faculties, U of A was the primary to offer an advanced diploma in agricultural and food law. California's elementary and middle school students will not be suspended for issues like falling asleep in school or speaking back to the instructor below a invoice signed by the state's governor.
Explore one of the best legislation schools in New York and join with any variety of high ranked law colleges along with their average financial support packages, printed tuition rates, LSAT scores, in style online levels, enrollment developments, student to instructor ratios, and rather more to search out the best faculty for you with our proprietary search expertise platform. …
Yahoo Search Preferences
The College of Michigan Regulation Faculty, situated in Ann Arbor, is a unit of the College of Michigan. Legislation Faculty Rankings Analyzing the varied law school rankings and rating methodologies may be useful in deciding the place to apply and the place to attend. Texas Tech Regulation provides a sturdy scientific program, three academic centers, ten dual-degree programs, three focus packages, a regional externship program, a recognized legal practice program.
You will positively get a top notch legal training at this school although in case you manage to get accepted, as only the top college students do. It's the oldest law college in Canada and continually ranks among the greatest regulation colleges within the civil regulation diploma is ranked as one of the best in Canada, and constantly outranks Europe, Asia, and Latin America's prime civil regulation faculties.
The University of Pennsylvania ("Penn") is a nicely-regarded law college, typically as a prime ten regulation faculty. The faculties at UG stage are – The College- Arts and Sciences, Faculty of Engineering and Utilized Sciences, Faculty of Nursing, Wharton Business Faculty.
Stanford Law Faculty is a professional graduate school of Stanford College, positioned in Silicon Valley close to Palo Alto, California. There are plenty of advantages offered by the top legislation faculties as in comparison with any average college. From being in the 40s to now being in the top 20, actually ascending towards the top 15 — that may be a massive, large deal," DeSantis, a Yale University grad and Harvard Legislation College alum, mentioned.
Law Schools. Top-of-the-line online law colleges, U of A was the primary to offer an advanced degree in agricultural and food regulation. California's elementary and middle school students will not be suspended for things like falling asleep in school or speaking again to the instructor below a invoice signed by the state's governor. …
Prime Regulation Faculties Forum
Building a profession as an attorney is a activity that requires a number of research, arduous work, stamina and above all, aim orientation. It's tied with the College of Michigan as the top public regulation college within the U.S. Harvard Law School is by far the most widely recognised legislation school on the earth and it houses an incredible variety of resources. Stanford Legislation School (also called Stanford Regulation or SLS) is knowledgeable graduate faculty of Stanford University, positioned in Silicon Valley near Palo Alto, California.
Meet with the Stanford Pre-legislation advisor for an outline of the application process, to make sure that you already know about resources for Stanford applicants to regulation college, and for answers to any questions you've about making use of. The 25 Law Schools Whose Grads Earn The Most Forbes turned to to seek out the regulation college schools whose graduates take advantage of within the early phases of their career.
You could think about the academic skills of a regulation faculty's scholar physique. Regulation colleges are rated by many different sources resembling Kaplan, the Princeton Review and media sources reminiscent of US News. Established in 1893, Stanford Law has been ranked one of many high three regulation schools in the country, with Yale Law College and Harvard Law School, yearly since 1992.
They are also have good applications in other specialties as effectively, so you will get a nicely rounded authorized schooling. For out of province students, the undergraduate diploma is $6155.forty and $5858.10 for a masters. The Faculty of Regulation is likely one of the skilled graduate faculties of McGill University in Montreal, Quebec.
LSAT (Law School Admission Test): This is a three hour entrance exam that an applicant has to take to get into regulation colleges. See if Stanford University is ranked and get information on applications, admission, tuition, and more. It is the oldest non-public university in US. Greatest known for its law school, business faculty and medical college, the university also affords diverse choices to select from. …
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200 boat migrants arrive on Lampedusa
Two large dinghies carrying 204 asylum-seekers landed in Italy on Monday after being intercepted by coast guards south of the Italian island of Lampedusa.
Published: 26 August 2013 14:27 CEST
Boat migrants arriving in Italy. Photo: Italian coast guard press office/AFP
The arrivals were mostly from sub-Saharan Africa and the vessels were on a cross-Mediterranean route taken by boats arriving from Libya, officials said.
One dinghy was spotted some 70 nautical miles south of Lampedusa, Italy's southernmost point and a major gateway for economic migrants and refugees entering the European Union.
The second dinghy was drifting and was rescued 35 nautical miles south of the first one.
The asylum-seekers have been taken to a temporary shelter on Lampedusa, where there are also around 100 migrants from Eritrea who arrived on Sunday.
Improved weather conditions and renewed upheaval in north Africa and the eastern Mediterranean have caused a surge in boat landings in Italy in recent weeks.
Most of the arrivals are from sub-Saharan Africa but some arrive from Egypt and Syria or further afield from countries like Afghanistan and Bangladesh.
IMMIGRATIONLIBYALAMPEDUSA
Italy's Meloni in Libya to discuss energy and migration
'More will drown': Italy accused of breaking international law on migrant rescues
|
{
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| 6,264
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Flood resilience research project presents roadmap
114 (1416), March, 2019
The European funded DAREnet project will present its research, development and innovation roadmap for improved flood resilience in the Danube River Region in Budapest this month
DAREnet stands for 'Danube river region Resilience Exchange Network' and is a practitioner network which aims to strengthen flood resilience in the EU Danube River Region. The transnational, multi-disciplinary network brings together a unique combination of renowned institutions and players in flood management and civil protection in order to deepen and broaden the research, development and innovation related collaboration in the field of flood management. The DAREnet project, which started on September 1, 2017, runs for five years and is supported by the European Union's Horizon 2020 Research and Innovation programme with €3.5 million.
EU Danube River Region – a Flood History and Perspectives
Between 2002 and 2014 seven major floods occurred in the Danube River basin which cost the lives of dozens of people and caused several billion Euro of damage. In 2010 alone, one of the most severe floods affected mainly the central and eastern parts of the basin and caused 35 casualties and generated total damages estimated at €2 billion. On top to that, the magnitude of the floods required the mobilisation of more than 100,000 responders in Slovakia and Hungary to ensure flood mitigation and the evacuation of the affected population. As a result of climate change, it is assumed that the general flood risk for the Danube River Region will increase further in the future. With this risk, the risk of further casualties and economic damage is rising, too. This is where the DAREnet projects steps in and seeks to increase the flood resilience of the Danube Region countries.
Practitioner Driven Innovation Needed
Flood practitioners will have to adapt fast to the increasing flood risk as well as keeping pace with an ever faster changing society as an aging population and increasing urbanisation makes their work more challenging. In this context, research, development and innovation (RDI) become even more key-drivers for an improved performance and effectiveness of flood response across borders and disciplines. Innovations driven by the practitioners themselves are needed in order to enhance flood mitigation and response throughout the entire region. DAREnet will enable flood management practitioners in the Danube River Region to identify and analyse by and for themselves relevant innovation gaps and translate them into a joint innovation strategy to improve flood resilience in the future.
The DAREnet RDI Roadmap: Defining Needs and Innovation Opportunities
"DAREnet is a wonderful opportunity for all colleagues from disaster and civil protection to network, to exchange ideas and good practices and to formulate future needs – all of which are formulated in the project's RDI Roadmap," says Gerry Foitik, Federal Commander in charge of the Austrian Red Cross. The DAREnet RDI Roadmap is the result of an iterative process of identifying, assessing and prioritising promising innovation opportunities to cope with the main environmental and societal challenges of the Danube River Region. It maps RDI requirements and gaps and emerged from a broad practitioner/expert dialogue and the regular consultation of competent national disaster management authorities.
The roadmap provides a well-balanced RDI strategy and programme which reflects both the needs on the ground and RDI policies. It also provides concrete perspectives for the further development, industrialisation and uptake of innovations of highest relevance for practitioners. The roadmap will further be a contribution to support current or planned standardisation activities in the field of civil protection. The roadmap therewith builds a unique portfolio of joint innovation concepts for the Danube River Region.
DAREnet Supports New Practitioner Initiatives
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 655
|
\section{Introduction}
\label{sec:introduction}
\IEEEPARstart{L}{ight} field imaging has gained in popularity due to its potential for computer vision or computational photography applications. However, light fields represent very large volumes of data, hence the need for compact representations and efficient compression algorithms. Many solutions have been designed for compressing light fields which encode the set of input views using either video compression techniques as HEVC or variants of this standard \cite{Conti2016Bi, Ahmad2019}.
Light field views are reordered as a pseudo video sequence (PVS) which is then fed into the video codec. A predefined scan order such as raster and spiral~\cite{Raster,amirpour2018high} is typically used to generate a PVS.
Approaches based on low rank models \cite{FDL, INRIA_LF_dataset} or 4D steered Gaussian mixture of experts \cite{TMM1} have also been proposed for light field compression. The
Multidimensional Light field Encoder (MuLE)~\cite{mule}, which has been adopted in JPEG Pleno Coding standard as a transform-based coding approach, exploits the 4D redundancy of light field images by dividing them into 4D blocks. Thereafter, a 4D-DCT transform is applied to the blocks to exploit the redundancy \cite{4D-DCT}. Similarly the use of 6D transforms is investigated in \cite{krivokuca2021compression} for plenoptic point cloud compression.
The authors in \cite{liu2019content}
describe a prediction method based on a Gaussian Process Regression technique applied on different classes of light field textures.
Other methods consist in first synthesizing the entire light field from a subset of input views with the help of estimated disparity maps \cite{tb, DIBR1,zhang2022light,huang2020low}.
Here, we propose a completely different approach based
on Neural Radiance Fields (NeRF) which have been recently
introduced for scene representation and light field view
synthesis \cite{mildenhall2020nerf}. NeRF is an implicit Multi-Layer Perceptron-based
model that maps 5D vectors—3D coordinates plus 2D
viewing directions—to opacity and color values, computed
by fitting the model to a set of training views. The resulting neural model can then be used to generate any view of the light field using volume rendering techniques.
Several variants have been proposed to reduce the number of input views as in \cite{Yu2021pixelNeRFNR}, or to make the rendering more efficient \cite{Liu2020NeuralSV}.
A generalizable radiance field reconstruction is also proposed in \cite{MVSNeRF} which can reconstruct radiance fields from only three nearby input views via fast network inference, and which can be used for rendering scenes different from those on which the network has been trained.
An end-to-end framework, called NeRF--, is proposed in \cite{Wang2021NeRFNR} for training NeRF models without pre-computed camera parameters.
The authors in
\cite{jeong2021selfcalibrating} consider more complex non-linear camera models and propose a new geometric loss function to jointly learn the geometry of the scene and the camera parameters. The authors in \cite{Bemana2020xfields} generalize the usage of implicit neural representation to solve the problem of time, light and view interpolation.
NeRF can thus be seen as a neural representation of a scene which is learned from a set of input views. While existing light field compression solutions usually consider encoding and transmitting a subset of light field views which are then used at the decoder to synthesize and render the entire light field, we consider an alternative approach which optimizes and compresses the NeRF on the sender side, so that the network itself is transmitted to the receiver. The light field compression problem is thus cast into a problem of neural network compression. However, unlike compressing networks used in image classification or recognition tasks \cite{han2016deep}, compressing a view synthesis network is more challenging, due to the fact that the light field reconstruction quality is sensitive to network weight changes.
The model should not only be compact, but should also preserve as much as possible high reconstruction quality.
In this paper, we first consider a simplified NeRF model based on only one MLP for rendering instead of the coarse and fine MLP in \cite{mildenhall2020nerf}, which halves the number of parameters of the network.
We optimize the network under a low rank constraint. The learning problem is formulated as a tensor rank optimization problem, solved using the Alternating Direction Method of Multipliers (ADMM) iterative optimization method.
This low rank constraint allows us, following principles of network distillation \cite{Hinton2015DistillingTK}, to transfer knowledge from this initial NeRF to a model of a much smaller dimension based on a Tensor Train (TT) decomposition.
In other words, the weights of NeRF are decomposed into TT components using a distillation network, to decrease the number of parameters to be encoded. The TT parameters are further quantized using an optimized codebook.
The knowledge transfer is made possible thanks to the low rank constrained optimization of the large NeRF model.
The performance in terms of compression efficiency of the
proposed Quantized Distilled Low Rank Neural Radiance Field (QDLR-NeRF) for light fields has been assessed against the one obtained with a HEVC-based method \cite{SullivanHEVC, HEVCstandard}
and the Jpeg-pleno standard \cite{jpegpleno}
in the 4D Prediction Mode. We also compare the obtained performances with those of recent deep learning video compression methods, in particular with the Hierarchical Learned Video Compression (HLVC) \cite{yang2020Learning}, the Recurrent Learned
Video Compression (RLVC) \cite{yang2021learning} methods,
and the OpenDVC \cite{yang2020opendvc} solution based on Deep Video Compression (DVC) \cite{Lu2019DVC}. These video compression methods are applied to the sequence of light field views. While achieving very good distortion-rate performance, such motion estimation-based deep compression networks, as well as similar methods such as in \cite{lin2020m,Hu2020,Zou2020,Yilmaz2020}, often have complex structures, thus are not easy to train, and often need pre-trained optical flow estimators.
Our experimental results show that our method outperforms very recent deep video
compression methods requiring training on large datasets. It is also competitive against the standardized and highly optimized HEVC video compression tools applied to the sequence of views, as well as Jpeg-Pleno, a compression tool specifically designed for light fields.
So, in summary the contributions of this paper are:
\begin{itemize}
\item A low rank constrained simplified NeRF for compact light field representation.
\item A network distillation operation that transfers knowledge from the LR-NeRF to a more compact scene light field representation model DLR-NeRF via Tensor Train decomposition.
\item An efficient quantization operation guided by a global codebook, which tremendously reduces the total size of the representation with a limited distortion.
\item A complete light field compression algorithm
that integrates ADMM-based low rank optimization, network distillation and optimized quantization, giving superior performances when compared with
light field reference compression methods.
\end{itemize}
Note that the proposed approach can be used beyond light field compression, in particular to reduce the memory footprint of NeRF, which can be critical for devices with low memory resources.
\begin{figure*}[!h]
\centering
\includegraphics[width=0.99\linewidth]{figures/workflow.png}
\caption{Overall workflow of our proposed QDLR-NeRF method. A simplified NeRF (formed by only one MLP) is first trained from the set of input views, under a low rank (LR) constraint. The information from this LR-NeRF is distilled to a model of a much smaller dimension DLR-NeRF via the Tensor Train decomposition. The weight distillation is used to transfer knowledge in parameters of the large LR-NeRF to a smaller DLR-NeRF while keeping high performance. A codebook $C$ with $N$ centroids is learned to quantize DLR-NeRF to obtain the final compact QDLR-NeRF.}
\label{fig:workflow}
\end{figure*}
\section{Workflow and notations}
We consider a light field represented by a 4D function $L(x,y,u,v)$ \cite{levoy1996light}, with $(x,y)\in\llbracket 1,X \rrbracket \times \llbracket 1,Y \rrbracket$
and $(u,v)\in\llbracket 1,U \rrbracket \times \llbracket 1,V \rrbracket$ respectively its angular and spatial coordinates.
The overall workflow of our method is shown in Fig~\ref{fig:workflow}. The workflow is divided into three phases: 1) The low rank-constrained neural radiance field (LR-NeRF) optimization for scene reconstruction. 2) The network distillation for transferring knowledge from the LR-NeRF to a smaller model DLR-NeRF based on the Tensor Train decomposition. 3) The quantization of the TT components with an optimized codebook.
In the first step, a simplified NeRF with one MLP having weights $\{W_{i},b_{i}\}$ ($i$ is the layer index) is trained as an implicit scene representation, with the goal of having the best scene reconstruction given the set of input views. The obtained NeRF is finetuned under a low rank constraint by applying Alternating Direction Method of Multipliers (ADMM) optimization. The tensor of the finetuned weights of LR-NeRF $\{W^{r}_{i},b_{i}\}$ becomes low-rank after this step, where $r$ is the target rank. In the network distillation step, the weights of LR-NeRF are decomposed into a Tensor Train (TT) format as $W^{r}_{i} = Q^{1}_{i}\cdot Q^{2}_{i}$, and we use $\{Q^{1}_{i}, Q^{2}_{i}, b_{i}\}$ to initialize a distilled version of LR-NeRF noted DLR-NeRF. This step bonds the low rank optimization in previous step and the quantization in the next step. It can, on one hand, guarantee low rank property of $W^{r}_{i}$, on the other hand, allow quantifying $Q^{1}_{i}, Q^{2}_{i}$ without degrading the final compression performance. The last quantization step aims at reducing the model size by quantifying the network weights. A global codebook $C$ with $N$ centroids is learned from $Q^{1}_{i}, Q^{2}_{i}$ to quantify the values within the interval [-1,1] of DLR-NeRF, from the first layer to the last layer gradually. Larger values outside the interval [-1,1] are quantized with a uniform $16$-bit quantizer. Thereafter, both sets of values inside and outside the interval [-1,1] are coded using Huffman coding for optimal bitrate. The biases of the network $b_{i}$ are converted to 16 bits for further compacting the model size. We denote the quantized weights of QDLR-NeRF as $\{\hat{Q}^{1}_{i},\hat{Q}^{2}_{i},\hat{b}_{i}\}$
\section{Method}
\subsection{Simplified Neural Radiance Field}
In our method, we adopt NeRF to implicitly represent the scene, where 5D coordinates (location and view direction) of light rays $(x, y, z, \theta, \phi)$ are fed into an MLP to produce a color and volume density $(RGB,\sigma)$ for volumetric rendering. This procedure can be formulated as:
\begin{equation}
RGB,\sigma = F_{\Theta}(x,y,z,\theta,\phi),
\end{equation}
with $\Theta = \{W_{i},b_{i}\}$ being weights and biases of the MLP.
Let us note that the original version of NeRF uses two MLPs to respectively coarsely and densely sample rays (i.e. performing a hierarchical volume sampling). The camera pose parameters are estimated from given views using the COLMAP structure-from-motion package \cite{schonberger2016structure}. We instead adopt one
unique MLP for rendering, which halves the number of parameters of the network. Since COLMAP may fail to estimate the camera pose parameters, especially for narrow-baseline light fields, we set the camera pose parameters as trainable parameters like in \cite{Wang2021NeRFNR}. Focal length $f$ and offset $\Delta$ (proportional to the baseline) are the two camera pose parameters to be additionally optimized in our method (compared with unstructured views, the estimation of camera pose parameters of structured light fields is simpler). In this step, the rendering error is used as the loss function to supervise the initialization of NeRF and the update of its parameters $\{W_{i},b_{i},f,\Delta \}$ as:
\begin{equation}
argmin_{\{W_{i},b_{i},f,\Delta\}}||c'-c_{gt}||^{2}_{2},
\end{equation}
where $c'$ is the rendered pixel value and $c_{gt}$ is ground-truth pixel value.
\subsection{Low Rank NeRF approximation with ADMM}
Although the initial NeRF \cite{mildenhall2020nerf} gives a good scene reconstruction and could be used for light field compression, its model size makes transmitting such a network less efficient than transmitting the compressed light field views. We therefore further reduce the model size by applying a TT decomposition \cite{oseledets2011tensor} to the learned NeRF. The network weights $W_{i}\in \mathbb{R}^{n_{1}\times n_{2}}, \forall i$ are decomposed into the TT format as
\begin{equation}
\label{eq:TT}
W_{i} = Q^{1}_{i}\cdot Q^{2}_{i},
\end{equation}
where $Q^{1}_{i}\in \mathbb{R}^{1\times n_{1}\times r}$ and $Q^{2}_{i}\in \mathbb{R}^{r\times n_{2}\times 1}$ are the TT cores, and $r$ is the target rank controlling the compression ratio.
Straightforwardly decomposing the full-rank tensor $W_{i}$ into a low-rank TT format inevitably causes a large approximation error, which degrades the light field reconstruction quality and the compression efficiency. To guarantee the low rank property of the tensor $W_{i}$ without performance degradation, the authors in \cite{yin2021towards} formulate the model compression as a tensor rank optimization problem, and leverage Alternating Direction Method of Multipliers(ADMM) to solve this optimization problem in an iterative manner. In this section, we adopt this ADMM-based low rank approximation to finetune the learned NeRF. This optimization can be formulated as
\begin{gather}
argmin_{\{W_{i},b_{i}\}} ||c'-c_{gt}||^{2}_{2}\\
s.t. \ \ rank(W_{i}) < r,
\end{gather}
where $r$ is the desired rank of $W_{i}$.
This non-convex optimization with constraints can be solved using the ADMM optimization method, after introducing an auxiliary variable $Z$ and an indicator function $g(\cdot)$, as
\begin{equation}
\label{indicator_function}
g(W_{i}) = \!
\begin{cases}
0, rank(W_{i}) < r \\
+\infty, otherwise.
\end{cases}
\end{equation}
The original optimization problem can then be rewritten as:
\begin{gather}
argmin_{\{W_{i},Z_{i}\}} ||c'-c_{gt}||^{2}_{2} +g(Z_{i})\\
s.t. \ \ W_{i} = Z_{i}
\end{gather}
and the corresponding augmented Lagrangian in the scaled dual form of such an optimization problem is defined as
\begin{equation}
\mathcal{L}(W_{i},Z_{i},U_{i}) = l(W_{i})+g(Z_{i})+\frac{\rho}{2}||W_{i}-Z_{i}+U_{i}||^2_{F}+\frac{\rho}{2}||U_{i}||^{2}_{F},
\end{equation}
where $\rho$ is a positive penalty parameter, $U_{i}$ is the dual multiplier, and $l = ||c'-c_{gt}||^2_{2}$ is the reconstruction error. The optimization of this Lagrangian term can be performed in an alternative way, as
\begin{align}
\label{w_problem}
W_{i}^{t+1} &= argmin_{\{W_{i}\}} \mathcal{L}(W_{i}^{t},Z_{i}^{t},U_{i}^{t}),\\
\label{z_problem}
Z_{i}^{t+1} &= argmin_{\{Z_{i}\}}\mathcal{L}(W_{i}^{t+1},Z_{i}^{t},U_{i}^{t}),\\
U_{i}^{t+1} &= U_{i}^{t} + W_{i}^{t+1} - Z_{i}^{t+1}
\end{align}
Eq.\ref{w_problem} corresponding to the updates of $W_{i}$ can be solved using gradient descent. Eq.\ref{z_problem} can be solved according to \cite{boyd2011distributed} as
\begin{equation}
Z_{i}^{t+1} = \Pi_{r}(W^{t+1}_{i}+U^{t}_{i}),
\end{equation}
where $\Pi_{r}$ is the operation that decomposes the matrix into the TT format truncated to the desired rank $r$. One can refer to \cite{yin2021towards} for details on the ADMM procedure.
After this ADMM-based optimization procedure, the weights of the network $W^{r}_{i}$ are low rank, hence can be decomposed into the TT format as in Eq.~\ref{eq:TT}, with a small approximation error. For sake of simplicity, in the following, we neglect the first dimension of $Q^{1}_{i}$ and the last dimension of $Q^{2}_{i}$, hence $Q^{1}_{i}$ and $Q^{2}_{i}$ are respectively with size $n_{1}\times r$ and $r\times n_{2}$. As the vector of bias parameters of each layer $b_{i}$ is of rank 1, they are not considered in this optimization. In summary, after this low-rank optimization step, the parameters of the layers $\{W^{r}_{i},b_{i}\}$ are approximated by their TT components $\{Q^{1}_{i},Q^{2}_{i},b_{i}\}$ for the following processing steps.
\begin{figure}[!t]
\centering
\subfigure[Weight distribution before quantization]{
\label{fig:weight_distribution_before}
\includegraphics[width=0.8\linewidth]{figures/quantization/ft.png}}\\
\subfigure[Weight distribution after quantization, the number of centroid is 256.]{
\label{fig:weight_distribution_after}
\includegraphics[width=0.8\linewidth]{figures/quantization/quant.png}}
\vspace{-0.2cm}
\caption{The weight distribution of $\{Q^{1}_{i},Q^{2}_{i}\}$ before\&after rate-constrained quantization, we take light field scene `\textit{sideboard}' as an example, the target rank $r=40$ and number of centroid for quantization is $N=256$.}
\label{fig:weight_distribution}
\end{figure}
\begin{figure}[t]
\centering
\setlength{
\tabcolsep}{1pt}
\centering
\begin{tabular}{cc}
\includegraphics[width=0.48\linewidth]{figures/anchor_basic/lf_5_5_ft.png} &
\includegraphics[width=0.48\linewidth]{figures/anchor_basic/lf_5_5_anchor.png} \\
\end{tabular}
\caption{Reconstructed views (`\textit{boxes}(5,5)') using (left) $16$ bits quantization and (right) coarse quantization of the weights outside the interval $[-1,1]$.}
\label{fig:anchor_basic}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.85\linewidth]{figures/quantization_layers.png}
\caption{PSNR evolution after quantizing each layer. We take the light field scene `\textit{sideboard}' with diffrent ranks $r=\{ 40,50,70,90\}$ as an example.}
\label{fig:quantization}
\end{figure}
\subsection{Rate-Constrained Quantization}
\label{sec:quantization}
The decomposition of the weights $W_{i}$ of the finetuned LR-NeRF into TT components reduces the model size. Beyond this low rank approximation, to further reduce the model size, one can in addition quantify the TT components $\{Q^{1}_{i}, Q^{2}_{i}, b_{i}\}$ as follows.
We quantify $\{Q^{1}_{i}, Q^{2}_{i}\}$ and $\{b_{i}\}$ in different manners. As $\{Q^{1}_{i}, Q^{2}_{i}\}$ occupy a much larger proportion of the total number of parameters, quantization is mainly performed on $\{Q^{1}_{i}, Q^{2}_{i}\}$. Fig.~\ref{fig:weight_distribution_before} shows the weight distribution of $\{Q^{1}_{i}, Q^{2}_{i}\},\forall i$. One can observe that most of the parameters are within the interval $[-1,1]$. Quite few parameters are outside the interval [-1,1]. These parameters represent about 0.5\% of the total number of parameters of $\{Q^{1}_{i}, Q^{2}_{i}\}$. However, as we show in Fig.~\ref{fig:anchor_basic}, the weights outside the interval [-1,1] are essential to have a good light field reconstruction and should not be coarsely quantized, which explains our choice of using a fine $16$ bit quantizers for these low probability values.
Therefore we quantize the weights inside and outside the interval $[-1,1]$ in two different manners. More specifically, the weights outside $[-1,1]$ are quantized using a uniform $16$ bits quantizer to keep enough precision. In contrary, the weights within $[-1,1]$ are quantized using a non uniform optimized quantizer, whose codebook $C$ is obtained by applying the k-means method to cluster weights into $N$ centroids. This is motivated by the fact that the two sets of weights have very different distributions. The weights outside the interval $[-1,1]$ have a low and close to uniform probability, making the use of a k-means based optimized quantizer less relevant for this set of weights. In addition, the low number of values would make the clustering, hence the quantization, not very effective.
Unlike in \cite{fan2020training}, where the authors learn a codebook for each layer of the network, we learn a unique codebook $C$ to quantize the weights within [-1,1] in all layers. Fig.~\ref{fig:weight_distribution_after} shows the weight distribution after rate-constrained quantization with 256 centroids. To alleviate the performance loss caused by this quantization, we adopt a quantization-aware training strategy in this step, i.e., after quantizing $\{Q^{1}_{n},Q^{2}_{n}\}$ of layer $n$, we continue to train the other layers and update $\{Q^{1}_{i},Q^{2}_{i}\} \forall i>n$ and $\{b_{i}\} \forall i$. Once all layers have been quantized, we update the codebook and proceed with a new quantization. In our experiment, we however found that, in most of cases, only one round of codebook update is enough. We show in Fig.~\ref{fig:quantization} the performance loss after quantizing layers from the first to the last, one can notice that thanks to our quantization-aware training procedure, there is barely any PSNR loss after quantizing first several layers, performance degradation is mainly caused by quantization of some layers and is quite limited. When the weights of all the layers have been quantized, we losslessly encode them using Huffman Coding.
While we could encode separately the two sets of weights,
we instead construct a Huffman code table for all the values (within and outside the interval $[-1,1]$). Separately encoding each set with an entropy code (e.g. Huffman code) would require sending an extra flag to signal whether the weight belongs to one set or the other, which would penalize the entire bit rate. Even if having a unique Huffman codebook for a larger number of weight values (the union of the two sets) would in theory increase the average Huffman code length, the number of large value is sufficiently small so that this average code length is not significantly increased. Simulations have shown that this solution was indeed more efficient in terms of bitrate.
Biases $\{b_{i}\}$ are simply saved using 16 bits.
One could think of integrating both constraints of low rank approximation and weight quantization within the ADMM framework. However, this is extremely challenging. Indeed, since the low rank tensor approximation and the weight quantization are not convex functions, their integration in the ADMM framework may raise convergence issues.
Another option is to consecutively apply these two techniques, i.e., finetuning the network with a low rank constraint (getting $W^{r}_{i}$), then decomposing $W^{r}_{i}$ into TT components and quantizing them (getting $\hat{Q}^{1}_{i}$ and $\hat{Q}^{2}_{i}$) finally retrieving the weights $\hat{W}^{r}_{i}$. Although this option avoids considering low rank constraint and quantization at the same time in ADMM, due to the fact that the quantization operation is performed on TT components $Q^{1}_{i}, Q^{2}_{i}$ instead of $W_{i}$ itself, any subtle perturbation on $Q^{1}_{i}, Q^{2}_{i}$ may lead to significant variations of the weights $W^{r}_{i}$. Hence such an option is unstable and the light fields reconstructed using $\hat{W}^{r}_{i}$ are prone to artifacts.
In order to avoid the above difficulties, and better bond the low rank optimization and the quantization of the TT components, we propose a `distilled' version of LR-NeRF. More specifically, for weights and bias $\{W^{r}_{i}, b_{i}\}$ in each layer of LR-NeRF, we use the corresponding TT components $Q^{1}_{i}, Q^{2}_{i}$ and bias $b_{i}$ to initialize two distilled layers, which finally gives us a distilled architecture.
\begin{figure*}[ht]
\centering
\setlength{
\tabcolsep}{1pt}
\centering
\begin{tabular}{ccccc}
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/r40_c32_paper.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/r40_c64_paper.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/r40_c256_paper.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/r70_c256_paper.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/r90_c256_paper.png} \\
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/WD_r40_c32.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/WD_r40_c64.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/WD_r40_c256.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/WD_r70_c256.png} &
\includegraphics[width=0.2\linewidth]{figures/rank_centroid/WD_r90_c256.png}\\
$(r=40,N=32)$ & $(r=40,N=64)$&$(r=40,N=256)$ &$(r=70,N=256)$ & $(r=90,N=256)$\\
PSNR = 24.60dB & PSNR = 27.17dB & PSNR = 31.10dB & PSNR = 34.71dB & PSNR = 35.22dB \\
\end{tabular}
\caption{We show in the first row the central view of the light field `\textit{sideboard}' reconstructed by quantized DLR-NeRF with different rank\¢roid settings. The second row shows the weight distribution of each quantized DLR-NeRF. Larger is the rank of the model and higher is the number of centroids, better will be the reconstructed view.}
\label{fig:rank_centroid}
\end{figure*}
\subsection{Network Distillation}
\label{sec:distillation}
The distillation of LR-NeRF is crucial to our workflow, since it leads to a smaller network whose weights are defined by the matrices $Q^{1}_{i}$ and $Q^{2}_{i}$.
This distillation mechanism also allows quantizing
$Q^{1}_{i}$ and $Q^{2}_{i}$ without necessity to reconstruct $W^{r}_{i}$, as $Q^{1}_{i}$ and $Q^{2}_{i}$ are the weights of the smaller distilled network. Therefore the low-rank constrained ADMM optimization in the first step and quantization-aware training in the last step are `physically' separated by this network distillation. The rank optimization and the bitrate optimization will not mutually interfere.
Please note that a layer with weight $W^{r}_{i}$ is actually distilled into two layers with weights $Q^{1}_{i}$ and $Q^{2}_{i}$ only if the resulting number of parameters is reduced compared to the number of weight values in the matrix $W^{r}_{i}$.
We further train DLR-NeRF for a certain number of epochs after initializing it using $Q^{1}_{i}, Q^{2}_{i}, b_{i}$.
Please note that one could also skip the previous NeRF initialization and low rank finetuning procedures, and train a distilled NeRF from scratch. However, as we will discussed in Sec.~\ref{sec:random_init}, the weights trained from scratch follow a different distribution from the one of the low-rank weights, and they fail to reconstruct high quality scene views.
After applying the quantization operation on this DLR-NeRF, the obtained QDLR-NeRF can be used to represent a light field in the compression context. One can indeed transmit the quantized network weights $\hat{Q}^{1}_{i}, \hat{Q}^{2}_{i}$ (after Huffman Coding), $\hat{b}_{i}$ (16 bits), the codewords (32 bits) and the camera parameters $f,\Delta$ (32 bits) from the sender to the receiver.
\begin{figure*}[!ht]
\centering
\setlength{
\tabcolsep}{1pt}
\centering
\begin{tabular}{cc}
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/boxes_rate.png} &
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/sideboard_rate.png} \\
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/cotton_rate.png} &
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/dino_rate.png} \\
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/Bikes_rate.png} &
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/Danger_rate.png} \\
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/Stone_rate.png} &
\includegraphics[width=0.43\linewidth,height=0.23\textheight]{figures/rate_distortion/Fountain_rate.png} \\
\end{tabular}
\caption{Rate-distortion curves of different compression methods, with tested light fields from the HCI synthetic dataset \cite{honauer2016dataset} and the EPFL real-world dataset \cite{EPFLLFdataset}.}
\label{fig:rate_distortion}
\end{figure*}
\section{Training schedule and hyperparameters}
The training of such a workflow has four phases,
as follows.
a).\textbf{Training the simplified NeRF:} We simplified the architecture of NeRF by adopting one single MLP for inference. The depth of the adopted MLP is $8$ and the number of channels is 256. We set the sampling rate along the rays to $128$ and the camera pose parameters $(f,\Delta)$ are initialized to $f= 0.01W$ ($W$ is the width of the light field views), $\Delta=10$. We adopt normalized depth for rendering. When training such a network, we followed the default configuration in \cite{mildenhall2020nerf}, with the initial learning rate set to $5\times 10^{-4}$ and the exponential decay rate to $0.1$. We finally trained the network for $3\times 10^{5}$ iterations.
b).\textbf{Finetuning LR-NeRF:} We finetuned LR-NeRF following the same configuration as in the previous step, except that in this step, the camera pose parameters are no longer updated. We finetune LF-NeRF for $3\times 10^{5}$ iterations. The penalty factor $\rho$ for ADMM is set to $10$.
c).\textbf{Finetuning DLR-NeRF:} After the TT decomposition of the LR-NeRF weights and the initialization of DLR-NeRF, we continued to finetune DLR-NeRF for $2\times 10^{5}$ iterations, during which the camera pose parameters are kept fixed.
d).\textbf{Quantizing DLR-NeRF:} The quantization of the layers of DLR-NeRF is gradually carried out from the first to the last layer.
After quantizing each layer, we train the other layers for $3 \times 10^{4}$ iterations. The initial codebook for the interval $[-1,1]$ is obtained after $20$ iterations of clustering in the k-means algorithm. Although the codebook can be updated after each round of quantization, we just update it once in practice.
Our proposed workflow has been implemented using pytorch and has been trained on a GPU of type GeForce RTX 2080 Ti with 11 GB memory.
\begin{figure*}[!ht]
\centering
\setlength{
\tabcolsep}{1pt}
\centering
\begin{tabular}{cccccc}
GT view(5,5) & RLVC & HLVC & HEVC & JPL & Ours\\
\includegraphics[width=0.16\linewidth]{figures/error_maps/boxes_5_5.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/boxes_error_rlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/boxes_error_hlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/boxes_error_hevc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/boxes_error_jpl.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/boxes_error_ours.png}\\
boxes & PSNR=35.49dB & PSNR=34.68dB & PSNR=35.73dB & PSNR=36.51 & PSNR=38.19dB\\
& bpp=0.110 & bpp=0.094 & bpp=0.099 & bpp=0.100 & bpp=0.105\\
\includegraphics[width=0.16\linewidth]{figures/error_maps/sideboard_5_5.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/sideboard_error_rlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/sideboard_error_hlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/sideboard_error_hevc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/sideboard_error_jpl.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/sideboard_error_ours.png}\\
sideboard & PSNR=30.36dB & PSNR=28.52dB & PSNR=30.21dB & PSNR=32.02 & PSNR=34.18dB\\
& bpp=0.156 & bpp=0.139 & bpp=0.133 & bpp=0.130 & bpp=0.128\\
\includegraphics[width=0.16\linewidth]{figures/error_maps/Danger_5_5.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Danger_error_rlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Danger_error_hlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Danger_error_hevc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Danger_error_jpl.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Danger_error_ours.png}\\
FountainVincent & PSNR=31.50dB & PSNR= 31.86dB & PSNR=31.39dB & PSNR=32.79 & PSNR=33.04dB\\
& bpp=0.104 & bpp=0.141 & bpp=0.110 & bpp=0.100 & bpp=0.110\\
\includegraphics[width=0.16\linewidth]{figures/error_maps/Fountain_5_5.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Fountain_error_rlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Fountain_error_hlvc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Fountain_error_hevc.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Fountain_error_jpl.png} &
\includegraphics[width=0.16\linewidth]{figures/error_maps/Fountain_error_ours.png}\\
Danger & PSNR=30.48dB & PSNR= 30.51dB & PSNR=30.25dB & PSNR=30.62 & PSNR=30.96dB\\
& bpp=0.110 & bpp=0.090 & bpp=0.110 & bpp=0.100 & bpp=0.103\\
\end{tabular}
\caption{Averaged reconstruction error maps of decompressed light fields, when using the RLVC, HLVC, HEVC, Jpeg-pleno methods and our method, along with the corresponding PSNR and bitrate values.}
\label{fig:error_map}
\end{figure*}
\section{Compression performance analysis}
\subsection{Settings}
We first trained a simplified NeRF with full rank. This initial model is then finetuned and distilled using four different ranks $r = \{150, 90, 70, 40\}$, and we finally quantized the distilled models with $N =256$ centroids.
The quantized models having a lower rank have fewer parameters, hence give a lower bitrate. We found that, when the target rank $r$ is lower than $40$, the light field reconstructed with the distilled Low-Rank NeRF (DLR-NeRF) is prone to artifacts.
Therefore, we do not decrease the rank below $40$, and to decrease the bitrate, we reduce the number of centroids to further reduce the model size.
More precisely, we set $N = \{256, 64, 32\}$ when $r = 40$.
To test the effectiveness of our method, we carry out experiments using both synthetic and real-world light fields. Both of them are from widely used light field benchmark. For synthetic light fields, we took four scenes \textit{boxes, sideboard, cotton, dino} from the HCI dataset \cite{honauer2016dataset}, each of them has an angular resolution $(U,V)=(9,9)$ and a spatial resolution $(X,Y)=(512,512)$. While for real-world light fields, we took four scenes \textit{Bikes, Danger, StonePillarsOutside, FountainVincent2} from the EPFL light field dataset \cite{EPFLLFdataset}, which have been captured using a plenoptic Lytro Illum camera. We took the central $9\times9$ views, each view having a spatial resolution of $432\times 624$. Although ground truth camera poses are already available for synthetic data, we estimated the camera poses for both the synthetic and real-world data to show that our workflow is not limited by the availability of the camera pose parameters.
\subsection{Rate-Distortion Performance}
Fig.~\ref{fig:rank_centroid} shows the central view reconstructed using the QDLR-NeRF with different $(r,N)$ settings, and their corresponding weight probability distributions. One can easily notice that, larger is the rank of the DLR-NeRF model or higher is the number of centroids better is the reconstructed view. This is quite intuitive, as a larger rank means more parameters a model has, and more centroid means less quantization noise.
However, in the compression context, besides the quality of the `compressed views', we also need to take bitrate into account, i.e. the rate-distortion performance. To investigate the compression performance of our proposed method, we measure the rate-distortion performances with different rank\¢roid settings, and compare them with those obtained when applying State-Of-The-Art (SOTA) video compression methods to light fields, by encoding the views as a pseudo video sequence. The codecs that we consider are the HEVC-Lozenge \cite{rizkallah2016impact}, the
Jpeg-pleno VM2.0 standard designed specifically for light field compression,
and learning-based RLVC \cite{yang2021learning}, HLVC \cite{yang2020Learning} and OpenDVC \cite{yang2020opendvc} compression methods. OpenDVC is an open implementation of the DVC \cite{Lu2019DVC}.
For the settings of each reference method, we use the HEVC HM-16.10 implementation in our test, with a GOP size equal to $4$.
The Jpeg-pleno standard needs an input disparity map that we estimated using the technique in \cite{shi2019depth}.
When considering the RLVC, HLVC and OpenDVC methods, we directly used the authors' codes with the recommended configurations, i.e., for the RLVC method, we set the P-frames number to $6$ for both the forward and backward directions, which means a GOP size of $13$, while for the HLVC and OpenDVC methods, we used the default setting of GOP size equal to 10. When testing the reference methods RLVC, HLVC and OpenDVC, we used their trained models. There are four pre-trained models for each method, with an optional hyper-parameter $\lambda = \{256, 512, 1024, 2048\}$ that controls the trade-off between distortion and bitrate. Higher $\lambda$ means less distortion but larger bitrate.
Fig.~\ref{fig:rate_distortion} shows the PSNR-Rate curves of each method with different light fields.
The bitrate is evaluated by bit per pixel (bpp). One can observe from the figures, that our proposed method outperforms the reference methods on synthetic data at moderate bitrate by a margin about 1dB in most of the tested scenes. While on real-world light fields, though the margin is smaller than that of synthetic data, our method still shows superiority than other referenced methods in most of cases.
Actually, due to the fact that light fields captured by Lytro Illum may contain artifacts such as vignetting, blurriness etc., which are caused by its hardware. When applying a NeRF-based compression method, these artifacts will prevent our method from reconstructing the accurate scene, hence lowering the PSNR of the reconstructed views.
Figure \ref{fig:error_map} shows the averaged error maps for the different methods. Note that the error maps are averaged over all the views, to account for the fact that some methods, such as Jpeg-Pleno, RLVC, OpenDVC, lead to strong variations in quality on the different views (see Fig.~\ref{fig:psnr_indices}).
We can observe that our method yields lower error and better compression results than other methods on synthetic data (\textit{boxes}, \textit{sideboard}). When using real-world Lytro light fields suffering from color inconsistency between angular views, our method may learn inaccurate scene information and hence generate some errors (like the windows in scene \textit{FountainVincent}). However, it can still well capture scene geometry information and better reconstruct the object contours (like the contours of the person in the scene).
Compared with the referenced methods that compress each input frame, our method focuses on retrieving the entire scene with as fewer parameters as possible. This distinct design endows our method with two advantages:
\begin{figure}
\centering
\includegraphics[width=0.99\linewidth]{figures/psnr_indices/psnr_indices.png}
\caption{PSNR variation along the viewpoints for the light field `\textit{boxes}'. All views have been compressed at a similar bitrate.}
\label{fig:psnr_indices}
\end{figure}
1). Better consistency across views. Fig.~\ref{fig:psnr_indices} shows the PSNR variations in terms of viewpoints (For Jpeg-pleno, the central view serves as the reference view and has higher PSNR).
Similarly, the RLVC, DLVC and OpenDVC methods first intra code key frames, and then compress the other frames within the GOP using motion-compensated inter-coding. The quality of the compressed light fields is therefore not stable and varies across the different viewpoints. In contrast, our method yields views with a more consistent quality and higher PSNR values. Each view is indeed rendered independently, thus enabling full random access, which is not the case of methods relying on inter-coding.
2). Capacity of rendering views in any angular position. Different from other methods that compress a set of input views, our method, thanks to NeRF, encodes the scene information. Hence the scene can be flexibly reconstructed by rendering the light field in any angular position on the decoder side.
\begin{figure*}[!ht]
\centering
\setlength{
\tabcolsep}{1pt}
\centering
\begin{tabular}{ccccc}
\includegraphics[width=0.2\linewidth,height=0.2\linewidth]{figures/rand_lr/rand.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/boxes_rand_5_5.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/sideboard_rand_5_5.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/cotton_rand_5_5.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/dino_rand_5_5.png} \\
\includegraphics[width=0.2\linewidth,height=0.2\linewidth]{figures/rand_lr/lr.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/boxes_lr_5_5.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/sideboard_lr_5_5.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/cotton_lr_5_5.png} &
\includegraphics[width=0.2\linewidth]{figures/rand_lr/dino_lr_5_5.png} \\
Weight distribution & boxes(5,5) & sideboard(5,5) & cotton(5,5) & dino(5,5)
\end{tabular}
\caption{Weight distribution and views reconstructed using NeRF-rand (1st row) and NeRF-lr (2nd row), with several scenes.}
\label{fig:rand_lr}
\end{figure*}
\subsection{Ablation Study}
In this section, we evaluate different aspects of the proposed method.
\subsubsection{Random initialization vs Low-rank initialization}
\label{sec:random_init}
As aforementioned in Sec.~\ref{sec:distillation}, instead of the proposed NeRF initialization and finetuning steps, one could directly train a distilled NeRF with randomly initialized weights. Although this variant has a simpler training schedule, we show that it severely degrades the quality of the reconstruction. To evaluate the interest of the proposed distillation approach, we adopted the architecture of the distilled NeRF with rank $40$, and respectively initialized it using random weights (noted as NeRF-rand) and low-rank weights (noted as NeRF-lr). We then trained the two models until convergence. To guarantee the same experimental conditions, the two variants share the same camera pose and are trained without quantization.
Table~\ref{table:rand_lr} shows the PSNR of the light fields generated by NeRF-rand and NeRF-ft, with the same camera pose. The distilled NeRF trained with randomly initialized weights yields poor reconstruction quality. While NeRF trained with low-rank weights gives a good reconstruction quality. Fig.~\ref{fig:rand_lr} shows views reconstructed when using the two variants, and an example of weight distribution (for the light field `\textit{boxes}'). From the figure, we can observe that the weights of NeRF-rand and NeRF-lr follow different distributions. NeRF-lr has more values around 0 and long tails, NeRF-rand has fewer values around 0. Most weights are within the interval
$[-0.25,0.25]$ and the distribution does not have long tails. In terms of reconstruction
quality, NeRF-rand produces views with severe blurriness, while NeRF-lr gives views with subtle details, which means that it is better to use the low-rank NeRF to initialize the distilled version. The difference in terms of performance between NeRF-lr and NeRF-rand can be explained by the fact that, due to its low number of parameters of the distilled network, the optimization of the distilled network from scratch (with random initialization) may fall in local minima, giving a lower performance compared to the use of weights resulting from the low rank approximation of the large network.
\begin{table}[t]
\begin{center}
\scalebox{0.9}{
\begin{tabular}{c|c|c|c|c|c}
\hline
Variants & boxes & sideboard & dino & cotton & \textbf{average}\\
\hhline{------}
\hline
NeRF-rand & 25.18dB & 19.88dB & 23.27dB & 32.56dB & \textbf{25.22dB}\\
\hhline{------}
NeRF-lr & 37.85dB & 30.93dB & 40.90dB & 45.18dB & \textbf{38.72dB}\\
\hline
\end{tabular}}
\end{center}
\caption{Average PSNR of views generated by NeRF initialized with random weights and with low-rank weights (with $r=40$). Both variants have fully converged.}
\label{table:rand_lr}
\end{table}
\subsubsection{Quantization strategy analysis}
\noindent
\textbf{Local quantization vs global quantization }
Instead of using a global codebook of $N$ centroids for quantizing all layers, one can also utilize one codebook optimized for each layer. Table~\ref{table:quantization_option} shows the average PSNR and bitrate obtained when using the different quantization options, i.e. with no quantization (DLR-NeRF-noQuant), with a quantizer optimized for each layer (DLR-NeRF-localQuant) and a global codebook for all layers (DLR-NeRF-globalQuant).
The local quantization suffers less from distortion but increases significantly the bitrate compared with the global quantization. While global quantization brings more distortion, its compression ratio is higher.
Therefore, we adopted a global quantizer as it gives a lower bitrate with acceptable performance loss. Moreover, learning one codebook is much easier than learning several codebooks per layer.
\begin{table}[!t]
\begin{center}
\scalebox{0.9}{
\begin{tabular}{c|c|c}
\hline
Quantization options & PSNR & Bitrate\\
\hhline{---}
\hline
DLR-NeRF-noQuant & 38.72dB & 0.30bpp\\
\hhline{---}
DLR-NeRF-localQuant & 38.70dB & 0.12bpp\\
\hhline{---}
DLR-NeRF-globalQuant & 38.18dB & 0.06bpp\\
\hhline{---}
\hline
\end{tabular}}
\end{center}
\caption{Average PSNR and Bitrate obtained when using different quantization options: with no quantization (DLR-NeRF-noQuant), with one codebook for each layer (DLR-NeRF-localQuant), and when using a shared codebook for all layers (DLR-NeRF-globalQuant).}
\label{table:quantization_option}
\end{table}
\subsubsection{Contribution of the different blocks of the architecture}
To justify the contribution of each building block of the workflow, we measure the averaged PSNR and the model size after each step of our algorithm, and set original NeRF \cite{mildenhall2020nerf} (NeRF-org) as our baseline, with whose size being 100\%. The original NeRF has coarse and fine MLPs, and uses grund truth camera poses for synthesis. In our workflow, we instead adopt a simplified NeRF with only one MLP to learn scene information, and optimize it with a low rank constraint (LR-NeRF). The camera poses are estimated during the optimization of the LR-NeRF. Then this LR-NeRF is distilled into the DLR-NeRF with respect to the desired rank, here, we set desired the rank to $r=40$ for LR-NeRF and DLR-NeRF. DLR-NeRF is finally quantized with the number of centroids set to $N=256$ to obtain QDLR-NeRF.
Table~\ref{table:building_block} gives the PSNR and the model size evolution after each step of our workflow. The PSNR and size values are averaged over four synthetic scenes. We can observe from the table that, the transition from NeRF-org to LR-NeRF brings about 3dB PSNR loss. The loss is due to two factors:
1.) The camera poses are estimated instead of being ground truth camera poses, which introduces some errors 2.) The low rank constraint slightly decreases the synthesis performance.
One could also think that this loss is caused by using only one MLP for synthesis. However, with most of light fields, the default sampling rate of $128$ along light rays is enough for one single MLP to yield high quality reconstruction. The replacement of two MLPs by one barely bring any performance loss.
From LR-NeRF to DLR-NeRF, by distilling the network with the desired rank $r=40$, we reduce the model size by a factor of $3$ with only a 0.1dB PSNR loss. This small loss means, that the target rank of $40$ (the full rank being 256) can already store most of scene information for reconstruction, which also proves the effectiveness of our low rank approximation.
From DLR-NeRF to QDLR-NeRF, the network is quantized from the first to the last layer, this gradual quantization step effectively reduces the model size to 1/5, with a limited performance loss of 0.6dB.
In summary, thanks to the proposed low rank optimization, network distillation and quantization operations, we ultimately reduce the model size from 100\% (the reference being the bit number of the original NeRF) to 3.3\%, which is crucial in a context of light field compression, but also simply in terms of storage requirement for the NeRF model.
\begin{table}[t]
\begin{center}
\scalebox{0.9}{
\begin{tabular}{c|c|c|c|c}
\hline
Metrics & NeRF-org & LR-NeRF & DLR-NeRF & QDLR-NeRF \\
\hhline{-----}
\hline
PSNR & 41.98dB & 38.83dB & 38.72dB & 38.18dB \\
\hhline{-----}
Size & 100\% & 50\% & 16.7\% & 3.3\% \\
\hline
\end{tabular}}
\end{center}
\caption{PSNR averaged on the $8$ test light fields at the different steps of the proposed workflow: Original NERF (NeRF-org), NERF with the low rank constraint (LR-NeRF), Distilled low-rank NeRF (DLR-NeRF) and after quantization of DLR-NeRF (QDLR-NeRF).}
\label{table:building_block}
\end{table}
\section{Discussion}
Although our proposed method is able to effectively compress light fields, due to the fact that, it is based on the NeRF method, factors that limit the performance of NeRF will consequently become limitations of our method. For example, when applying NeRF to learn light fields captured by Lytro, blurriness and vignetting in each sub-aperture view may prevent the network from reconstructing precise scenes. As a result, the compression performance of our QDLR-NeRF is limited by these artifacts. While better performance is obtained on synthetic data, as they do not include these artifacts. That also explains why the gaps between the rate-distortion curves of our method and those of the reference methods on synthetic light fields are larger than those on Lytro-captured light fields.
Finally, please note that, even if we have chosen the original NeRF to demonstrate the interest of the proposed method, the method can obviously apply to different variants of NeRF implementations, e.g., SIREN\cite{sitzmann2019siren}, PlenOctrees\cite{Yu_2021_ICCV}, including to the recent SIGNET solution \cite{Feng_2021_ICCV}.
\section{Conclusion}
In this paper, we have proposed a Quantized Distilled Low Rank Neural Radiance Field (QDLR-NeRF) representation for light field compression. The method optimizes a NeRF with a low rank constraint using an ADMM optimization framework to obtain the so-called LR-NeRF, the weights in LR-NeRF are low-rank, hence can be decomposed into a Tensor Train format. The decomposed weights are then used to initialize a distilled version of NeRF named DLR-NeRF, which has fewer parameters. Finally, we gradually quantize the layers of DLR-NeRF from the first layer to the last one using a global codebook learned by k-means, to get QDLR-NeRF. The distillation operation avoids tackling the rank-constrained optimization and the rate-constrained quantization simultaneously, making the entire pipeline work stably to compress a light field. The low rank optimization and quantization operations effectively reduce the size of the model without significantly degrading the reconstruction performance. Experimental results, using both synthetic and real-world light fields, show that our method outperforms the reference methods with a large margin. Furthermore, due to the fact that our method is based on synthesis method, it also has the advantage of generating novel views as densely as possible.
\ifCLASSOPTIONcompsoc
\section*{Acknowledgments}
\else
\section*{Acknowledgment}
\fi
This work was supported in part by the french ANR research agency in the context of the artificial intelligence project DeepCIM, and in part by the EU H2020 Research and Innovation Programme under grant agreement No 694122 (ERC advanced grant CLIM). We would also like to show our gratitude to Prof. Zhaolin Xiao, Dr. Xi Wang and Mr. Kai Gu for inspiring discussions.
\bibliographystyle{IEEEtran}
\normalem
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"redpajama_set_name": "RedPajamaArXiv"
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{"url":"https:\/\/www.physicsforums.com\/threads\/complex-problem-please-help-f-z-sqrt-xy-in-x-iy-form.289134\/","text":"1. Feb 1, 2009\n\n### saraaaahhhhhh\n\n1. The problem statement, all variables and given\/known data\n\nIn the title: f(z) = sqrt(|xy|)...show that this satisfies the Cauchy-Riemann equations at z=0, but is not differentiable there.\n\n2. Relevant equations\n\nCauchy-Riemann just states that partial u partial x = partial v partial y and partial u partial y = - partial v partial x.\n\n3. The attempt at a solution\n\nI think all the partials du\/dx, du\/dy, dv\/dx, and dv\/dy are 0. Because f(0) is 0 in this case, right? Maybe that's wrong. Maybe I'm assumign too much by saying that if z=0, x and y also are 0.\n\nAnyway, then I just need to show the limit as h->0 for differentiation doesn't exist, right? If what I said above is right, than it would just be plugging in some x_0 and y_0 (if h = x_0 + iy_0) for x and y and than finding the limit for when x_0 = 0 and when y_0 = 0, and as long as those aren't equal then it's not differentiable.\n\nDoes this sound right, or totally off?\n\n2. Feb 2, 2009\n\n### gabbagabbahey\n\nYou're supposed to take the partial derivatives first and then evaluate them at z=0; not the other way around!\n\n3. Feb 2, 2009\n\n### saraaaahhhhhh\n\nWouldn't that mean the Cauchy-Riemann equations don't hold? I'm a little unsure on what u would be in this case.\n\nDo I need to separate sqrt(|xy|) into the real and imaginary parts? Or can I just assume all is real and then take the partial derivates of u, and the partials of v would just be 0, since there's no complex part?\n\nThis is why I think Cauchy-Riemann wouldn't hold, but I'm not sure.\n\nThanks so much for the response! I do appreciate it.\n\n4. Feb 2, 2009\n\n### saraaaahhhhhh\n\nJust to go ahead and try this: would partial u partial x be y(xy)^(-1\/2)?\nAnd then partial u partial y be x(xy)^(-1\/2)?\nAnd both partials of v be 0? This is assuming that sqrt(xy) is just the 'real' part...if f(z) takes the form u + iv.\n\nI have a feeling this is wrong, since Cauchy-Riemann is supposed to hold and doesn't hold using this method. But if it's wrong, how am I supposed to figure out what u and v are in cases like this?\n\n5. Feb 2, 2009\n\n### gabbagabbahey\n\nYes, x and y are real numbers, so |xy| is a positive, real number and so sqrt(|xy|) is real.\n\nCareful, what do you get for $$\\frac{\\partial u}{\\partial x}$$ and $$\\frac{\\partial u}{\\partial y}$$....where do they equal zero?\n\n6. Feb 2, 2009\n\n### saraaaahhhhhh\n\nI'm not sure what you're saying here. I think you get that they don't exist or are undefined, because there would be 0 on the bottom of a fraction? But I'm not sure where you're going with this.","date":"2016-12-09 02:14:14","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\": 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\": 0.8018235564231873, \"perplexity\": 727.9235888908103}, \"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-2016-50\/segments\/1480698542668.98\/warc\/CC-MAIN-20161202170902-00291-ip-10-31-129-80.ec2.internal.warc.gz\"}"}
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\section{INTRODUCTION}
An accurate and real-time estimation of the vehicle sideslip angle is essential to strengthen the performance of active vehicle control systems. The state-of-the-art estimation of sideslip angle mostly relies on model-based approaches using an Unscented Kalman Filter (UKF). Despite its efficiency and robustness, the process and observation noise parameters must be accurately tuned to achieve good performance \cite{chen2018weak, abbeel2005discriminative}. The noise parameters selection is particularly relevant because they need to capture the following aspects:
\begin{itemize}
\item Process and observation model mismatch with respect to the real vehicle dynamics.
\item Discretisation error because the time-step in the Kalman filter influences the noise parameters to achieve the best state estimation \cite{chen2021time}.
\item Different working conditions of the sensors installed in the vehicle.
\end{itemize}
If the tuning is obtained through numerical optimisation, the cost function is highly non-convex, non-smooth and nonlinear, calling for robust optimisation methods \cite{chen2018weak}.
Several optimisation algorithms for UKF tuning \cite{acosta2019optimized} have been studied: GA, Sequential Quadratic Programming, Nelder-Mead, Artificial Bee Colony, Fruit Fly Optimisation (FFO) and Differential Evolution. The comparison demonstrates that each algorithm leads to different optimum locations, illustrating the importance of the optimization method. However, a comparison regarding the amount of data and the optimisation time has been omitted. Furthermore, only stochastic optimisation algorithms have been compared that can be inefficient if the UKF takes a long simulation time. For vehicle sideslip angle estimation, large-scale training sets representing vehicle behaviour \cite{mazzilli2021benefit} make the cost function evaluation very time-consuming. In different engineering applications, several solutions have been proposed, e.g. Reinforcement Learning (RL) \cite{tang2021reinforcement} or Bayesian Optimisation (BO) \cite{chen2018weak}. However, the majority of these are tested only on simulation data or toy examples. A more detailed analysis of previous works is in Section II. \newline
\begin{figure}[t]
\centering
\setlength{\fboxrule}{0pt}
\framebox{\parbox{3in}{\includegraphics[scale=0.35]{Pictures/Drawing1.jpg}}}
\caption{Framework utilizing a Two-Stage Bayesian Optimisation (TSBO) to tune the process noise parameters of a UKF.}
\label{Framework}
\end{figure}
This paper proposes a new UKF tuning methodology using Two-Stage Bayesian Optimisation (TSBO) \cite{torun2018global}, based on a t-Student Process (tSP) for vehicle sideslip angle estimation. The proposed methodology to tune the process noise parameters reduces the optimisation time and improves the optimum localisation. Both process and observation noise are assumed Gaussian, zero mean and uncorrelated, as for the majority of the model-based vehicle state estimation filters \cite{heidfeld2020ukf}. The methodology framework is represented in Figure \ref{Framework}, a more detailed explanation will be presented in Section IV. The observation noise parameters are tuned by performing a statistical analysis of the vehicle sensor measurements \cite{mazzilli2021benefit}. The process noise parameters' tuning is based on optimising a cost function defined as the sum of the Normalized Root Mean Squared Errors (NRMSE) of the vehicle states and measurements for 8 manoeuvres. The 8 manoeuvres which compose the training set and the 23 forming the test set are selected from a real-world experimental dataset composed of 216 manoeuvres recorded at the Automotive Testing Papenburg GmbH. The manoeuvres are chosen to cover a wide range of vehicle motions. The cost function is optimised using the modified TSBO
\cite{torun2018global}. It consists of a fast exploration and a pure exploitation stage to find the optimum, reducing the number of simulations required. Differently from the TSBO proposed in \cite{torun2018global}, the surrogate model is a tSP to enhance the robustness and the ability to capture heavy-tailed NRMSE. The methodology is experimentally validated using a UKF, but can also be applied to an Extended Kalman Filter (EKF). \looseness = -1
\section{PREVIOUS WORKS}
Despite the extensive use of UKF for vehicle sideslip angle estimation, the tuning of the process and observation noise parameters is rarely investigated in the literature. The observation noise parameters are usually tuned through statistical analysis, obtained after sensor calibration tests \cite{mazzilli2021benefit}. The only exception is when the observation noise parameters are tuned together with the process noise parameters \cite{heidfeld2021optimization}. This rarely happens because the filter performance depends mainly on the ratio between the eigenvalues of the observation and process covariance matrices. Thus, it is more convenient to fix the observation noise parameters, which can be determined through sensor calibration, and optimise the process noise parameters.The methodologies for process noise parameters tuning can be split into three different categories: \emph{manual tuning}, \emph{metaheuristic} optimisation and \emph{data-driven} techniques. An overview of optimisation algorithms for UKF tuning is shown in Table \ref{Table_Overview}. \looseness = -1
\emph{Manual tuning} is a trial-and-error approach driven by the user experience. The idea is to perform a grid search in the parameter space and reach the best tuning iteratively. Despite the oversimplicity of the concept, it is still very often used, especially for vehicle sideslip angle estimation \cite{van2018adaptive}, because the performance of Kalman filters is stable for a range of process noise parameters settings \cite{mazzilli2021benefit}.
The main drawback is the inefficiency of the approach.
Moreover, there is no proof to reach the optimal performance. This leads to an unreliable comparison when different filter architectures are analysed.
Thus, Kalman filter tuning with numerical optimisation techniques are widely used. Gradient-based optimisations are the most straightforward algorithms which can be implemented \cite{kerst2019}, but the non-convex and nonlinear cost functions let them easily be trapped into local minima. Thus, gradient-free optimisation algorithms are introduced. One of the simplest algorithms is the coordinate descent algorithm \cite{abbeel2005discriminative} which consists of a cycling increase or decrease of each parameter of the process covariance.
A similar optimisation technique is the downhill simplex algorithm \cite{powell2002automated}, which consists of evaluating the cost function at the simplex vertices of the predefined sample space. After this, the algorithm should converge to the optimum through a series of movements: reflection, expansion, and contraction. Interested reader can find more information on both algorithms in \cite{abbeel2005discriminative} and \cite{powell2002automated} respectively. These algorithms may easily fall in local optima when the cost function is non-smooth, so more advanced metaheuristic optimisations have been proposed.
\emph{Metaheuristics} are procedures that can provide an acceptable solution to an optimisation problem with incomplete information about the cost function. Examples of metaheuristic algorithms are: the already cited downhill simplex algorithm \cite{powell2002automated}, GA \cite{oshman2000optimal} or the Multi-Objective GA \cite{mazzilli2021benefit}, SA \cite{heidfeld2021optimization} and FFO \cite{acosta2019optimized}. A comparison of different metaheuristic algorithms for Kalman filter tuning \cite{acosta2019optimized} shows that GA and FFO found the best cost function optimum. This explains why GA is the current state-of-the-art for UKF tuning for vehicle sideslip angle estimation, which is applied in many recent publications \cite{mazzilli2021benefit}. GA is an evolutionary algorithm that tries to emulate Darwin's theory of natural evolution.
Due to the high number of generations required, GA can be very time-consuming when the cost function is costly to evaluate.
\begin{table}[t]
\caption{Overview of the optimisation algorithm most used to tune the noise parameters of nonlinear Kalman filter.}
\label{Table_Overview}
\begin{center}
\begin{tabular}{| >{\centering\arraybackslash}m{1in} | >{\centering\arraybackslash}m{1in} | >{\centering\arraybackslash}m{0.6in} |}
\hline
\textbf{Authors} & \textbf{Process noise tuning} & \textbf{Dataset}\\
\hline
van Aalst, 2018 \cite{van2018adaptive} & Manual Tuning & Experimental \\
\hline
Abbeel, 2005 \cite{abbeel2005discriminative} & Coordinate Ascent Algorithm & Experimental \\
\hline
Powell, 2002 \cite{powell2002automated} & Downhill Simplex Algorithm & Simulated \\
\hline
Mazzilli, 2021 \cite{mazzilli2021benefit}, Oshman, 2000 \cite{oshman2000optimal} & Multi-Objective GA, GA & Experimental \\
\hline
Acosta, 2019 \cite{acosta2019optimized} & FFO & Simulated \\
\hline
Heidfeld, 2021 \cite{heidfeld2021optimization} & Simulated Annealing & Experimental \\
\hline
Tang, 2021 \cite{tang2021reinforcement} & RL & Experimental \\
\hline
Escoriza, 2021 \cite{Escoriza2021} & Recurrent Neural Network & Experimental \\
\hline
Chen, 2018 \cite{chen2018weak}, Chen, 2019 \cite{chen2019kalman} & BO based on Gaussian \& t-Student Process & Simulated \\
\hline
\textbf{Current Paper} & \textbf{TSBO with t-Student Process} & \textbf{Experimental} \\
\hline
\end{tabular}
\end{center}
\end{table}
\emph{Data-driven} optimisation algorithms such as BO are based on the creation of a surrogate model, Gaussian Processes GP \cite{chen2018weak}, or tSP \cite{chen2019kalman}, using as inputs the tuning parameters and as output the value of the cost function. The surrogate model does not only approximate the cost function, but also it is associated with a model probability distribution. The acquisition function takes this information to find the new parameters with the highest probability of being the best new optimum. Standard BO fits the surrogate model on parameters randomly taken from the sample space, but this can lead to a non-optimal surrogate model. Furthermore, it will require many cost function evaluations if the sample space is broad.
Other data-driven approaches can be implemented; for instance, Reinforcement Learning RL can be applied to choose the parameters of the process noise, or RL can compensate for the error of the Kalman filter \cite{tang2021reinforcement} due to not-optimal process noise parameters. A similar concept is the so-called "KalmanNet" \cite{Escoriza2021} which uses a Recurrent Neural Network RNN to compute the Kalman gain, reducing the problems of non-optimal Kalman tuning. Despite the potential of RL and RNN, the amount of data required to train the Neural Networks makes them impractical for the tuning/improvement of Kalman filter for sideslip angle estimation. \looseness = -1
The main contributions of this paper are twofold. The first is the development of a new TSBO based on a tSP for tuning the process noise parameters of UKF for vehicle sideslip angle estimation. The TSBO in this paper differs from a recent TBSO related to electronic design \cite{torun2018global} because the surrogate model is based on a tSP to increase its robustness and ability to reach a better global optimum without increasing the required computational power.
The second contribution is that the developed TSBO reduces the number of simulations required to tune the Kalman filter with respect to the state-of-the-art GA \cite{mazzilli2021benefit,acosta2019optimized} and it improves the accuracy of the tuning respect GA. The tuning performance is tested and validated using an experimental dataset for vehicle sideslip angle estimation.
\section{BAYESIAN OPTIMISATION}
Filter tuning consists of minimising a nonlinear, non-convex and non-smooth cost function due to the reasons already expressed in section I. A minimisation problem is:
\begin{equation}
\begin{aligned}
& \text{min}_{\;q\;\in\;Q}\;J\left(q\right) \\
& \text{where} \;\; Q \subseteq\;\Re^d
\end{aligned}
\label{eq1}
\end{equation}
\noindent
where $q$ is the parameter vector of dimension $d$, $J\left(q\right)$ is the cost function, and $Q \subseteq\;\Re^d$ is the solution space. The function $J\left(q\right)$ is a "black-box" function because it is not accessible, but its outputs are observed based on some given inputs. Thus, "black-box" stochastic optimisation algorithms are considered. It is time-consuming to perform a dense sampling of the solution space $Q$, so the algorithm should focus on sampling the subset of $Q$ with the highest probability to contain the cost function optimum $q^*$. BO can deal with incomplete and sparse knowledge of the solution thanks to its probabilistic approach. It is based on the Bayes' theorem
\begin{equation}
P\left(\text{beliefs}\; |\; \text{data}\right) = \dfrac{P\left(\text{beliefs}\right) \times P\left(\text{data}\; |\; \text{beliefs}\right) }{P\left(\text{data}\right) }
\label{eq2}
\end{equation}
\noindent
where data are the available observations of the function $J\left(q\right)$, beliefs are the beliefs of the shape of $J\left(q\right)$, and $P\left(\text{beliefs}\; |\; \text{data}\right)$, $P\left(\text{data}\; |\; \text{beliefs}\right)$, $P\left(\text{beliefs}\right)$, and $P\left(\text{data}\right) $ are the posterior, likelihood, and the marginal probabilities respectively. Thus, BO aims to find $q^*$ learning the shape of $J\left(q\right)$ through Bayesian inference. The TSBO overcomes the standard BO due to its ability to define a better ratio between exploration (function shape learning) and exploitation (approaching the optimum).
BO can be split into two steps: creating a stochastic process of the cost function, called "Surrogate Model", and building an "Acquisition Function" that uses the surrogate model to approach the optimum $q^*$.
\subsection{Surrogate Model}
\begin{figure}[t]
\centering
\setlength{\fboxrule}{0pt}
\framebox{\parbox{3in}{\includegraphics[scale=0.28]{Pictures/DEF_GPVSTP.JPG}}}
\caption{GP and sTP model of the cost function varying the process noise parameter related with the vehicle lateral velocity. The tSP allows more outliers and it can follow the measurements better than the GP. The shadow area is the variance of the tSP and the uncertainty for the GP.}
\label{tSPvsGP}
\end{figure}
BO approximates the "black-box" cost function through a stochastic process called the surrogate model. It represents a probabilistic prior over the space of functions. The prior is updated as soon as the cost function is evaluated thanks to the Bayes' Theorem. Different priors are eligible for being the surrogate model; a partial list comprises: GP, tSP, Bayesian neural networks and polynomial chaos expansion. GP are the current state-of-art because it is a non-parametric model \cite{torun2018global}, and the Bayesian update step is analytical. Despite this, in this paper a tSP prior is selected for the surrogate model due to two reasons. The first one is that the t-Student distribution allows defining the level of Kurtosis, so it allows much more likely outliers \cite{shah2014student,tracey2018upgrading} than GP. The second reason is that the observations directly influence the predictive covariance \cite{shah2014student,tracey2018upgrading}. Both properties are beneficial for the tuning of UKF because the cost function can have discontinuities, for instance, due to the noise. Figure \ref{tSPvsGP} shows the explained differences between tSP and GP modelling in an example that models the cost function varying the process noise parameter related with lateral velocity. It is visible how tSP reduces the influence of the outliers, allowing the mean to have a better fitting.
The tSP is defined as:
\begin{equation}
f\left(q\right) = tSP\left(m\left(q\right),\;k\left(q,q'\right),\; \nu \right)
\label{eq3}
\end{equation}
\noindent
where $m\left(q\right)$ represents the mean which is assumed equal to constant zero mean function because there is no prior \cite{torun2018bayesian}, $\nu$ are the degrees of freedom of the t-Student distribution, which defines the level of Kurtosis, and $k\left(q,q'\right)$ is the Kernel function between the inputs pair $q$ and $q'$. The choice of the Kernel is essential to have a reliable model fitting. This paper chooses the automatic relevance determination Matérn $5/2$ function, due to its generalisation capabilities and interpretability properties:
\begin{equation}
k_{q,\;q'} = k(q,\;q')=\sigma_f^2\left(1+\frac{\sqrt{5}r}{\sigma_d}+\frac{5\,r^2}{3\,\sigma_d^2}\right)e^{-\frac{\sqrt{5}r}{\sigma_d}}
\label{eq4}
\end{equation}
\noindent
where $r$ is the Euclidean distance between the two points $q$ and $q'$ calculated as:
\begin{equation}
r = \sqrt{\left(q-q'\right)^T\left(q-q'\right)}
\label{eq5}
\end{equation}
\noindent
where $\sigma_f$ and $\sigma_d$ are two hyperparamters, which are trained to minimize the negative log marginal likelihood of the tSP. It is essential to highlight that tSP should be accurate only when there are higher chances of finding the cost function optimum. Thus, every time a new observation is available, the surrogate model is retrained. tSP are implemented using the GPML Matlab Code version 4.2 \cite{williams2006gaussian}.
\subsection{Acquisition Function}
The Acquisition Function AF is responsible for moving the BO towards the optimum region, choosing the next sample point to be evaluated. Thus, it is responsible for defining the ratio between exploration, moving the search towards the area where the surrogate model is uncertain, and exploiting, moving the search towards the area with a higher chance of improving the current optimum. Ideally, the more focus is given to the exploration stage, the higher the chances to find the global optimum; however, it increases the computational time due to a larger number of cost function evaluations.
The next point to be evaluated ($q_{t+1}$) is usually obtained through an additional optimisation of the AF. This paper evaluates the AF on some candidate points obtained through the process that will be explained in Section IV to avoid further optimisation. The AF is evaluated on the candidate points \cite{williams2006gaussian, tracey2018upgrading} according to:
\begin{equation}
\hat{\mu}_{\,tSP}\left(q_{t+1}\right) = k_{q,\,q}^T\,K_{\tilde{q},\;\tilde{q}}^{-1}\,f\left(\tilde{q}\right)
\label{eq6}
\end{equation}
\noindent
where $\tilde{q}$ are the sampling points already evaluated, $\hat{\mu}_{\,tSP}$ is the posterior mean of a tSP for a new sampling point $q$ and $k$ is defined in Eq. \ref{eq4}.
\begin{multline}
\hat{\sigma}^2_{\,tSP}\left(q_{t+1}\right) = \left(\frac{\nu+f\left(\tilde{q}\right)^T\,K_{\tilde{q},\;\tilde{q}}^{-1}\,J\left(\tilde{q}\right)-2}{\nu + |D| -2}\right)\times(k\left(q,q\right) + \\-k_{q,\;\tilde{q}}^T\,K_{\tilde{q},\;\tilde{q}}^{-1}\,k_{q,\;\tilde{q}})
\label{eq7}
\end{multline}
\noindent
where $\hat{\sigma}_{\,tSP}$ is the posterior covariance, and $D$ is the set of samples $D=\left[\left(\tilde{q}_1,J\left(\tilde{q}_1\right)\right),\; \left(\tilde{q}_2,J\left(\tilde{q}_2\right)\right), \; \left(\tilde{q}_3,J\left(\tilde{q}_3\right)\right),\;...\,\right]$. \newline
Two AFs are selected: the Expected Improvement (EI) and the Confidence Bound Minimisation (CBM) \cite{clare2020expected}.
The EI is defined as:
\begin{multline}
EI_{\,tSP}\left(q\right)= \hat{\sigma}_{\,tSP}\left(q\right)\,\left(\frac{\nu}{\nu-1}\right)\,\left(1+\frac{z_s^2}{\nu}\right)\,\phi\left(z_s\right)+\\
+ \left[ \hat{y} - \hat{\mu}_{\,tSP}\right]\,\Phi\left(z_s\right)
\label{eq8}
\end{multline}
\noindent
where $\phi\left(z_s\right)$ and $\Phi\left(z_s\right)$ are the probability density function and the cumulative distribution function of an univariate standard t-Student's random variable, $z_s$, and $\hat{y}$ is the current optimum sampled by the BO.
The CBM is formulated as:
\begin{equation}
CBM_{\,tSP}\left(q\right)= \hat{\sigma}_{\,tSP}\left(q\right)\,\sqrt{\beta} + \left[f^*- \hat{\mu}_{\,tSP}\right]
\label{eq9}
\end{equation}
\noindent
where the $\beta$ defines the ratio between exploitation and exploration, and $f^*$ is the best known optimum, representing the prior knowledge of the optimum.
\section{TWO-STAGE BAYESIAN OPTIMISATION}
This paper proposes an evolution of the BO to tune the process noise parameters of the UKF. It is called TSBO, code by \cite{torun2018global}, and aims to reduce the number of function evaluations, and improve the ratio between exploitation and exploration. The trade-off improvement is obtained thanks to the subdivisions of the BO in two stages. The first, "fast exploration", aims to find the sample space region where the optimum is contained. The second, "pure exploitation", aims to fine-tune the restricted sample space obtained from the first stage. The first stage allows starting the surrogate model training from a single evaluation at the centre of the sample space. This allows the user not to evaluate a random set of process noises to fit the first surrogate model.
\subsection{Fast Exploration}
The fast exploration aims to narrow the sample space $Q\subseteq \Re^d$ where the BO search the optimum as fast as possible. It consists of subdividing the sample space into $2^d$ hyper-rectangles. Every hyper-rectangle centre point is a candidate point, which the AF evaluates to choose the next sampling point $q_{\,t+1}$ where the cost function is evaluated. The following sampling point is not obtained as in the standard BO through an auxiliary optimisation of the AF, but it is the candidate point with the maximum value of the AF between the other candidate points. The cost function is only evaluated at points $q_{\,t+1}$. A new set of hyper-rectangles is generated starting from the hyper-rectangle enclosing the best candidate point. The two available AFs, EI and CBM, are alternatively used to evaluate the candidate points. After a predefined number of iterations $MAX_{AF}$, the AF which would have had the greatest gain to the optimisation is selected as final AF.
The fast exploration stage is repeated until the euclidean distance between the new best sampling point $q_{t+1,\;max}$ and the previous best sampling point $q_{t\;max}$ is below a user-defined threshold $TR_{FE}$ for a number of times $MAX_{FE}$:
\begin{equation}
n = \begin{cases}
n+1\,, \;\;\;\;\;\;\;& \text{if} \;\;\; ||q_{\,t+1,\,max} - q_{\,t,\,max}|| < TR_{FE}\\
0\,, \;\;\;\;\;\;\; & \text{otherwise} \\
\end{cases}
\label{eq10}
\end{equation}
Every time the cost function is evaluated and a new measurement is available; the surrogate model is retrained to improve the fitting with the black-box function.
Algorithm \ref{alg1} sums up the fast exploration stage of the TSBO.
\begin{algorithm}
\caption{Fast Exploration stage of the TSBO}
\label{alg1}
\begin{algorithmic}
\Require A sample space $Q$ and an evaluated sampling point at the center of $Q$
\State Fit the tSP Surrogate model
\State Subdivide $Q$ in $2^d$ hyper-rectangles
\While{$n \le MAX_{FE}$}
\State Compute candidate points at the center of hyper-rectangles
\State Evaluate AF at the candidate points
\State Pick the candidate points with the maximum AF
\If{$||q_{\,t+1\,max} - q_{\,t\,max}|| < TR_{FE}$}
\State $n+1 \gets n$
\ElsIf{$||q_{\,t+1\,max} - q_{\,t\,max}|| \geq TR_{FE}$}
\State $n \gets n$
\EndIf
\State Evaluate the cost function in the sampling points
\State Train the tSP of the Surrogate with the new observation
\State Subdivide the hyper-rectangle which were enclosing the best candidate points in $2^d$ hyper-rectangles
\EndWhile
\end{algorithmic}
\end{algorithm}
\begin{algorithm}
\caption{Pure Exploitation stage of the TSBO}
\label{alg2}
\begin{algorithmic}
\Require $n = MAX_{FE}$
\While{$n_{iter} \le MAX_{PE}$, and the output from Algorithm 1}
\State Compute candidate points at the center of hyper-rectangles
\State Evaluate AF at the candidate points
\State Pick the candidate points with the maximum AF
\State Evaluate the cost function in the sampling points
\If{$n_{iter} \le MAX_{SM}$}
\State Train the tSP of the Surrogate with the new observation
\EndIf
\State Subdivide the hyper-rectangle which were enclosing the best candidate points in $3^d$ hyper-rectangles
\EndWhile
\end{algorithmic}
\end{algorithm}
\subsection{Pure Exploitation}
The pure exploitation stage follows a procedure similar to the fast exploration, but it specialises in refining the optimum position. The first step is the computation of the sample space $\tilde{Q}^d$ around the optimum computed in the fast exploration stage:
\begin{equation}
\tilde{Q}^d = \begin{bmatrix}
\left(1-\alpha\right)\,q^*_{\,1} & \left(1+\alpha\right)\,q^*_{\,1}\\
\vdots & \vdots\\
\left(1-\alpha\right)\,q^*_{\,d} & \left(1+\alpha\right)\,q^*_{\,d}
\end{bmatrix}
\label{eq11}
\end{equation}
\noindent
where $\alpha$ is a hyper-parameter that defines how wide the sample space should be, and $q^*_i$ is the optimum sampling point obtained in the fast exploration stage. The new sample space $\tilde{Q}^d$ is divided into $3^d$ hyper-rectangles to have more candidate points to evaluate. The higher number of candidate points helps the pure exploitation stage to converge faster to the global optimum of the function. The rest of the procedure is the same of the fast exploration. The only difference is that when the number of evaluated sampling points $n_{iter}$ is higher than a predefined threshold $MAX_{SM}$, the tSP is no more retrained.
Algorithm \ref{alg2} summarises the pure exploitation stage of the TSBO, which is iterated until $n_{iter}$ is lower than a user-defined threshold $MAX_{PE}$.
\section{APPLICATION: UKF TUNING}
The proposed TSBO based on tSP is tested on the tuning of the process noise parameters of a UKF for vehicle sideslip angle estimation. In this paper, the single-track model with tyre axle forces computed by the Dugoff tyre is chosen as the vehicle model. The states are the longitudinal velocity at the Center-of-Gravity CoG $V_x$, the lateral velocity at the CoG $V_y$ and the yaw rate $\dot{\psi}$ while the vehicle measurements are the $V_x$, the lateral acceleration at the CoG $a_y$ and the $\dot{\psi}$. The vehicle sideslip angle $\beta_s$ is obtained as $\beta_s = \arctan{\frac{V_y}{V_x}}$:
\subsection{Dataset}
All the manoeuvres that compose the training set and test set are taken from a real-world experimental dataset composed of 216 manoeuvres which correspond to 2 hrs of driving. It puts together standard vehicle dynamics manoeuvres, e.g. double lane change, slalom, random steer, J-turn, spiral, braking in a turn, and steady-state circular tests, together with recorded laps at the Papenburg track. All manoeuvres were performed on dry asphalt with tyres inflated according to the vehicle specifications.
All manoeuvres are recorded using the BMW test platform instrumented by the inertial measurement unit, wheel force transducers for all four wheels, GPS and an optical sensor from Corrsys-Datron to measure the sideslip angle. The high-end optical speed sensor is not present in consumer vehicles and will be used as a reference for TBSO tuning and validation.
The UKF should be tuned for different working conditions, so various vehicle maneuvers are jointly considered in the training set. The training set is composed of 8 manoeuvres: 1 braking in a turn, 1 skidpad, 2 J-turn, 2 slaloms and 2 lance change.
A test set composed of 23 manoeuvres is taken to prove the generalization capability of the approach. All 23 maneuvers of the test set are different from the training set even if, some of them have similar characteristics. The manoeuvres are: 2 braking in a turn, 2 skidpad, 5 J-turn, 4 slalom, 4 lane change, 2 random steer, 1 lap track and 3 spiral. The characteristics of the manoeuvres cover a wide range of vehicle driving behaviours and different settings of the Electronic Stability Control.
\subsection{Cost Function Formulation}
In this paper, the UKF tuning aims to improve the accuracy of the vehicle state estimation, therefore, this paper focuses on an objective function defined by minimising the Normalised Root Mean Squared Error NRMSE rather than maximising the negative log-likelihood \cite{abbeel2005discriminative}.
The minimisation problem is described as:
\begin{equation}
\begin{aligned}
& \text{min}_{\;q\;\in\;Q} \;J\left(q\right) \\
& \text{where} \;\; Q =\;\begin{bmatrix}
q_{\,1,\, min} & q_{\,1,\, max}\\
\vdots & \vdots\\
q_{\,d,\, min} & q_{\,d,\, max}
\end{bmatrix}
\end{aligned}
\label{eq13}
\end{equation}
\noindent
where $J$ is the cost function defined as:
\begin{equation}
\begin{aligned}
& J = W_1\,E_{\beta} + W_2\,E_{\dot{\psi}} + W_3\,E_{a_y} \\
&\text{where}\;\; E_j = \sqrt{\frac{\sum_{i=1}^{N{\,man}}\left(NRMSE_{j,\;i}\right)^2\,N_{s,\;i}}{\sum_{i=1}^{N_{\,man}}N_{s,\;i}}}
\end{aligned}
\label{eq14}
\end{equation}
\noindent
where $W_1$, $W_2$, $W_3$ are the weights of the cost function, $N_s$ is the length of the manoeuvre measured in sampling points, $N_{man}$ is the number of manoeuvres considered in the training set, and $NRMSE$ is computed as follow:.
\begin{equation}
NRMSE = \sqrt{\frac{\sum_{k=1}^{N_s}\left(\hat{X}_k-X_k\right)^2}{N_s}}\frac{1}{\text{max}\left(|X|\right)}
\label{eq15}
\end{equation}
\noindent
where $X$ and $\hat{X}$ are the vectors of the measured and estimated states respectively.
\subsection{Key Performance Indicator}
The accuracy of the estimation of sideslip angle is evaluated through the use of the root mean squared error RMSE, maximum absolute error MAE, the RMSE and the MAE when the absolute vehicle acceleration $a_y$ is greater than \SI{4}{m/s^2}, which are respectively abbreviated with RMSE\textsubscript{NON} and MAE\textsubscript{NON}. The latter is used to analyse how the UKF tuning is especially relevant when the vehicle behaves in a nonlinear way.
\section{RESULTS}
The performance in terms of minimisation time and optimum localisation of the TSBO based on tSP is compared with the current state-of-the-art technique GA and with a TSBO based on GP. All optimisations perform in the same sample space $Q$ where all the process noise parameters for $V_x$, $V_y$ and $\dot{\psi}$ vary from $10^{-10}$ to 1.
The optimisation parameters for TSBO based on tSP and GP are summarised in Table \ref{par_TSBO}. The parameters for GA are summarized in Table \ref{par_GA}.
\begin{table}[b]
\caption{User-defined parameters for TSBO optimisations.}
\label{par_TSBO}
\begin{center}
\begin{tabular}{| >{\centering\arraybackslash}m{0.9in} | >{\centering\arraybackslash}m{0.7in} | >{\centering\arraybackslash}m{0.7in} |}
\hline
\textbf{Parameters} & \textbf{TSBO - tSP} & \textbf{TSBO - GP} \\
\hline
Likelihood function & t-Student 's & Gaussian \\
\hline
Inference & Variational Bayes & Exact \\
\hline
Kernel function & Matérn ARD $5/2$ & Matérn ARD $5/2$ \\
\hline
Mean function & Constant & Constant \\
\hline
$\nu$ & 15 & NA \\
\hline
$MAX_{FE}$ & 15 & 15 \\
\hline
$MAX_{PE}$ & 40 & 40 \\
\hline
$MAX_{SM}$ & 38 & 38 \\
\hline
$TR_{FE}$ & $0.01\parallel \;q^* \parallel$ & $0.01\parallel \;q^* \parallel$ \\
\hline
$\beta$ & 0.01 & 0.01 \\
\hline
$\alpha$ & 0.15 & 0.15 \\
\hline
$W_1$, $W_2$, $W_3$ & 5, 1, 1 & 5, 1, 1\\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}[t]
\caption{User-defined parameters for GA optimisation.}
\label{par_GA}
\begin{center}
\begin{tabular}{| >{\centering\arraybackslash}m{0.9in} | >{\centering\arraybackslash}m{0.9in} |}
\hline
\textbf{Parameters} & \textbf{GA} \\
\hline
Population size & 15 \\
\hline
Max generations & 15\\
\hline
Élite count & 0.75 \\
\hline
Crossover fraction & 0.8 \\
\hline
$W_1$, $W_2$, $W_3$ & 5, 1, 1 \\
\hline
\end{tabular}
\end{center}
\end{table}
The optimum cost and optimisation time for the TSBO based on tSP, TSBO based on GP and GA are summarised in Table \ref{res_com_tab} and Figure \ref{res_com_pic}.
\begin{table}[t]
\caption{Numerical results of the optimum cost function and optimisation time using different algorithms for UKF tuning.}
\label{res_com_tab}
\begin{center}
\begin{tabular}{| >{\centering\arraybackslash}m{0.9in} | >{\centering\arraybackslash}m{0.9in} | >{\centering\arraybackslash}m{0.9in} |}
\hline
\textbf{Algorithm} & \textbf{Total cost [-] } & \textbf{Optim. time [s]}\\
\hline
Manual tuning & 1.714 & NA\\
\hline
GA & 0.378 & 1599\\
\hline
TSBO - GP & 0.400 & \textbf{306}\\
\hline
TSBO - tSP & \textbf{0.316} & 320\\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{figure}[b]
\centering
\setlength{\fboxrule}{0pt}
\framebox{\parbox{3in}{\includegraphics[scale=0.3]{Pictures/Number_of.JPG}}}
\caption{Performance comparison of TSBO based on tSP, TSBO based on GP and GA.}
\label{res_com_pic}
\end{figure}
Figure \ref{res_com_pic} shows how both TSBOs approach the global optimum faster than GA. Where TSBO converges after 40 evaluations of the cost function, the GA needs at least 220 evaluations, resulting in TSBO being on average \SI{79}{\%} faster than GA. Thus, TSBOs are particularly convenient when the cost function evaluation is computationally heavy, for instance, due to numerous manoeuvres considered in the training set. Despite the faster optimisation, TSBO based on tSP reaches an optimum \SI{16.4}{\%} lower than the GA optimum. The proposed algorithm outperforms the state-of-the-art approach both in terms of optimisation time and optimisation accuracy. TSBO based on GP is \SI{4.4}{\%} faster than TSBO based on tSP. The rise in optimisation time is due to the surrogate model's training phase, which is slower for the tSP due to the more optimisation parameters. The better optimisation accuracy, \SI{21}{\%}, of the tSP than the GP is due to the higher Kurtosis of the t-Student's distribution which makes the non-parametric model capable of dealing with outliers. A much higher optimisation accuracy compensates for the slight higher computational time. \newline
Table \ref{Trai} presents the RMSE, MAE, RMSE\textsubscript{NON} and MAE\textsubscript{NON} of the sideslip angle for the various optimised UKFs. The reported values are the average of all manoeuvres composing the training set. Table \ref{Trai} highlights how the cost function's minimisation is related to the KPIs used to compare the estimation accuracy because TSBO based on tSP outperforms the other algorithms. On average, the RMSE of the sideslip angle optimised with tSBO based on tSP is \SI{15.4}{\%} lower than the one with GA, and the MAE is \SI{15}{\%} lower. Particularly important is the improvement of the RMSE\textsubscript{NON} and of the MAE\textsubscript{NON} because when the $|a_y| \ge$ \SI{4}{m/s^2} the sideslip angle estimation becomes more critical for vehicle stability control. The UKF optimised by the TSBO based on tSP reduces the RMSE\textsubscript{NON}, and the MAE\textsubscript{NON} of the UKF optimised by GA of \SI{24.6}{\%} and \SI{12.5}{\%}, respectively. The accuracy of the UKF tuned by GA is higher than the one optimised by TSBO based on GP.
Table \ref{Vali} reports the same information as Table \ref{Trai}, but for the test set, to check that the numerical optimisation algorithms do not overfit the training set leading to worse performance in other manoeuvres. Table \ref{Vali} shows that TSBO based on tSP still behaves better than all other algorithms for the 4 KPIs, proving better performance in tuning the process noise UKF parameters.
On average, the RMSE of the sideslip angle optimised with tSBO based on tSP is \SI{9.9}{\%} lower than the one with GA, and the MAE is \SI{17.6}{\%} lower. The improvement of the RMSE\textsubscript{NON} and of the MAE\textsubscript{NON} is particularly significant because when the $|a_y| \ge$ \SI{4}{m/s^2}, the sideslip angle estimation becomes more critical for vehicle stability control. The UKF optimised with the TSBO based on tSP reduces the RMSE\textsubscript{NON}, and the MAE\textsubscript{NON} of the UKF optimised with GA of \SI{10.6}{\%} and \SI{9.8}{\%}, respectively. The improvement in the test set is lower than the one obtained in the training set but still particularly relevant, especially for what concerns the MAE. \newline
\begin{table}[t]
\caption{Comparison of the average KPIs for the UKF tuned by manual tuning, GA, TSBO based on GP and TSBO based on sTP. Results of the training set.}
\label{Trai}
\begin{center}
\begin{tabular}{| >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} |}
\hline
\textbf{KPI} & \textbf{Manual} & \textbf{GA} & \textbf{TSBO - GP}& \textbf{TSBO - tSP}\\
\hline
RMSE [deg] & 1.028 & 0.500 & 0.634 & \textbf{0.423} \\
\hline
MAE [deg] & 1.196 & 0.900 & 1.252 & \textbf{0.765} \\
\hline
RMSE\textsubscript{NON} [deg] & 0.716 & 0.568 & 0.855 & \textbf{0.428} \\
\hline
MAE\textsubscript{NON} [deg] & 0.818 & 0.671 & 0.961 & \textbf{0.587} \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}[b]
\caption{Comparison of the average KPIs for the UKF tuned by manual tuning, GA, TSBO based on GP and TSBO based on sTP. Results of the test set.}
\label{Vali}
\begin{center}
\begin{tabular}{| >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} | >{\centering\arraybackslash}m{0.5in} |}
\hline
\textbf{KPI} & \textbf{Manual} & \textbf{GA} & \textbf{TSBO - GP}& \textbf{TSBO - tSP}\\
\hline
RMSE [deg] & 0.577 & 0.383 & 0.431 & \textbf{0.345} \\
\hline
RMSE [deg] & 0.672 & 0.529 & 0.689 & \textbf{0.436} \\
\hline
RMSE\textsubscript{NON} [deg] & 1.328 & 0.860 & 1.030 & \textbf{0.769} \\
\hline
MAE\textsubscript{NON} [deg] & 1.047 & 0.746 & 0.902 & \textbf{0.673} \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{figure}[t]
\centering
\setlength{\fboxrule}{0pt}
\framebox{\parbox{3in}{\includegraphics[scale=0.27]{Pictures/BAR.JPG}}}
\caption{Relative improvement of the UKF tuned by TSBO based on tSP with respect to the UKF tuned by the state-of-the-art GA. The improvement is measured through the sideslip angle's RMSE for 6 different maneuver chosen from the test set.}
\label{bar}
\end{figure}
\begin{figure}[t]
\centering
\setlength{\fboxrule}{0pt}
\framebox{\parbox{3in}{\includegraphics[scale=0.12]{Pictures/SKIDPAD.jpg}}}
\caption{Sideslip angle estimation in a skidpad maneuver.}
\label{SKIDPAD}
\end{figure}
\begin{figure}[t]
\centering
\setlength{\fboxrule}{0pt}
\framebox{\parbox{3in}{\includegraphics[scale=0.12]{Pictures/SLALOM.jpg}}}
\caption{Sideslip angle estimation in a slalom maneuver.}
\label{SLALOM}
\end{figure}
\begin{figure}[ht]
\centering
\setlength{\fboxrule}{0pt}
\framebox{\parbox{3in}{\includegraphics[scale=0.12]{Pictures/JTURN.jpg}}}
\caption{Sideslip angle estimation in a J-turn maneuver.}
\label{JTURN}
\end{figure}
Figure \ref{bar} shows the relative improvement of the UKF tuned by TSBO based on tSP and GA in 6 different maneuvers of the test set. The relative improvement is measured with the RMSE of the sideslip angle, $a_y$ and $\dot{\psi}$. In 5 out of 6 maneuvers the TSBO reaches higher performance than the GA. The spiral maneuver is the only one which shows a degraded accuracy in the RMSE of sideslip angle of \SI{8}{\%}. Performance degradation in this particular maneuver is considered acceptable due to the various driving conditions of the test set. The relative improvement is significant especially for the sideslip angle and for the $a_y$, while the $\dot{\psi}$ does not have this. The reason is that the $\dot{\psi}$ has lower maximum absolute error compared with the other variables, so the relative improvement is less noticeable. Figure \ref{bar} shows how TSBO can enhance the performance of the UKF for both transient (J-turn, slalom) and steady state (skidpad) maneuvers. Significant is the improvement in the skidpad, see also Figure \ref{SKIDPAD}. The reason is that during a steady-state maneuver the vehicle yaw acceleration is almost null so the difference between estimated and measured tyre forces becomes essential for the $V_y$ estimation. The best way to reduce the tyre force error is to optimise the process noise parameters.
Despite this, the improvement in sideslip angle estimation is noticeable also for a J-turn, see Figure \ref{JTURN}, and a slalom manoeuvre, see Figure \ref{SLALOM}.
Figure \ref{SLALOM} shows how the improvement in the tuning of the UKF is noticeable at the sideslip angle peaks of the slalom maneuver. The improvement at the peaks is more remarkable when the sideslip angle is above \SI{3}{deg} while when it is between 0 and \SI{3}{deg} the difference is not visible due to the lower absolute error of both UKFs.
Figure \ref{JTURN} shows the sideslip angle estimation in J-turn and it highlights another time how the UKF tuned by TSBO based on tSP reduces the estimation error especially when the sideslip angle is above \SI{4}{deg}.
\section{CONCLUSIONS}
This paper presented a two-stage Bayesian optimisation approach based on t-Student process to tune the process noise parameters of a unscented Kalman filter for sideslip angle estimation. The proposed approach reaches the cost function optimum \SI{79.9}{\%} faster than the state-of-the-art GA and the optimum is \SI{16.4}{\%} better than the one obtained by GA. The obtained results are tested on an experimental test set composed by transient and quasi-steady state maneuvers. Furthermore, two-stage Bayesian optimisation creates a physical representation of the black-box cost function thanks to surrogate model training. The performance of the two-stage Bayesian optimisation based on t-Student process is also compared with the two-stage Bayesian optimisation based on Gaussian process. The algorithm based on t-Student process is \SI{4.4}{\%} slower than the one based on Gaussian process but it reaches a \SI{21}{\%} better optimum. As future research, the plan is to tune not only the process noise parameters of the unscented Kalman filter but also the parameters defining the location of the sigma points.
\addtolength{\textheight}{-15cm}
\bibliographystyle{IEEEtran}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,922
|
INTERVIEW: An interview with Hydee on Toronto's Bass scene, Summer 2014
By Serafina Thoma on August 13, 2014 INTERVIEWS
I had the chance to talk to Toronto's very own Ruben "HYDEE" Reyes, one of Embrace's long time residents who's opened for artists like Skrillex, Nero, Flux Pavillion and many more. He's played at WEMF and Digital Dreams and soon to play again at the Hoxton this August 22nd alongside Kill Paris, Dr. Ozi and Decibel. This expert in drum & bass as well as dubstep has again and again proved to be a leader in the scene with his skills, experience, and motivation. I've seen him play a countless number of times in Toronto and he always knows how to set people off and get the good vibes goin' for the night. Get to know another artist in your city who loves music just as much as you do.
1. How did you get started in Toronto's Bass scene?
I started going to Bassmentality and checked out Zeds Dead and the Killabits. I got hooked up with Embrace and they started booking me for shows and for Bassmentality. That's basically how it started.
2. Do you still play the drums and have you ever considered recording drums for production purposes?
I haven't played the drums in probably, 5 years now. Although I did start almost 20 years ago, but I just don't have any of the space or equipment to record the drums, otherwise that would definitely be a cool thing to do.
3. Would you say you have your own style of mixing or that you have many influences from other DJs?
I feel like I've been influenced by other DJs, but also at the same time, I do throw in my own style where I just like to keep it heavy and flowing, keep you guessing a little bit with some surprises, keep the vibes going and have a good time.
4. How does it feel to see the Bass scene grow over the past few years, let alone be seen as a leader?
I love it. Toronto's got a huge bass scene. There's so much talent comes out of here, and so much talent comes through here. We got huge festivals like Digital Dreams and Veld, as well as big powerhouse promotional companies like Embrace, Destiny, Live Nation, INK… you know the talent is endless and the scene is amazing. It just keeps growing and growing and I love it.
5. Who do you think is reinventing the bass scene right now?
Well there's a lot of big influences right now like Tantrum Desire, Metrik, Shockone. As for dubstep, Zomboy is fucking amazing, Cookie Monsta crushes it… there's too many names to specify but there's a lot of good heads out there.
6. Drum and Bass has always seemed to bring in the best crowds. Do you think DnB will ever become commercialized EDM, especially after being featured on Z103.5's Drive at 5 Street Mix?
Z103.5 was doing a promotional feature for local artists in the Digital Dreams festival lineup. I don't think it'll ever become commercialized, but it was good to get it out there as good exposure. But Drum and Bass will forever be a part of the underground scene, it'll always be there. I don't think it'll ever be commercialized though, I hope not anyways.
7. Which artists are still on our bucket list to open for/ play with/ collab with?
Sub Focus would be amazing to play with. Metrik, I really love him. I would love to play with him one day. Barely Alive, those guys are amazing. Bear Grillz… there's tons! But I have already played with a lot, so that's actually a hard questions for me to choose.
8. The Dubstep scene in thriving in the US compared to Canada. Do you think the Dubstep scene is dying over here like people say?
Hell no, I mean look at tonight (Zomboy The Outbreak Tour, June 20) ; it's pretty slammed in there and its not even 12 o'clock yet. I think Dubstep just kind of grew really fast and artists are just getting paid a ridiculous amount of money because it grew that fast until it plateaued a bit. I think it's a little bit in hibernation, but I don't think it's dead by any means. Skrillex just came through Toronto and there were 10,000 people there. Digital Dreams has a bunch of huge artists, and now Zomboy and Cookie Monsta are here. Definetly not dead.
How stoked are you for the Kill Paris and Dr. Ozi show at the Hoxton in August? Have you played with locals Dr. Ozi before? What do you think of their tracks?
I'm actually really excited. I believe this is their first show at the Hoxton. Nix and Christian are really good guys. I've seen them grow from the beginning. They make solid tracks, they're dedicated, they love what they do. I love their attitude and I can't wait to share the stage with them and have a really good night.
Do you see a strong alliance forming among local Toronto Djs?
There's some DJs who work together. I think strength in numbers is key. If you have people working against each other then it really doesn't help anyone. Everyone should be working in the same direction full force, working together to make the scene that much better.
What inspires you to keep pushing yourself every day?
Basically just for the love of music. I've had a passion for music ever since I was a kid. My dad was a musician, my brother is a musician, my sister is a singer. Music is in my blood and I just love playing it and making people dance. I love seeing people go off and seeing the positive energy that music brings.
What kind of original material can we expect from you in the near-future? Any collabs?
To be honest, I haven't produced in a couple years and it's only being due to being crazy busy with work and Djing, but I'd love to get back into it. Hopefully sooner than later and hopefully I can perfect my own craft in time to collaborate with some other artists.
Catch Hydee alongside Kill Paris, Dr. Ozi, Decibel and more at the Hoxton on August 22nd, doors open at 10 pm! 19+ event! Get tickets online here.
Hydee
Serafina Thoma – EDM TOR
Serafina Thoma
It has been since late elementary school when Serafina Thoma came across artists like Benny Benassi, Ratatat, and Daft Punk and instantly bonded her soul to electronic music forever. Throughout high school, her taste in EDM expanded when introduced to artists Pendulum, Skrillex, Glitch Mob and Justice through various groups of friends over the years. She is an OSHEAGA 2012 veteran, a Veld 2013 warrior, and is an Electric Forest 2014 enthusiast. She uses her vast skills in writing, multimedia, and social media to be as vocal as possible about her opinions of new tracks, shows and albums. She'll make sure to speak her mind openly and honestly. Her knowledge in the scene continues to grow throughout many encounters and experiences in the Greater Toronto Area. Serafina and can be seen jammin' often at the back of The Hoxton to deep or electro house.
INTERVIEW: A Team EDMTOR Interview with Tempo Giusto, February 2019
INTERVIEW: Sheridan Grout speaks about his successes, Ottawa's trance scene, and the road ahead.
INTERVIEW: Sam Jones on His Influences and What's Next
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,596
|
Q: Build an array with previous three months from current month in javascript I showing a report which brings three months data from current month. For example, this month is june so it brings, April, May and June data.
I want to build an array in javascript/angularjs which gives me the previous three months from current date like this:
$scope.montharray = [
{
monthname: "All",
Monthnumber: "4,5,6"
},
{
monthname: "April",
MonthNumber:"4",
},
{
monthname: "May",
MonthNumber:"5",
},
{
monthname: "June",
MonthNumber:"6",
}
]
Can someone help me how i can achieve to get the rolling three months array like this?
TIA
A: You will need an array to look up the month names. Work out the current month with a new date. Use Array.from to create your array. Make sure to % mod by 12 to wrap back to January if you go over 12.
const monthNames = [
'January',
'February',
'March',
'April',
'May',
'June',
'July',
'August',
'September',
'October',
'November',
'December'
];
const currentMonth = new Date().getMonth() + 1;
const monthArray = Array.from({ length: 4 }, (_, index) =>
index === 0
? { monthname: 'All', monthNumber: `${currentMonth},${(currentMonth + 1) % 12},${(currentMonth + 2) % 12}` }
: { monthName: monthNames[(currentMonth + index - 2) % 12], monthNumber: `${(currentMonth + index - 1) % 12}` }
);
console.log(monthArray);
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,118
|
Posted on January 17, 2019 March 15, 2019 by Tee Watts
Featured Interview – Kirk Fletcher
Upon connecting with Kirk Fletcher, I had to let him know that I think his latest release Hold On is fire. The playing is super clean, with no muddled notes or sound. From the opening track, Two Steps all the way through his tribute track to Cornell Dupree to the end of the album. Joe Bonamassa says Fletcher is one of the best guitarists in the world.
The accolades and nominations are pouring in for the guitarist. His stint as lead guitarist of Kim Wilson & The Fabulous Thunderbirds, in addition to his performances with Pinetop Perkins, Hubert Sumlin and James Cotton, as well as his collaborations with Charlie Musselwhite and others, have vaulted him to the head of the class of current trend setting Blues and R&B guitarists. In a free ranging discussion with Blues Blast, Kirk expounded on his world of music and career.
"Blues and soul are similar to me, you know? I don't mean Soul music. I mean being soulful. When I hear Blues that are soulful, I can feel that." So states Fletcher, the Southern California raised son of a preacher man, who spent a considerable amount of his formative years in Compton.
"You know, I'm actually from Lakewood, California, kind of a suburb, close to Long Beach. I spent a lot of time in Compton though. My father's church was in Compton and I lived there for a lot of years. People took the Compton part and ran with it. Oh, he's from Compton!"
And yes, he did dabble in other genres before settling on the Blues. I asked him about any connections to Hip Hop.
"During that time, I was plugged into it a little bit. I would do like, little guitar parts for people who had beats and stuff. I was in that scene for just a short while. Those were just the times. In the '90s, everybody played guitar and had a MPC60 and did samples. I didn't do anything major. I had friends that were really into it. My brother and his friends. I was more into songs; R&B, Blues and Gospel."
Kirk started following in his brother's guitar footsteps at age eight, playing in their father's church. It was a Pentecostal Church of God In Christ, from where many a musician has honed his or her chops. Sly and Freddie Stone, Stevie Wonder, Natalie Cole and Michelle Shocked have all been members of a COGIC Church at one time or another.
Unfortunately Kirk's brother passed away some years ago. Before he passed he took young Kirk to an L.A. music store, Guitar Works. It was there he met Robben Ford's guitar tech, Jeff Rivera.
"Yeah, my buddy Jeff and I are still friends to this day. From the time I was about sixteen. By the time I graduated high school, I was going to Guitar Works every day. I mean, every day! I was also playin' four and five nights a week in church as well as little side gigs. So I was pretty much a regular guitar player, whatever that is, you know, playin' lot of music and practicin' all the time.
"Luckily Jeff, Robben Ford's guitar tech would hire me as an extra set of hands to help with the setup of everything. I got to see a lot of rehearsals, recording sessions and gigs around L.A. whenever Robben had something. Robben didn't even know I played until later on. Robben and I are pretty good friend now."
Another stepping stone in Kirk's career was Al Blake, lead singer and harmonica player of the Hollywood Fats Band.
"Al Blake is very much responsible for exposing me to a lot of obscure Blues artists. The whole Blues spectrum, really. He showed me how to play in different positions and styles like Country Blues. The differences in styles between for example, the Jimmy Rogers/Muddy Waters style. The Luther Tucker/Robert Lockwood, Jr. style. And the Louis and Dave Myers style. He introduced me to so many other West Coast Blues artists and taught me about the interplay between harmonica and guitar. I could easily identify with the call and response aspect of it which is what we did in my father's church.
"Today when I play, I try to let everything go and let the music take over. It comes from playin' on the road. I try to be a pretty spiritual person in general without getting too religious. I let that flow through my music. And I'm a fan first. Of B.B. King, Albert King, Luther Tucker, Eddie Taylor, Jimmy Dawkins. So I try to make it exciting for people as they did and do for me . I really try to impart that into my guitar playing.
"The mark of a good night is not how well I played, but actually how much I played for myself, how I got in the moment, even how I mess up. It's like, I can break through and make something happen in the middle of a gig or something. I think where that started was when I began doing gigs under my own name, playing music that I like. When you are playing for an audience and they can feel it, it's an earth-shattering moment. When I get to play with my heroes it's earth-shattering too. When I was younger, being friends with people like Kim Wilson, Rusty Zinn and Billy Flynn was really advantageous. They understood that I was a younger cat and hadn't had a chance to play with a lot of the older guys. There were like, 'Cool man, we'll make it happen.'
"I believe the first time I played with Pinetop was maybe at Antone's Blues Club in Austin, Texas. It was one of those Blues Anniversaries and Kim made that happen. It was like the Muddy Waters Blues Band and different guitar players would come in and out. That was the kind of thing where the young musicians could play with the older ones. Clifford Antone was always doin' that in his club. I think that's where I got to play with Hubert Sumlin and Mojo Beauford in addition to Pinetop the first time.
"Another time I was playing with Rusty Zinn at a Blues Festival that I think was in Wisconsin where I got to play with Pinetop again, one of several times. I talked to him about the old days. He told me how he started out as a guitarist but injured his hand in a knife fight which is why he switched to piano. I also found out that he loved McDonald's as comfort food!"
As Kirk Fletcher seemed fully comfortable as we talked shop, I decide to take a fun turn with him. I ask him to briefly respond to guitar players I randomly name. Here are his responses:
James Armstrong- "I definitely know who he is."
James "Super Chikan" Johnson – "Yeah. Absolutely. I just don't know that much about his musical work and it's not because he isn't fantastic. It's just there aren't enough hours in a day to study all the great ones sufficiently."
Freddie Stone – "Oh man! Know you done…Oh my God! Freddie Stone. I mean that's like textbook guitar right there. One of the first people to bring that church, changa langa, scratch guitar amalgamation of Black music in Sly & The Family Stone. I listen to them probably every day. Freddie Stone is one of my all time favorite guitar players."
Jimi Hendrix -" Oh man. Jimi Hendrix. It's like I'm still learning stuff. It's a never ending book with him. He's been there for my whole life and I'm sure his music will rule in my head forever. He touches so many levels. When I was young, it was all about the fantastic guitar work and the sounds being so innovative and fresh, even in the '80s and '90s. And now, it's like the whole package; the songwriting, the way he progressed from the chitlin' circuit to the world stage. Amazing. So he's like ground zero for me."
Keith Richards – "Oh my God. Keith Richards is amazing. I mean his songwriting, his complete ensemble playing, the encyclopedic knowledge of all the music before him. He's not some drunk, druggy guy. He's a serious musician, a serious scholar of music. I have nothing but the utmost respect for him."
Shuggie Otis – "Oh man, Shuggie Otis and Sly Stone are people I probably listen to everyday. Shuggie was and is so innovative and ahead of his time. He's a serious Blues guitar player too. Him and Sly were a lot of the inspiration on my latest record too. Just trying things and taking your own path and not letting anyone tell you what to do. That's what Shuggie did. He had the chance to let Quincy Jones produce his record, but chose not to. I figured if he could do that, then I better get going. Big inspiration all the way around."
T-Bone Walker – "Aww man. Textbook. I mean, the guy deserves a lot of credit. The Father of electric guitar. There were people before him, but that single note style and bending laid the groundwork for B.B. King who is probably my favorite all time Blues guitar player. When you think about it T-Bone Walker was like the Black Elvis or Sinatra. I really like those pictures of him playing while doing the splits with Lottie The Body soaring over him."
The gear discussion also comes up. Kirk reveals his current penchant for experimentation.
"At the moment I'm playin' a lot of different guitars. It's kind of a new thing. I'm trying to marry the beautiful Gibson warm sustain tones with others, for various reasons. So right now, I'm either playing a 335, a Les Paul, a Strat or a Tele. In the studio the Tele seems to work really well. I guess it's kinda the ultimate roots guitar. A lot of my favorite tracks were recorded using a Tele or 335 so, I don't know. A lot of my friends have played Strats and I don't like all of them. Next week it will be something different out of those four. Amp wise, if I can, I usually use some kind of Fender reverb. Preferably an old Fender Super Reverb. I still have my Super Reverb's in L.A."
These days Kirk lives in Switzerland, but comes into L.A. several times a year. I asked, how he came to live in Switzerland.
"Man, my woman and playin' a lot. I was already comin' over here a lot to play and actually met my girlfriend several years ago here. We reconnected a few years ago. The timing was right. My daughter was in college, so I thought, 'Why not?' I like it. I go back to L.A. every few months so I'm really kinda back and forth. It does take some getting used to though cuz I miss my friends. The way of life in Switzerland is really cool. With the rail system going to so many countries, gigging and touring is easy."
As far as the press accolades and heavy praise being heaped upon him, Kirk Fletcher keeps a level head. As January 2019 closes, he is in L.A. doing a few gigs in the wake of his appearance at the NAMM Convention. Then it's back to Switzerland to get ready to hit the road in Europe followed by Joe Bonamassa's Blues Cruise.
"Man, I don't know about all the heaps of praise in the press. It's nice to be recognized for what you do and I appreciate it. You read some of it and use it to get gigs, to make some sort of living playing music. I'm glad that I'm in a position to be talked about, period. Other than that, I don't really look at it in a competitive way and I don't think they mean it that way. I think what they mean is you are a musician that moves people. I think of all my buddies that I would put on that list; Chris Cain, Jr. Watson, the list goes on and on. The more known I get, the more I can talk about all the people I love. Hopefully, it's a win, win for everybody."
Visit Kirk's website at:http://kirkfletcherband.com/.
CategoriesInterviews TagsAl Blake, Albert King, B.B. King, Billy Flynn, Chris Cain, Clifford Antone, Dave Myers, Eddie Taylor, Freddie Stone, Hubert Sumlin, James 'Super Chikan' Johnson, James Armstrong, James Cotton, Jeff Rivera, Jimmy Dawkins, Jimmy Hendrix, Jimmy Rogers, Jr. Watson, Keith Richards, Kim Wilson & The Fabulous Thunderbirds, King Curtis, Louis Myers, Luther Tucker, Michelle Shocked, Mojo Beauford, Muddy Waters, Natalie Cole, Pinetop Perkins, Robben Ford, Robert Lockwood Jr, Rusty Zinn, Shuggie Otis, sly stone, Stevie Wonder, T-Bone Walker
Previous PostPrevious Dane Phillip Smith – Looks Like Down To Me | Album Review
Next PostNext Issue 13-3 January 17 2019
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{"url":"https:\/\/studiogypsies.com\/blog\/electric-potential-unit-588787","text":"Superposition of Electric Potential: The electric potential at point L is the sum of voltages from each point charge (scalars). The case of the electric potential generated by a point charge is important because it is a case that is often encountered. with the difference that the electric field drops off with the square of the distance while the potential drops off linearly with distance. This is analogous to the relationship between the gravitational field and the gravitational potential. Note the symmetry between electric potential and gravitational potential \u2013 both drop off as a function of distance to the first power, while both the electric and gravitational fields drop off as a function of distance to the second power. Note that there are cases where you might need to sum potential contributions from sources other than point charges; however, that is beyond the scope of this section. Summing voltages rather than summing the electric simplifies calculations significantly, since addition of potential scalar fields is much easier than addition of the electric vector fields. September 18, 2013. September 17, 2013. (4), Connected to a terminal with zero electrical potential (7), What unit of electrical charge is equal to the quantity of electricity conveyed in one second by a current of one ampere (7), One billion of the standard unit of electrical power, Reciprocal ___ (unit of electrical conductance). The potential of the charged conducting sphere is the same as that of an equal point charge at its center. The electric potential tells you how much potential energy a single point charge at a given location will have. Enter letters or a clue and click 'Find Anagrams' to find anagrams. To find the voltage due to a combination of point charges, you add the individual voltages as numbers. The equation for the electric potential due to a point charge is $\\text{V}=\\frac{\\text{kQ}}{\\text{r}}$, where k is a constant equal to 9.0\u00d710, To find the voltage due to a combination of point charges, you add the individual voltages as numbers. The change in potential energy, \u0394PE, is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, W = \u2013\u0394PE. One electron volt equals 1.602E-19 (J). September 18, 2013. One electron volt is the potential energy change of moving one electron's worth of charge, e, through one volt. The potential at an infinite distance is often taken to be zero. A spherical sphere of charge creates an external field just like a point charge, for example. Electric Potential Difference We use the letters PE to denote electric potential energy, which has units of joules (J). Another way of saying this is that because PE is dependent on q, the q in the above equation will cancel out, so V is not dependent on q. Since the charge of the test particle has been divided out, the electric potential is a \u201cproperty\u201d related only to the electric field itself and not the test particle. Typically, the reference point is the Earth or a point at infinity, although any point can be used. This is consistent with the fact that V is closely associated with energy, a scalar, whereas E is closely associated with force, a vector. The electric potential is a scalar while the electric field is a vector. December 13, 2012. What unit of electrical charge is equal to the quantity of electricity conveyed in one second by a current of one ampere (7) GIGAWATT One billion of the standard unit of electrical power Using calculus to find the work needed to move a test charge q from a large distance away to a distance of r from a point charge Q, and noting the connection between work and potential (W=\u2013q\u0394V), it can be shown that the electric potential V of a point charge is, $\\text{V}=\\frac{\\text{kQ}}{\\text{r}}$ (point charge). Also electronvolts may be used, 1 eV = 1.602\u00d710 J. It is much easier to sum scalars than vectors, so often the preferred method for solving problems with electric fields involves the summing of voltages. (adsbygoogle = window.adsbygoogle || []).push({}); The electric potential of a point charge Q is given by $\\text{V}=\\frac{\\text{kQ}}{\\text{r}}$. An electric potential (also called the electric field potential, potential drop, or the electrostatic potential) is the amount of work needed to move a unit of electric charge from a reference point to a specific point in an electric field without producing an acceleration. Explain how the total electric potential due to a system of point charges is found. The SI unit of electric potential energy is joule (named after the English physicist James Prescott Joule). OpenStax College, College Physics. The Crossword Solver found 20 answers to the. Units: Since the work done is measured in joules and charge in coulombs, the unit of electric potential is joules \/coulombs, the unit of electric potential is joules\/coulomb or volts. The electric potential due to a point charge is, thus, a case we need to consider. OpenStax College, Electric Potential in a Uniform Electric Field. Van de Graaff Generator: The voltage of this demonstration Van de Graaff generator is measured between the charged sphere and ground. Since the charge of the test particle has been divided out, the electric potential is a \u201cproperty\u201d related only to the electric field itself and not the test particle. where k is a constant equal to 9.0\u00d7109 N\u22c5m2\/C2 . CC licensed content, Specific attribution, http:\/\/en.wiktionary.org\/wiki\/electric_potential, http:\/\/cnx.org\/content\/m42324\/latest\/?collection=col11406\/1.7, http:\/\/en.wikipedia.org\/wiki\/Electric_potential, http:\/\/cnx.org\/content\/m42328\/latest\/?collection=col11406\/1.7, http:\/\/www.boundless.com\/\/physics\/definition\/superposition, http:\/\/commons.wikimedia.org\/wiki\/File:Potencial_eletrico_resultante.PNG. $\\text{V}=\\frac{\\text{PE}}{\\text{q}}$. Optionally, provide word lengths or an answer pattern to improve results. The electric potential at a point is equal to the electric potential energy (measured in joules) of any charged particle at that location divided by the charge (measured in coulombs) of the particle. The summing of all voltage contributions to find the total potential field is called the superposition of electric potential. The summing of all voltage contributions to find the total potential field is called the superposition of electric potential. Hence a body is said to have an electrical potential of 1 volt if one joule of work is done to charge the body to one coulomb. We\u2019ve also seen that the electric potential due to a point charge is, where k is a constant equal to 9.0\u00d7109 N\u22c5m2\/C2. To find the total electric potential due to a system of point charges, one adds the individual voltages as numbers. The electric potential at a point is equal to the electric potential energy (measured in joules) of any charged particle at that location divided by the charge (measured in coulombs) of the particle. We\u2019ve seen that the electric potential is defined as the amount of potential energy per unit charge a test particle has at a given location in an electric field, i.e. The potential at infinity is chosen to be zero. Recall that the electric potential V is a scalar and has no direction, whereas the electric field E is a vector. Recall that the electric potential is defined as the potential energy per unit charge, i.e. OpenStax College, College Physics. Crossword Solver, Scrabble Word Finder, Scrabble Cheat, Crossword Solver,Scrabble Cheat, Scrabble Help, Word Finder, Units of electric potential and current in siren (4), Light using large unit of electrical current (4), What are units of electrical resistance called? Express the electric potential generated by a single point charge in a form of equation, Recall that the electric potential is defined as the electric potential energy per unit charge, $\\text{V}=\\frac{\\text{PE}}{\\text{q}}$. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta. So for example, in the electric potential at point L is the sum of the potential contributions from charges Q. It is named after the Italian physicist Alessandro Volta (1745\u20131827). So for example, in the figure above the electric potential at point L is the sum of the potential contributions from charges Q1, Q2, Q3, Q4, and Q5 so that, $\\text{V}_{\\text{L}}=\\text{k}[\\frac{\\text{Q}_{1}}{\\text{d}_{1}}+\\frac{\\text{Q}_{2}}{\\text{d}_{2}}+\\frac{\\text{Q}_{3}}{\\text{d}_{3}}+\\frac{\\text{Q}_{4}}{\\text{d}_{4}}+\\frac{\\text{Q}_{5}}{\\text{d}_{5}}]$. The potential difference between two points \u0394V is often called the voltage and is given by $\\Delta \\text{V} = \\text{V}_{\\text{B}} - \\text{V}_{\\text{A}} = \\frac{\\Delta \\text{PE}}{\\text{q}}$. The equation for the electric potential of a point charge looks similar to the equation for the electric field generated for a point particle. OpenStax College, College Physics. In the CGS system the erg is the unit of energy, being equal to 10 J. To find the total electric field, you must add the individual fields as vectors, taking magnitude and direction into account. The volt (symbol: V) is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. 1V = 1J\/C A convenient unit of electric potential energy is the electron volt (eV).","date":"2022-06-25 05:22:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8265298008918762, \"perplexity\": 273.5304977599311}, \"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-2022-27\/segments\/1656103034170.1\/warc\/CC-MAIN-20220625034751-20220625064751-00408.warc.gz\"}"}
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Ein Blendling (von mhd. blenden "mischen"; vgl. auch englisch to blend und dänisch at blande) ist ein Nachkomme von Eltern, die derselben Art angehören, jedoch nicht derselben Unterart, Rasse oder Sorte.
Verwendung
Der Begriff Blendling wird heute allgemein in der Biologie verwendet, speziell in der Zucht (Tier- und Pflanzenzüchtung).
Das Synonym Mistus (lat. mixtus oder mistus "gemischt") wird seltener gebraucht.
In der deutschen Übersetzung von Charles Darwins Über die Entstehung der Arten werden die Begriffe Blendling und Bastard unterschieden:
Blendling (engl. mongrel) steht für die Nachkommen von Eltern verschiedener Varietäten. Sie sind in der Regel fruchtbar.
Bastard (engl. hybrid) steht für die Nachkommen von Eltern, die verschiedenen Arten angehören. Sie sind in der Regel unfruchtbar.
Nach dieser historischen Definition wären Blendlinge zum Beispiel die fruchtbaren Nachkommen von rot- und weißblühenden Erbsen, mit denen Gregor Mendel arbeitete. Ein Bastard wäre dagegen das Maultier, der meist unfruchtbare Nachkomme einer Pferdestute und eines Eselhengstes.
Siehe auch
Hybride
Einzelnachweise
Pflanzenveredelung
Tierzucht
Feldwirtschaft
Hybride
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from transmute_core import *
from .url_dispatcher import TransmuteUrlDispatcher
from .swagger import add_swagger_api_route, create_swagger_json_handler, add_swagger
from .route import add_route
route = add_route
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"redpajama_set_name": "RedPajamaGithub"
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Holmegaard é um município da Dinamarca, localizado na região sul, no condado de Storstrom.
O município tem uma área de 66 km² e uma população de 7 237 habitantes, segundo o censo de 2004.
Ligações externas
Site oficial
Municípios da Dinamarca
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Q: Python: *args, grouped by type I have a class __init__ that accepts variable length arguments. I am trying to figure out how to separate the *args into str, and floats/ints.
So, for example, in my mind that might look like:
class Example():
def __init__(self, *legs, *vals, named_input: float, named_input_2: str):
*legs are a string. *vals are floats & ints.
My goal is that the user can do:
a = Example('1y', '5y', named_input = 100, named_input_2 = 'setting_1')
a.legs = ['1y', '5y']
a.vals = []
a = Example('1y', '5y', 15, named_input = 100, named_input_2 = 'setting_1')
a.legs = ['1y', '5y']
a.vals = [15]
a = Example('1y', 0, 15, 30, named_input = 100, named_input_2 = 'setting_1')
a.legs = ['1y']
a.vals = [ 0, 15, 30,]
At least 1 *leg must always be supplied. vals can be None though.
A: Overcomplicated it.. just had to do this:
class test():
def __init__(self, *args):
self.legs = []
self.vals = []
for x in args:
if type(x) in [str]:
self.legs.append(x)
elif type(x) in [float, int]:
self.vals.append(x)
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Alexandre Pottier né le à Paris, est un acteur, réalisateur et scénariste français.
Biographie
Alexandre Pottier est d'origine mexicaine par son père. Il passe une partie de son enfance dans le Sud. Il suit des études d'anglais et d'histoire. Il acquiert également une solide formation musicale au conservatoire de Toulouse et au conservatoire de Tours en chant et trompette. Avec quelques diplômes en poche, il retourne dans sa ville natale pour suivre des cours d'art dramatique.
Il commence sa carrière en tant que comédien au TAI théâtre dans L'Écume des jours de Boris Vian. On a pu également le voir aux côtés de Jean Marais dans Hernani ou dans Viens chez moi, j'habite chez une copine.
Il a été, à la télévision, « Syntaxerror » dans Objectif Nul (récompensé par un sept d'or) et a participé à de nombreux téléfilms et séries tels que Julie Lescaut, Une femme d'honneur, Chère Marianne, Un drôle de cadeau, Plus belle la vie, Sous le soleil, Avocats et Associés, RIS police scientifique et Préjudices.
Il a également participé à l'écriture de plusieurs émissions ou séries pour la télévision et la radio : Zap 6, Coucou !, Abricot et pamplemousse, Plus belle la vie, ainsi que pour de nombreux programmes pour la jeunesse : Les Minikeums, Casimir et Léonard, Inspecteur Casimir et Ozie boo. Il a reçu la médaille d'honneur de la SACD. Il est aussi réalisateur de plusieurs courts-métrages dont Perte de vue et Le et l'auteur d'une série sur l'équitation Tagada. On lui doit aussi plusieurs documentaires : Bienvenue au Club, L'Équitation Western, A cheval mon grand, Les joies de l'attelage et La Police montée de New York.
Il enseigne l'Art Dramatique depuis de nombreuses années. il est professeur à l'Académie Oscar Sisto.
Il pratique l'escrime depuis de nombreuses années, il est également bon cavalier.
Il enseigne également l'Art Dramatique au conservatoire de Marolles-en-Brie.
Filmographie
Télévision
Séries télévisées
1987 : Objectif Nul : Syntaxeror
1989 : Le Destin du docteur Calvet : Inspecteur Gosset
1989 : Juliette en toutes lettres
1989 : Crossbow : un garde (saison 3, épisode 8 : The Gods)
1994 : Placé en garde à vue
1994 : Extrême Limite : Vincent (saison 1, épisode 15 : La clandestine)
1996 : Sous le soleil : Bruno Collin (saison 1, épisode 3 : Comportement modèle)
1996 – 1997 : L'histoire du samedi : Jeannot (2 épisodes)
1997 : Docteur Sylvestre : Matthieu (saison 3, épisode 2 : Un esprit clairvoyant)
1998 : Une femme d'honneur : Philippe Langlois (saison 2, épisode 1 : Brûlé vif)
1999 : Chère Marianne : le gardien de prison (épisode : Cellule familiale)
2000 : Blague à part : Morgos (saison 2, épisode : Mariage)
2003 : Julie Lescaut : Cheny (saison 12, épisode 3 : Hors-la-loi)
2004 – 2005 : Plus belle la vie : Antoine Frémont/Antoine Tailleroche (42 épisodes)
2006 : Avocats et Associés : Avocat Sandra Bess (saison 14, épisode 6 : Le coup de grâce)
2006 : Préjudices (saison 1, épisode 9 : Un flic attaque)
2007 : Boulevard du Palais : policier friche (saison 9, épisode 3 : La cité des coupables)
2008 : Central Nuit : le serrurier (saison 6, épisode 5 : Cauchemars)
2012 : RIS police scientifique : Henri Dumas (saison 7, épisode 4 : Magie noire)
2012 : Si près de chez vous : Paul (saison 1, épisode 106 : Un domaine viticole vandalisé)
2013 : Les Limiers : le responsable caisse (saison 1, épisode 2 : Passé trouble)
2013 : Falco (saison 1, épisode 6 : Tête à tête avec la mort)
Téléfilms
1995 : Lulu roi de France
2000 : Le blanc et le rouge : le gendarme
2002 : La Victoire des vaincus : Gugu enfant
2005 : 1905 : M. Goldstein
Cinéma
1991 : Isabelle Eberhardt (non crédité)
1993 : Aéroport (court-métrage)
1996 : Mémoires d'un jeune con
2000 : Scénarios sur la drogue (épisode : Speed ball)
2001 : Un aller simple : le photographe
2001 : Méfiez-vous des apparences (court-métrage) : Alex
2014 : Grace de Monaco : Rainier Minister
Réalisateur
2014 : A cheval, mon grand
2015 : Les Joies de l'Attelage
Doublage
1996-1998 : Sacatruc : Doc / Isidore
Notes et références
Liens externes
Naissance à Paris
Acteur français de cinéma
Acteur de Plus belle la vie
Réalisateur français
Les Nuls
Élève du conservatoire à rayonnement régional de Toulouse
Élève du conservatoire à rayonnement régional de Tours
Naissance en juin 1961
Acteur français de doublage
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When it comes to a thirsty nappy, this is it. Matched with a bombproof wrap it'll absorb most of what your baby can throw at it.
All bamboo nappies come with a fast dry fold-out bamboo booster sewn in place except for the size 1 which now comes with a separate bamboo booster as parents told us that on a newborn the extra absorption wasn't needed. Each bamboo nappy also comes with a free washable fleecy liner.
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{"url":"https:\/\/mitpress.mit.edu\/books\/cornucopia-limited","text":"Hardcover | $9.75 Short | \u00a36.95 | ISBN: 9780262033367 | 294 pp. | 6 x 9 in | September 2005 Paperback |$3.75 Short | \u00a32.99 | ISBN: 9780262532983 | 294 pp. | 6 x 9 in | September 2007\neBook | \\$20.00 Short | ISBN: 9780262251051 | 294 pp. | September 2007\n\n## Cornucopia Limited\n\nDesign and Dissent on the Internet\n\n## Overview\n\nThe network economy presents itself in the transactions of electronic commerce, finance, business, and communications. The network economy is also a social condition of discontinuity, indefinite limits, and in-between spaces. In Cornucopia Limited, Richard Coyne uses the liminality of design -- its uneasy position between creativity and commerce -- to explore the network economy. He argues that design, with its open-ended and transgressive explorations, provides a new way to think about the world of commerce; design\u2019s inter-territorial precinct, its in-between condition, offers a way to frame the problems of the Internet economy -- for profit vs. for free, private vs. public, security vs. open access, defense vs. permeability.Design, says Coyne, has a natural affinity with the edge condition and the position between polar opposites. Edgy design starts with an idea, brings to mind its opposite, and then works with what emerges from the friction between the two. The designer of a Web portal, for example, might take on the problem of security by focusing on the limits of permeability. Design is edgy, and risky, argues Coyne, in the same way that breaches in network security are risky. In Cornucopia Limited he examines the threshold between conditions exemplified by the boundary between design and commerce. Coyne uses five metaphors of design to develop his argument: the household (in economics, historically opposed to the market), with its relationship to the street mediated by various portals; the machine, rampant and glitchy; the game, competitive but simulated; the gift, precursor to commerce; and the threshold. The threshold condition, Coyne says, is the site of edgy design and a portal into the new. The threshold, he argues, provides the most potent metaphor for understanding the liminal dwellers of the network economy.","date":"2016-05-05 22:57:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2008621096611023, \"perplexity\": 5745.786163252691}, \"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-2016-18\/segments\/1461861623301.66\/warc\/CC-MAIN-20160428164023-00077-ip-10-239-7-51.ec2.internal.warc.gz\"}"}
| null | null |
Ranoidea is een geslacht van kikkers uit de familie Pelodryadidae.
Het geslacht werd voor het eerst wetenschappelijk beschreven door Johann Jakob von Tschudi in 1838. De groep werd lange tijd tot de familie boomkikkers (Hylidae) gerekend. In de literatuur wordt daarom vaak de verouderde situatie vermeld.
Er zijn 74 soorten, die leven in Australië en delen van Azië zoals in Nieuw-Guinea en Indonesië.
Soorten
Ranoidea alboguttata
Ranoidea andiirrmalin
Ranoidea aruensis
Ranoidea auae
Gouden boomkikker (Ranoidea aurea)
Ranoidea australis
Ranoidea barringtonensis
Ranoidea becki
Ranoidea bella
Ranoidea booroolongensis
Ranoidea brevipes
Ranoidea brongersmai
Ranoidea bulmeri
Koraalteenboomkikker (Ranoidea caerulea)
Ranoidea callista
Ranoidea cavernicola
Ranoidea chloris
Ranoidea citropa
Ranoidea cryptotis
Ranoidea cultripes
Ranoidea cyclorhynchus
Ranoidea dahlii
Ranoidea daviesae
Ranoidea dayi
Ranoidea dorsivena
Ranoidea elkeae
Ranoidea eschata
Ranoidea eucnemis
Ranoidea exopthalmia
Ranoidea fuscula
Ranoidea genimaculata
Ranoidea gilleni
Ranoidea gracilenta
Ranoidea graminea
Ranoidea impura
Ranoidea jungguy
Ranoidea kroombitensis
Ranoidea kumae
Ranoidea lesueurii
Ranoidea longipes
Ranoidea lorica
Ranoidea macki
Ranoidea maculosa
Ranoidea maini
Ranoidea manya
Ranoidea moorei
Ranoidea myola
Ranoidea nannotis
Ranoidea napaea
Ranoidea novaehollandiae
Ranoidea nudidigita
Ranoidea nyakalensis
Ranoidea occidentalis
Ranoidea pearsoniana
Ranoidea phyllochroa
Ranoidea piperata
Ranoidea platycephala
Ranoidea pratti
Ranoidea raniformis
Ranoidea rara
Ranoidea rheocola
Ranoidea rivicola
Ranoidea robinsonae
Ranoidea rueppelli
Ranoidea sauroni
Ranoidea serrata
Ranoidea spenceri
Ranoidea spinifera
Ranoidea splendida
Ranoidea subglandulosa
Ranoidea vagitus
Ranoidea verrucosa
Ranoidea wilcoxi
Ranoidea xanthomera
Pelodryadidae
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,310
|
{"url":"https:\/\/tex.stackexchange.com\/questions\/257894\/capitalize-every-word-in-an-acronym-acl-command-in-the-acro-package","text":"capitalize every word in an acronym (\\acl command in the acro-package)\n\nI would like to have a command which capitalizes every word when I use an \\acl command of the acro-package.\n\n\\DeclareAcronym{t}{short={t},long={this is a test}}\n\\capitalizingcommand{\\acl{t}}\n\n\nMy desired output would be:\n\nThis Is A Test\n\nas far as i know the acro-package only supports the capitalization of the first word via \\Acl{t}.\n\nSo far I tried the \\ecapitalisewords command from the mfirstuc-package, but the expansion seems not to work and latex tries to capitalise the shortcut which results in an error.\n\nThis is my working or rather not working example.\n\n\\documentclass{article}\n\\usepackage{mfirstuc}\n\\usepackage{acro}\n\n\\DeclareAcronym{t}{short={t},long={this is a test}}\n\\begin{document}\n\n\\acl{t}\n%\\ecapitalisewords{\\acl{t}}\n\n\\end{document}\n\n\nYou can't do this directly. However, you can define a macro which sets long-format to \\capitalisewords in a group:\n\n\\documentclass{article}\n\\usepackage{mfirstuc}\n\\usepackage{acro}\n\n\\DeclareAcronym{t}{short={t},long={this is a test}}\n\n\\newcommand*\\accapitalizelong[1]{%\n\\begingroup\n\\acsetup{long-format=\\capitalisewords}%\n#1%\n\\endgroup\n}\n\n\\begin{document}\n\n\\acl{t}\n\n\\accapitalizelong{\\acl{t}}\n\n\\acl{t}\n\n\\end{document}\n\n\nIf you instead want to generally change the uppercasing behaviour of all the \\Ac... macros you can set the option uc-cmd:\n\n\\documentclass{article}\n\\usepackage{mfirstuc}\n\\usepackage{acro}\n\n\\DeclareAcronym{t}{short={t},long={this is a test}}\n\n\\acsetup{uc-cmd=\\capitalisewords}\n\n\\begin{document}\n\n\\acl{t}\n\n\\Acl{t}\n\n\\end{document}\n\n\nOf course you can also define a similar command like in my first suggestion to locally change uppercasing. Or even define a \\ACL:\n\n\\documentclass{article}\n\\usepackage{mfirstuc}\n\\usepackage{acro}\n\n\\DeclareAcronym{t}{short={t},long={this is a test}}\n\n\\NewDocumentCommand\\ACL{sm}{%\n\\begingroup\n\\acsetup{uc-cmd=\\capitalisewords}%\n\\IfBooleanTF{#1}{\\Acl*{#2}}{\\Acl{#2}}%\n\\endgroup\n}\n\n\\begin{document}\n\n\\acl{t}\n\n\\Acl{t}\n\n\\ACL{t}\n\n\\end{document}","date":"2020-11-01 01:51:58","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\": 0.9051560163497925, \"perplexity\": 2402.309753232398}, \"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-2020-45\/segments\/1603107922746.99\/warc\/CC-MAIN-20201101001251-20201101031251-00703.warc.gz\"}"}
| null | null |
{"url":"https:\/\/www.shaalaa.com\/question-bank-solutions\/following-are-cannot-be-probability-event-3-5-type-event-complementry_29591","text":"Share\n\n# Following Are Cannot Be the Probability of an Event ? 3\/5 - Mathematics\n\nCourse\n\n#### Question\n\nWhich of following cannot be the probability of an event ?\n\n 3\/5\n\n#### Solution\n\nThe probability of an event lies betweet '0' and '1' i.e 0 \u2264 P(E) \u22641.\n\n3\/5=0.6\n\n\u2235 0<=0.6<=1\n\nHence, it can be the probability of an event.\n\nIs there an error in this question or solution?","date":"2020-08-14 17:24:28","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\": 0.6894469261169434, \"perplexity\": 1514.1629814388361}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-34\/segments\/1596439739347.81\/warc\/CC-MAIN-20200814160701-20200814190701-00565.warc.gz\"}"}
| null | null |
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← Leeds Candlelit Vigil to mark one week of badger slaughter
LAP Newsletter November 2013 →
LAP Newsletter October 2013
Posted on September 25, 2013 by Andy P
Hello to all Leeds Animal Protection members and supporters
SOME RECENT EVENTS AND NEWS
We have held very busy information stalls at Chapel Allerton Arts Festival, Otley Vehicle Transport Extravaganza and in Leeds City Centre.
We campaigned to get the badger cull stopped and to get snares banned. Many people knew about snares and the horrific suffering they cause and are surprised that they are still legal. We have also been collecting signatures on a petition for "Safer Medicines" and have given people BUAV "Little Books of Cruelty Free", which contains a list of cruelty free companies. We have also given out lots of lovely veggie recipes and nutritional information.
One week after the start of the cull, campaigners from Leeds and York gathered in Briggate in Leeds one evening to hold a candlelit vigil for the badgers. We were able to talk to the people who were around and some signed Brian May's petition there and then. Photos of the vigil were sent to campaigners in the cull areas, to show our support for those who are enduring the difficulties and demands of witnessing the slaughter, and caring for the badgers.
THE BADGER CULL
The government's pilot cull of badgers began in Somerset on August 26th and in Gloucestershire on September 3rd. The shooting of badgers, by shotgun or rifle, will last for up to six weeks. It is reported that the marksmen have not been able to kill anywhere near the number of animals they intended to, thanks in part to the wonderful work of campaigners in the cull areas.
On the Animal Aid website there are links to Somerset Badger Patrol and Gloucester Against Badger Shooting. These groups would really appreciate more help if anyone can get there for a night or a weekend, or even make a donation to enable someone else to go. There is a link on the Animal Aid website to an article by a Somerset County Councillor – Mike Rigby – which is well worth reading.
Humaneness – What is it? Well don't ask the government's Chief Veterinary Officer because he doesn't know! Despite the fact that one of the government's stated aims of the trial culls is to assess it. Although the assessment of badger suffering was ordered to be released in August, Humane Society International are still waiting for DEFRA to reply to their questions about badger cull humaneness assessments and also about how badger carcases will be selected for post mortem examination.
Brian May's e-petition to stop the cull closed on September 7th and achieved 304,028 signatures – the most signed e-petition ever.
Please check that your MP has signed EDM 299 [if they are able to sign EDMs]. This is calling for a debate and vote in parliament before any extension of the culling to other areas of the country. If they haven't done so then please ask them!
SNARING
League Against Cruel Sports "Snare Aware" continues for the rest of September. On their website you can find details about different kinds of snares and how they are used. If anyone has not signed the petition please go to www.league.org.uk/bansnares
Animal Aid have a campaign to end the sale of gun magazines to children, which we will be supporting on our stalls. The aim is to get magazines that encourage the killing of animals for "sport" to be consigned to the "top shelf" positions in shops and sales to be restricted to over 18s.
Such magazines act as front-line advocates for the shooting lobby and are on sale in high street newsagents. A recent poll shows that the overwhelming majority of people want these magazines kept away from children. You can help by signing the petition at http://tinyurl.com/Ban-shoot-mags
If you would like to receive Animal Aid's E-news to receive their updates – please go to www.animalaid.org.uk
SAFER MEDICINES
On our stalls recently we have had a petition for "Safer Medicines Campaign". The petition calls for the Government to mandate the use of new technologies that can predict the safety of medicines for patients more reliably than current methods. Safer Medicines are an independent group of scientists and doctors, with extensive expertise in drug discovery, development and testing. Their aim is to change the way that medicines are tested, so that they are safer for human beings – moving from a system based mainly on tests in animals – to one focused firmly on human biology.
To sign the petition and for details of their work – please go to www.SaferMedicines.org
At www.buav.org we can download a Schools Guide about animal experiments. This is a good overview for students – and for everyone else. On their website we can also read about how BUAV are showcasing their campaigns such as Broken Promises, Our Best Friends and Licensed to Kill at the various party conferences. They are asking MPs from all parties to sign EDM 442, which calls on the Government to uphold its pledge to reduce animal experiments and also EDM 514, which calls for an end to cats and dogs in research.
BADGER CULL PROTEST outside the Conservative Party Conference in Manchester. This is at Manchester Central Convention Complex [formerly known as the GMEX centre], Windmill Street, Manchester M2 3GX – Sunday September 29th at 1.00pm – please wear black and white – for the badgers details at www.animalrightsuk.org/
DR HADWEN TRUST COLLECTION – we will be holding a collection for Dr Hadwen Trust at Leeds Railway Station on Saturday October 19th. This is a really good chance to collect some funds, meet people, give them a leaflet to introduce them to the work of DHT and encourage them to look at the website. Dr Hadwen Trust funds and promotes non-animal research to replace the use of animals in medical research. Please see their website www.drhadwentrust.org for details. We need people to help collect at the Railway Station. Please get in touch with Jenny jenny@bluecloud.plus.com for details if you can help. Please state which times you could do. We have to sign in and have a brief safety talk – The times are 10.00 – 12.00, 12.00 – 2.00 and 2.00 – 4.00. We could stay till 6.00 if anyone is interested. Anyone collecting will need to show photo ID – valid passport or photo driving licence – Thanks.
There may be some actions when the pilot badger culls end in October. If so – there will be info on Leeds Animal Protection website and Facebook page; we will also send out an action alert by e-mail.
Two dates for your diaries for November:
Remembrance Day Ceremony at Leeds Cenotaph, where we will be laying a wreath of purple poppies in memory of the animals who died in warfare – Sunday November 10th.
Bradford Peace Fair at Victoria Hall, Saltaire – Saturday November 23rd
The next meetings will be:
Wednesday September 25th
Wednesday October 22nd
Wednesday November 27th
LEEDS ANIMAL PROTECTION MEMBERSHIP
New members are always welcome at any time, but the Leeds Animal Protection year begins in September, so now is the perfect time to join (or renew your membership).
Jenny and Carla
This entry was posted in Newsletters and tagged Badger cull, BUAV, Dr Hadwen Trust, Remembrance Day, shooting, snares. Bookmark the permalink.
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,382
|
The Absolute Sound (TAS) is an American audiophile magazine which reviews high-end audio equipment, along with recordings and comments on various music-related subjects.
History
The Absolute Sound was founded in 1973 by Harry Pearson, who was its editor-in-chief and publisher. In the early years, TAS was a quarterly, digest-sized magazine and accepted no advertisements. During the 1970s and 1980s, TAS (along with Stereophile) was influential in the audiophile industry. Pearson is credited as being the most important figure in the rise of High-End audio.
Until the mid- to late 1990s, Pearson owned and directed all rights to TAS. The magazine was published by Pearson Publishing Inc., which also published a sister high-end video review magazine published quarterly called The Perfect Vision. Pearson remained the chairman of its editorial advisory board until 2006 and regularly contributed a feature entitled HP's Workshop until his departure in 2012. The magazine is now published by Absolute Multimedia, Inc., of Austin, Texas.
References
External links
Professional and trade magazines
1973 establishments in Texas
Magazines established in 1973
Magazines published in Austin, Texas
Music magazines published in the United States
Ten times annually magazines
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,876
|
Pell draws link between Vatican finances clean-up and child sex charges
Cardinal George Pell has inferred that his being charged with child sexual abuse in Victoria was due to his work on Vatican financial reform.
Pope promoted archbishop despite church sex abuse warnings
Pope John Paul II promoted ex-US Cardinal Theodore McCarrick in 2000 despite rumours of his sexual misconduct, a Vatican report found, in one of a series of failings by popes and officials who let him rise through the ranks.
Photo supplied
Pope's warm Vatican welcome for Pell
Pope Francis has warmly welcomed Cardinal George Pell for a private audience at the Vatican after the cardinal's sex abuse conviction and acquittal.
George Pell cites "manufactured obscurity" after High Court overturns child sex convictions
Cardinal George Pell has left Geelong's Barwon Prison after the High Court today set him free, saying that "justice prevailed" and he felt no ill will towards the man who accused him of child sexual abuse.
Pell to be stripped of Order of Australia
Catholic Cardinal George Pell will be stripped of his Order of Australia after losing an appeal against his child sex abuse conviction.
Daniel McCulloch Wednesday, August 21
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 782
|
Q: Upload image onclick on Mask image instead of choose file I am using the code below to upload the image on the mask image, so that the user needs to select the choose file button to upload image on mask.
Requirement :
But when the user clicks on the mask image, it should display the "Image upload" dialogue box & allow to upload image.
Here is a Codepen : https://codepen.io/kidsdial/pen/ywaxVY
var mask;
let jsonData = {
"path" : " love shape\/",
"info" : {
"author" : "",
"keywords" : "",
"file" : "love shape",
"date" : "sRGB",
"title" : "",
"description" : "Normal",
"generator" : "Export Kit v1.2.8"
},
"name" : "love shape",
"layers" : [
{
"x" : 0,
"height" : 612,
"layers" : [
{
"x" : 0,
"color" : "0xFFFFFF",
"height" : 612,
"y" : 0,
"width" : 612,
"shapeType" : "rectangle",
"type" : "shape",
"name" : "bg_rectangle_1"
},
{
"x" : 49,
"height" : 480,
"layers" : [
{
"x" : 0,
"height" : 480,
"src" : "TZwOgSa.png",
"y" : 0,
"width" : 514,
"type" : "image",
"name" : "mask_image_1"
},
{
"radius" : "27 \/ 27",
"color" : "0xACACAC",
"x" : 233,
"y" : 205,
"height" : 53,
"width" : 53,
"shapeType" : "ellipse",
"type" : "shape",
"name" : "useradd_ellipse1"
}
],
"y" : 66,
"width" : 514,
"type" : "group",
"name" : "user_image_1"
}
],
"y" : 0,
"width" : 612,
"type" : "group",
"name" : "loveshape_18"
}
]
};
$(document).ready(function() {
function json(data)
{
var width = 0;
var height = 0;
let layer1 = data.layers;
width = layer1[0].width;
height = layer1[0].height;
let layer2 = layer1[0].layers;
for (i = 1; i < layer2.length; i++) {
var x = layer2[i].x;
var y = layer2[i].y;
var src = layer2[i].layers[0].src;
$(".container").css('width', width + "px").css('height', height + "px").addClass('temp');
var mask = $(".container").mask({
maskImageUrl: 'https://i.imgur.com/' + src,
onMaskImageCreate: function(img) {
img.css({
"position": "absolute",
"left": x + "px",
"top": y + "px"
});
}
});
fileup.onchange = function() {
mask.loadImage(URL.createObjectURL(fileup.files[0]));
};
}
}
json(jsonData);
}); // end of document ready
// jq plugin for mask
(function($) {
var JQmasks = [];
$.fn.mask = function(options) {
// This is the easiest way to have default options.
var settings = $.extend({
// These are the defaults.
maskImageUrl: undefined,
imageUrl: undefined,
scale: 1,
id: new Date().getUTCMilliseconds().toString(),
x: 0, // image start position
y: 0, // image start position
onMaskImageCreate: function(div) {},
}, options);
var container = $(this);
let prevX = 0,
prevY = 0,
draggable = false,
img,
canvas,
context,
image,
timeout,
initImage = false,
startX = settings.x,
startY = settings.y,
div;
container.mousePosition = function(event) {
return {
x: event.pageX || event.offsetX,
y: event.pageY || event.offsetY
};
}
container.selected = function(ev) {
var pos = container.mousePosition(ev);
var item = $(".masked-img canvas").filter(function() {
var offset = $(this).offset()
var x = pos.x - offset.left;
var y = pos.y - offset.top;
var d = this.getContext('2d').getImageData(x, y, 1, 1).data;
return d[0] > 0
});
JQmasks.forEach(function(el) {
var id = item.length > 0 ? $(item).attr("id") : "";
if (el.id == id)
el.item.enable();
else el.item.disable();
});
};
container.enable = function() {
draggable = true;
$(canvas).attr("active", "true");
div.css({
"z-index": 2
});
}
container.disable = function() {
draggable = false;
$(canvas).attr("active", "false");
div.css({
"z-index": 1
});
}
container.onDragStart = function(evt) {
container.selected(evt);
prevX = evt.clientX;
prevY = evt.clientY;
//evt.originalEvent.dataTransfer.setData('text/plain', 'anything');
};
container.getImagePosition = function() {
return {
x: settings.x,
y: settings.y,
scale: settings.scale
};
};
container.onDragOver = function(evt) {
if (draggable && $(canvas).attr("active") === "true") {
var x = settings.x + evt.clientX - prevX;
var y = settings.y + evt.clientY - prevY;
if (x == settings.x && y == settings.y)
return; // position has not changed
settings.x += evt.clientX - prevX;
settings.y += evt.clientY - prevY;
prevX = evt.clientX;
prevY = evt.clientY;
container.updateStyle();
}
};
container.updateStyle = function() {
clearTimeout(timeout);
timeout = setTimeout(function() {
context.clearRect(0, 0, canvas.width, canvas.height);
context.beginPath();
context.globalCompositeOperation = "source-over";
image = new Image();
image.setAttribute('crossOrigin', 'anonymous');
image.src = settings.maskImageUrl;
image.onload = function() {
canvas.width = image.width;
canvas.height = image.height;
context.drawImage(image, 0, 0, image.width, image.height);
div.css({
"width": image.width,
"height": image.height
});
};
img = new Image();
img.src = settings.imageUrl;
img.setAttribute('crossOrigin', 'anonymous');
img.onload = function() {
settings.x = settings.x == 0 && initImage ? (canvas.width - (img.width * settings.scale)) / 2 : settings.x;
settings.y = settings.y == 0 && initImage ? (canvas.height - (img.height * settings.scale)) / 2 : settings.y;
context.globalCompositeOperation = 'source-atop';
context.drawImage(img, settings.x, settings.y, img.width * settings.scale, img.height * settings.scale);
initImage = false;
};
}, 0);
};
// change the draggable image
container.loadImage = function(imageUrl) {
if (img)
img.remove();
// reset the code.
settings.y = startY;
settings.x = startX;
prevX = prevY = 0;
settings.imageUrl = imageUrl;
initImage = true;
container.updateStyle();
};
// change the masked Image
container.loadMaskImage = function(imageUrl, from) {
if (div)
div.remove();
canvas = document.createElement("canvas");
context = canvas.getContext('2d');
canvas.setAttribute("draggable", "true");
canvas.setAttribute("id", settings.id);
settings.maskImageUrl = imageUrl;
div = $("<div/>", {
"class": "masked-img"
}).append(canvas);
div.find("canvas").on('touchstart mousedown', function(event) {
if (event.handled === false) return;
event.handled = true;
container.onDragStart(event);
});
div.find("canvas").on('touchend mouseup', function(event) {
if (event.handled === false) return;
event.handled = true;
container.selected(event);
});
div.find("canvas").bind("dragover", container.onDragOver);
container.append(div);
if (settings.onMaskImageCreate)
settings.onMaskImageCreate(div);
container.loadImage(settings.imageUrl);
};
container.loadMaskImage(settings.maskImageUrl);
JQmasks.push({
item: container,
id: settings.id
})
return container;
};
}(jQuery));
.temp {}
.container {
background: black;
}
.masked-img {
overflow: hidden;
margin-top: 30px;
position: relative;
}
<script src="https://code.jquery.com/jquery-3.3.1.min.js"></script>
<input id="fileup" type="file" >
<div class="container">
</div>
Thanks in advance.
A: You should use label element with for attribute, the for attribute should match the input file id
var mask;
let jsonData = {
"path" : " love shape\/",
"info" : {
"author" : "",
"keywords" : "",
"file" : "love shape",
"date" : "sRGB",
"title" : "",
"description" : "Normal",
"generator" : "Export Kit v1.2.8"
},
"name" : "love shape",
"layers" : [
{
"x" : 0,
"height" : 612,
"layers" : [
{
"x" : 0,
"color" : "0xFFFFFF",
"height" : 612,
"y" : 0,
"width" : 612,
"shapeType" : "rectangle",
"type" : "shape",
"name" : "bg_rectangle_1"
},
{
"x" : 49,
"height" : 480,
"layers" : [
{
"x" : 0,
"height" : 480,
"src" : "e5bcf5edf9e0a4a1df715231f995f878_frame0.png",
"y" : 0,
"width" : 514,
"type" : "image",
"name" : "mask_image_1"
},
{
"radius" : "27 \/ 27",
"color" : "0xACACAC",
"x" : 233,
"y" : 205,
"height" : 53,
"width" : 53,
"shapeType" : "ellipse",
"type" : "shape",
"name" : "useradd_ellipse1"
}
],
"y" : 66,
"width" : 514,
"type" : "group",
"name" : "user_image_1"
}
],
"y" : 0,
"width" : 612,
"type" : "group",
"name" : "loveshape_18"
}
]
};
$(document).ready(function() {
function json(data)
{
var width = 0;
var height = 0;
let layer1 = data.layers;
width = layer1[0].width;
height = layer1[0].height;
let layer2 = layer1[0].layers;
for (i = 1; i < layer2.length; i++) {
var x = layer2[i].x;
var y = layer2[i].y;
var src = layer2[i].layers[0].src;
$(".container").css('width', width + "px").css('height', height + "px").addClass('temp');
var mask = $(".container").mask({
maskImageUrl: 'http://piccellsapp.com:1337/parse/files/PfAppId/' + src,
onMaskImageCreate: function(img) {
img.css({
"position": "absolute",
"left": x + "px",
"top": y + "px"
});
}
});
fileup.onchange = function() {
mask.loadImage(URL.createObjectURL(fileup.files[0]));
};
}
}
json(jsonData);
}); // end of document ready
// jq plugin for mask
(function($) {
var JQmasks = [];
$.fn.mask = function(options) {
// This is the easiest way to have default options.
var settings = $.extend({
// These are the defaults.
maskImageUrl: undefined,
imageUrl: undefined,
scale: 1,
id: new Date().getUTCMilliseconds().toString(),
x: 0, // image start position
y: 0, // image start position
onMaskImageCreate: function(div) {},
}, options);
var container = $(this);
let prevX = 0,
prevY = 0,
draggable = false,
img,
canvas,
context,
image,
timeout,
initImage = false,
startX = settings.x,
startY = settings.y,
div;
container.mousePosition = function(event) {
return {
x: event.pageX || event.offsetX,
y: event.pageY || event.offsetY
};
}
container.selected = function(ev) {
var pos = container.mousePosition(ev);
var item = $(".masked-img canvas").filter(function() {
var offset = $(this).offset()
var x = pos.x - offset.left;
var y = pos.y - offset.top;
var d = this.getContext('2d').getImageData(x, y, 1, 1).data;
return d[0] > 0
});
JQmasks.forEach(function(el) {
var id = item.length > 0 ? $(item).attr("id") : "";
if (el.id == id)
el.item.enable();
else el.item.disable();
});
};
container.enable = function() {
draggable = true;
$(canvas).attr("active", "true");
div.css({
"z-index": 2
});
}
container.disable = function() {
draggable = false;
$(canvas).attr("active", "false");
div.css({
"z-index": 1
});
}
container.onDragStart = function(evt) {
container.selected(evt);
prevX = evt.clientX;
prevY = evt.clientY;
//evt.originalEvent.dataTransfer.setData('text/plain', 'anything');
};
container.getImagePosition = function() {
return {
x: settings.x,
y: settings.y,
scale: settings.scale
};
};
container.onDragOver = function(evt) {
if (draggable && $(canvas).attr("active") === "true") {
var x = settings.x + evt.clientX - prevX;
var y = settings.y + evt.clientY - prevY;
if (x == settings.x && y == settings.y)
return; // position has not changed
settings.x += evt.clientX - prevX;
settings.y += evt.clientY - prevY;
prevX = evt.clientX;
prevY = evt.clientY;
container.updateStyle();
}
};
container.updateStyle = function() {
clearTimeout(timeout);
timeout = setTimeout(function() {
context.clearRect(0, 0, canvas.width, canvas.height);
context.beginPath();
context.globalCompositeOperation = "source-over";
image = new Image();
image.setAttribute('crossOrigin', 'anonymous');
image.src = settings.maskImageUrl;
image.onload = function() {
canvas.width = image.width;
canvas.height = image.height;
context.drawImage(image, 0, 0, image.width, image.height);
div.css({
"width": image.width,
"height": image.height
});
};
img = new Image();
img.src = settings.imageUrl;
img.setAttribute('crossOrigin', 'anonymous');
img.onload = function() {
settings.x = settings.x == 0 && initImage ? (canvas.width - (img.width * settings.scale)) / 2 : settings.x;
settings.y = settings.y == 0 && initImage ? (canvas.height - (img.height * settings.scale)) / 2 : settings.y;
context.globalCompositeOperation = 'source-atop';
context.drawImage(img, settings.x, settings.y, img.width * settings.scale, img.height * settings.scale);
initImage = false;
};
}, 0);
};
// change the draggable image
container.loadImage = function(imageUrl) {
if (img)
img.remove();
// reset the code.
settings.y = startY;
settings.x = startX;
prevX = prevY = 0;
settings.imageUrl = imageUrl;
initImage = true;
container.updateStyle();
};
// change the masked Image
container.loadMaskImage = function(imageUrl, from) {
if (div)
div.remove();
canvas = document.createElement("canvas");
context = canvas.getContext('2d');
canvas.setAttribute("draggable", "true");
canvas.setAttribute("id", settings.id);
settings.maskImageUrl = imageUrl;
div = $("<div/>", {
"class": "masked-img"
}).append(canvas);
div.find("canvas").on('touchstart mousedown', function(event) {
if (event.handled === false) return;
event.handled = true;
container.onDragStart(event);
});
div.find("canvas").on('touchend mouseup', function(event) {
if (event.handled === false) return;
event.handled = true;
container.selected(event);
});
div.find("canvas").bind("dragover", container.onDragOver);
container.append(div);
if (settings.onMaskImageCreate)
settings.onMaskImageCreate(div);
container.loadImage(settings.imageUrl);
};
container.loadMaskImage(settings.maskImageUrl);
JQmasks.push({
item: container,
id: settings.id
})
return container;
};
}(jQuery));
.temp {}
.container {
background: black;
position: relative;
}
.masked-img {
overflow: hidden;
margin-top: 30px;
position: relative;
}
.file-label {
position: absolute;
height: 100%;
width: 100%;
top:0;
left: 0;
}
<script src="https://code.jquery.com/jquery-3.3.1.min.js"></script>
<input id="fileup" name="fileup" type="file" >
<div class="container">
<label for="fileup" class="file-label">
</label>
</div>
https://codepen.io/bearnithi/pen/NJROxr
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,008
|
Perpich
Why Arts Education Is Important
Center Administration
Careers at Perpich
Arts High School Alumni News
Arts High School News
Celebrating National Arts in Education Week 2021
This week we celebrate National Arts in Education Week. Recently I came across an article by Americans for the Arts that highlights 10 Reasons to Support the Arts in 2021. I encourage you to check out the article. After reading it, the…
Perpich Success in MN Scholastic Art & Writing Awards
The Minnesota Scholastic Art & Writing Awards have been announced.
The Minnesota Scholastic ART Awards have been announced. This year, Perpich Arts High School students received 63 total awards: 14 Gold, 17 Silver, and 32 Honorable Mentions.
There are 97 schools in Minnesota receiving awards. Of…
Samantha Rei (Visual Arts 1999) Fashions a Piece of History
Samantha (Crossland) Rei was a contestant on Season 16 of Project Runway.
When Peggy Flanagan entered the One Minnesota Party on Saturday, January 12, 2019, as the new Minnesota Lt. Governor, she did it wearing a Samantha Rei original. Samantha (Crossland) Rei (Visual Arts 1999)…
Mandy (Wolf) Meisner '93 Sworn in as Anoka County Commissioner
Mandy studied music and graduated from Perpich in 1993.
On Tuesday, January 8, 2019 Perpich alum Mandy (Wolf) Meisner took the oath of office to become the newest Anoka County Commissioner. Mandy studied music and graduated from Perpich in 1993.
Meisner broke many barriers when she…
Perpich Regional Arts Teacher-Leader Network Announced
Perpich Center for Arts Education is proud to introduce the Regional Arts Teacher-Leader network. Regional Arts Teacher-Leaders comprise a collaborative network of 62 distinguished teachers of dance, media arts, music, visual arts, and theater coming together to increase professional development opportunities across the state….
Noted MN Composer also at Home in the Perpich Music Department
Janika Vandervelde, who retired in December 2015 as music teacher at Perpich, is not one to toot her own horn (although she does happen to play French horn). As a result of her modesty, many parents and non-music students and alumni are unaware that…
Previous Page 1 … Page 21 Page 22 Page 23
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,656
|
49ers thought Bears were trading up for Solomon Thomas
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Japan Releases "What To Do If North Korea Nukes You" Guide
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Prisoners suffer health deterioration as they enter 10th day of strike
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Arkansas inmate convulses during deadline-beating execution
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United Airlines and the passenger reach a settlement
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1 killed, 7 injured in San Diego shooting
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Turkey demands US stop supporting Syrian Kurdish militants
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Valtteri Bottas credits home comforts to first GP victory in Russian GP
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CIA chief visits South Korea after latest missile test raises tension
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Tear gas in France as Le Pen, Macron hold May Day rallies
Under Marine Le Pen "we'd have the franc in the morning and then the euro in the afternoon", said Macron. "The euro is dead", she told Le Parisien this we...
Queen Elizabeth's birthday celebrated
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South Korea says THAAD can defend against attack
As the tensions continued, Donald Trump offered Kim an olive branch. A statement from the Foreign Ministry spokesman on Monday that was circulated by North Ko...
Berkeley hails peaceful debate over Ann Coulter
The two sides were separated by a wall of riot police, while hundreds of other officers were deployed around the city and campus. "I think we're not doing eno...
Gorsuch Full of Questions in First US Supreme Court Argument
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Trump Admin Working With Allies To Pressure North Korea
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F1: Valtteri Bottas has 'an unbelievable future ahead,' says Mika Hakkinen
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Iranian Defense Minister Believes Israel Should Be 'Completely Disarmed'
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Trump administration to roll back some school meal standards
She then asked where the new USDA chief thinks the future of agriculture is headed. "We've seen a reduction in milk consumption in schools because of this p...
Trump slams sanctuary city ruling, says opponents are 'judge shopping!'
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NKorea says it will speed up nuke program in response to US
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'You have a true friend,' Trump tells NRA
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Hill settles on $1T spending bill, vote likely by Wednesday
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Palestinians say dozens wounded at protests for prisoners
But the group's decision to appoint Yehya al-Sinwar - a hardline founder of Hamas' military wing in the 1980s - as Hamas's Gaza leader is a sign that the group ...
Trump will sign executive order while visiting central Pa. factory
Trump tells the television network of congressional Republicans: "I like nearly all of them a lot" and "I think you're going to see the Republican party really ...
Marine Le Pen Lays Wreath At Holocaust Memorial
While supporters from fringe movements often disrupt protest marches in the French capital, they usually don't carry signs. He said two police officers were c...
Hamas loses out as Palestinian hunger strike benefits Fatah
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Chelsea keeps Tottenham 4 points behind in title pursuit
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,719
|
\section{Our Models}
\label{sec:models}
\subsection{Style-Controlled Backtranslation (+ \textsc{bt})}
\label{sec:bt-at-inference}
While the Universal Rewriter model has a strong tendency to exactly copy input sentences while rewriting sentences in the same language (\sectionref{sec:universal-rewriter-shortcomings}), we found it is an effective style-controlled translation system. This motivates a simple \emph{inference-time} trick to improve model outputs and reduce copying --- translate sentences to English (\texttt{en}) in a style-agnostic manner with a zero style vector $\mathbf{0}$, and translate back into the source language (\texttt{lx}) with stylistic control.
\begin{align*}
\mathbf{s}_A,~\mathbf{s}_B &= \frac{1}{N} \sum_{y \in S_A,~S_B} f_\text{style}(y)\\
x^{\texttt{en}} &= f_\text{ur}(\texttt{en} \oplus x, \mathbf{0}) \\
\bar{x} &= f_\text{ur}(\texttt{lx} \oplus x^{\texttt{en}}, \lambda (\mathbf{s}_B - \mathbf{s}_A))
\end{align*}
where $x$ is the input sentence, $S_A, S_B$ are exemplars of the styles we want to transfer between, \texttt{en, lx} are language codes prepended to indicate the output language (
\section{The Universal Rewriter (\textsc{ur}) model}
\label{sec:universal-rewriter-modeling}
We will start by discussing the Universal Rewriter (\textsc{ur}) model from~\citet{garcia2021towards}, upon which our proposed \textsc{diffur}~model is built. The \textsc{ur}~model extracts a style vector $\mathbf{s}$ from an exemplar sentence $e$, which reflects the desired target style. This style vector is used to style transfer an input sentence $x$. Consider $f_\text{enc}, f_\text{dec}$ to be encoder \& decoder Transformers initialized with mT5~\citep{xue-etal-2021-mt5}, which are composed to form the model $f_\text{ur}$.
\begin{align*}
f_\text{style}(e) = \mathbf{s} &= f_\text{enc}(\texttt{[CLS]} \oplus e)[0] \\
f_\text{ur}(x, \mathbf{s}) &= f_\text{dec}(f_\text{enc}(x) + \mathbf{s})
\end{align*}
where $\oplus$ is string concatenation, $+$ is vector addition. The Universal Rewriter is trained on three next-word prediction cross entropy objectives which are based on self supervised style transfer and supervised machine translation.\\
\noindent \textbf{Learning Style Transfer by Exemplar-driven Denoising}: To learn a style extractor, the Universal Rewriter uses the idea that two non-overlapping spans of text in the same document are likely to have the same style. Concretely, let $x_1$ and $x_2$ be two non-overlapping spans in mC4. Style extracted from one span is used to denoise the other,
\begin{align*}
\bar{x}_2 &= f_\text{ur}(\text{noise}(x_2), f_\text{style}(x_1)) \\
\mathcal{L}_\text{denoise} &= \mathcal{L}_\text{CE}(\bar{x}_2, x_2)
\end{align*}
where $\mathcal{L}_\text{CE}$ is the standard next-word prediction cross entropy loss function and noise($\cdot$) refers to 20-60\% random token dropping and token replacement. This objective is used on the mC4 dataset~\citep{xue-etal-2021-mt5} with 101 languages.\\
To build a general-purpose rewriter which can do translation as well as style transfer, the model is \textbf{additionally trained on two objectives}: (1) supervised machine translation using the OPUS-100 parallel dataset~\citep{zhang-etal-2020-improving}, and (2) a self-supervised objective to learn effective style-controlled translation. Details of these two objectives are provided in
\section*{Acknowledgements}
We are very grateful to the Task Mate team (especially Auric Bonifacio Quintana) for their support and helping us crowdsource data and evaluate models on their platform. We thank John Wieting, Timothy Dozat, Manish Gupta, Rajesh Bhatt, Esha Banerjee, Yixiao Song, Marzena Karpinska, Aravindan Raghuveer, Noah Constant, Parker Riley, Andrea Schioppa, Artem Sokolov, Mohit Iyyer and Slav Petrov for several useful discussions during the course of this project. We are also grateful to Rajiv Teja Nagipogu, Shachi Dave, Bhuthesh R, Parth Kothari, Bhanu Teja Gullapalli and Simran Khanuja for helping us annotate model outputs in several Indian languages during pilot experiments. This work was mostly done during Kalpesh Krishna (KK)'s internship at Google Research India, hosted by Bidisha Samanta and Partha Talukdar. KK was partly supported by a Google PhD Fellowship.
\section{Evaluation}
\label{sec:evaluation}
Automatic evaluation of style transfer is a challenging problem~\citep{pang-2019-towards,mir-etal-2019-evaluating,tikhonov2019style}, and the lack of resources (such as evaluation datasets, style classifiers) make evaluation trickier for Indic languages. To tackle this issue, we first collect a small dataset of formality and semantic similarity annotations in four Indic languages (\sectionref{sec:meta-eval-dataset}). We leverage this dataset to guide the design of an evaluation suite, which measures output style accuracy using cross-lingual transfer (\sectionref{sec:accuracy-eval}), semantic similarity using language-agnostic representations (\sectionref{sec:semantic-similarity}), overall performance by aggregating metrics (\sectionref{sec:aggregation-overall-style-transfer}) and style magnitude control using $\lambda$ (\sectionref{sec:evaluating-control}).\footnote{Unlike some prior work, we do not evaluate fluency due to the lack of Indic language resources; more in
\section{Conclusion}
We present a recipe for building and evaluating controllable few-shot style transfer systems which need only 3-10 style examples at inference. These systems are especially useful in low-resource settings where no large-scale labelled style corpus is available. We focus on one such setting, style transfer in Indian languages. Our proposed methods outperform prior work in formality transfer and code-mixing addition for several Indian languages, and we see promising qualitative results for several other attribute transfer tasks. Future work includes (1) further improving systems, especially for gender neutralization / author anonymization; (2) studying style transfer for languages where little to no machine translation data is available.
\section*{Ethical Considerations}
Recent work has highlighted issues of stylistic bias in text generation systems, specifically machine translation systems~\citep{hovy2020you}. We acknowledge these issues, and consider style transfer and style-controlled generation technology as an opportunity to work towards fixing them (for instance, gender neutralization as presented in \sectionref{sec:analysis}). Note that it is important to tread down this path carefully --- In Chapter 9, ~\citet{blodgett2021sociolinguistically} argue that style is inseparable from social meaning (as originally noted by~\citealp{eckert2008variation}), and humans may perceive automatically generated text very differently compared to automatic style classifiers.
Our models were trained on 32 Google Cloud TPUs. As discussed in \sectionref{sec:experimental-setup}, the \textsc{ur}~\& \textsc{ur-indic}~model take roughly 18 hours to train. The \textsc{diffur}-* and \textsc{multitask}~models are much cheaper to train (2 hours) since we finetune the pretrained \textsc{ur}-* models. The Google 2020 environment report mentions,\footnote{\url{https://www.gstatic.com/gumdrop/sustainability/google-2020-environmental-report.pdf}} ``TPUs are highly efficient chips which have been specifically designed for machine learning applications''. These accelerators run on Google Cloud, which is carbon neutral today, and is aiming to ``run on carbon-free energy, 24/7, at all of Google's data centers by 2030'' (\url{https://cloud.google.com/sustainability}).
\section{Introduction}
\begin{figure}[t]
\centering
\includegraphics[width=0.48\textwidth]{figs/diffur-fig1.pdf}
\caption{An illustration of our few-shot style transfer system during inference. Our model extracts style vectors from exemplar English sentences as input (in this case formal/informal sentences) and uses their vector difference to guide style transfer in other languages (Hindi). $\lambda$ is used to control the magnitude of transfer: in this example our model produces more high Sanskrit words \& honorifics (more formal) with higher $\lambda$.}
\vspace{-0.1in}
\label{fig:diffur-model-inference}
\end{figure}
Style transfer is a natural language generation task in which input sentences need to be re-written into a target style, while preserving semantics. Style transfer has many applications such as creative writing assistance~\citep{heidorn2000intelligent}, controlling text generation systems for attributes like formality or persuasiveness~\citep{smith2020controlling,niu2020controlling}, data augmentation~\citep{xie2019unsupervised, lee2021neural}, author obfuscation~\citep{shetty2018a4nt}, text simplification~\citep{xu2015problems}.
Most prior work in style transfer either assumes access to supervised data with parallel sentences between the two styles~\citep{jhamtani2017shakespearizing}, or access to large corpus of unpaired sentences with style labels~\citep{prabhumoye-etal-2018-style,subramanian2018multiple}. Models built are style-specific and cannot generalize to new styles during inference, which is needed for real-time adaptation to a user's style in a dialog or writing application. Moreover, \textbf{access to a large unpaired corpus with style labels is a strong assumption}. Most standard ``unpaired'' style transfer datasets have been carefully curated~\citep{shen2017style} or were originally parallel datasets~\citep{xu-etal-2012-paraphrasing,rao-tetreault-2018-dear}. This is especially relevant in settings outside English, where NLP tools and labelled datasets are largely underdeveloped~\citep{joshi-etal-2020-state}.
We consider one such setting, and take the \textbf{first steps} in studying \textbf{style transfer for five Indian languages}, which have nearly a billion native speakers in total.\footnote{We consider Hindi, Bengali, Telugu, Gujarati, Kannada. In the latest Census \shortcite{india2011census}, 67\% Indians consider one of these five languages as their first language. India's current population is estimated to be 1.4 billion~\citep{worldometers2021india}.} Since no training data exists for these languages, we analyzed the current state-of-the-art in few-shot multilingual style transfer, the Universal Rewriter (\textsc{ur}) from~\citet{garcia2021towards}. Unfortunately, we found it often copied inputs verbatim (\sectionref{sec:universal-rewriter-shortcomings}) \emph{without transferring style}.
We propose a simple inference-time trick of style-controlled translation through English, which improves the output diversity from \textsc{ur}~(\sectionref{sec:bt-at-inference}). To further boost performance, \textbf{we propose the \textsc{diffur}~algorithm},\footnote{``\textbf{Diff}erence \textbf{U}niversal \textbf{R}ewriter'', pronounced as \emph{differ}.} which uses the recent finding that paraphrasing leads to stylistic changes~\citep{krishna-etal-2020-reformulating}. \textsc{diffur}~extracts edit vectors from paraphrase pairs, which are used to condition and train a rewriter model, as shown in \figureref{fig:diffur-model}. On formality transfer and code-mixing addition, our best performing \textsc{diffur}~variant significantly outperforms \textsc{ur}~across all languages (by 2-3x) using automatic \& human evaluation.
In addition to better rewriting, our system is better able to \textbf{control the magnitude of style transfer} than prior work (\figureref{fig:diffur-model-inference}). Control is provided via a scalar knob ($\lambda$) which can be adjusted to make the output text reflect the target style (provided by exemplars) more or less. We also observe \textbf{promising qualitative results in several attribute transfer directions} (\sectionref{sec:analysis}) including sentiment transfer, text simplification, gender neutralization and text anonymization, all \emph{without retraining the model} and using just 3-10 exemplars at inference.
Finally, we found it hard to precisely evaluate our models due to the lack of evaluation datasets and style classifiers (often used as metrics) for Indic languages. To facilitate further research in formality transfer for Indic languages, we crowdsource \textbf{formality annotations for 4000 sentence pairs in four Indic languages} (\sectionref{sec:meta-eval-dataset}), and use this dataset to \textbf{design the automatic evaluation suite} used in this work (\sectionref{sec:evaluation}).
\noindent In summary, our contributions provide an end-to-end recipe for developing and evaluating style transfer models and evaluation in a low-resource setting.
\section{Related Work}
\noindent \textbf{Multilingual style transfer} is mostly unexplored in prior work --- in a survey of 35 papers by~\citet{briakou-etal-2021-ola} only a single work in each of Chinese~\citep{shang2019semi}, Russian~\citep{tikhonov2018sounds}, Latvian \& Estonian~\citep{korotkova2019grammatical} and French~\citep{niu2018multi} was found.~\citet{briakou-etal-2021-ola} further introduced XFORMAL, the first multilingual formality transfer \emph{evaluation} dataset in French, Brazilian Portugese and Italian.\footnote{We do not use this data since it does not cover Indian languages, and due to Yahoo! L6 corpus restrictions for industry researchers (confirmed via correspondence with authors).} In Hindi, formality has been studied in linguistics, with a focus on politeness~\citep{kachru2006hindi,agnihotri2013hindi,kumar-2014-developing} and code-mixing~\citep{bali2014borrowing}. Due to its prevalence in India, English-Hindi code-mixed has received attention in language modeling literature~\citep{pratapa2018language, samanta2019deep} and natural language understanding~\citep{khanuja2020gluecos}. To the best of our knowledge, we are the first to study style \emph{transfer} for Indian languages.
\vspace{0.05in}
\noindent \textbf{Few-shot methods} are a recent development in English style transfer, with prior work using variational autoencoders with a fixed number of latent factors~\citep{pmlr-v119-xu20a}, or clever prompts to large pretrained English language models at inference~\citep{reif2021recipe}. Most related to our work is the state-of-the-art TextSETTR model from~\citet{riley-etal-2021-textsettr} which uses a neural style encoder to map sentences to a style vector space. At inference, a few exemplar sentences are encoded to style vectors and used to control generation. To train this encoder,~\citet{riley-etal-2021-textsettr} use the idea that adjacent sentences in a document have a similar style. The model can modify a variety of attributes (formality, dialect, sentiment) at inference without re-training.
Recently, the \textbf{Universal Rewriter}~\citep{garcia2021towards} extended the TextSETTR model to 101 languages and developed a general-purpose rewriter which can perform translation, few-shot style transfer and stylized translation. To the best of our knowledge, the Universal Rewriter is the only prior few-shot style transfer system outside English, and the baseline in our work. We discuss the shortcomings of this approach in \sectionref{sec:universal-rewriter-shortcomings}, and propose alternative strategies in \sectionref{sec:models}.
\vspace{0.05in}
A few prior works have developed methods to \textbf{control the degree of style transfer} using a scalar input~\citep{wang2019controllable, samantahierarchical}. However, these models are style-specific and need large unpaired corpora in each style for training. We adopt the method used in~\citet{garcia2021towards} for controlling the style transfer degree (\sectionref{sec:universal-rewriter-modeling}) and notice the method is much better at style transfer control after our proposed fixes (\sectionref{sec:main-results}).
\section{Main Experiments}
\label{sec:main-experiments}
\subsection{Experimental Setup}
\label{sec:experimental-setup}
\noindent In this section we describe our setup comparing models on 1) formality transfer; 2) adding code-mixing to text. In our experiments, we \textbf{compare the following models} ---
\begin{itemize}
\setlength{\itemsep}{0.1pt}
\item \textsc{ur}: the Universal Rewriter~\citep{garcia2021towards}, which is our main baseline (\sectionref{sec:universal-rewriter-modeling});
\item \textsc{diffur}: our model with paraphrase vector differences (\sectionref{sec:diffur-model})
\item \textsc{ur-indic}, \textsc{diffur-indic}: Indic~variants of \textsc{ur}~and \textsc{diffur}~models~(\sectionref{sec:indic-variants})
\item \textsc{multitask}: Multitask training between \textsc{ur-indic}~and \textsc{diffur-indic}~(\sectionref{sec:multitask})
\item +~\textsc{bt}: models with style-controlled backtranslation at inference time (\sectionref{sec:bt-at-inference});
\end{itemize}
\noindent \textbf{Training Details}: Our models are implemented in JAX~\citep{jax2018github} using the T5X library.\footnote{\url{https://github.com/google-research/google-research/tree/master/flax_models/t5x}} We re-use the \textsc{ur}~checkpoint from~\citet{garcia2021towards}. To train the \textsc{ur-indic}~model, we follow the setup in~\citet{garcia2021towards} and initialize the model with mT5-XL~\citep{xue-etal-2021-mt5}, which has 3.7B parameters. We fine-tune the model for 25K steps with a batch size of 512 inputs and a learning rate of 1e-3, using the objectives in \sectionref{sec:universal-rewriter-modeling}. Training was done on 32 Google Cloud TPUs which took a total of 17.5 hours. To train the \textsc{diffur}~and~\textsc{diffur-indic}~models, we further fine-tune \textsc{ur}~and \textsc{ur-indic}~for a total of 4K steps using the objective from \sectionref{sec:diffur-model}, which takes 2 hours. \\
\noindent \textbf{Training Datasets}: To train the \textsc{ur-indic}~model, we use mC4~\citep{xue-etal-2021-mt5} for the self-supervised objectives and Samanantar~\citep{ramesh2021samanantar} for the supervised translation. For creating paraphrase data for training our \textsc{diffur}~models (\sectionref{sec:diffur-model}), we again leverage Indic language side of Samanantar sentence pairs. \emph{No paired/unpaired data with style labels is used during training} --- the model determines the target style at inference using 3-10 exemplars sentences. \\
\noindent \textbf{Evaluation Datasets}: Our models are evaluated on formality transfer and the task of adding code-mixing in text. Since we do not have access to any formality evaluation dataset,\footnote{We do not use GYAFC~\citep{rao-tetreault-2018-dear} and XFORMAL~\citep{briakou-etal-2021-ola} due to reasons in footnote 3. Our dataset from \sectionref{sec:meta-eval-dataset} has already been used for classifier selection, and has machine generated sentences.} we hold out 11K sentences from Samanantar in each language for validation, and another 11K sentences per language for testing. These sets have roughly equal number of formal / informal sentences, as marked by our formality classifiers (\sectionref{sec:accuracy-eval}). These sentences are used as inputs for both directions of formality transfer (depending on their formality labels), and one direction of code-mixing addition.\\
\textbf{Five Indic languages} with varying scripts and morphological richness are used to evaluate our systems --- Hindi, Bengali, Kannada, Telugu and Gujarati. As discussed in \sectionref{sec:indic-variants}, the \textsc{ur}~model saw translation data only for Hindi \& Bengali, whereas \textsc{ur-indic}~sees translation data for all these five languages. In addition, to test the generalization capability of the \textsc{diffur}-* models, no paraphrase data for Gujarati is used for training.\\
As \textbf{exemplars} for few-shot formality transfer, we use three formal English sentences, and three informal English sentences. These exemplars were taken from~\citet{garcia2021towards}, and have been provided in
\section*{Appendices for ``Few-shot Controllable Style Transfer for Low-Resource Settings: \\ A Study in Indian Languages''}
\section{More details on the translation-specific Universal Rewriter objectives}
\label{sec:details-ur-model}
In this section we describe the details of the supervised translation objective and the style-controlled translation objective used in the Universal Rewriter model. See \sectionref{sec:universal-rewriter-modeling} for details on the exemplar-based denoising objective.
\noindent \textbf{Learning translation via direct supervision}: This objective is the standard supervised translation setup, using zero vectors for style. The output language code is prepended to the input. Consider a pair of parallel sentences $(x, y)$ in languages with codes \texttt{lx}, \texttt{ly} (prepended to the input string),
\begin{align*}
\bar{y} &= f_\text{ur}(\texttt{ly} \oplus x, \mathbf{0}) \\
\mathcal{L}_\text{translate} &= \mathcal{L}_\text{CE}(\bar{y}, y)
\end{align*}
The Universal Rewriter is trained on English-centric translation data from the high-resource languages in OPUS-100~\citep{zhang-etal-2020-improving}.\\
\noindent \textbf{Learning style-controlled translation}: This objective emulates "style-controlled translation" in a self-supervised manner, via backtranslation through English. Consider $x_1$ and $x_2$ to be two non-overlapping spans in mC4 in language \texttt{lx},
\begin{align*}
x_2^{\texttt{en}} &= f_\text{ur}(\texttt{en} \oplus x_2, -f_\text{style}(x_1)) \\
\bar{x}_2 &= f_\text{ur}(\texttt{lx} \oplus x_2^{\texttt{en}}, f_\text{style}(x_1)) \\
\mathcal{L}_\text{BT} &= \mathcal{L}_\text{CE}(\bar{x}_2, x_2)
\end{align*}
\section{Choice of Exemplars}
\label{appendix:exemplar-choice}
\textbf{Formal exemplars}
\noindent 1. This was a remarkably thought-provoking read.
\noindent 2. It is certainly amongst my favorites.
\noindent 3. We humbly request your presence at our gala in the coming week.
\noindent \textbf{Informal exemplars}
\noindent 1. reading this rly makes u think
\noindent2. Its def one of my favs
\noindent 3. come swing by our bbq next week if ya can make it\\
\begin{figure}[h]
\centering
\includegraphics[width=0.48\textwidth]{figs/code-mix-exemplars}
\caption{Exemplars used for adding code-mixing.}
\label{fig:code-mixing-exemplars}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=0.48\textwidth]{figs/gender-neutral-exemplars}
\caption{Exemplars used for gender neutralization.}
\label{fig:gender-exemplars}
\end{figure}
\noindent \textbf{Complex exemplars}
\noindent 1. The static charges remain on an object until they either bleed off to ground or are quickly neutralized by a discharge.
\noindent 2. It is particularly famous for the cultivation of kiwifruit.
\noindent 3. Notably absent from the city are fortifications and military structures.
\noindent \textbf{Simple exemplars}
\noindent 1. Static charges last until they are grounded or discharged.
\noindent 2. This area is known for growing kiwifruit.
\noindent 3. Some things important missing from the city are protective buildings and military buildings.\\
\noindent \textbf{Positive sentiment exemplars}
\noindent 1. The most comfortable bed I've ever slept on, I highly recommend it.
\noindent 2. I loved it.
\noindent 3. The movie was fantastic.
\noindent \textbf{Negative sentiment exemplars}
\noindent 1. The most uncomfortable bed I've ever slept on, I would never recommend it.
\noindent 2. I hated it.
\noindent 3. The movie was awful.
\begin{figure}[h]
\centering
\includegraphics[width=0.48\textwidth]{figs/anonymization-exemplars}
\caption{Exemplars used for text anonymization. All entities in the deanonymized exemplars are random.}
\label{fig:anonymization-exemplars}
\end{figure}
\section{Evaluation Appendix}
\subsection{Multilingual Classifier Selection}
\label{appendix:classifier}
Due to the absence of a style classification dataset in Indic languages, we built our multilingual classifier drawing inspiration from recent research in zero-shot cross-lingual transfer~\citep{conneau-etal-2018-xnli, conneau2019cross, pfeiffer-etal-2020-mad}. We experimented with three zero-shot transfer techniques while selecting our classifiers for evaluating multilingual style transfer. \\
\noindent \textsc{translate train}: The first technique uses the hypothesis that style is preserved across translation. We classify the style of English sentences in the Samanantar translation dataset~\cite{ramesh2021samanantar} using a style classifier trained on English formality data from~\citet{krishna-etal-2020-reformulating}. We use the human translated Indic languages sentences as training data. This training data is used to fine-tune a large-scale multilingual language model. \\
\noindent \textsc{zero-shot}: The second technique fine-tunes large-scale multilingual language models on a English style transfer dataset, and applies it zero-shot on multilingual data during inference. \\
\noindent \textsc{mad-x}: Introduced by~\citet{pfeiffer-etal-2020-mad}, this technique is similar to \textsc{zero-shot} but additionally uses language-specific parameters (``adapters'') during inference. These language-specific adapters have been originally trained using masked language modeling on the desired language data. \\
\noindent \textbf{Dataset for evaluating classifiers}: We conduct our experiments on Hindi formality classification, leveraging our evaluation datasets from \sectionref{sec:meta-eval-dataset}. We removed pairs which did not have full agreement across the three annotators and those pairs which had the consensus rating of ``Equal'' formality. This filtering process leaves us with 316 pairs in Hindi (out of 1000). In our experiments, we check whether the classifiers give a higher score to the more formal sentence in the pair.\\
\noindent \textbf{Models}: We leverage the multilingual classifiers open-sourced\footnote{\url{https://github.com/martiansideofthemoon/style-transfer-paraphrase/blob/master/README-multilingual.md}} by~\citet{krishna-etal-2020-reformulating}. These models have been trained on the English GYAFC formality classification dataset~\citep{rao-tetreault-2018-dear}, and have been shown to be effective on the XFORMAL dataset~\citep{briakou-etal-2021-ola} for formality classification in Italian, French and Brazilian Portuguese.\footnotemark[13] These classifiers were trained on preprocessed data which had trailing punctuation stripped and English sentences lower-cased, encouraging the models to focus on lexical and syntactic choices. As base multilingual language models, we use (1) mBERT-base from~\citet{devlin-etal-2019-bert}; (2) XLM-RoBERTa-base from~\citet{conneau-etal-2020-unsupervised}.\\
\noindent \textbf{Results}: Our results on Hindi are presented in \tableref{tab:multilingual-classifier-eval-hindi} and other languages in \tableref{tab:multilingual-classifier-eval-indic}. Consistent with~\citet{pfeiffer-etal-2020-mad}, we find \textsc{mad-x} to be a superior zero-shot cross lingual transfer method compared to baselines. We also find XLM-R has better multilingual representations than mBERT. Unfortunately, AdapterHub~\citep{pfeiffer2020AdapterHub} has XLM-R language adapters available only for Hindi \& Tamil (among Indic languages). For other languages we use the \textsc{zero-shot} technique on XLM-R, consistent with the recommendations\footnotemark[13] provided by~\citet{krishna-etal-2020-reformulating} based on their experiments on XFORMAL~\citep{briakou-etal-2021-ola}.
\begin{table}[h]
\begin{center}
\begin{tabular}{ llr }
\toprule
Method & Model & Accuracy ($\uparrow$) \\
\midrule
\textsc{translate train} & mBERT & 66\% \\
\textsc{zero-shot} & mBERT & 72\% \\
& XLM-R & 76\% \\
\textsc{mad-x} & XLM-R & \textbf{81}\% \\
\bottomrule
\end{tabular}
\end{center}
\caption{Hindi formality classification accuracy on our crowdsourced dataset (\sectionref{sec:meta-eval-dataset}) using different cross-lingual transfer methods. Our results indicate that \textsc{mad-x} is the most effective method, and XLM-R is a better pretrained model than mBERT.}
\label{tab:multilingual-classifier-eval-hindi}
\end{table}
\begin{table}[h]
\begin{center}
\begin{tabular}{ lrr }
\toprule
Language & mBERT & XLM-R \\
\midrule
bn & 65.3\% & 82.2\% \\
kn & 76.3\% & 76.9\% \\
te & 72.6\% & 74.6\% \\
\bottomrule
\end{tabular}
\end{center}
\caption{Formality classification on our crowdsourced Bengali, Kannada and Telugu dataset (\sectionref{sec:meta-eval-dataset}) using the \textsc{zero-shot} technique described in
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Jordan Davis Was Killed Because of America's Fear of Young Black Men
ByEdward Williams
In November 2012, Michael Dunn, a 47-year-old white male stopped at a local gas station in Jacksonville, Fla. with his then-fiancée. When he pulled up at the gas station parking lot, he parked next to a car full of young, black male teens playing loud music. In the backseat of the car of teens was Jordan Davis, a 17-year-old from Marietta, Ga.
Dunn apparently asked the teens to turn down their music. A verbal altercation ensued between Dunn and Davis. According to Dunn, Davis pulled out some object that appeared to be a shotgun. Dunn pulled his 9mm gun out of his glove compartment and fired eight or nine times into the car full of young teens. Jordan Davis was killed. Police never found any gun or object that Davis could possibly have used that Dunn would have mistaken for a gun.
Dunn left the scene of the shooting, went back to his hotel with his fiancée and ordered pizza. He never called the police.
Based on these facts, why couldn't a diverse jury find Dunn guilty of murder (rather than attempted murder)? The answer is simple: The law of self-defense in Florida does not require an individual to flee to avoid using lethal force. And, at least two Florida juries have interpreted the law to mean that anytime a young black male is present, the "reasonable fear" requirement (that allows a person to use lethal force) is satisfied.
On the first issue, the requirement to flee, if possible, is one that was embedded into the law of self-defense when it was developed centuries ago, except in certain circumstances, namely when in defense of one's own home. To law students, this is known as the castle doctrine, with the underlying idea being that a person has a right to defend his or her castle/home/property. Florida and several other states have extended the castle doctrine far beyond its initial use and have effectively made it permissible for an individual to defend herself instead of fleeing in any and every circumstance. This is slightly different from the "Stand Your Ground" law, but only as a matter of procedure.
Neither Michael Dunn nor George Zimmerman used the Florida "Stand Your Ground" law, in that they did not request a special pre-trial hearing by the judge to determine if they actually stood their ground according to the law. Dunn and Zimmerman used the stand your ground principle that changed the dynamics of self-defense law in Florida. It is this shift in principle that makes it okay for Dunn to raise a self-defense claim when he could have simply pulled out of the parking lot, and for Zimmerman to raise a self-defense claim when he could have simply stayed in his vehicle as told by officers.
The second fundamental issue is even more disturbing. It is not based on an actual shift in law as enacted by the Florida state legislature, but rather is based on an interpretation of "reasonable apprehension" that brings to bear all of the fears of young black men that are inculcated into society through media, "news" and political fearmongering.
The question before the jury was whether it was reasonable for Dunn to fear for his life when he thought he saw something that could have been a gun (although no gun was recovered and no object similar to a gun could be found) coming through the back window of a car filled with four young black men listening to loud "thug" music or "rap crap?" For some members of the jury, the answer to this question was "yes," and for others the answer was "no."
When jury members start to do television interviews, I would not be surprised if we find that it was the non-white jurors who answered "no" and the white jurors that answered "yes." But why am I making this racial? Isn't this just playing into the same ol' racial infighting that we should be past in a post-racial America? My answer is no. Why? Because if four white teens bumping rock music had pulled up to Dunn, I believe that regardless of a phantom gun, those four kids would still be alive today. And, if one of them had been killed, a jury would have found Dunn's apprehension unreasonable.
This is a tough pill to swallow, but as a society, we have demonized young black men so much, for so long, that it is ingrained into our national psychology. It is easier for a jury to simply throw up their hands in irreconcilable disagreement than to find a middle-aged white man's fear of a young black man, in the absence of an actual weapon, unreasonable. I am frustrated by the fact that a jury has failed to hold accountable someone with the ability to do one simple thing: walk (or in this case, drive) away.
Dunn spoke to the teens first. He pulled out his gun, fired about eight shots into a car full of young teens, went to his hotel and ordered pizza instead of calling police, and for now, Dunn remains unaccountable for the murder of Jordan Davis.
So what now? How do we move forward? As I see it, there two options: one that is difficult but possible, and one that seems out-of-reach. First, we must push states like Florida to reinstate a common law definition of the castle doctrine, meaning that the only time you have a right not to flee, if possible, is when you are in your own home. Second, we must deprogram our society's fear of young black men. On the second issue, I welcome any and all suggestions, as I fear it may be an insurmountable task.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,692
|
Het WCW World Tag Team Championship was een professioneel worstelkampioenschap voor tag teams dat georganiseerd werd door World Championship Wrestling (WCW). Het was de originele wereld-tag team-titel van WCW en bleef actief totdat het verenigd was met het WWF Tag Team Championship, een wereld-tag team-titel van World Wrestling Federation (WWF).
Geschiedenis
Het WCW Tag Team Championship was origineel bekend als het NWA World Tag Team Championship van Mid-Atlantic Championship Wrestling gerund door Jim Crockett Promotions. De introductie van de titel in 1975, de Minnesota Wrecking Crew bekwam op 29 januari 1975 de inaugurele kampioenen. In 1991 werd de titel van naam veranderd in het WCW World Tag Team Championship wanneer Ted Turner de Jim Crockett Promotions inkocht en bekwam de World Championship Wrestling. Ondanks dat de naam van de titel Mid-Atlantic Championship Wrestling, de National Wrestling Alliance (NWA) erkende hun kampioenen tot 1992 niet wanneer Terry Gordy en Steve Williams een toernooi wonnen voor de titel. Als resultaat dat Gordy en Williams de WCW World Tag Team Champions waren wanneer beiden officieel de inaugurele NWA World Tag Team Champions bekwamen en beide titels samen waren verdedigd tot de WCW in september 1993 de NWA verliet. Op 17 januari 2008 nam de NWA hun erkenning terug van elke WCW World Tag Team Champion, die in 1995 hun titels waren gevormd, officieel gelinkt waren naar het NWA World Tag Team Championship.
De World Wrestling Federation kocht in maart 2001 de WCW in. Kort daarna vond de "The Invasion" plaats, waar uiteindelijk de WCW/ECW Alliance werd ontmanteld. Tijdens deze tijd, de titel was verwezen als het WCW Tag Team Championship. Op SummerSlam 2001 was de titel in een Steel Cage match verenigd met het WWF Tag Team Championship wanneer de toenmalige huidige WCW Tag Team Champions Kane en The Undertaker (Brothers of Destruction) Chris Kanyon en Diamond Dallas Page versloegen voor de WWF Tag Team titels. De titels waren alleen tijdelijk verenigd, als Kane en The Undertaker eerst, in Monday Night Raw op 17 september 2001, de WWF Tag Team titels verloren aan Dudley Boyz, gevolgd door het verlies van de WCW Tag Team titels aan Booker T en Test in de SmackDown aflevering op 25 september 2001. Op Survivor Series 2001 versloegen de toenmalige huidige WCW Tag Team Champions, Dudley Boyz, de toenmalige huidige WWF Tag Team Champions, Hardy Boyz, om de WCW en WWF Tag Team Championships te verenigen. De verenigde titels was dan opgeborgen en de WWE (vroeger WWF) erkende de Dudley Boyz officieel als de laatste WCW Tag Team Champions.
Statistieken
Zie ook
Externe links
NWA World Tag Team Championship (Mid-Atlantic) geschiedenis op Wrestling-titels.com
WCW World Tag Team Championship geschiedenis op Wrestling-titels.com
National Wrestling Alliance kampioenschap
World Championship Wrestling kampioenschap
WWE-kampioenschap
Professioneel worstelkampioenschap
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,291
|
Similar to Peaucellier linkage, Hart's linkage (Hart's inversor or Hart's cell) employs inversion to convert between circular and rectilinear motion. Compared to the Peaucellier linkage, Hart's device uses fewer rods.
for 0 < m < 1. In ΔABD, (1) implies OP||BD. Similarly, in ΔABC, AQ||AC. Because of the symmetry, or since ΔABC = ΔADC), the quadrilateral ABDC is an isosceles trapezoid, so that BD||AC. It then follows from (1) that the three points O, P, Q are collinear and belong to a line parallel to both AC and BD.
(2) OP·OQ = m(1 - m)·(AD2 - AB2).
and S is fixed, then P will trace a circle that passes through the center O of inversion. It follows that Q will then describe a segment of a straight line.
The applet below demonstrates this property. The points A, B, D, O, and S are draggable for the purpose of defining (or redefining) the attributes of the configuration. However, when P is dragged both O and S remain fixed.
Note that the dimensions of the rods impose certain limitations on the relative positions of the rods. When these are about to be violated while P is being dragged, the applet stops tracing the points. If this happens, return P into the arc already drawn and reconfigure from here.
Let's now prove the claim (2), as promised.
EB2 + AE2 = AB2.
(5) AC·BD = AD2 - AB2.
OQ/AC = OB/AB = 1 - m.
= m(1 - m)(AD2 - AB2).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,006
|
The black art of news management
In his latest column for the New Statesman, John Pilger describes the "master illusions" which have formed the basis of black propaganda and provided "false flags" for political chicanery and for wars and atrocities, such as Iraq and the Israeli assault on the Gaza peace flotilla.
How do wars begin? With a "master illusion", according to Ralph McGehee, one of the CIA's pioneers in "black propaganda", known today as "news management". In 1983, he described to me how the CIA had faked an "incident" that became the "conclusive proof of North Vietnam's aggression". This followed a claim, also fake, that North Vietnamese torpedo boats had attacked an American warship in the Gulf of Tonkin in August 1964.
"The CIA," he said, "loaded up a junk, a North Vietnamese junk, with communist weapons - the Agency maintains communist arsenals in the United States and around the world. They floated this junk off the coast of central Vietnam. Then they shot it up and made it look like a fire fight had taken place, and they brought in the American press. Based on this evidence, two Marine landing teams went into Danang and a week after that the American air force began regular bombing of North Vietnam." An invasion that took three million lives was under way.
The Israelis have played this murderous game since 1948. The massacre of peace activists in international waters on 31 May was "spun" to the Israeli public for most of last week, preparing them for yet more murder by their government, with the unarmed flotilla of humanitarians described as terrorists or dupes of terrorists. The BBC was so intimidated that it reported the atrocity primarily as a "potential public relations disaster for Israel", the perspective of the killers, and a disgrace for journalism.
A similar master illusion currently preoccupies Asian governments. On 20 May, South Korea announced that it had "overwhelming evidence" that one of its warships, the Cheonan, had been sunk by a torpedo fired by a North Korean submarine in March with the loss of 46 sailors. The United States maintains 28,000 troops in South Korea, where popular sentiment has long backed a détente with Pyongyang.
On 26 May, US Secretary of State Hillary Clinton flew to Seoul and demanded that the "international community must respond" to "North Korea's outrage". She flew on to Japan, where the new "threat" from North Korea conveniently eclipsed the briefly independent foreign policy of Japanese prime minister Yukio Hatoyama, elected last year with popular opposition to America's permanent military occupation of Japan. The "overwhelming evidence" is a torpedo propeller that "had been corroding at least for several months," reported the Korea Times. In April, the director of South Korea's national intelligence, Won See-hoon, told a parliamentary committee that there was no evidence linking the sinking of the Cheonan to North Korea. The defence minister agreed. The head of South Korea's military marine operations said, "No North Korean warships have been detected [in] the waters where the accident took place." The reference to "accident" suggests the warship struck a reef and broke in two.
To the American media, North Korea's guilt is beyond doubt, just as North Vietnam's guilt was beyond doubt, just as Saddam Hussein had weapons of mass destruction, just as Israel can terrorise with impunity. However, unlike Vietnam and Iraq, North Korea has nuclear weapons, which helps explain why it has not been attacked, not yet: a salutary lesson to other countries, such as Iran, currently in the crosshairs.
In Britain, we have our own master illusions. Imagine someone on state benefits caught claiming £40,000 of taxpayers' money in a second home scam. A prison sentence would almost certainly follow. David Laws, chief secretary to the Treasury, does the same and is described as follows:
"I have always admired his intelligence, his sense of public duty and his personal integrity" (Nick Clegg, deputy prime minister). "You are a good and honourable man. I am sure that throughout you have been motivated by wanting to protect your privacy rather than anything else." (David Cameron, prime minister). Laws is "a man of quite exceptional nobility" (Julian Glover, the Guardian). A "brilliant mind" (BBC).
The Oxbridge club and its associate members in politics and the media have tried to link Laws's "error of judgement" and "naivety" to his "right to privacy" as a gay man, an irrelevance. The "brilliant mind" is a wealthy Cambridge-groomed investment banker and gilts trader devoted to the noble task of cutting the public services of mostly poor and honest people.
Now imagine another public official, the force behind one of the great war criminals and liars. This official "spun" the illegal invasion of a defenceless country that resulted in the deaths of at least a million people and the dispossession of many more: in effect, the crushing of a human society. If this was the Balkans or Africa, he would very likely have been indicted by the International Criminal Court.
But crime pays for the clubbable. In quick step with the Laws affair, this truth was demonstrated by the continuing celebration of Alastair Campbell, whose frequent media appearances provide a vicarious thrill for the liberal intelligentsia. To the Guardian, Campbell is "bullish, sometimes misdirected, but unafraid to press on where others might have faltered". The Guardian's immediate interest is its "exclusive" publication of Campbell's "politically explosive" and "uncut" diaries. Here is a flavour: "Saturday 14 May. I called Peter [Mandelson] and asked why he didn't return my calls yesterday. 'You know why.' 'No, I don't.' He said he was incandescent at my Newsnight interview...' "
In a promotional interview with the Guardian, Campbell dispensed more of this dated incest, referring just once to the bloodbath for which he was a principal apologist. "Did Iraq lose us support in 2005?" he asked rhetorically. "Without a doubt..." Thus, a criminal tragedy equal in scale to the Rwandan genocide was dismissed as a "loss" for New Labour: a master illusion of notable profanity.
Another fake Shareholders wanted the Mirror editor out long before the allegedly bogus photos. Does anyone care that the BBC and other papers fall for the hoaxes of US and UK rulers?
The pursuit of Julian Assange is an assault on freedom and a mockery of journalism John Pilger describes the augmented Anglo-American government and media campaign against Julian Assange and WikiLeaks as Assange is granted political asylum by Ecuador and remains in that country's London embassy.
Obama, the prince of bait-and-switch John Pilger describes the devaluing of civilian casualties in colonial wars, and the anointing of Barack Obama, as he tours the battlefields, sounding more and more like George W. Bush.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,231
|
We asked a bunch of seventeen year olds if they knew what an emo was and we were met with blank stares. They suggested maybe hipsters would have been better suited as a character subject for a 2016-set high school film.
Nevertheless, the teaser trailer for Neil Triffitt's Emo The Musical looks great and marks a major achievement for Triffitt and his dedicated team having originally released the concept as a short film. The Cinema Australia team couldn't be any more excited to see what they've come up with.
Emo The Musical will have its world premiere film at this year's Melbourne International Film Festival with Triffitt as a special guest. You can get tickets here.
Having been kicked out of his old school, Ethan just wants to start afresh. And after being accepted to join his new school's grungy emo band, Worst Day Ever, he thinks he's finally found his place. But when the school's sunshine-and-rainbows Hope Group decides to compete alongside Worst Day Ever in the local band comp, it pits the ideologically and musically opposed bands against each other. There couldn't be a worse time for Emo Ethan and the Hope Group's kind-hearted, faithful singer Trinity to fall in love.
Expanded from his Berlinale 2013 award-winning short film, Neil Triffett's debut feature is a cheerfully irreverent take on Romeo and Juliet-style star-crossed love, via High School Musical and Glee. Supported by the MIFF Premiere Fund, and featuring Rahart Adams (Nowhere Boys, MIFF 2013), Benson Jack Anthony (800 Words) and newcomer Jordan Hare alongside Adam Zwar, Bridie Carter and Dylan Lewis, it's a sweetly satirical (and, given this year's Safe Schools controversies, timely) story about tolerance, individuality and harmonising.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,684
|
package com.amazonaws.services.mgn.model.transform;
import java.util.Map;
import javax.annotation.Generated;
import com.amazonaws.SdkClientException;
import com.amazonaws.services.mgn.model.*;
import com.amazonaws.protocol.*;
import com.amazonaws.annotation.SdkInternalApi;
/**
* SsmDocumentMarshaller
*/
@Generated("com.amazonaws:aws-java-sdk-code-generator")
@SdkInternalApi
public class SsmDocumentMarshaller {
private static final MarshallingInfo<String> ACTIONNAME_BINDING = MarshallingInfo.builder(MarshallingType.STRING)
.marshallLocation(MarshallLocation.PAYLOAD).marshallLocationName("actionName").build();
private static final MarshallingInfo<Boolean> MUSTSUCCEEDFORCUTOVER_BINDING = MarshallingInfo.builder(MarshallingType.BOOLEAN)
.marshallLocation(MarshallLocation.PAYLOAD).marshallLocationName("mustSucceedForCutover").build();
private static final MarshallingInfo<Map> PARAMETERS_BINDING = MarshallingInfo.builder(MarshallingType.MAP).marshallLocation(MarshallLocation.PAYLOAD)
.marshallLocationName("parameters").build();
private static final MarshallingInfo<String> SSMDOCUMENTNAME_BINDING = MarshallingInfo.builder(MarshallingType.STRING)
.marshallLocation(MarshallLocation.PAYLOAD).marshallLocationName("ssmDocumentName").build();
private static final MarshallingInfo<Integer> TIMEOUTSECONDS_BINDING = MarshallingInfo.builder(MarshallingType.INTEGER)
.marshallLocation(MarshallLocation.PAYLOAD).marshallLocationName("timeoutSeconds").build();
private static final SsmDocumentMarshaller instance = new SsmDocumentMarshaller();
public static SsmDocumentMarshaller getInstance() {
return instance;
}
/**
* Marshall the given parameter object.
*/
public void marshall(SsmDocument ssmDocument, ProtocolMarshaller protocolMarshaller) {
if (ssmDocument == null) {
throw new SdkClientException("Invalid argument passed to marshall(...)");
}
try {
protocolMarshaller.marshall(ssmDocument.getActionName(), ACTIONNAME_BINDING);
protocolMarshaller.marshall(ssmDocument.getMustSucceedForCutover(), MUSTSUCCEEDFORCUTOVER_BINDING);
protocolMarshaller.marshall(ssmDocument.getParameters(), PARAMETERS_BINDING);
protocolMarshaller.marshall(ssmDocument.getSsmDocumentName(), SSMDOCUMENTNAME_BINDING);
protocolMarshaller.marshall(ssmDocument.getTimeoutSeconds(), TIMEOUTSECONDS_BINDING);
} catch (Exception e) {
throw new SdkClientException("Unable to marshall request to JSON: " + e.getMessage(), e);
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,793
|
Q: Using getopts in Bash to specify variables results in an illegal option error I was attempting to specify variables' values using getopts in Bash. But whenever trying to use flag -l or -c, I get an error: illegal option -- l.
DIR="./"
LENGTH=0
CHAR="a"
while getopts "hd:" arg; do
case ${arg} in
d)
DIR=${OPTARG};;
l)
LENGTH=$OPTARG;;
c)
CHAR=$OPTARG;;
h)
echo "Flags:"
echo "-h: display help"
echo "-d: specify directory"
echo "-l: specify length"
echo "-c: specify character"
exit 0;;
esac
done
echo $DIR
echo $LENGTH
echo $CHAR
Could you please tell what I'm doing wrong?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,528
|
Kuma Coffee - Single Origin Espresso Roasters Choice - 12 oz.
read more h America. As our coffee lineup changes so often, you can expect the SOE we choose to change with it. And even though it will be the roaster's choice, we promise you are going to love what you get!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,889
|
\section{Conclusions}
\label{sec:conclusions}
The divide and conquer principle is one of the fundamental concepts for learning dynamical systems with high complexity. With a focus on ResNet based learning methods, we have proposed a deep neural network based adaptive learning (DNN-AL) approach. Through adaptively decomposing the datasets associated with large validation errors, deep neural networks (DNNs) are hierarchically constructed to efficiently learn local governing equations, and the unknown switching time instants are identified gradually. Especially, during the adaptive procedure, the network parameters at the previous iteration steps are reused as initial parameters for the current iteration step, which provides an efficient initialization strategy for training local DNNs. From our analysis, prediction error bounds are established for the DNNs obtained in DNN-AL. Several numerical examples demonstrate the effectiveness of DNN-AL. As this work is limited to switched systems under time-dependent switching, developing adaptive learning methods for systems with both time and state dependent switching will be the focus of our future work.
\section*{Acknowledgments}
This work is supported by the National Natural Science Foundation of China (No. 12071291), the Science and Technology Commission of Shanghai Municipality (No. 20JC1414300) and the Natural Science Foundation of Shanghai (No. 20ZR1436200).
\bibliographystyle{elsarticle-num}
\section{Method and analysis}
\label{sec:method}
Our goal is to construct efficient neural network approximations for the $\Delta$-lag flow map associated with the switched system \eqref{eq:swithed-system}, which is written as
\begin{equation}
\label{eq:flow-swithced}
\begin{aligned}
\Phi_{\Delta}^{\mathrm{switched}}(\mathbf{x}(t_0))&:=
\mathbf{x}(t_0+\Delta)\\
&=\mathbf{x}(t_0)+
\begin{cases}
\int_0^\Delta \mathbf{f}^{(1)}(\mathbf{x}(t_0+s))\dif s,\quad 0=T_0<t_0\le t_0+\Delta \le T_1\\
\cdots\\
\int_0^\Delta \mathbf{f}^{(i)}(\mathbf{x}(t_0+s))\dif s,\quad T_{i-1}<t_0\le t_0+\Delta \le T_i\\
\cdots\\
\int_0^\Delta\mathbf{f}^{(K)}(\mathbf{x}(t_0+s))\dif s,\quad T_{K-1}<t_0\le t_0+\Delta \le T_K,\\
\end{cases}
\end{aligned}
\end{equation}
where $T_1,\ldots,T_K$ are the switching time instants introduced in \eqref{eq:switch-signal}, $\mathbf{f}^{(\cdot)}(\cdot)$ refers to the governing equation associated with the switching signal (see \eqref{eq:swithed-system}), and $\phi_{\Delta}^{(i)}(\mathbf{x}(t_0)):=\int_0^\Delta \mathbf{f}^{(i)}(\mathbf{x}(t_0+s))\dif s$ denotes the effective increment corresponding to $\mathbf{f}^{(i)}$.
For this purpose, we propose a deep neural network based adaptive learning (DNN-AL) approach. In DNN-AL, training datasets of the $\Delta$-lag flow map are adaptively decomposed, and local neural network approximations are constructed using the decomposed datasets, so that the switching time instants can be identified, and the local networks can approximate the $\Delta$-lag flow map well.
During the adaptive procedure, the networks at the current iteration step are reused in the next iteration step, which results in efficient initial guesses for training deep ResNets. Details of our DNN-AL approach are presented in Section \ref{subsec:DNN-AL}, and error bounds of the predicated states are analyzed in Section \ref{subsec:theo}.
\subsection{Adaptive learning for switched systems}
\label{subsec:DNN-AL}
To begin with, the adaptivity iteration step is denoted by $\widehat{K}$, and the time interval $(0,T_{\max}]$ is partitioned into $\widehat{K}$ sub-intervals at the step $\widehat{K}$ (details are given in the following).
The double index $\dindex{\widehat{K}}{i}$ is used to denote the $i$-th sub-interval at adaptivity iteration step $\widehat{K}$.
Endpoints of the sub-intervals are denoted by $\{\hat{t}^{(\widehat{K},i)}\}_{i=0}^{\widehat{K}}$, where $0=\hat{t}^\dindex{\widehat{K}}{0} <\cdots<\hat{t}^\dindex{\widehat{K}}{\widehat{K}}=T_{\max}$.
Here, the validation data is the last trajectory of the $N$ collected orbits \eqref{eq:each-trajectory} at the time between 0 and $T_{\max}$, $\mathbf{Y}^{(N)}$, and let $\mathbf{y}_\text{validate}^{(j)}=\mathbf{y}_{j}^{(N)},$ for $j=1,\ldots,J$, where $J$ is the number of discrete states at each trajectory.
Details of DNN-AL to approximate switched systems are presented as follows.
For the first step, i.e.\ $\widehat{K}=1$,
let $\hat{t}^{(1,0)}=0$, $\hat{t}^\dindex{1}{1}=T_{\max}$, and partition the dataset \eqref{eq:data-pairs} into a training dataset $\mathcal{D}_{\mathrm{train}}^\dindex{1}{1}$ and a validation dataset $\mathcal{S}_{\mathrm{validate}}^\dindex{1}{1}$, which are defined as
\begin{equation}
\label{eq:initial-dataset}
\begin{aligned}
\mathcal{D}_{\mathrm{train}}^\dindex{1}{1}&:=\left\{(\mathbf{y}_j^{(n)}, \mathbf{y}_{j+1}^{(n)}):\quad n=1,\ldots,N-1,\quad j=1,\ldots, J-1\right\}, \\
\mathcal{S}_{\mathrm{validate}}^\dindex{1}{1}&:=\left\{(\mathbf{y}_{\text{validate}}^{(j)},\mathbf{y}_{\text{validate}}^{(j+1)}):\quad j=1,\ldots,J-1\right\}.
\end{aligned}
\end{equation}
A deep neural network (see \eqref{eq:RT-ResNet}) with (untrained) parameters is initialized,
and it is denoted by $\mathcal{N}^\dindex{1}{1}_0(\cdot;\Theta^\dindex{1}{1}_0)$, where $\Theta^\dindex{1}{1}_0$ are the parameters. We then train a deep ResNet
using Algorithm \ref{alg:trining-ResNet} with the initial network $\mathcal{N}^\dindex{1}{1}_0$ and the training dataset $\mathcal{D}_{\mathrm{train}}^\dindex{1}{1}$,
and denote the trained deep neural network by $\mathcal{N}^\dindex{1}{1}(\cdot; \Theta^\dindex{1}{1})$.
To assess the accuracy of the trained network,
the following validation error is considered,
\[
\mathcal{E}_{\mathrm{validate}}^\dindex{1}{1} = \frac{1}{\left|\mathcal{S}_{\mathrm{validate}}^\dindex{1}{1}\right|}\sum_{(\mathbf{y}_{\text{in}},\mathbf{y}_{\text{out}})\in\mathcal{S}_{\mathrm{validate}}^\dindex{1}{1}}\ell_{\text{se}}(\mathbf{y}_{\text{in}},\mathbf{y}_{\text{out}};\Theta^{(1,1)})\,,
\]
where $\ell_{\text{se}}$ is the square error function defined in \eqref{eq:square-loss}.
If the $\mathcal{E}_{\mathrm{validate}}^\dindex{1}{1}$ is larger than a given tolerance $tol$, the interval $(\hat{t}^\dindex{1}{0},\hat{t}^\dindex{1}{1}]$ is equally divided into two parts, i.e., $(\hat{t}^\dindex{1}{0},\hat{t}^\dindex{1}{1}]=(\hat{t}^\dindex{1}{0},t^{(1)}]\cup (t^{(1)},\hat{t}^\dindex{1}{1}]$, where
$t^{(1)}= (\hat{t}^\dindex{1}{0}+\hat{t}^\dindex{1}{1})/2$,
and the datasets are divided and associated with these two intervals. After that, the adaptivity iteration step is updated, i.e.\ $\widehat{K}=2$, and the new deep neural networks are trained based on the divided datasets.
In general, after $\widehat{K}$ adaptivity iteration steps, the time domain $(0,T_{\max}]$ is partitioned into $\widehat{K}$ intervals
$(\hat{t}^\dindex{\widehat{K}}{i-1},\hat{t}^\dindex{\widehat{K}}{i}]$ for $i=1,\ldots,\widehat{K}$, where
$0=\hat{t}^\dindex{\widehat{K}}{0}<\cdots<\hat{t}^\dindex{\widehat{K}}{\widehat{K}}=T_{\max}$, and
the trained neural networks $\mathcal{N}^\dindex{\widehat{K}}{i}$, the associated training sets $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}}{i}$, the validation sets $\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}}{i}$ and the validation errors $\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}}{i}$ are obtained.
The procedures for the next iteration step
are as follows.
First, the index of the local deep neural network
with the maximum validation error is identified as,
\begin{eqnarray} \label{eq:max_error}
i^{*}=\argmax_{i=1,\ldots,\widehat{K}} \mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}}{i} \,.
\end{eqnarray}
When the maximum validation error is not unique,
$i^*$ in \eqref{eq:max_error} is set to an arbitrary
index with the maximum value.
Next, the interval associated with the maximum error $(\hat{t}^\dindex{\widehat{K}}{i^*-1},\,\hat{t}^\dindex{\widehat{K}}{i^*}]$ is equally divided into two intervals. Denoting
$t^{(\widehat{K})}= (\hat{t}^\dindex{\widehat{K}}{i^*-1} + \hat{t}^\dindex{\widehat{K}}{i^*})/2$,
the time domain are partitioned by $0=\hat{t}^\dindex{\widehat{K}+1}{0}<\cdots<\hat{t}^\dindex{\widehat{K}+1}{\widehat{K}+1}=T_{\max}$ with
\begin{equation}
\label{eq:update-time-instants}
\hat{t}^\dindex{\widehat{K}+1}{i}=
\begin{cases}
\hat{t}^\dindex{\widehat{K}}{i},\quad &0\leq i< i^*\\
t^{(\widehat{K})},\quad &i=i^*\\
\hat{t}^\dindex{\widehat{K}}{i-1},\quad & \widehat{K}+1\geq i>i^*.
\end{cases}
\end{equation}
From the iteration step $\widehat{K}$
to the step $\widehat{K}+1$, the time intervals,
datasets, local deep neural networks and validation errors are the same, except those associated with the
index $i^*$.
So, for $i=1,\ldots,i^*-1$, we define
\begin{equation}
\label{eq:left-data}
\begin{aligned}
&\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i}:= \mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}}{i}, \,\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i}:=\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}}{i},\\
&\mathcal{N}^\dindex{\widehat{K}+1}{i}(\cdot;\Theta^\dindex{\widehat{K}+1}{i}):= \mathcal{N}^\dindex{\widehat{K}}{i}(\cdot;\Theta^\dindex{\widehat{K}}{i}),\\
&\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i}:=\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}}{i},
\end{aligned}
\end{equation}
and for $i=i^*+2,\ldots,\widehat{K}+1$,
\begin{equation}
\label{eq:right-data}
\begin{aligned}
&\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i} :=\mathcal{D}_{\mathrm{train}}^{(\widehat{K},i-1)},\, \mathcal{S}_{\mathrm{validate}}^{(\widehat{K}+1,i)}:=\mathcal{S}_{\mathrm{validate}}^{(\widehat{K},i-1)},\\
&\mathcal{N}^{(\widehat{K}+1,i)}(\cdot;\Theta^{(\widehat{K}+1,i)}):=\mathcal{N}^{(\widehat{K},i-1)}(\cdot;\Theta^{(\widehat{K},i-1)}), \\
&\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i}:=\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}}{i-1}.
\end{aligned}
\end{equation}
Next, new local deep ResNets are constructed for $(\hat{t}^\dindex{\widehat{K}+1}{i^*-1},\hat{t}^\dindex{\widehat{K}+1}{i^*}]$ and $(\hat{t}^\dindex{\widehat{K}+1}{i^*},\hat{t}^\dindex{\widehat{K}+1}{i^*+1}]$. For the interval $(\hat{t}^\dindex{\widehat{K}+1}{i^*-1},\hat{t}^\dindex{\widehat{K}+1}{i^*}]$, a training dataset $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*}$ and a validation dataset $\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*}$ are
constructed as
\begin{equation}
\label{eq:sub-dataset}
\begin{aligned}
\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*}&:=\left\{(\mathbf{y}^{(n)}_j,\mathbf{y}^{(n)}_{j+1}): n=1,\ldots,N-1,\, t_j\in (\hat{t}^\dindex{\widehat{K}+1}{i^*-1}, \hat{t}^\dindex{\widehat{K}+1}{i^*}]\right\},\\
\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*}&:=\left\{(\mathbf{y}_{\text{validate}}^{(j)},\mathbf{y}_{\text{validate}}^{(j+1)}):t_j\in (\hat{t}^\dindex{\widehat{K}+1}{i^*-1}, \hat{t}^\dindex{\widehat{K}+1}{i^*}]\right\}.
\end{aligned}
\end{equation}
Initial deep ResNets for these two intervals are set to the trained neural network $\mathcal{N}^\dindex{\widehat{K}}{i^*}$,
i.e., $\mathcal{N}_0^\dindex{\widehat{K}+1}{i^*}:=\mathcal{N}^\dindex{\widehat{K}}{i^*}$ and
$\mathcal{N}_0^\dindex{\widehat{K}+1}{i^*+1}:=\mathcal{N}^\dindex{\widehat{K}}{i^*}$.
Then the trained neural network $\mathcal{N}^\dindex{\widehat{K}+1}{i^*}$ is obtained using Algorithm \ref{alg:trining-ResNet} with inputs $\mathcal{N}^\dindex{\widehat{K}+1}{i^*}_0$ and $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*}$.
The validation error for $\mathcal{N}^\dindex{\widehat{K}+1}{i^*}$ is computed as
\begin{equation}
\begin{aligned}
\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*} = \frac{1}{\left |\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*}\right |}
\sum_{(\mathbf{y}_{\text{in}},\mathbf{y}_{\text{out}})\in \mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*}} \ell_{\text{se}}(\mathbf{y}_{\text{in}},\mathbf{y}_{\text{out}};\Theta^\dindex{\widehat{K}+1}{i^*})\,,
\end{aligned}
\label{eq:valid-error}
\end{equation}
where $\ell_{\text{se}}$ is defined in \eqref{eq:square-loss}.
Similarly, for the interval $(\hat{t}^\dindex{\widehat{K}+1}{i^*},\, \hat{t}^\dindex{\widehat{K}+1}{i^*+1}]$, the datasets $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*+1}$ and $\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*+1}$ are constructed, the neural network $\mathcal{N}^\dindex{\widehat{K}+1}{i^*+1}$ is trained, and the validation error $\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*+1}$ is computed. After that,
the iteration step is updated $\widehat{K}=\widehat{K}+1$, and the above procedures are repeated until the maximum validation error is smaller than a given tolerance.
Our DNN-AL approach is summarized in Algorithm \ref{alg:main-alg}, where $tol$ is the given tolerance.
The major ingredients at each iteration step of DNN-AL include: (1) training deep neural networks to learn flow maps using datasets associated with time intervals,
(2) decomposing the interval with the largest validation error.
\figurename{\ref{fig:DNN-AL-train-valid}} illustrates the simple schematic of DNN-AL. \figurename{\ref{fig:train-phase}} and \figurename{\ref{fig:validation-phase}} show the flow charts of the training procedure and the validation procedure respectively. The network architecture used in the algorithm is illustrated in \figurename{\ref{fig:ResNet-used}}.
\begin{figure}
\centering
\subfigure[Training.]{
\label{fig:train-phase}
\includegraphics[scale=0.42]{figs/DDOT-train.pdf}
}
\subfigure[Validation.]{\label{fig:validation-phase}\includegraphics[scale=0.38]{figs/DDOT-valid.pdf}}
\subfigure[Network architecture.]{\label{fig:ResNet-used}\includegraphics[scale=0.9]{figs/ResNet-used.pdf}}
\caption{DNN-AL for switched systems: (a)
Two new training datasets and the corresponding neural networks are obtained at each adaptivity iteration;
(b) The validation errors are computed, and the interval with the largest error is identified and decomposed;
(c) Neural networks with recurrent structures.
}
\label{fig:DNN-AL-train-valid}
\end{figure}
\begin{algorithm}[!htp]
\caption{Adaptive learning for unknown switched systems}
\label{alg:main-alg}
\begin{algorithmic}[1]
\REQUIRE{Dataset $\mathcal{D}=\left\{
(\mathbf{y}_j^{(n)}, \mathbf{y}_{j+1}^{(n)}): j =1,\ldots,J-1,\quad n=1,\ldots,N\right\}$.}
\STATE{Initialize $\widehat{K}=1$.}
\STATE{Partition $\mathcal{D}$ into the training dataset $\mathcal{D}_{\mathrm{train}}^\dindex{1}{1}$ and the validation dataset $\mathcal{S}_{\mathrm{validate}}^\dindex{1}{1}$ (see \eqref{eq:initial-dataset}).}
\STATE{Initialize a deep ResNet $\mathcal{N}_0^\dindex{1}{1}$ (see network structure in \eqref{eq:RT-ResNet}).}
\STATE{Obtain the trained deep ResNet $\mathcal{N}^\dindex{1}{1}$ using Algorithm \ref{alg:trining-ResNet} with
the initial network $\mathcal{N}_0^\dindex{1}{1}$ and the data set $\mathcal{D}_{\mathrm{train}}^\dindex{1}{1}$.
}
\STATE{Compute the validation error $\mathcal{E}_{\mathrm{validate}}^\dindex{1}{1}$ for $\mathcal{N}^\dindex{1}{1}$ with $\mathcal{S}_{\mathrm{validate}}^\dindex{1}{1}$ (see \eqref{eq:valid-error}).}
\WHILE{$\max\left( \{\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}}{i} \}_{i=1}^{\widehat{K}}\right)\geq tol$}
\STATE{Find the index of the maximum error: $i^*= \argmax_{i=1:\widehat{K}} \mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}}{i}$.}
\STATE{Determine the time instant $t^{(\widehat{K})}:= \left(\hat{t}^\dindex{\widehat{K}}{i^*-1}+\hat{t}^\dindex{\widehat{K}}{i^*}\right)/2$.}
\STATE{Divide the interval $\left(\hat{t}^\dindex{\widehat{K}}{i^*-1},\hat{t}^\dindex{\widehat{K}}{i^*}\right]$ into $\left(\hat{t}^\dindex{\widehat{K}}{i^*-1},t^{(\widehat{K})}\right]$ and $\left(t^{(\widehat{K})},\hat{t}^\dindex{\widehat{K}}{i^*}\right]$.}
\STATE{Update time instants (see \eqref{eq:update-time-instants}).}
\STATE{Update datasets, neural networks and others for unchanged sub-intervals (see \eqref{eq:left-data} and \eqref{eq:right-data}).}
\STATE{Obtain the training and the validation sets $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*}$, $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*+1}$, $\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*}$ and $\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*+1}$ (see \eqref{eq:sub-dataset}).}
\STATE{Initialize $\mathcal{N}_0^\dindex{\widehat{K}+1}{i^*}:=\mathcal{N}^\dindex{\widehat{K}}{i^*}$ and
$\mathcal{N}_0^\dindex{\widehat{K}+1}{i^*+1}:=\mathcal{N}^\dindex{\widehat{K}}{i^*}$}.
\STATE{Obtain $\mathcal{N}^\dindex{\widehat{K}+1}{i^*}$ using Algorithm \ref{alg:trining-ResNet} with $\mathcal{N}_0^\dindex{\widehat{K}+1}{i^*}$ and $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*}$.}
\STATE{Obtain $\mathcal{N}^\dindex{\widehat{K}+1}{i^*+1}$ using Algorithm \ref{alg:trining-ResNet} with $\mathcal{N}_0^\dindex{\widehat{K}+1}{i^*+1}$ and $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}+1}{i^*+1}$.}
\STATE{Compute the validation errors $\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*},\,\mathcal{E}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*+1}$ for $\mathcal{N}^\dindex{\widehat{K}+1}{i^*}$ and $\mathcal{N}^\dindex{\widehat{K}+1}{i^*+1}$ with $\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*}$ and $\mathcal{S}_{\mathrm{validate}}^\dindex{\widehat{K}+1}{i^*+1}$ (see \eqref{eq:valid-error}).}
\STATE{Let $\widehat{K}=\widehat{K}+1$.}
\ENDWHILE
\ENSURE{Trained DNN models $\mathcal{N}^\dindex{\widehat{K}}{i}$ for $i=1,\ldots,\widehat{K}$, identified time points $\left\{t^{(i)}\right\}_{i=1}^{\widehat{K}-1}$ and the endpoints of sub-intervals $\left\{\hat{t}^\dindex{\widehat{K}}{i}\right\}_{i=0}^{\widehat{K}}$.}
\end{algorithmic}
\end{algorithm}
\section{Introduction}
\label{sec:intro}
Many problems arising in computational science and engineering are described by dynamical systems with high complexity.
In many practical applications of these systems, measurement data typically can be collected, but mechanisms or governing equations may not be given a priori, which causes difficulties in understanding the underlying physical phenomena and predicting future dynamics. How to discover or learn the governing equations then becomes a crucial problem. For this purpose, there has been a rapid development in system identification methods during the past few decades. Early methods to learn unknown dynamical systems include the eigen-system realization algorithm \cite{juang1985eigensystem} and the observer/Kalman filter identification \cite{juang1993identification}. To seek exact expressions of governing equations, sparse identification of nonlinear dynamics is developed in \cite{brunton2016discovering}, that for noisy and corrupted data is studied in \cite{schaeffer2017sparse,zhang2018robust,tran2017exact}, and extracting dynamics with limited data is studied in \cite{schaeffer2018extracting}.
In addition, symbolic regression for learning nonlinear dynamical systems is proposed in \cite{schmidt2009distilling}, and equation-free modeling is developed in \cite{kevrekidis2003equation}. Recently, variants of deep neural networks (DNNs) have been interpreted and analyzed with dynamical systems \cite{chen2018neural,lu2018beyond,weinan2017proposal}. For instance, residual networks (ResNets) can be considered as dynamical systems with forward Euler discretization \cite{he2016deep,qin2019data}. Furthermore, ResNet based methods are proposed to approximate the governing equations for autonomous systems \cite{qin2019data}, non-autonomous systems \cite{qin2021data} and reduced systems \cite{fu2020learning}.
More specifically, the ResNet block used in the work \cite{qin2019data} is considered as a one-step exact integrator without temporal error, and the proposed networks consisting of multiple ResNet blocks are applied to approximate the evolution operator without requiring time derivatives, so as to avoid additional numerical errors. A general framework for recovering missing dynamical systems is presented in \cite{shixiaojiang21}.
In this work, we focus on dynamical systems with structural changes at discrete time instants, which are referred to as switched systems.
Switched systems have wide applications, which include epidemiology \cite{keeling2001seasonally}, legged locomotion \cite{holmes2006dynamics}, cascading failures on the electrical grid \cite{dobson2007complex}, and the design of cyber-physical systems \cite{sanfelice2016analysis}.
For example, in the process of robotic manipulation, interactions with the environment naturally give switching time instants \cite{van2000introduction,cortes2008discontinuous,liberzon2003switching}. Recently, a hybrid-sparse identification approach has been proposed to identify hybrid systems in \cite{mangan2019model}. In switched systems, discontinuities exist in the governing equations, such that constructing their global approximations becomes challenging. In addition, the number of switching time instants and their locations are not given a priori, which causes significant difficulties in learning the underlying systems.
To efficiently learn switched systems, we propose a deep neural network based adaptive learning (DNN-AL) approach. In our approach, neural network models to approximate underlying governing equations are hierarchically constructed, and the deep ResNets developed in \cite{qin2019data} are applied to construct local models.
As the switching time instants are not given, we gradually decompose global DNN models into local models, so that the switching time instants can be identified. That is, for a given adaptivity iteration step, the overall time interval are decomposed into small local intervals, and the observed dataset is decomposed associated with them. Then, with the decomposed datasets, local DNNs are trained, and their validation errors are computed. For the next iteration step, the local interval with the largest validation error is decomposed. Especially, local DNNs for the newly decomposed intervals are initialized with the previous network parameters, which results in an efficient initialization strategy. The adaptive procedure stops when the maximum validation error is small enough. To summarize, the main contributions of this work are three-fold: first, we propose a DNN-AL approach to learn governing equations in switched systems with unknown switching time instants; second, our hierarchical initialization approach results in efficient training procedures for local DNNs; third, for the models constructed by our DNN-AL, our analysis gives the bound of the prediction errors.
The rest of the paper is organized as follows. In Section \ref{sec:setup}, we present the general problem setup. Section \ref{sec:learn-autonomous-dnn} reviews ResNet based learning methods for autonomous systems. In Section \ref{sec:method}, our main DNN-AL algorithm is presented, and its error analysis is conducted. Numerical studies are discussed in Section \ref{sec:experiments}. Finally, Section \ref{sec:conclusions} concludes the paper.
\subsection{Theoretical properties}
\label{subsec:theo}
In this section, we present a theoretical analysis of our proposed algorithm.
The analysis provides an error bound between the solution of switched systems \eqref{eq:swithed-system} and the predictions of neural networks given by Algorithm \ref{alg:main-alg}. Our analysis processes through the following three steps. First, an auxiliary system is introduced, and a bound of the error between the solution of the auxiliary system and the original system \eqref{eq:swithed-system} is given. Second, a bound of the error between solution states of the auxiliary system and predictions by neural networks is provided.
Finally, based on results obtained in the first and the second steps, the bound of the error between the solution of the switched system \eqref{eq:swithed-system} and the predictions of neural networks in Algorithm \ref{alg:main-alg} is given.
To simplify the presentation in this section, we assume that the switched system has only one switching time instant, i.e.,
\begin{equation}
\label{eq:2seg-signal}
\sigma(t)=
\begin{cases}
1,\, t\in (T_0=0,T_1]\\
2,\, t\in(T_1,T_2=T_{\max}].
\end{cases}
\end{equation}
We note that the following analysis can be extended to switched systems with multiple switching time instants.
Based on the time instants obtained in Algorithm \ref{alg:main-alg}, an auxiliary system is defined as follows.
\begin{definition}[Auxiliary system]
\label{def:auxiliary-system}
Given the time instants $\{\hat{t}^{(\widehat{K},i)}\}_{i=0}^{\widehat{K}}$ obtained using Algorithm \ref{alg:main-alg}, denoting
\[
\breve{t}=\underset{t\in \{\hat{t}^{(\widehat{K},i)}\}_{i=0}^{\widehat{K}}}{\argmin} |t - T_1|,
\]
an auxiliary system is defined as
\begin{equation}
\label{eq:auxiliary-system}
\frac{\mathrm{d}\tilde{\mathbf{x}}(t)}{\mathrm{d}t}=\mathbf{f}^{(\tilde{\sigma}(t))}(\tilde{\mathbf{x}}(t)),\quad \tilde{\mathbf{x}}(0)=\mathbf{x}_0,
\end{equation}
where $\mathbf{f}^{(1)}$ and $\mathbf{f}^{(2)}:\mathbb{R}^d\rightarrow \mathbb{R}^d$ are introduced in \eqref{eq:swithed-system},
$\mathbf{x}_0$ is an initial state
and $\tilde{\sigma}(t)$ is the signal function defined as
\[\tilde{\sigma}(t)=\begin{cases}
1,\quad t\in (0, \breve{t}]\\
2,\quad t\in (\breve{t}, T_2].
\end{cases}\]
\end{definition}
Here, we give a bound for the error between the solution $\mathbf{x}(t)$ of the original system \eqref{eq:swithed-system} and the solution $\tilde{\mathbf{x}}(t)$ of the auxiliary system \eqref{eq:auxiliary-system}.
\begin{proposition}
\label{proposition:reconstruct-system}
Assume that the functions $\mathbf{f}^{(k)}(\mathbf{x})$ for $k=1,2$ in \eqref{eq:swithed-system} and \eqref{eq:auxiliary-system} are Lipschitz continuous
with Lipschitz constants $L_k$ for $\mathbf{x}\in\mathbb{R}^d$,
and there exist constants $\mu,\eta >0$ such that $\max_{\mathbf{x}\in \mathbb{R}^d}\|\mathbf{f}^{(1)}(\mathbf{x})-\mathbf{f}^{(2)}(\mathbf{x})\|\leq \mu$ and $|\breve{t}-T_1|\leq \eta$, where $\breve{t}$ is introduced in Definition \ref{def:auxiliary-system}. Without loss of generality, we assume that $\breve{t}\geq T_1$. The difference between the solution $\mathbf{x}(t)$ of the original switched system
\eqref{eq:swithed-system}
and the solution $\tilde{\mathbf{x}}(t)$ of the auxiliary system \eqref{eq:auxiliary-system}
is bounded as
\[\|\mathbf{x}(t)-\tilde{\mathbf{x}}(t)\|\leq \begin{cases}
0,\quad &t\in (0, T_1]\\
\mu(t-T_1)\exp(\max(L_1,L_2)(t-T_1)),\quad &t\in(T_1, \breve{t}]\\
\mu\eta\exp(L_2(t-\breve{t})+\max(L_1,L_2)\eta),\quad &t\in(\breve{t}, T_2].
\end{cases}\]
\end{proposition}
\begin{proof}
First, for any $t\in (0,T_1]$, given the initial condition $\tilde{\mathbf{x}}(0)=\mathbf{x}(0)=\mathbf{x}_0$,
\[
\begin{aligned}
\|\mathbf{x}(t)-\tilde{\mathbf{x}}(t)\| &=\left \|\mathbf{x}(0)-\tilde{\mathbf{x}}(0)+\int_0^{t} \mathbf{f}^{(1)}(\mathbf{x}(s))-\mathbf{f}^{(1)}(\tilde{\mathbf{x}}(s))\dif s \right\| = 0.
\end{aligned}
\]
Second, for any $t\in (T_1, \breve{t}]$,
\[
\begin{aligned}
\|\mathbf{x}(t)-\tilde{\mathbf{x}}(t)&\|=\left\|\mathbf{x}(T_1)-\tilde{\mathbf{x}}(T_1) + \int_{T_1}^{t} \mathbf{f}^{(\sigma(s))}(\mathbf{x}(s)) - \mathbf{f}^{(\tilde{\sigma}(s))}(\tilde{\mathbf{x}}(s))\dif s\right\| \\
&\leq \|\mathbf{x}(T_1)-\tilde{\mathbf{x}}(T_1)\| +
\int_{T_1}^{t} \|\mathbf{f}^{(\sigma(s))}(\mathbf{x}(s)) - \mathbf{f}^{(\tilde{\sigma}(s))}(\tilde{\mathbf{x}}(s))\|\dif s\\
&\leq 0 + \int_{T_1}^{t} \|\mathbf{f}^{(\sigma(s))}(\mathbf{x}(s)) - \mathbf{f}^{(\tilde{\sigma}(s))}(\mathbf{x}(s))\|\dif s\\
&\quad +\int_{T_1}^{t} \|\mathbf{f}^{(\tilde{\sigma}(s))}(\mathbf{x}(s)) - \mathbf{f}^{(\tilde{\sigma}(s))}(\tilde{\mathbf{x}}(s))\|\dif s \\
&\leq \mu(t-T_1) + \int_{T_1}^{t} L_{\tilde{\sigma}(s)}\|\mathbf{x}(s) - \tilde{\mathbf{x}}(s)\|\dif s \\
&\leq \mu(t-T_1) + \int_{T_1}^{t} \max(L_1,L_2)\|\mathbf{x}(s) - \tilde{\mathbf{x}}(s)\|\dif s.
\end{aligned}
\]
By using Gronwall-Bellman inequality, $\|\mathbf{x}(t)-\tilde{\mathbf{x}}(t)\|\leq \mu(t-T_1)\exp(\max(L_1,L_2)(t-T_1))$.
Lastly, for $t\in ( \breve{t}, T_2]$,
\[
\begin{aligned}
\|\mathbf{x}(t)-\tilde{\mathbf{x}}(t)\|&=
\|\mathbf{x}(\breve{t})-\tilde{\mathbf{x}}(\breve{t})+\int_{\breve{t}}^{t} \mathbf{f}^{(2)}(\mathbf{x}(s)) - \mathbf{f}^{(2)}(\tilde{\mathbf{x}}(s))\dif s\|\\
&\leq \|\mathbf{x}(\breve{t})-\tilde{\mathbf{x}}(\breve{t})\|+\int_{\breve{t}}^{t} \|\mathbf{f}^{(2)}(\mathbf{x}(s)) - \mathbf{f}^{(2)}(\tilde{\mathbf{x}}(s))\|\dif s\\
&\leq \|\mathbf{x}(\breve{t})-\tilde{\mathbf{x}}(\breve{t})\|+\int_{\breve{t}}^{t} L_2\|\mathbf{x}(s) - \tilde{\mathbf{x}}(s)\|\dif s\\
&\leq \exp(L_2(t-\breve{t}))\|\mathbf{x}(\breve{t})-\tilde{\mathbf{x}}(\breve{t})\|(\text{Using Gronwall-Bellman inequality})\\
&\leq \mu(\breve{t}-T_1)\exp(L_2(t-\breve{t})) \exp(\max(L_1,L_2)(\breve{t}-T_1))\\
&\leq \mu\eta\exp(L_2(t-\breve{t})) \exp(\max(L_1,L_2)\eta)\\
&=\mu\eta\exp(L_2(t-\breve{t})+\max(L_1,L_2)\eta).
\end{aligned}
\]
\end{proof}
Similarly, under the same assumptions of Proposition \ref{proposition:reconstruct-system}, when $\breve{t}<T_1$,
the differences between the states of the switched system and the auxiliary system are concluded
\[\|\mathbf{x}(t)-\tilde{\mathbf{x}}(t)\|\leq \begin{cases}
0,\quad &t\in (0, \breve{t}]\\
\mu(t-\breve{t})\exp(\max(L_1,L_2)(t-\breve{t})),\quad &t\in(\breve{t}, T_1]\\
\mu\eta\exp(L_2(t-T_1)+\max(L_1,L_2)\eta),\quad &t\in(T_1, T_2].
\end{cases}\]
\par
For the system involving $\mathbf{f}^{(1)}$ and $\mathbf{f}^{(2)}$, the flow map of the system can be shown it is locally Lipschitz.
\begin{lemma}
\label{lemma:flow-map}
For $k=1,2$, the $\Delta$-lag flow map associated with function $\mathbf{f}^{(k)}$ is defined as
\begin{equation}
\label{eq:flow-map-with-function}
\Phi_{\Delta}^{(k)}(\mathbf{x}_0):=\mathbf{x}_0 + \int_0^\Delta \mathbf{f}^{(k)}(\mathbf{x}(t)) \dif t,
\end{equation}
where $\mathbf{x}(0)= \mathbf{x}_0\in\mathbb{R}^d$ is a given initial state. If the assumptions in Proposition \ref{proposition:reconstruct-system} hold,
for any given initial conditions $\mathbf{x},\mathbf{y}\in \mathbb{R}^d$, we have
\[
\|\Phi_{\Delta}^{(k)}(\mathbf{x}) - \Phi_{\Delta}^{(k)}(\mathbf{y})\|\leq \exp(L_k \Delta)\|\mathbf{x}-\mathbf{y}\|.
\]
\end{lemma}
\begin{proof}
The proof directly follows the continuity of the dynamical system with respect to the initial condition \cite[p.~43]{teschl2012ordinary}.
\end{proof}
Since neural networks are employed, the universal approximation property is recalled.
\begin{lemma}(see \cite{pinkus1999approximation})
\label{lemma:universal-approximation}
For any compact set $D\subset \mathbb{R}^d$, any continuous function $F: \mathbb{R}^d\rightarrow \mathbb{R}^d$ and any positive real number $\varepsilon$,
there exists a single-hidden-layer neural network $\mathcal{N}(\cdot, \Theta)$ with the parameters $\Theta$ such that
\[\max_{\mathbf{y}\in D}|F(\mathbf{y}) - \mathcal{N}(\mathbf{y};\Theta)|\leq \varepsilon,\] if and only if the activation functions are continuous and are not polynomials.
\end{lemma}
\begin{proof}
The proof is given in the \cite{pinkus1999approximation}.
\end{proof}
As in Algorithm \ref{alg:main-alg}, the neural networks to approximate the flow maps \eqref{eq:flow-map-with-function} are denoted by $\{\mathcal{N}^\dindex{\widehat{K}}{i}\}_{i=1}^{\widehat{K}}$.
Letting $\mathcal{C}_i$ be the convex hull of the training dataset $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}}{i}$, and
denoting
\[
i' = \argmin_{i\in \{0,\ldots,\widehat{K}\}} |\hat{t}^\dindex{\widehat{K}}{i} - \breve{t}|,
\]
it is assumed that the learned neural networks $\{\mathcal{N}^\dindex{\widehat{K}}{i}\}_{i=1}^{\widehat{K}}$ have sufficient accuracy, i.e., for a sufficiently small number $\varepsilon\geq 0$,
\begin{equation}
\label{eq:neural-network-flow}
\begin{cases}
\max_{\mathbf{y}_\text{in}\in \mathcal{C}_i}
\|\mathcal{N}^\dindex{\widehat{K}}{i}(\mathbf{y}_\text{in};\Theta^\dindex{\widehat{K}}{i})-\Phi_{\Delta}^{(1)}(\mathbf{y}_\text{in})\| \le \varepsilon\,,\quad i=1,\ldots,i',\\
\max_{\mathbf{y}_\text{in}\in \mathcal{C}_i}
\|\mathcal{N}^\dindex{\widehat{K}}{i}(\mathbf{y}_\text{in};\Theta^\dindex{\widehat{K}}{i})-\Phi_{\Delta}^{(2)}(\mathbf{y}_\text{in})\| \le \varepsilon\,,\quad i=i'+1,\ldots,\widehat{K}.\\
\end{cases}
\end{equation}
We utilize the trained networks to predict the states of the unknown switched system \eqref{eq:swithed-system}.
For a given initial condition $\widehat{\mathbf{y}}(0)$, the prediction at time $t_{j+1}$ is generated as
\begin{equation}
\label{eq:nn-predictions}
\widehat{\mathbf{y}}(t_{j+1}) = \begin{cases}
\mathcal{N}^\dindex{\widehat{K}}{1}(\widehat{\mathbf{y}}(t_j);\Theta^\dindex{\widehat{K}}{1}),\quad &t_j\in (\hat{t}^\dindex{\widehat{K}}{0}=0,\hat{t}^\dindex{\widehat{K}}{1}]\\
\ldots\\
\mathcal{N}^\dindex{\widehat{K}}{i}(\widehat{\mathbf{y}}(t_j);\Theta^\dindex{\widehat{K}}{i}),\quad &t_j\in (\hat{t}^\dindex{\widehat{K}}{i-1},\hat{t}^\dindex{\widehat{K}}{i}]\\
\ldots \\
\mathcal{N}^\dindex{\widehat{K}}{\widehat{K}}(\widehat{\mathbf{y}}(t_j);\Theta^\dindex{\widehat{K}}{\widehat{K}}),\quad &t_j\in (\hat{t}^\dindex{\widehat{K}}{\widehat{K}-1},\hat{t}^\dindex{\widehat{K}}{\widehat{K}}=T_{\max}],
\end{cases}
\end{equation}
where $j=1,\ldots,J-1$.
In this section, the initial state for neural networks predictions \eqref{eq:nn-predictions}, the initial condition of the switched system \eqref{eq:swithed-system} and the auxiliary system \eqref{eq:auxiliary-system} are considered to be the same, i.e., $\widehat{\mathbf{y}}(0)=\mathbf{x}(0)=\tilde{\mathbf{x}}(0)$.
\begin{proposition}
\label{proposition:neural-network-approximation}
Suppose the assumptions in Lemma \ref{lemma:flow-map} hold.
For $\widehat{\mathbf{y}}(t_{j-1})\in \mathcal{C}_i$ (where $i=1,\ldots,\widehat{K}$, and $\mathcal{C}_i$ is the convex hull of the training set $\mathcal{D}_{\mathrm{train}}^\dindex{\widehat{K}}{i}$) and $\widehat{\mathbf{y}}(t_j)=\mathcal{N}^\dindex{\widehat{K}}{i}(\widehat{\mathbf{y}}(t_{j-1});\Theta^\dindex{\widehat{K}}{i})$ with $j=1,\ldots,J$, assume that $\widehat{\mathbf{y}}(t_j)\in \mathcal{C}_i$
and the neural networks are sufficiently accurate such that \eqref{eq:neural-network-flow} holds.
Then the difference between the prediction using neural networks $\widehat{\mathbf{y}}(t_j)$ and the solution of the auxiliary system $\tilde{\mathbf{x}}(t_j)$ is bounded by
\[\|\widehat{\mathbf{y}}(t_j)-\tilde{\mathbf{x}}(t_j)\|\leq \begin{cases}
\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon,\quad &t_j\in(t_1=0,\breve{t}] \\
\frac{1-\exp(L_2 (t_j-\breve{t}))}{1-\exp(L_2\Delta)}\varepsilon \\
\quad +\exp(L_2(t_j-\breve{t}))\frac{1-\exp(L_1 \breve{t})}{1-\exp(L_1\Delta)}\varepsilon,
\quad &t_j\in(\breve{t},T_2] .
\end{cases}\]
\end{proposition}
\begin{proof}
When $t_j\in(t_1=0,\breve{t}]$ and $\hat{t}^{(\widehat{K},i-1)}<t_j<\hat{t}^{(\widehat{K},i)}$,
we have
\[
\begin{aligned}
\|\widehat{\mathbf{y}}(t_j)-\tilde{\mathbf{x}}(t_j)\|&=\|\mathcal{N}^\dindex{\widehat{K}}{i} (\widehat{\mathbf{y}}(t_{j-1});\Theta^\dindex{\widehat{K}}{i})-\Phi_{\Delta}^{(1)}(\tilde{\mathbf{x}}(t_{j-1}))\|\\
&\leq \|\mathcal{N}^\dindex{\widehat{K}}{i} (\widehat{\mathbf{y}}(t_{j-1});\Theta^\dindex{\widehat{K}}{i})-\Phi_{\Delta}^{(1)}(\widehat{\mathbf{y}}(t_{j-1}))\|\\
&\quad +\|\Phi_{\Delta}^{(1)}(\widehat{\mathbf{y}}(t_{j-1}))-\Phi_{\Delta}^{(1)}(\tilde{\mathbf{x}}(t_{j-1}))\| \\
&\leq \varepsilon + \exp(L_1 \Delta)\|\widehat{\mathbf{y}}(t_{j-1})-\tilde{\mathbf{x}}(t_{j-1})\| \\
&\quad \ldots \\
&\leq \frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon + \exp(L_1 t_j)\|\widehat{\mathbf{y}}(0)-\tilde{\mathbf{x}}(0)\|\\
&=\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon,
\end{aligned}
\]
where the last equation is obtained as $\widehat{\mathbf{y}}(0)=\tilde{\mathbf{x}}(0)$.
Similarly, for $t_j\in(\breve{t},T_2]$, the error bound satisfies
\[
\begin{aligned}
\|\widehat{\mathbf{y}}(t_j)-\tilde{\mathbf{x}}(t_j)\|&\leq \varepsilon + \exp(L_2 \Delta)\|\widehat{\mathbf{y}}(t_{j-1})-\tilde{\mathbf{x}}(t_{j-1})\| \\
&\quad \ldots\\
&\leq \frac{1-\exp(L_2 (t_j-\breve{t}))}{1-\exp(L_2\Delta)}\varepsilon + \exp(L_2(t_j-\breve{t}))\|\widehat{\mathbf{y}}(\breve{t})-\tilde{\mathbf{x}}(\breve{t})\|\\
&\leq \frac{1-\exp(L_2 (t_j-\breve{t}))}{1-\exp(L_2\Delta)}\varepsilon \\
&\quad + \exp(L_2(t_j-\breve{t}))\frac{1-\exp(L_1 \breve{t})}{1-\exp(L_1\Delta)}\varepsilon.
\end{aligned}
\]
\end{proof}
The bounds in Proposition \ref{proposition:reconstruct-system} and Proposition \ref{proposition:neural-network-approximation} result in
the following error bounds for the neural networks
obtained using Algorithm \ref{alg:main-alg}.
\begin{theorem}
\label{thm:nn-error-bound}
Supposing assumptions of Proposition \ref{proposition:reconstruct-system} and Proposition \ref{proposition:neural-network-approximation} hold, the error of the predictions using the neural networks \eqref{eq:nn-predictions} is bouned as
\[
\|\widehat{\mathbf{y}}(t_j) - \mathbf{x}(t_j)\|\leq
\begin{cases}
\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon, &t_j\in(0,T_1] \\
\mu(t_j-T_1)\exp(\max(L_1,L_2)(t_j-T_1))\\
\quad +\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon, &t_j\in(T_1,\breve{t}]\\
\mu\eta\exp(L_2(t_j-\breve{t})+\max(L_1,L_2)\eta) \\
\quad + \frac{1-\exp(L_2 (t_j-\breve{t}))}{1-\exp(L_2\Delta)}\varepsilon\\
\quad + \exp(L_2(t_j-\breve{t}))\frac{1-\exp(L_1 \breve{t})}{1-\exp(L_1\Delta)}\varepsilon, &t_j\in(\breve{t},T_2],
\end{cases}
\]
where $\mathbf{x}(t)$ is the accurate solution of the original system \eqref{eq:swithed-system}
and $t_{j}:=(j-1)\Delta$ with $\Delta:=T_{\max}/(J-1)$ for $j=1,\ldots,J$.
\end{theorem}
\begin{proof}
Using Proposition \ref{proposition:reconstruct-system}, we have
\[
\begin{aligned}
\|\tilde{\mathbf{x}}(t_j) - \mathbf{x}(t_j)\|\leq
\begin{cases}
0,\quad &t_j\in(0,T_1]\\
\mu(t_j-T_1)\exp(\max(L_1,L_2)(t_j-T_1)),\quad &t_j\in(T_1,\breve{t}]\\
\mu\eta\exp(L_2(t_j-\breve{t})+\max(L_1,L_2)\eta),\quad &t_j\in(\breve{t},T_2].
\end{cases}
\end{aligned}
\]
The bounds in Proposition \ref{proposition:neural-network-approximation} give
\[
\begin{aligned}
\|\widehat{\mathbf{y}}(t_j)-\tilde{\mathbf{x}}(t_j)\|\leq
\begin{cases}
\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon,\quad &t_j\in(0,T_1]\\
\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon,
\quad &t_j\in(T_1,\breve{t}]\\
\frac{1-\exp(L_2 (t_j-\breve{t}))}{1-\exp(L_2\Delta)}\varepsilon \\
\quad +\exp(L_2(t_j-\breve{t}))\frac{1-\exp(L_1 \breve{t})}{1-\exp(L_1\Delta)}\varepsilon,
\quad &t_j\in(\breve{t},T_2].
\end{cases}
\end{aligned}
\]
Finally, using the triangle inequality gives
\[
\begin{aligned}
\|\widehat{\mathbf{y}}(t_j) - \mathbf{x}(t_j)\| &\leq \|\widehat{\mathbf{y}}(t_j) - \tilde{\mathbf{x}}(t_j)\| + \|\tilde{\mathbf{x}}(t_j) - \mathbf{x}(t_j)\|\\
&\leq
\begin{cases}
\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon + 0,\quad &t_j\in(0,T_1] \\
\mu(t_j-T_1)\exp(\max(L_1,L_2)(t_j-T_1))
\\
\quad +\frac{1-\exp(L_1 t_j)}{1-\exp(L_1\Delta)}\varepsilon ,
\quad &t_j\in(T_1,\breve{t}] \\
\mu\eta\exp(L_2(t_j-\breve{t})+\max(L_1,L_2)\eta)\\ \quad +\frac{1-\exp(L_2 (t_j-\breve{t}))}{1-\exp(L_2\Delta)}\varepsilon\\
\quad +\exp(L_2(t_j-\breve{t}))\frac{1-\exp(L_1 \breve{t})}{1-\exp(L_1\Delta)}\varepsilon
,
\quad &t_j\in(\breve{t},T_2].
\end{cases}
\end{aligned}
\]
\end{proof}
From Theorem \ref{thm:nn-error-bound},
it is clear that the prediction error of the neural networks obtained from Algorithm \ref{alg:main-alg} is bounded by the error of the neural network approximation for the $\Delta$-lag flow maps \eqref{eq:flow-map-with-function} and the error for the switching point \eqref{eq:switch-signal}.
\section{Numerical experiments}
\label{sec:experiments}
In this section,
numerical experiments are conducted to illustrate the effectiveness of our DNN-AL approach presented in Algorithm \ref{alg:main-alg}.
Four test problems are considered---the first and the second ones consider the forced damped oscillator problem with two and three subsystems respectively, the third one considers a forced damped pendulum problem, and the fourth test problem focuses on the heat equation.
In this work, deep neural networks are implemented based on the open-source machine library Pytorch \cite{paszke2019pytorch}.
To train deep neural networks (see Algorithm \ref{alg:trining-ResNet}), the size of each mini-batch is set to $100$, and the number of epochs is set to $100$.
The SGD method used in this paper is AdamW \cite{loshchilov2017decoupled}, and the initial learning rate is set to 0.001. In addition, we implement the cosine annealing part of \cite{loshchilov2016sgdr} to tune the learning rate. To initialize the deep ResNet on line 3 of Algorithm \ref{alg:main-alg}, the Kaiming initialization \cite{he2015delving} is used, and all the biases are initially set to zeros. The tolerance $tol$ in Algorithm \ref{alg:main-alg} is set to $0.005$.
\subsection{Forced damped oscillator with two subsystems}\label{sec:test1}
We start with the following forced damped oscillator equation
\begin{equation}
\left\{
\begin{array}{ll}
\frac{\dif }{\dif t}x_1 = x_2\,,\\
\frac{\dif }{\dif t}x_2 = -k x_1 - \nu x_2 +f\,,
\end{array}
\right.
\label{eq:oscillator}
\end{equation}
where $\nu$ is the damping term from the friction force, $f$ is the external force term, $k$ is the spring constant, and $t\in (0,40]$.
Following the generic notation in \eqref{eq:switch-signal}--\eqref{eq:swithed-system}, the governing equations for this test problem are set to
\[
\mathbf{f}^{(1)} =
\left ( \begin{array}{cc}
x_2 \\
-x_1 - 0.1 x_2 + 2
\end{array} \right),\,
\mathbf{f}^{(2)}=
\left ( \begin{array}{cc}
x_2 \\
- x_1 - 0.5 x_2 + 10
\end{array} \right),\]
and the time-dependent signal function is set to
\[\sigma(t)=\left\{
\begin{array}{ll}
1\, ,t\in (0,27.6] \\
2\,,t\in (27.6,40].
\end{array}\right.\]
The spatial domain considered is $D=[-3,3]^2$. The time lag is set to $\Delta=0.05$ and then $J=801$.
To generate the observed datasets, 200 initial states are generated using the uniform distribution with the range $D$. Then the switched system is solved using the LSODA solver provided in SciPy \cite{petzold1983automatic,2020SciPy-NMeth} for each initial state, and 200 trajectories are collected. The datasets are constructed through the procedures in Section \ref{sec:setup}. For our DNN-AL approach, the neural network for this test problem consists of 10 ResNet blocks with 2 fully connected layers per block. The 2 fully connected layers in each block have 20 nodes and 2 nodes respectively.
To assess the effectiveness of our DNN-AL approach, the orbit with the initial state $\mathbf{x}_0=[2,1]^T$ is considered, which is not included in our observed datasets. A reference result for this orbit is computed with the LSODA solver for comparison.
\figurename{\ref{fig:force-damp-oscillator-plots}} shows the orbits obtained by DNN-AL and the LSODA solver. From \figurename{\ref{fig:force-damp-oscillator-plots}}(a) (for $x_1$) and \figurename{\ref{fig:force-damp-oscillator-plots}}(b) (for $x_2$), it can be seen that at adaptivity iteration step one of DNN-AL, i.e., just using a deep RestNet to approximate the $\Delta$-lag flow map of the whole system, the predictions of the neural networks are inaccurate, especially for the states at the time after the switching time instant $t=27.6$. \figurename{\ref{fig:force-damp-oscillator-plots}}(c) and \figurename{\ref{fig:force-damp-oscillator-plots}}(d) show that, at adaptivity iteration step three in DNN-AL, the predictions of the neural networks get closer to the results of the LSODA solver. From \figurename{\ref{fig:force-damp-oscillator-plots}}(e) and \figurename{\ref{fig:force-damp-oscillator-plots}}(f), it is clear that, after seven adaptivity iteration steps, predictions of the neural networks obtained by DNN-AL and the results of the LSODA solver are visually indistinguishable, which shows that DNN-AL effectively learns this switched system.
\begin{figure}[htp!]
\centering
\subfigure[Iteration step 1, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-2segment-noise0-block10/RT-ResNetoscillator-2seg_pred_epoch0_blk_1_x1.pdf}
\label{fig:osci-x1-k1}
}
\subfigure[Iteration step 1, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-2segment-noise0-block10/RT-ResNetoscillator-2seg_pred_epoch0_blk_1_x2.pdf}
\label{fig:osci-x2-k1}
}
\subfigure[Iteration step 3, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-2segment-noise0-block10/RT-ResNetoscillator-2seg_pred_epoch0_blk_3_x1.pdf}
\label{fig:osci-x1-k3}
}
\subfigure[Iteration step 3, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-2segment-noise0-block10/RT-ResNetoscillator-2seg_pred_epoch0_blk_3_x2.pdf}
\label{fig:osci-x2-k3}
}
\subfigure[Iteration step 7, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-2segment-noise0-block10/RT-ResNetoscillator-2seg_pred_epoch0_blk_7_x1.pdf}
\label{fig:osci-x1-k7}
}
\subfigure[Iteration step 7, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-2segment-noise0-block10/RT-ResNetoscillator-2seg_pred_epoch0_blk_7_x2.pdf}
\label{fig:osci-x2-k7}
}
\caption{The neural network predictions and solutions of the LSODA solver, $\mathbf{x}_0=[2,1]^T$, forced damped oscillator equation with two subsystems.}
\label{fig:force-damp-oscillator-plots}
\end{figure}
At time $t_j$ (for $j=1,\ldots,J$), let $\mathbf{x}(t_j)=[x_1(t_j),x_2(t_j)]^T$ be the state obtained by the LSODA solver, and $\widehat{\mathbf{y}}(t_j)=[\widehat{y}_1(t_j),\widehat{y}_2(t_j)]^T$ be the prediction of the deep ResNets obtained by DNN-AL. The error for $x_1$ is given by $|x_1(t_j) - \widehat{y}_1(t_j)|$, and the error for $x_2$ is given by $|x_2(t_j) - \widehat{y}_2(t_j)|$.
The relative error
is defined as \begin{equation}
\label{eq:test-relative-err}
\ell_{\mathrm{relative}}:=\frac{\|\mathbf{x}(t_j) - \widehat{\mathbf{y}}(t_j)\|^2}{\|\mathbf{x}(t_j)\|^2}.
\end{equation}
\figurename{\ref{fig:oscilator-2seg-loss}} shows the errors for this test problem where seven adaptivity iterations are conducted in DNN-AL.
The approximate switching time instant is $\breve{t}=27.5$ (see Definition \ref{def:auxiliary-system}), which is very close to the true switching time instant $27.6$. It can be seen that the errors are very small in the time interval $(0,27.5]$, which are mainly caused by the neural network approximation error. There is a clear jump in the relative error (and the errors for $x_1$ and $x_2$) around the switching time instant ($t=2.76$). This is because the trained deep ResNets are built with the approximate switching time instant $\breve{t}=27.5$. However, the relative error is still bounded (clearly less than $10^{-1}$). These results are consistent with Theorem \ref{thm:nn-error-bound}.
\begin{figure}[htp!]
\centering
\includegraphics[scale=0.36]{figs/oscillator-2segment-noise0-block10/RT-ResNetoscillator-2seg_pred_epoch0_blk_7_loss.pdf}
\caption{Errors of DNN-AL predictions, forced damped oscillator equation with two subsystems.}
\label{fig:oscilator-2seg-loss}
\end{figure}
We next consider the situation of noisy data. The noise in \eqref{eq:each-trajectory} is set to $\epsilon^{(n)}_j:=\xi^{(n)}_j\mathbf{x}(t_{j};\mathbf{x}_0^{(n)})$, where $\xi^{(n)}_j$ is drawn from the uniform distribution over $[0,\,\eta_{\mathrm{noise}}]$ and $\eta_{\mathrm{noise}}$ is a given positive number. The test set is again set to the orbit with the initial state $\mathbf{x}_0=[2,\,1]^T$. To quantify the accuracy of the neural networks obtained through DNN-AL,
the mean square error (MSE) is considered, which is defined as
\begin{equation}
\label{eq:test-mse}
\ell_{\mathrm{mse}}:=\frac{1}{J}\sum_{j=1}^J \|\mathbf{x}(t_j) - \widehat{\mathbf{y}}(t_j)\|^2,
\end{equation}
where $\mathbf{x}(t_j)$ is the state obtained by the LSODA solver, and
$\widehat{\mathbf{y}}(t_j)$ is the prediction of the neural networks.
The MSEs for this test problem are shown in Table \ref{tab:err-noise}, where different ranges of the noises are tested. In this table, the test MSE is defined in \eqref{eq:test-mse}, and the validation MSE is computed through replacing the test set for \eqref{eq:test-mse} by the validation set (see \eqref{eq:initial-dataset}). Table \ref{tab:err-noise} shows that the validation MSE is smaller than the test MSE, which is expected.
It also can be seen that the test MSE increases approximately in proportion to the noise, which shows that the performance of the trained neural networks of DNN-AL is stable with respect to the noise.
\begin{table}[htp!]
\centering
\begin{tabular}{cccc}
\hline
$\eta_{\mathrm{noise}}$ & 2e-2 & 5e-2 & 1e-1\\
\hline
Validation MSE & 4.769e-03 &4.645e-03 &6.731e-03\\
Test MSE &2.442e-02 &4.451e-02&1.061e-01\\
\hline
\end{tabular}
\caption{Errors with different noisy levels, forced damped oscillator equation with two subsystems.}
\label{tab:err-noise}
\end{table}
The efficiency of our hierarchical initialization strategy is investigated herein. As shown on line $13$ of Algorithm \ref{alg:main-alg}, the initial deep ResNets are hierarchically constructed using the trained ResNets at the previous adaptivity iteration steps. For comparison, a direct initialization strategy is tested, which is to use the standard Kaiming initialization \cite{he2015delving} to construct the initial ResNets at every adaptivity iteration step.
As the identified interval with the largest validation error is decomposed into two parts at each adaptivity iteration step (line $9$ of Algorithm \ref{alg:main-alg}), two new deep ResNets need to be trained, which are referred to as the left and the right ones.
\figurename{\ref{fig:adaptive-train-loss}} shows the values of the training loss \eqref{eq:train-loss} at adaptivity iteration step three, five and seven respectively.
It can be seen that our hierarchical initialization strategy results in smaller training loss values than the direct initialization approach.
\figurename{\ref{fig:adaptive-test-error}} shows the test MSEs (see \eqref{eq:test-mse}) associated with the two initialization strategies, where the initial state is $\mathbf{x}_0=[2,\,1]^T$.
It is clear that our hierarchical initialization results in smaller test errors after two adaptivity iteration steps.
\begin{figure}[htp!]
\centering
\subfigure[Iteration step 3, left]{
\includegraphics[scale=0.33]{figs/Adaptive-initialization/oscillator-2seg-iter3-net1-train_loss_adaptive.pdf}
}
\subfigure[Iteration step 3, right]{
\includegraphics[scale=0.33]{figs/Adaptive-initialization/oscillator-2seg-iter3-net2-train_loss_adaptive.pdf}
}
\subfigure[Iteration step 5, left]{
\includegraphics[scale=0.33]{figs/Adaptive-initialization/oscillator-2seg-iter5-net1-train_loss_adaptive.pdf}
}
\subfigure[Iteration step 5, right]{
\includegraphics[scale=0.33]{figs/Adaptive-initialization/oscillator-2seg-iter5-net2-train_loss_adaptive.pdf}
}
\subfigure[Iteration step 7, left]{
\includegraphics[scale=0.33]{figs/Adaptive-initialization/oscillator-2seg-iter7-net1-train_loss_adaptive.pdf}
}
\subfigure[Iteration step 7, right]{
\includegraphics[scale=0.33]{figs/Adaptive-initialization/oscillator-2seg-iter7-net2-train_loss_adaptive.pdf}
}
\caption{Training loss at different adaptivity iteration steps, forced damped oscillator equation with two subsystems.}
\label{fig:adaptive-train-loss}
\end{figure}
\begin{figure}[htp!]
\centering
\includegraphics[scale=0.35]{figs/Adaptive-initialization/oscillator-2seg-test_loss_adaptive.pdf}
\caption{Test errors at different adaptivity iteration steps, forced damped oscillator equation with two subsystems.}
\label{fig:adaptive-test-error}
\end{figure}
\subsection{Forced damped oscillator with three subsystems}
Here, we consider the forced damped oscillator problem with three subsystems. That is, the equation \eqref{eq:oscillator} is considered again, and the signal function and the governing equations are set to
\[\sigma(t)=
\begin{cases}
1\,,\quad t\in (0,17.4]\\
2\,,\quad t\in (17.4,27.6]\\
3\,,\quad t\in (27.6,40],
\end{cases}
\]
and
\[
\begin{aligned}
\mathbf{f}^{(1)}=\left ( \begin{array}{cc}
x_2 \\
2-0.1x_2-x_1
\end{array} \right),\mathbf{f}^{(2)}=\left ( \begin{array}{cc}
x_2 \\
4-0.2x_2-x_1
\end{array} \right),\mathbf{f}^{(3)}=\left ( \begin{array}{cc}
x_2 \\
8-0.4x_2-x_1
\end{array} \right).
\end{aligned}
\]
Other settings for this test problem are the same as those for the two-subsystem test problem in Section \ref{sec:test1}, and $200$ trajectories with different initial states are generated to construct the observed data. The neural network structure and the settings for Algorithm \ref{alg:main-alg} are the same as those in Section \ref{sec:test1}.
To test the effectiveness of our DNN-AL approach, the orbit with the initial state $\mathbf{x}_0=[1,0]^T$ is considered, which is not included in the observed dataset. \figurename{\ref{fig:force-damp-oscillator-3seg-plots}} shows the reference solution (generated by the LSODA solver) and the predictions of the trained deep ResNets obtained through Algorithm \ref{alg:main-alg}, where the trajectories at adaptivity iteration step two, six, and eight are presented. It is clear that, as the adaptivity iteration step increases, the predictions of the trained deep ResNets get closer to the reference results.
Especially at adaptivity iteration step eight, the predictions of the trained deep ResNets and the reference results are almost indistinguishable.
\begin{figure}[htp!]
\centering
\subfigure[Iteration step 2, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-3segment-noise0-block10/RT-ResNetoscillator-3seg_pred_epoch0_blk_2_x1.pdf}
\label{fig:osci-3seg-x1-k2}
}
\subfigure[Iteration step 2, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-3segment-noise0-block10/RT-ResNetoscillator-3seg_pred_epoch0_blk_2_x2.pdf}
\label{fig:osci-3seg-x2-k2}
}
\subfigure[Iteration step 6, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-3segment-noise0-block10/RT-ResNetoscillator-3seg_pred_epoch0_blk_6_x1.pdf}
\label{fig:osci-3seg-x1-k6}
}
\subfigure[Iteration step 6, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-3segment-noise0-block10/RT-ResNetoscillator-3seg_pred_epoch0_blk_6_x2.pdf}
\label{fig:osci-3seg-x2-k6}
}
\subfigure[Iteration step 8, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-3segment-noise0-block10/RT-ResNetoscillator-3seg_pred_epoch0_blk_8_x1.pdf}
\label{fig:osci-3seg-x1-k8}
}
\subfigure[Iteration step 8, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/oscillator-3segment-noise0-block10/RT-ResNetoscillator-3seg_pred_epoch0_blk_8_x2.pdf}
\label{fig:osci-3seg-x2-k8}
}
\caption{The neural network predictions and solutions of the LSODA solver, $\mathbf{x}_0=[1,0]^T$, forced damped oscillator equation with three subsystems.}
\label{fig:force-damp-oscillator-3seg-plots}
\end{figure}
\subsection{Forced damped pendulum}
The ordinary differential equation system for the forced damped pendulum considered is,
\begin{equation}
\left\{
\begin{array}{ll}
\frac{\mathrm{d}}{\mathrm{d}t} x_1=x_2,\\
\frac{\mathrm{d}}{\mathrm{d}t} x_2=-a x_2 - g\sin x_1 + b ,
\end{array}
\right.
\label{eq:pendulum}
\end{equation} where $-a x_2$ represents a friction force, $g$ is a gravity constant in a constant gravitational field, and $ b$ refers to an external force.
Following the generic notation in \eqref{eq:switch-signal}--\eqref{eq:swithed-system}, the two governing equations of the subsystems for this test problem are,
\[
\mathbf{f}^{(1)} =
\left ( \begin{array}{cc}
x_2 \\
-0.15x_2 - 9.8\sin x_1
\end{array} \right),\,
\mathbf{f}^{(2)}=
\left ( \begin{array}{cc}
x_2 \\
-0.15 x_2 - 9.8\sin x_1 + 2
\end{array} \right),\]
and the corresponding signal function is set to \[\sigma(t) = \begin{cases}
1\,,\quad t\in (0,15.2]\\
2\,,\quad t\in (15.2,40].
\end{cases}\]
The spatial domain is set to $D=[-\pi/2,\pi/2]\times [-\pi,\pi] $, and the time step is set to $\Delta=0.05$. Similar to Section \ref{sec:setup}, 200 initial states are generated through the uniform distribution with the range $D$, and trajectories associated with these initial states are obtained with the LSODA solver, which are used to construct the datasets (see Section \ref{sec:setup}).
For this test problem, the neural network in DNN-AL consists of 10 ResNet blocks with 2 fully connected layers per block. For each block, the 2 fully connected layers have 20 nodes and 2 respectively.
For comparison, the orbit with the initial state $\mathbf{x}_0=[0,-2]^T$ is considered, which is not included in the observed dataset. \figurename{\ref{fig:force-damp-pendulum-plots}} shows the reference solution (generated by the LSODA solver) and the predictions of the trained deep ResNets obtained through Algorithm \ref{alg:main-alg}, where the trajectories at adaptivity iteration step one, three, and five are presented. It is clear that, as the adaptivity iteration step increases, the predictions of the trained deep ResNets get closer to the reference results, and the predictions of the trained deep ResNets at adaptivity iteration step five are very close to the reference results.
\begin{figure}[htp!]
\centering
\subfigure[Iteration step 1, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/pendulum-2segment-noise0-block10/RT-ResNetpendulum-2seg_pred_epoch0_blk_1_x1.pdf}
\label{fig:pendulum-x1-k1}
}
\subfigure[Iteration step 1, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/pendulum-2segment-noise0-block10/RT-ResNetpendulum-2seg_pred_epoch0_blk_1_x2.pdf}
\label{fig:pendulum-x2-k1}
}
\subfigure[Iteration step 3, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/pendulum-2segment-noise0-block10/RT-ResNetpendulum-2seg_pred_epoch0_blk_3_x1.pdf}
}
\subfigure[Iteration step 3, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/pendulum-2segment-noise0-block10/RT-ResNetpendulum-2seg_pred_epoch0_blk_3_x2.pdf}
}
\subfigure[Iteration step 5, $x_1(t)$]{
\includegraphics[scale=0.34]{figs/pendulum-2segment-noise0-block10/RT-ResNetpendulum-2seg_pred_epoch0_blk_5_x1.pdf}
\label{fig:pendulum-x1-k5}
}
\subfigure[Iteration step 5, $x_2(t)$]{
\includegraphics[scale=0.34]{figs/pendulum-2segment-noise0-block10/RT-ResNetpendulum-2seg_pred_epoch0_blk_5_x2.pdf}
\label{fig:pendulum-x2-k5}
}
\caption{The neural network predictions and solutions of the LSODA solver, $\mathbf{x}_0=[0,-2]^T$, forced damped pendulum.}
\label{fig:force-damp-pendulum-plots}
\end{figure}
\subsection{Heat equation}
In this test problem, we consider the following heat equation
\begin{equation}
\begin{aligned}
&\frac{\partial u}{\partial t} =\kappa\frac{\partial^2 u}{\partial x^2}+q(t,\,x)\,,\quad x\in (0,1) \textrm{ and } t\in (0,2],\\
&u(0,\,x)=u_0(x),\\
&u(t,\,0)=u(t,\,1)=0,\\
\end{aligned}
\label{eq:heat-eqn}
\end{equation}
where $\kappa>0$ is the thermal diffusivity of the medium, $u$ is the unknown temperature and $q(t,\,x)$ is a source function.
The initial condition is set to
\begin{eqnarray}
u_0(x) = a\cdot x(1-x),
\label{eq:heat_a}
\end{eqnarray}
where $a\in \mathbb{R}$ is a parameter.
To generate data and reference solutions, the spatial domain is discretized with a uniform grid with $I_{\text{grid}}=21$ nodes, and the time lag is set to $\Delta=0.01$ (then $J=201$).
To result in a discretized problem, $\partial^2 u/\partial x^2$ in \eqref{eq:heat-eqn} is approximated by the second-order centered difference method, and the LSODA solver provided in SciPy \cite{2020SciPy-NMeth} is again applied to solve this problem.
The thermal diffusivity of the medium $\kappa$ is set to $0.2$.
The source function $q(t,\,x)$ in \eqref{eq:heat-eqn} is set to
\[
q(t,x) = \begin{cases}
20\exp\left(-\frac{(x-1)^2}{0.25}\right),\quad t\in (0,1.2]\\
10\exp\left(-\frac{(x-1)^2}{0.25}\right),\quad t\in (1.2,2].
\end{cases}
\]
The signal function of this test problem is set to
\[\sigma(t) = \begin{cases}
1,\quad t\in(0,1.2]\\
2,\quad t\in(1.2,2].
\end{cases}\]
To generate the observed datasets, 5000 different values of the parameter $a$ in \eqref{eq:heat_a} are generated using the uniform distribution with the range $[0,1]$, and the corresponding trajectories are computed using SciPy. For DNN-AL, each deep ResNet for this test problem contains 10 ResNet blocks, with two fully-connected layers per block. The two layers have 50 nodes and 21 nodes respectively.
For comparison, a reference solution with $a=1$ is computed using SciPy, which is not included in the training datasets. \figurename{\ref{fig:heat-eqn-reference}} shows the reference solution.
For each $x_i$ and $t_j$ ($i=1,\ldots,I_{\text{grid}}$ and $j=1,\ldots,J$), the prediction of the deep ResNets obtained by Algorithm \ref{alg:main-alg} is denoted by $\hat{u}(t_j,x_i)$, and the point-wise absolute error is defined as $|u(t_j,x_i)-\hat{u}(t_j,x_i)|$.
\figurename{\ref{fig:heat-equation-plots}} shows the predictions of the trained DNNs and the corresponding errors.
It can be seen that after three adaptivity iteration steps, the DNN predictions are very close to the reference solution, and the maximum error is only around $0.04$ for the DNNs obtained at the last iteration step (step six).
Finally, the DNN predictions and the reference solutions at $t=1$ and $t=1.5$ are shown in \figurename{\ref{fig:heat-eqn-sample}}, where it can be seen that each DNN prediction and the corresponding reference solution are visually indistinguishable.
\begin{figure}[htp!]
\centering
\includegraphics[scale=0.17]{figs/Heat-2segment-noise0-block10/Heat-2seg-ref_sol.pdf}
\caption{Reference solution, heat equation.}
\label{fig:heat-eqn-reference}
\end{figure}
\begin{figure}[htp!]
\centering
\subfigure[Iteration step 1, $\hat{u}(t,x)$ and $|u(t,x)-\hat{u}(t,x)|$]{
\includegraphics[scale=0.18]{figs/Heat-2segment-noise0-block10/bestHeat-2seg_pred_epoch100_blk_1.pdf}
\label{fig:heat-k1}
}
\subfigure[Iteration step 3, $\hat{u}(t,x)$ and $|u(t,x)-\hat{u}(t,x)|$]{
\includegraphics[scale=0.18]{figs/Heat-2segment-noise0-block10/bestHeat-2seg_pred_epoch100_blk_3.pdf}
\label{fig:heat-k3}
}
\subfigure[Iteration step 6, $\hat{u}(t,x)$ and $|u(t,x)-\hat{u}(t,x)|$]{
\includegraphics[scale=0.18]{figs/Heat-2segment-noise0-block10/bestHeat-2seg_pred_epoch100_blk_6.pdf}
\label{fig:heat-k6}
}
\caption{
DNN predictions and errors, heat equation.}
\label{fig:heat-equation-plots}
\end{figure}
\begin{figure}[htp!]
\centering
\includegraphics[scale=0.2]{figs/Heat-2segment-noise0-block10/bestHeat-2seg_pred_epoch100_blk_6_sample.pdf}
\caption{
DNN predictions and reference solutions for $t=1$ and $t=1.5$, heat equation.}
\label{fig:heat-eqn-sample}
\end{figure}
\section{Problem setup and preliminary}
\label{sec:setup}
Let $I = \{1,\ldots,K\}$ denote a finite index set, and for each $k\in I$, $\mathbf{f}^{(k)}(\cdot):\mathbb{R}^d\rightarrow \mathbb{R}^d$ denotes a function, which is referred to as the governing equation.
Given a time interval $(0,T_{\max}]$,
a switching signal function is denoted by $\sigma(t):(0,T_{\max}] \to I$. The switching signal function
is typically assumed to be a piecewise constant function with a finite number of discontinuities, which are referred to as switching times \cite{liberzon2003switching}. In this paper, the switching signal function is defined as \begin{equation}
\label{eq:switch-signal}
\sigma(t) = \begin{cases}
1,\quad T_0:=0< t\leq T_1,\\
2,\quad T_1 < t \leq T_2,\\
\cdots\\
K,\quad T_{K-1} < t\leq T_K:=T_{\max},
\end{cases}
\end{equation}
where $\{T_k\}_{k=1}^{K-1}$ are the $K-1$ discontinuities (or switching times).
The dynamical system with time-dependent switching \eqref{eq:switch-signal} considered in this work is written as
\begin{equation}
\label{eq:swithed-system}
\frac{\mathrm{d}}{\mathrm{d}t} \mathbf{x}(t) = \mathbf{f}^{(\sigma(t))}(\mathbf{x}(t)),\quad \mathbf{x}(0) = \mathbf{x}_0,
\end{equation} where $\mathbf{x}(t)\in \mathbb{R}^d$
is a state vector of the system state variables, $\mathbf{x}_0$ is an initial state and $\sigma(t)$ specifies the active governing function for $t\in (0,T_{\max}]$.
This work focuses on the situation where the switched system \eqref{eq:swithed-system} is unknown, i.e., the governing functions, the discontinuity locations,
and the number of discontinuity points are not given a priori. Our aim is to construct its numerical model using observed measurement data.
The observed data are assumed to be available as a collection of several trajectories, where the number of collected trajectories is denoted by $N$, and the corresponding initial states are denoted by $\{\mathbf{x}_0^{(n)}\}^N_{n=1}$. The time interval is discretized with $J$ uniform grids, the time lag between any two adjacent grid points is denoted by $\Delta:=T_{\max}/(J-1)$, and each grid point is denoted by $t_{j}:=(j-1)\Delta$ for $j=1,\ldots,J$.
For an initial state $\mathbf{x}_0^{(n)}$, the state vector at time $t_{j}$ is written as $\mathbf{x}(t_{j};\mathbf{x}_0^{(n)})$, where $n=1,\ldots,N$ and $j=1,\ldots,J$.
For each $n=1,\ldots,N$, the observation of the trajectory is denoted by
\begin{equation}
\label{eq:each-trajectory}
\mathbf{Y}^{(n)} = \{ \mathbf{y}_j^{(n)} := \mathbf{x}(t_{j};\mathbf{x}_0^{(n)}) + \epsilon^{(n)}_j \}_{j=1}^{J}\,,
\end{equation}
where the measurement noises $\epsilon^{(n)}_j$ are assumed to be independent and identically distributed random variables.
We reorganize the overall observed trajectories $\{\mathbf{Y}^{(n)}\}_{n=1}^N$ as
\begin{equation}
\begin{aligned}
\mathcal{D}:=&\{
(\mathbf{y}_j^{(n)}, \mathbf{y}_{j+1}^{(n)}): j =1,\ldots,J-1,\quad n=1,\ldots,N\}.
\end{aligned}
\label{eq:data-pairs}
\end{equation}
The goal of this work is to develop a numerical model to capture the inherent evolution of the system \eqref{eq:swithed-system} with the limited observed measurement data \eqref{eq:each-trajectory}.
Precisely speaking,
we train local models with the data \eqref{eq:each-trajectory}, and for an arbitrary initial state $\mathbf{x}_0$, we use the models to make predictions $\widehat{\mathbf{y}}$ to approximate the true solutions $\mathbf{x}$
as follows
\[\widehat{\mathbf{y}}(t_j;\mathbf{x}_0)\approx \mathbf{x}(t_j;\mathbf{x}_0),\quad j=1,\ldots,J.\]
\section{Review of learning autonomous systems via deep Residual networks}
\label{sec:learn-autonomous-dnn}
In this section, we review neural network based methods in learning autonomous systems following the presentation in work \cite{qin2019data}.
Consider an autonomous system
\begin{equation}
\label{eq:autonomous-system}
\frac{\mathrm{d} \mathbf{x}(t)}{\mathrm{d} t} = \mathbf{f}(\mathbf{x}(t)),\quad \mathbf{x}(0) = \mathbf{x}_0,
\end{equation} where $\mathbf{f}(\cdot):\mathbb{R}^d\rightarrow \mathbb{R}^d$ is a Lipschitz continuous governing equation and $\mathbf{x}_0\in\mathbb{R}^d$ is an initial state.
Given the state $\mathbf{x}(t_0)$ at $t_0 \geq 0$ and the governing equation $\mathbf{f}$, for $t>0$, the flow of the system \eqref{eq:autonomous-system} is represented by
\[\Phi_t(\mathbf{x}(t_0)) := \mathbf{x}(t_0 + t)=\mathbf{x}(t_0)+\int_0^t \mathbf{f}(\mathbf{x}(s+t_0)) \mathrm{d} s.\]
The exact $\Delta$-lag flow map of the autonomous system \eqref{eq:autonomous-system} is defined as
\begin{equation}
\begin{aligned}
\Phi_{\Delta}(\mathbf{x}(t_0))&:=
\mathbf{x}(t_{0}+\Delta) \\
& =\mathbf{x}(t_0) + \int_0^\Delta \mathbf{f}(\mathbf{x}(s+t_0))\mathrm{d}s\\
&= \mathbf{x}(t_0) + \Delta\cdot \mathbf{f}(\mathbf{x}(t_0+\gamma))\\
&= \mathbf{x}(t_0) + \Delta\cdot \mathbf{f}(\Phi_\gamma (\mathbf{x}(t_0))),
\quad \gamma \in [0,\Delta]\,,
\end{aligned}
\label{eq:flow_map}
\end{equation}
and $\phi_{\Delta}(\mathbf{x}(t_0);\mathbf{f}) := \Delta\cdot \mathbf{f}(\Phi_\gamma (\mathbf{x}(t_0)))$ is the \textit{effective increment}.
When the governing equation $\mathbf{f}$
and the time lag $\Delta$ are fixed,
the effective increment $\phi_{\Delta}$
is uniquely determined by
the input state $\mathbf{x}(t_0)$.
\par
In the following, we generically denote the input and the output of the
$\Delta$-lag flow map \eqref{eq:flow_map} as $\mathbf{y}_\text{in}$ and $\mathbf{y}_\text{out}$ (i.e., let $\mathbf{y}_\text{in}=\mathbf{x}(t_0)$ and $\mathbf{y}_\text{out}=\mathbf{x}(t_{0}+\Delta)$ for \eqref{eq:flow_map}).
An efficient residual network (ResNet) is proposed to model the
$\Delta$-lag flow map in \cite{qin2019data} (see \cite{he2016deep} for the original ResNet).
A feedforward neural network composing $L\in \mathbb{N}^+$ fully connected layers is defined as
\[
\mathcal{F}(\mathbf{x};\Theta):=\mathbf{w}_L\cdots h(\mathbf{w}_2(h(\mathbf{w}_1\mathbf{x}+\mathbf{b}_1))+\mathbf{b}_2) +\mathbf{b}_L,
\] where $h$ is the non-linear activation function, $\mathbf{w}_l$ and $\mathbf{b}_l$ are the weight and the bias in the $l$-th layer respectively,
and $\Theta:=\left\{\mathbf{w}_l,\mathbf{b}_l \right\}_{l=1}^{L}$ is the associated parameter set of the network.
Denoting the identity operator as $\mathcal{I}:\mathbb{R}^d \to\mathbb{R}^d$,
a ResNet block is defined as
\begin{equation}
\mathcal{R}(\mathbf{y}_\text{in};\Theta):=\mathbf{y}_\text{in} + \mathcal{F}(\mathbf{y}_\text{in}; \Theta), \label{eq:res}
\end{equation}
which can also be rewritten as $\mathcal{R}(\mathbf{y}_\text{in};\Theta):=( \mathcal{I}+ \mathcal{F}(\cdot; \Theta))(\mathbf{y}_\text{in})$.
The ResNet block \eqref{eq:res} can be considered as a one-step ``exact" integrator for solving autonomous systems \cite{qin2019data}.
Here, we choose the following element-wise hyperbolic tangent (tanh) as the activation function, that is
\[
\text{tanh}(x) = \frac{\mathrm{e}^{2x}-1}{\mathrm{e}^{2x}+1}
.\]
\par
Following \cite{qin2019data}, a ResNet block is stacked $M\in \mathbb{N}^+$ times to construct a deep neural network.
Based on the structure of the recurrent neural network (see \cite[ch.~10]{goodfellow2016deep}),
a deep ResNet is defined as
\begin{equation}
\label{eq:RT-ResNet}
\left\{
\begin{aligned}
\widehat{\mathbf{y}}_0 &= \mathbf{y}_\text{in},\\
\widehat{\mathbf{y}}_{m+1} &= \mathcal{R}(\widehat{\mathbf{y}}_m; \Theta),\quad m =0,\ldots,M-1,\\
\widehat{\mathbf{y}}_\text{out} &= \widehat{\mathbf{y}}_{M},
\end{aligned}
\right.
\end{equation}
where the output gives an approximation of
the output of the $\Delta$-lag flow map, i.e., $\widehat{\mathbf{y}}_\text{out}\approx \mathbf{y}_\text{out}$.
For the convenience of notation, the deep ResNet is denoted by $\mathcal{N}$, i.e., $\widehat{\mathbf{y}}_{\text{out}}=\mathcal{N}(\mathbf{y}_{\text{in}};\Theta)$.
\par
To train the deep ResNet, i.e., to find optimal values of $\Theta$ in \eqref{eq:RT-ResNet}, the following square error loss function is considered
\begin{equation}
\begin{aligned}
\ell_{\text{se}}(\mathbf{y}_{\text{in}},\mathbf{y}_{\text{out}};\Theta) &:=
\Big\|\mathcal{N}(\mathbf{y}_{\text{in}};\Theta) - \mathbf{y}_{\text{out}}
\Big\|^2,
\end{aligned}
\label{eq:square-loss}
\end{equation}
where $\|\cdot \|$ denotes the standard Euclidean norm.
Given a training dataset
$\mathcal{D}_{\mathrm{train}}= \{(\mathbf{y}^{(s)}_\text{in}, \mathbf{y}^{(s)}_\text{out}),s=1,\ldots,N_{\text{train}}\}$ with size $N_{\text{train}}$,
the training loss function of the deep neural network $\mathcal{N}$ is
\begin{equation}
\begin{aligned}
\mathcal{L}_{\text{train}}(\Theta) &= \frac{1}{N_{\text{train}}} \sum_{(\mathbf{y}_\text{in},\mathbf{y}_\text{out})\in \mathcal{D}_{\mathrm{train}}}
\ell_{\text{se}}(\mathbf{y}_\text{in},\mathbf{y}_\text{out};\Theta).
\end{aligned}
\label{eq:train-loss}
\end{equation}
Based on \eqref{eq:train-loss}, we choose the optimal parameters $\Theta^*$
\begin{equation}
\Theta^* = \argmin_{\Theta} (\mathcal{L}_{\text{train}}(\Theta)).
\label{eq:train-REsNet-autonomous}
\end{equation}
As the above optimization problem is highly non-convex and the amount of data is large,
the stochastic gradient descent (SGD) method \cite{bottou2018optimization} is applied, which is a common choice for training deep neural networks with backpropagation \cite{lecun1989backpropagation,krizhevsky2012imagenet,he2016deep}.
The training procedure is summarized as follows.
First,
the training dataset $\mathcal{D}_{\text{train}}$ is divided into $N_{\text{batch}}$ mini-batches.
Each mini-batch is denoted by $M_{r}$ with size $|M_{r}|$ for $r=1,\ldots,N_{\text{batch}}$, and the sizes of different mini-batches are similar.
Then for each mini-batch $M_{r}$, the expectation of the square error loss \eqref{eq:square-loss} and the corresponding gradient are estimated, and the parameters are updated as
\[
\Theta=\Theta - \tau \nabla_{\Theta}\frac{1}{|M_{r}|}\left(\sum_{(\mathbf{y}_\text{in},\mathbf{y}_\text{out})\in M_{r}} \Big\|\mathcal{N}(\mathbf{y}_{\text{in}};\Theta) - \mathbf{y}_{\text{out}}\Big\|^2 \right),
\]
where $\tau$ is a given learning rate.
For each epoch of the optimization procedure,
the above updating step is repeated $N_{\text{batch}}$ times.
At the end of each epoch, a pre-set learning rate scheduler is applied to decrease the learning rate $\tau$, and the mini-batch data are randomly reshuffled. The training procedure is summarized in Algorithm \ref{alg:trining-ResNet}, where $N_E$ is the number of epochs.
\begin{algorithm}[!ht]
\caption{Training a deep ResNet}
\label{alg:trining-ResNet}
\begin{algorithmic}[1]
\REQUIRE{Initial ResNet
$\mathcal{N}(\cdot;\Theta_0)$,
and training dataset $\mathcal{D}_{\mathrm{train}}=\left\{(\mathbf{y}_{\text{in}}^{(s)},\mathbf{y}_\text{out}^{(s)})\right\}_{s=1}^{N_{\text{train}}}$.}
\STATE{Set an initial learning rate $\tau$, and initialize a learning rate scheduler.}
\STATE{Set $\Theta=\Theta_0$.}
\FOR{training epoch $=1,\ldots, N_E$}
\FOR{$r =1,\ldots, N_{\text{batch}}$}
\STATE{Obtain the mini batch $M_{r}$ containing $|M_{r}|$ data pairs.}
\STATE{Update the parameters $\Theta$ by the stochastic gradient descent: $\Theta=\Theta - \tau \nabla_{\Theta}\frac{1}{|M_{r}|}\left (\sum_{(\mathbf{y}_\text{in},\mathbf{y}_\text{out})\in M_{r}} \Big\|\mathcal{N}(\mathbf{y}_{\text{in}};\Theta) - \mathbf{y}_{\text{out}}\Big\|^2 \right) $.}
\ENDFOR
\STATE{Decrease the learning rate $\tau$ using the learning rate scheduler.}
\ENDFOR
\STATE{Let $\Theta_*=\Theta$.}
\ENSURE{Trained RestNet $\mathcal{N}(\cdot;\Theta_*)$.}
\end{algorithmic}
\end{algorithm}
|
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| 6,742
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{"url":"https:\/\/www.trustudies.com\/question\/1114\/in-figure-oacb-is-a-quadrant-of-a-cir\/","text":"3 Tutor System\nStarting just at 265\/hour\n\n# In figure OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm , find the area of the (i) quadrant OACB, (ii) Shaded region,\n\n(i) Area of quadrant $$= \\ \\frac{1}{4} \\ \\pi r^2$$\n\n$$= \\ \\frac{1}{4} \\ \u00d7 \\ \\frac{22}{7} \\ \u00d7 \\ (3.5)^2$$\n\n$$= \\ \\frac{1}{4} \\ \u00d7 \\ \\frac{22}{7} \\ \u00d7 \\ ( \\frac{7}{2} )^2 \\ = \\ \\frac{77}{8}$$ cm2\n\n(ii) Area of \u2206 BOD = $$\\frac{1}{2}$$ Base \u00d7 Height\n\n$$= \\ \\frac{1}{2} \\ (OB \\ \u00d7 \\ OD)$$\n\n$$= \\ \\frac{1}{2} (3.5 \\ \u00d7 \\ 2) \\ = \\ \\frac{7}{2}$$ cm2\n\nSo, area of the shaded region\n\n= Area of quadrant - Area of \u2206 BOD\n\n$$= \\ \\frac{77}{8} \\ - \\ \\frac{7}{2} \\ = \\ \\frac{49}{8}$$ cm2","date":"2023-03-22 02:31:04","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\": 0.8039266467094421, \"perplexity\": 3151.7695409009198}, \"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-2023-14\/segments\/1679296943749.68\/warc\/CC-MAIN-20230322020215-20230322050215-00336.warc.gz\"}"}
| null | null |
{"url":"http:\/\/www.philipzucker.com\/category\/formal-methods\/","text":"## Linear Relation Algebra of Circuits with HMatrix\n\nOooh this is a fun one.\n\nI\u2019ve talked before about relation algebra and I think it is pretty neat. http:\/\/www.philipzucker.com\/a-short-skinny-on-relations-towards-the-algebra-of-programming\/. In that blog post, I used finite relations. In principle, they are simple to work with. We can perform relation algebra operations like composition, meet, and join by brute force enumeration.\n\nUnfortunately, brute force may not always be an option. First off, the finite relations grow so enormous as to be make this infeasible. Secondly, it is not insane to talk about relations or regions with an infinite number of elements, such as some continuous blob in 2D space. In that case, we can\u2019t even in principle enumerate all the points in the region. What are we to do? We need to develop some kind of finite parametrization of regions to manipulate. This parametrization basically can\u2019t possibly be complete in some sense, and we may choose more or less powerful systems of description for computational reasons.\n\nIn this post, we are going to be talking about linear or affine subspaces of a continuous space. These subspaces are hyperplanes. Linear subspaces have to go through the origin, while affine spaces can have an offset from the origin.\n\nIn the previous post, I mentioned that the finite relations formed a lattice, with operations meet and join. These operations were the same as set intersection and union so the introduction of the extra terminology meet and join felt a bit unwarranted. Now the meet and join aren\u2019t union and intersection anymore. We have chosen to not have the capability to represent the union of two vectors, instead we can only represent the smallest subspace that contains them both, which is the union closed under vector addition. For example, the join of a line and point will be the plane that goes through both.\n\nLinear\/Affine stuff is great because it is so computational. Most questions you cant to ask are answerable by readily available numerical linear algebra packages. In this case, we\u2019ll use the Haskell package HMatrix, which is something like a numpy\/scipy equivalent for Haskell. We\u2019re going to use type-level indices to denote the sizes and partitioning of these spaces so we\u2019ll need some helper functions.\n\nIn case I miss any extensions, make typos, etc, you can find a complete compiling version here https:\/\/github.com\/philzook58\/ConvexCat\/blob\/master\/src\/LinRel.hs\n\nIn analogy with sets of tuples for defining finite relations, we partition the components of the linear spaces to be \u201cinput\u201d and \u201coutput\u201d indices\/variables $\\begin{bmatrix} x_1 & x_2 & x_3 & ... & y_1 & y_2 & y_3 & ... \\end{bmatrix}$. This partition is somewhat arbitrary and easily moved around, but the weakening of strict notions of input and output as compared to functions is the source of the greater descriptive power of relations.\n\nRelations are extensions of functions, so linear relations are an extension of linear maps. A linear map has the form $y = Ax$. A linear relation has the form $Ax + By = 0$. An affine map has the form $y = Ax + b$ and an affine relation has the form $Ax + By = b$.\n\nThere are at least two useful concrete representation for subspaces.\n\n1. We can write a matrix $A$ and vector $b$ down that corresponds to affine constraints. $Ax = b$. The subspace described is the nullspace of $A$ plus a solution of the equation. The rows of A are orthogonal to the space.\n2. We can hold onto generators of subspace. $x = A' l+b$ where l parametrizes the subspace. In other words, the subspace is generated by \/ is the span of the columns of $A'$. It is the range of $A'$.\n\nWe\u2019ll call these two representations the H-Rep and V-Rep, borrowing terminology from similar representations in polytopes (describing a polytope by the inequalities that define it\u2019s faces or as the convex combination of it\u2019s vertices). https:\/\/inf.ethz.ch\/personal\/fukudak\/lect\/pclect\/notes2015\/PolyComp2015.pdf These two representations are dual in many respects.\n\nIt is useful to have both reps and interconversion routines, because different operations are easy in the two representations. Any operations defined on one can be defined on the other by sandwiching between these conversion functions. Hence, we basically only need to define operations for one of the reps (if we don\u2019t care too much about efficiency loss which, fair warning, is out the window for today). The bulk of computation will actually be performed by these interconversion routines. The HMatrix function nullspace performs an SVD under the hood and gathers up the space with 0 singular values.\n\nThese linear relations form a category. I\u2019m not using the Category typeclass because I need BEnum constraints hanging around. The identity relations is $x = y$ aka $Ix - Iy = 0$.\n\nComposing relations is done by combining the constraints of the two relations and then projecting out the interior variables. Taking the conjunction of constraints is easiest in the H-Rep, where we just need to vertically stack the individual constraints. Projection easily done in the V-rep, where you just need to drop the appropriate section of the generator vectors. So we implement this operation by flipping between the two.\n\nWe can implement the general cadre of relation operators, meet, join, converse. I feel the converse is the most relational thing of all. It makes inverting a function nearly a no-op.\n\nRelational inclusion is the question of subspace inclusion. It is fairly easy to check if a VRep is in an HRep (just see plug the generators into the constraints and see if they obey them) and by using the conversion functions we can define it for arbitrary combos of H and V.\n\nIt is useful the use the direct sum of the spaces as a monoidal product.\n\nA side note: Void causes some consternation. Void is the type with no elements and is the index type of a 0 dimensional space. It is the unit object of the monoidal product. Unfortunately by an accident of the standard Haskell definitions, actual Void is not a BEnum. So, I did a disgusting hack. Let us not discuss it more.\n\n### Circuits\n\nBaez and Fong have an interesting paper where they describe building circuits using a categorical graphical calculus. We have the pieces to go about something similar. What we have here is a precise way in which circuit diagrams can be though of as string diagrams in a monoidal category of linear relations.\n\nAn idealized wire has two quantities associated with it, the current flowing through it and the voltage it is at.\n\nWhen we connect wires, the currents must be conserved and the voltages must be equal. hid and hcompose from above still achieve that. Composing two independent circuits in parallel is achieve by hpar.\n\nWe will want some basic tinker toys to work with.\n\nA resistor in series has the same current at both ends and a voltage drop proportional to the current\n\nComposing two resistors in parallel adds the resistance. (resistor r1) <<< (resistor r2) == resistor (r1 + r2))\n\nA bridging resistor allows current to flow between the two branches\n\nComposing two bridge circuits is putting the bridge resistors in parallel. The conductance $G=\\frac{1}{R}$ of resistors in parallel adds. hcompose (bridge r1) (bridge r2) == bridge 1 \/ (1\/r1 + 1\/r2).\n\nAn open circuit allows no current to flow and ends a wire. open ~ resistor infinity\n\nAt branching points, the voltage is maintained, but the current splits.\n\nThis cmerge combinator could also be built using a short == bridge 0 , composing a branch with open, and then absorbing the Void away.\n\nWe can bend wires up or down by using a composition of cmerge and open.\n\nVoltage and current sources enforce current and voltage to be certain values\n\nMeasurements of circuits proceed by probes.\n\nInductors and capacitors could be included easily, but would require the entries of the HMatrix values to be polynomials in the frequency $\\omega$, which it does not support (but it could!). We\u2019ll leave those off for another day.\n\nWe actually can determine that the rules suggested above are being followed by computation.\n\n### Bits and Bobbles\n\n\u2022 Homogenous systems are usually a bit more elegant to deal with, although a bit more unfamiliar and abstract.\n\u2022 Could make a pandas like interface for linear relations that uses numpy\/scipy.sparse for the computation. All the swapping and associating is kind of fun to design, not so much to use. Labelled n-way relations are nice for users.\n\u2022 Implicit\/Lazy evaluation. We should let the good solvers do the work when possible. We implemented our operations eagerly. We don\u2019t have to. By allowing hidden variables inside our relations, we can avoid the expensive linear operations until it is useful to actually compute on them.\n\u2022 Relational division = quotient spaces?\n\u2022 DSL. One of the beauties of the pointfree\/categorical approach is that you avoid the need for binding forms. This makes for a very easily manipulated DSL. The transformations feel like those of ordinary algebra and you don\u2019t have to worry about the subtleties of index renaming or substitution under binders.\n\u2022 Sparse is probably really good. We have lots of identity matrices and simple rearrangements. It is very wasteful to use dense operations on these.\n\u2022 Schur complement https:\/\/en.wikipedia.org\/wiki\/Schur_complement are the name in the game for projecting out pieces of linear problems. We have some overlap.\n\u2022 Linear relations -> Polyhedral relations -> Convex Relations. Linear is super computable, polyhedral can blow up. Rearrange a DSL to abuse Linear programming as much as possible for queries.\n\u2022 Network circuits. There is an interesting subclass of circuits that is designed to be pretty composable.\n\nhttps:\/\/en.wikipedia.org\/wiki\/Two-port_network Two port networks are a very useful subclass of electrical circuits. They model transmission lines fairly well, and easily composable for filter construction.\n\nIt is standard to describe these networks by giving a linear function between two variables and the other two variables. Depending on your choice of which variables depend on which, these are called the z-parameters, y-parameters, h-parameters, scattering parameters, abcd parameters. There are tables of formula for converting from one form to the others. The different parameters hold different use cases for composition and combining in parallel or series. From the perspective of linear relations this all seems rather silly. The necessity for so many descriptions and the confusing relationship between them comes from the unnecessary and overly rigid requirement of have a linear function-like relationship rather than just a general relation, which depending of the circuit may not even be available (there are degenerate configurations where two of the variables do not imply the values of the other two). A function relationship is always a lie (although a sometimes useful one), as there is always back-reaction of new connections.\n\nThe relation model also makes clearer how to build lumped models out of continuous ones. https:\/\/en.wikipedia.org\/wiki\/Lumped-element_model\n\nnull\n\u2022 Because the type indices have no connection to the actual data types (they are phantom) it is a wise idea to use smart constructors that check that the sizes of the matrices makes sense.\n\u2022 Nonlinear circuits. Grobner Bases and polynomial relations?\n\u2022 Quadratic optimization under linear constraints. Can\u2019t get it to come out right yet. Clutch for Kalman filters. Nice for many formulations like least power, least action, minimum energy principles.\n\u2022 Quadratic Operators -> Convex operators. See last chapter of Rockafellar.\n\u2022 Duality of controllers and filters. It is well known (I think) that for ever controller algorithm there is a filter algorithm that is basically the same thing.\n\u2022 LQR \u2013 Kalman\n\u2022 Viterbi filter \u2013 Value function table\n\u2022 particle filter \u2013 Monte Carlo control\n\u2022 Extended Kalman \u2013 iLQR-ish? Use local approximation of dynamics\n\u2022 unscented kalman \u2013 ?\n\n## Failing to Bound Kissing Numbers\n\nhttps:\/\/en.wikipedia.org\/wiki\/Kissing_number\n\nCody brought up the other day the kissing number problem.Kissing numbers are the number of equal sized spheres you can pack around another one in d dimensions. It\u2019s fairly self evident that the number is 2 for 1-d and 6 for 2d but 3d isn\u2019t so obvious and in fact puzzled great mathematicians for a while. He was musing that it was interesting that he kissing numbers for some dimensions are not currently known, despite the fact that the first order theory of the real numbers is decidable https:\/\/en.wikipedia.org\/wiki\/Decidability_of_first-order_theories_of_the_real_numbers\n\nI suggested on knee jerk that Sum of Squares might be useful here. I see inequalities and polynomials and then it is the only game in town that I know anything about.\n\nApparently that knee jerk was not completely wrong\n\nhttps:\/\/arxiv.org\/pdf\/math\/0608426.pdf\n\nSomehow SOS\/SDP was used for bounds here. I had an impulse that the problem feels SOS-y but I do not understand their derivation.\n\nOne way the problem can be formulated is by finding or proving there is no solution to the following set of equations constraining the centers $x_i$ of the spheres. Set the central sphere at (0,0,0,\u2026) . Make the radii 1. Then$\\forall i. |x_i|^2 = 2^2$ and $\\forall i j. |x_i - x_j|^2 \\ge 2^2$\n\nI tried a couple different things and have basically failed. I hope maybe I\u2019ll someday have a follow up post where I do better.\n\nSo I had 1 idea on how to approach this via a convex relaxation\n\nMake a vector $x = \\begin{bmatrix} x_0 & y _0 & x_1 & y _1 & x_2 & y _2 & ... \\end{bmatrix}$ Take the outer product of this vector $x^T x = X$ Then we can write the above equations as linear equalities and inequalities on X. If we forget that we need X to be the outer product of x (the relaxation step), this becomes a semidefinite program. Fingers crossed, maybe the solution comes back as a rank 1 matrix. Other fingers crossed, maybe the solution comes back and says it\u2019s infeasible. In either case, we have solved our original problem.\n\nDidn\u2019t work though. Sigh. It\u2019s conceivable we might do better if we start packing higher powers into x?\n\nOk Round 2. Let\u2019s just ask z3 and see what it does. I\u2019d trust z3 with my baby\u2019s soft spot.\n\nIt solves for 5 and below. Z3 grinds to a halt on N=6 and above. It ran for days doin nothing on my desktop.\n\nOk. A different tact. Try to use a positivstellensatz proof. If you have a bunch of polynomial inequalities and equalities if you sum polynomial multiples of these constraints, with the inequalities having sum of square multiples, in such a way to = -1, it shows that there is no real solution to them. We have the distance from origin as equality constraint and distance from each other as an inequality constraint. I intuitively think of the positivstellensatz as deriving an impossibility from false assumptions. You can\u2019t add a bunch of 0 and positive numbers are get a negative number, hence there is no real solution.\n\nI have a small set of helper functions for combining sympy and cvxpy for sum of squares optimization. I keep it here along with some other cute little constructs https:\/\/github.com\/philzook58\/cvxpy-helpers\n\nand here is the attempted positivstellensatz.\n\nIt worked in 1-d, but did not work in 2d. At order 3 polynomials N=7, I maxed out my ram.\n\nI also tried doing it in Julia, since sympy was killing me. Julia already has a SOS package\n\nIt was faster to encode, but it\u2019s using the same solver (SCS), so basically the same thing.\n\nI should probably be reducing the system with respect to equality constraints since they\u2019re already in a Groebner basis. I know that can be really important for reducing the size of your problem\n\nI dunno.\n\nBlah blah blah blah A bunch of unedited trash\n\nhttps:\/\/github.com\/peterwittek\/ncpol2sdpa Peter Wittek has probably died in an avalanche? That is very sad.\n\nThese notes\n\nhttps:\/\/web.stanford.edu\/class\/ee364b\/lectures\/sos_slides.pdf\n\nPositivstullensatz.\n\nkissing number\n\nReview of sum of squares\n\nminimimum sample as LP. ridiculous problem\nmin t\nst. f(x_i) \u2013 t >= 0\n\ndual -> one dual variable per sample point\nThe only dual that will be non zero is that actually selecting the minimum.\n\nHm. Yeah, that\u2019s a decent analogy.\n\nHow does the dual even have a chance of knowing about poly airhtmetic?\nIt must be during the SOS conversion prcoess. In building the SOS constraints,\nwe build a finite, limittted version of polynomial multiplication\nx as a matrix. x is a shift matrix.\nIn prpducing the characterstic polynomial, x is a shift matrix, with the last line using the polynomial\nknown to be zero to\neigenvectors of this matrix are zeros of the poly.\n\nSOS does not really on polynomials persay. It relies on closure of the suqaring operaiton\n\nmaybe set one sphere just at x=0 y = 2. That breaks some symmettry\n\nset next sphere in plane something. random plane through origin?\n\norder y components \u2013 breaks some of permutation symmettry.\n\nno, why not order in a random direction. That seems better for symmettry breaking\n\n## Learn Coq in Y\n\nI\u2019ve been preparing a Learn X in Y tutorial for Coq. https:\/\/learnxinyminutes.com\/\n\nI\u2019ve been telling people this and been surprised by how few people have heard of the site. It\u2019s super quick intros to syntax and weirdness for a bunch of languages with inline code tutorials.\nI think that for me, a short description of that mundane syntactic and programming constructs of coq is helpful.\nSome guidance of the standard library, what is available by default. And dealing with Notation scopes, which is a pretty weird feature that most languages don\u2019t have.\nThe manual actually has all this now. It\u2019s really good. Like check this section out https:\/\/coq.inria.fr\/refman\/language\/coq-library.html . But the manual is an intimidating documents. It starts with a BNF description of syntax and things like that. The really useful pedagogical stuff is scattered throughout it.\n\nAnyway here is my draft (also here https:\/\/github.com\/philzook58\/learnxinyminutes-docs\/blob\/master\/coq.html.markdown where the syntax highlighting isn\u2019t so janked up). Suggestions welcome. Or if this gets accepted, you can just make pull requests\n\nBonus. An uneditted list of tactics. You\u2019d probably prefer https:\/\/pjreddie.com\/coq-tactics\/\n\n## Neural Networks with Weighty Lenses (DiOptics?)\n\nI wrote a while back how you can make a pretty nice DSL for reverse mode differentiation based on the same type as Lens. I\u2019d heard some interesting rumblings on the internet around these ideas and so was revisiting them.\n\nComposition is defined identically for reverse mode just as it is for lens.\n\nAfter chewing on it a while, I realized this really isn\u2019t that exotic. How it works is that you store the reverse mode computation graph, and all necessary saved data from the forward pass in the closure of the (dy -> dx). I also have a suspicion that if you defunctionalized this construction, you\u2019d get the Wengert tape formulation of reverse mode ad.\n\nSecond, Lens is just a nice structure for bidirectional computation, with one forward pass and one backward pass which may or may not be getting\/setting. There are other examples for using it like this.\n\nIt is also pretty similar to the standard \u201cdual number\u201d form type FAD x dx y dy = (x,dx)->(y,dy) for forward mode AD. We can bring the two closer by a CPS\/Yoneda transformation and then some rearrangement.\n\nand meet it in the middle with\n\nI ended the previous post somewhat unsatisfied by how ungainly writing that neural network example was, and I called for Conal Elliot\u2019s compiling to categories plugin as a possible solution. The trouble is piping the weights all over the place. This piping is very frustrating in point-free form, especially when you know it\u2019d be so trivial pointful. While the inputs and outputs of layers of the network compose nicely (you no longer need to know about the internal computations), the weights do not. As we get more and more layers, we get more and more weights. The weights are in some sense not as compositional as the inputs and outputs of the layers, or compose in a different way that you need to maintain access to.\n\nI thought of a very slight conceptual twist that may help.\n\nThe\u00a0idea\u00a0is we keep the weights out to the side in their own little type parameter slots. Then we define composition such that it composes input\/outputs while tupling the weights. Basically we throw the repetitive complexity appearing in piping the weights around into the definition of composition itself.\n\nThese operations are easily seen as 2 dimensional diagrams.\n\nHere\u2019s the core reverse lens ad combinators\n\nAnd here are the two dimensional combinators. I tried to write them point-free in terms of the combinators above to demonstrate that there is no monkey business going on. We\n\nI wonder if this is actually nice?\n\nI asked around and it seems like this idea may be what davidad is talking about when he refers to dioptics\n\nhttp:\/\/events.cs.bham.ac.uk\/syco\/strings3-syco5\/slides\/dalrymple.pdf\n\nPerhaps this will initiate a convo.\n\nEdit: He confirms that what I\u2019m doing appears to be a dioptic. Also he gave a better link http:\/\/events.cs.bham.ac.uk\/syco\/strings3-syco5\/papers\/dalrymple.pdf\n\nHe is up to some interesting diagrams\n\n### Bits and Bobbles\n\n\u2022 Does this actually work or help make things any better?\n\u2022 Recurrent\u00a0neural\u00a0nets\u00a0flip\u00a0my\u00a0intended\u00a0role\u00a0of\u00a0weights\u00a0and\u00a0inputs.\n\u2022 Do conv-nets naturally require higher dimensional diagrams?\n\u2022 This weighty style seems like a good fit for my gauss seidel and iterative LQR solvers. A big problem I hit there was getting all the information to the outside, which is a similar issue to getting the weights around in a neural net.\n\n## Gr\u00f6bner Bases and Optics\n\nGeometrical optics is a pretty interesting topic. It really is almost pure geometry\/math rather than physics.\n\nHuygens principle says that we can compute the propagation of a wave by considering the wavelets produced by each point on the wavefront separately.\n\nIn physical optics, this corresponds to the linear superposition of the waves produced at each point by a propagator function $\\int dx' G(x,x')$. In geometrical optics, which was Huygens original intent I think (these old school guys were VERY geometrical), this is the curious operation of taking the geometrical envelope of the little waves produced by each point.\n\nhttps:\/\/en.wikipedia.org\/wiki\/Envelope_(mathematics) The envelope is an operation on a family of curves. You can approximate it by a finite difference procedure. Take two subsequent curves close together in the family, find their intersection. Keep doing that and the join up all the intersections. This is roughly the approach I took in this post http:\/\/www.philipzucker.com\/elm-eikonal-sol-lewitt\/\n\nYou can describe a geometrical wavefront implicitly with an equations $\\phi(x,y) = 0$. Maybe the wavefront is a circle, or a line, or some wacky shape.\n\nThe wavelet produced by the point x,y after a time t is described implicitly by $d(\\vec{x},\\vec{x'})^2 - t^2 = (x-x')^2 + (y-y')^2 - t^2 = 0$.\n\nThis described a family of curves, the circles produced by the different points of the original wavefront. If you take the envelope of this family you get the new wavefront at time t.\n\nHow do we do this? Grobner bases is one way if we make $\\phi$ a polynomial equation. For today\u2019s purposes, Grobner bases are a method for solving multivariate polynomial equations. Kind of surprising that such a thing even exists. It\u2019s actually a guaranteed terminating algorithm with horrific asymptotic complexity. Sympy has an implementation. For more on Grobner bases, the links here are useful http:\/\/www.philipzucker.com\/dump-of-nonlinear-algebra-algebraic-geometry-notes-good-links-though\/. Especially check out the Cox Little O\u2019Shea books\n\nThe algorithm churns on a set of multivariate polynomials and spits out a new set that is equivalent in the sense that the new set is equal to zero if and only if the original set was. However, now (if you ask for the appropriate term ordering) the polynomials are organized in such a way that they have an increasing number of variables in them. So you solve the 1-variable equation (easy), and substitute into the 2 variable equation. Then that is a 1-variable equation, which you solve (easy) and then you substitute into the three variable equation, and so on. It\u2019s analogous to gaussian elimination.\n\nSo check this out\n\nThe envelope conditions can be found by introducing two new differential variables dx, and dy. They are constrained to lie tangent to the point on the original circle by the differential equation e3, and then we require that the two subsequent members of the curve family intersect by the equation e4. Hence we get the envelope. Ask for the Grobner basis with that variable ordering gives us an implicit equations for x2, y2 with no mention of the rest if we just look at the last equation of the Grobner basis.\n\nI set arbitrarily dy = 1 because the overall scale of them does not matter, only the direction. If you don\u2019t do this, the final equation is scaled homogenously in dy.\n\nThis does indeed show the two new wavefronts at radius 1 and radius 3.\n\nHere\u2019s a different one of a parabola using e1\u00a0=\u00a0\u00a0y1\u00a0\u2013\u00a0x1\u00a0+\u00a0x1**2\n\nThe weird lumpiness here is plot_implicit\u2019s inability to cope, not the actually curve shape Those funky prongs are from a singularity that forms as the wavefront folds over itself.\n\nI tried using a cubic curve x**3 and the grobner basis algorithm seems to crash my computer. \ud83d\ude41 Perhaps this is unsurprising. https:\/\/en.wikipedia.org\/wiki\/Elliptic_curve ?\n\nI don\u2019t know how to get the wavefront to go in only 1 direction? As is, it is propagating into the past and the future. Would this require inequalities? Sum of squares optimization perhaps?\n\nEdit:\n\nIt\u2019s been suggested on reddit that I\u2019d have better luck using other packages, like Macaulay2, MAGMA, or Singular. Good point\n\nAlso it was suggested I use the Dixon resultant, for which there is an implementation in sympy, albeit hidden. Something to investigate\n\nhttps:\/\/github.com\/sympy\/sympy\/blob\/master\/sympy\/polys\/multivariate_resultants.py\n\nhttps:\/\/nikoleta-v3.github.io\/blog\/2018\/06\/05\/resultant-theory.html\n\nAnother interesting angle might be to try to go numerical with a homotopy continuation method with phcpy\n\nhttps:\/\/www.semion.io\/doc\/solving-polynomial-systems-with-phcpy\n\n## Concolic Weakest Precondition is Kind of Like a Lens\n\nThat\u2019s a mouthful.\n\nLens are described as functional getters and setters. The simple lens type is\n\n. The setter is\n\nand the getter is\n\nThis type does not constrain lenses to obey the usual laws of getters and setters. So we can use\/abuse lens structures for nontrivial computations that have forward and backwards passes that share information. Jules Hedges is particular seems to be a proponent for this idea.\n\nI\u2019ve described before how to encode reverse mode automatic differentiation in this style. I have suspicions that you can make iterative LQR and guass-seidel iteration have this flavor too, but I\u2019m not super sure. My attempts ended somewhat unsatisfactorily a whiles back but I think it\u2019s not hopeless. The trouble was that you usually want the whole vector back, not just its ends.\n\nI\u2019ve got another example in imperative program analysis that kind of makes sense and might be useful though. Toy repo here: https:\/\/github.com\/philzook58\/wp-lens\n\nIn program analysis it sometimes helps to run a program both concretely and symbolically. Concolic = CONCrete \/ symbOLIC. Symbolic stuff can slowly find hard things and concrete execution just sprays super fast and can find the dumb things really quick.\n\nWe can use a lens structure to organize a DSL for describing a simple imperative language\n\nThe forward pass is for the concrete execution. The backward pass is for transforming the post condition to a pre condition in a weakest precondition analysis. Weakest precondition semantics is a way of specifying what is occurring in an imperative language. It tells how each statement transforms post conditions (predicates about the state after the execution) into pre conditions (predicates about before the execution).\u00a0 The concrete execution helps unroll loops and avoid branching if-then-else behavior that would make the symbolic stuff harder to process.\u00a0I\u2019ve been flipping through Djikstra\u2019s book on this. Interesting stuff, interesting man.\n\nI often think of a state machine as a function taking s -> s. However, this is kind of restrictive. It is possible to have heterogenous transformations s -> s\u2019. Why not? I think I am often thinking about finite state machines, which we really don\u2019t intend to have a changing state size. Perhaps we allocated new memory or something or brought something into or out of scope. We could model this by assuming the memory was always there, but it seems wasteful and perhaps confusing. We need to a priori know everything we will need, which seems like it might break compositionally.\n\nWe could model our language making some data type like\ndata Imp = Skip | Print String | Assign String Expr | Seq Imp Imp | ...\nand then build an interpreter\n\nBut we can also cut out the middle man and directly define our language using combinators.\n\nTo me this has some flavor of a finally tagless style.\n\nLikewise for expressions. Expressions evaluate to something in the context of the state (they can lookup variables), so let\u2019s just use\n\nAnd, confusingly (sorry), I think it makes sense to use Lens in their original getter\/setter intent for variables. So Lens structure is playing double duty.\n\ntype Var s a = Lens' s a\n\nWith that said, here we go.\n\nWeakest precondition can be done similarly, instead we start from the end and work backwards\n\nPredicates are roughly sets. A simple type for sets is\n\nNow, this doesn\u2019t have much deductive power, but I think it demonstrates the principles simply. We could replace Pred with perhaps an SMT solver expression, or some data type for predicates, for which we\u2019ll need to implement things like substitution. Let\u2019s not today.\n\nA function\n\nis equivalent to\n\n. This is some kind of CPS \/ Yoneda transformation thing. A state transformer\n\nto predicate transformer\n\nis somewhat evocative of that. I\u2019m not being very precise here at all.\n\nWithout further ado, here\u2019s how I think a weakest precondition looks roughly.\n\nFinally here is a combination of the two above that uses the branching structure of the concrete execution to aid construction of the precondition. Although I haven\u2019t expanded it out, we are using the full s t a b parametrization of lens in the sense that states go forward and predicates come back.\n\nNeat. Useful? Me dunno.\n\n## Relational Algebra with Fancy Types\n\nLast time, I tried to give a primer of relations and relational algebra using the Haskell type type Rel a b = [(a,b)]. In this post we\u2019re going to look at these ideas from a slightly different angle. Instead of encoding relations using value level sets, we\u2019ll encode relations in the type system. The Algebra of Programming Agda repo and the papers quoted therein are very relevant, so if you\u2019re comfortable wading into those waters, give them a look. You can find my repo for fiddling here\n\nAt this point, depending on what you\u2019ve seen before, you\u2019re either thinking \u201cYeah, sure. That\u2019s a thing.\u201d or you\u2019re thinking \u201cHow and why the hell would you do such a ridiculous thing.\u201d\n\nMost of this post will be about how, so let\u2019s address why first:\n\n1. Examining relations in this style illuminates some constructions that appear around the Haskell ecosystem, particularly some peculiar fellows in the profunctor package.\n2. More syntactic approach to relations allows discussion of larger\/infinite domains. The finite enumerations of the previous post is nice for simplicity, but it seems you can\u2019t get far that way.\n3. Mostly because we can \u2013 It\u2019s a fun game. Maybe a useful one? TBD.\n\nWith that out of the way, let\u2019s go on to how.\n\n### Translating Functions to Relation GADTs\n\nWe will be using some Haskell extensions in this post, at the very least GADTs and DataKinds. For an introduction to GADTs and DataKinds, check out this blog post. DataKinds is an extension that reflects every data constructor of data types to a type constructor. Because there are values True and False there are corresponding types created'True and 'False. GADTs is an extension of the type definition mechanism of standard Haskell. They allow you to declare refined types for the constructors of your data and they infer those refined type when you pattern match out of the data as well, such that the whole process is kind of information preserving.\n\nWe will use the GADT extension to define relational datatypes with the kind\n\n. That way it has a slot a for the \u201cinput\u201d and b for the \u201coutput\u201d of the relation. What will goes in these type slots will be DataKind lifted types like 'True, not ordinary Haskell types like Int. This is a divergence from from the uses of similar kinds you see in Category, Profunctor, or Arrow. We\u2019re doing a more typelevel flavored thing than you\u2019ll see in those libraries. What we\u2019re doing is clearly a close brother of the singleton approach to dependently typed programming in Haskell.\n\nSome examples are in order for what I mean. Here are two simple boolean functions, not and and defined in ordinary Haskell functions, and their equivalent GADT relation data type.\n\nYou can already start to see how mechanical the correspondence between the ordinary function definition and our new fancy relation type. A function is often defined via cases. Each case corresponds to a new constructor of the relation and each pattern that occurs in that case is the pattern that appears in the GADT. Multiple arguments to the relations are encoded by uncurrying everything by default.\n\nAny function calls that occur on the right hand side of a function definition becomes fields in the constructor of our relation. This includes recursive calls and external function calls. Here are some examples with a Peano style natural number data type.\n\nWe can also define things that aren\u2019t functions. Relations are a larger class of things than functions are, which is part of their utility. Here is a \u201cless than equal\u201d relation LTE.\n\nYou can show that elements are in a particular relation by finding a value of that relational type. Is ([4,7], 11) in the relation Plus? Yes, and I can show it with with the value PS (PS (PS (PS PZ))) :: Plus (4,7) 11 . This is very much the Curry-Howard correspondence. The type R a b corresponds to the proposition\/question is $(a,b) \\in R$ .\n\n### The Fun Stuff : Relational Combinators\n\nWhile you need to build some primitive relations using new data type definitions, others can be built using relational combinators. If you avoid defining too many primitive relations like the above and build them out of combinators, you expose a rich high level manipulation algebra. Otherwise you are stuck in the pattern matching dreck. We are traveling down the same road we did in the previous post, so look there for less confusing explanations of the relational underpinnings of these constructions, or better yet some of the references below.\n\nHigher order relational operators take in a type parameters of kind\n\nand produce new types of a similar kind. The types appearing in these combinators is the AST of our relational algebra language.\n\nThe first two combinators of interest is the composition operator and the identity relation. An element $(a,c)$ is in $R \\cdot Q$ if there exists a $b$ such that $(a,b) \\in R$ and $(b,c) \\in Q$. The fairly direct translation of this into a type is\n\nThe type of the composition is the same as that of Profunctor composition found in the profunctors package.\n\nAlongside a composition operator, it is a knee jerk to look for an identity relation and we do have one\n\nThis is also a familiar friend. The identity relation in this language is the Equality type.\n\nWe can build an algebra for handling product and sum types by defining the appropriate relational combinators. These are very similar to the combinators in the Control.Arrow package.\n\nThe converse of relations is very interesting operation and is the point where relations really differ from functions. Inverting a function is tough. Conversing a relation always works. This data type has no analog in profunctor to my knowledge and probably shouldn\u2019t.\n\nRelations do not have a notion of currying. The closest thing they have is\n\n### Lattice Operators\n\nFor my purposes, lattices are descriptions of sets that trade away descriptive power for efficiency. So most operations you\u2019d perform on sets have an analog in the lattice structure, but it isn\u2019t a perfect matching and you\u2019re forced into approximation. It is nice to have the way you perform these approximation be principled, so that you can know at the end of your analysis whether you\u2019ve actually really shown anything or not about the actual sets in question.\n\nThe top relation holds all values. This is represented by making no conditions on the type parameters. They are completely phantom.\n\nBottom is a relation with no inhabitants.\n\nThe meet is basically the intersection of the relations, the join is basically the union.\n\nA Lattice has an order on it. This order is given by relational inclusion. This is the same as the :-> combinator can be found in the profunctors package.\n\nRelational equality can be written as back and forth inclusion, a natural isomorphism between the relations. There is also an interesting indirect form.\n\n#### Relational Division\n\nIf we consider the equation (r <<< p) :-> q with p and q given, in what sense is there a solution for r? By analogy, this looks rather like r*p = q, so we\u2019re asking a kind of division question. Well, unfortunately, this equation may not necessarily have a solution (neither do linear algebraic equations for that matter), but we can ask for the best under approximation instead. This is the operation of relational division. It also appears in the profunctor package as the right Kan Extension. You\u2019ll also find the universal property of the right division under the name curryRan and uncurryRan in that module.\n\nOne formulation of Galois connections can be found in the adjunctions file. Galois Connections are very slick, but I\u2019m running out of steam, so let\u2019s leave that one for another day.\n\n### Properties and Proofs\n\nWe can prove many properties about these relational operations. Here a a random smattering that we showed using quickcheck last time.\n\n### Odds and Ends\n\n\u2022 Recursion Schemes \u2013 Recursion schemes are a methodology to talk about recursion in a point free style and where the rubber meets the road in the algebra of programming. Here is an excellent series of articles about them. Here is a sample of how I think they go:\n\u2022 Higher Order Relations?\n\u2022 Examples of use. Check out the examples folder in the AoP Agda repo. These are probably translatable into Haskell.\n\u2022 Interfacing with Singletons. Singletonized functions are a specialized case or relations. Something like?\n\u2022 A comment to help avoid confusion. What we\u2019ve done here feels confusingly similar to profunctor, but it is in fact distinct I think. Profunctors are described as a categorical generalization of relations , but to be honest, I kind of don\u2019t get it. Despite many of our constructions appearing in the profunctor package, the profunctor typeclass itself appears to not play a role in our formulation. There just isn\u2019t a good way to dimap under our relations as written, unless you construct free profunctors. Converse at the least is a wrench in the works.\n\u2022 Star and graphs. Transition relations are a powerful methodology. A transition relation is in some respects the analog of a square matrix. We can iteratively compose it with itself.\n\n## CAV 2019 Notes: Probably Nothin Interestin\u2019 for You. A bit of noodling with Liquid Haskell\n\nI went to the opening workshops of CAV 2019 in New York this year (on my own dime mind you!) after getting back from joining Ben on the long trail for a bit. The tutorials on Rosette and Liquid Haskell were really fun. Very interesting technology. Also got some good ramen and mochi pudding, so it\u2019s all good. Big Gay Ice Cream was dece.\n\n## Day 1 workshops\n\nCalin Belta http:\/\/sites.bu.edu\/hyness\/calin\/.Has a new book. Control of Temporal logic systems. Automata. Optimized. Partition space into abstraction. Bisimulation https:\/\/www.springer.com\/gp\/book\/9783319507620\n\nControl Lyapunov Function (CLF) \u2013 guarantees you are going where you want to go\n\nControl Barrier Function \u2013 Somehow controls regions you don\u2019t want to go to.\n\nLyapunov function based trajectory optimization. You somehow have (Ames 2014) http:\/\/ames.gatech.edu\/CLF_QP_ACC_final.pdf Is this it?\n\nDifferential flatness , input output linearization\n\nTemproal logic with\n\n#### Rise of Temporal Logic\n\nLinear Temporal Logic vs CTL\n\nFixpoint logic,\n\nBuchi automata \u2013 visit accepting state infinite times\n\nequivalency to first order logic\n\nmonadic logic, propositions only take 1 agrument. Decidable. Lowenheim. Quantifier elimination. Bounded Mondel property\n\nLanguages: ForSpec, SVA, LDL, PSL, Sugar\n\nmethod of tableau\n\nPolytopic regions. Can push forward the dynmaics around a trajectory and the polytope that you lie in. RRT\/LQR polytopic tree. pick random poitn. Run.\n\nEvauating branching heuristics\n\nbranch and prune icp. dreal.\n\nbranch and prune. Take set. Propagate constraints until none fire.\n\nbranching heuristics on variables\n\nlargest first, smearing, lookahead. Try different options see who has the most pruning. Non clear that helped that muhc\n\nQF_NRA. dreal benchmarks. flyspeck, control, robotics, SMT-lib\n\nhttp:\/\/capd.sourceforge.net\/capdDynSys\/docs\/html\/index.html\n\n#### Rosette\n\nverify \u2013 find an input on which the assertions fail. exists x. not safe\n\ndebug \u2013 Minimal unsat core if you give an unsat query. x=42\/\\ safe(s,P(x))\\$ we know thia is unsat because of previous step\n\nsolve \u2013 exists v si.t safe(v)\n\nsynthesis \u2013 exists e forall x safe(x,P(x))\n\ndefine-symbolic, assert, verify, debug, solve, sythesis\n\nRosette. Alloy is also connected to her. Z Method. Is related to relational logic?\n\nhttps:\/\/homes.cs.washington.edu\/~emina\/media\/cav19-tutorial\/index.html\n\nhttp:\/\/emina.github.io\/rosette\/\n\nBuilding solver aided programming tool.\n\nsymbolic compiler. reduce program all possible paths to a constraint\n\nCling \u2013 symbolic execution engine for llvm\n\nimplement intepreter in rosette\n\nSymbolic virtual machine\n\nlayering of languages. DSL. library (shallow) embedding. interpreter (deep) embedding.\n\ndeep embedding for sythesis.\n\nI can extract coq to rosette?\n\nhow does it work?\n\nreverse and filter keeping only positive queries.\n\nsymbolic execution vs bounded model checking\n\nsymbolic checks every possible branch of the program. Cost is expoentntial\n\nCBMC.\n\ntype driven state merging. Merge instances of primitiv types. (like BMC), value types structurally ()\n\ninstance Merge Int, Bool, Real \u2014 collect up SMT context\n\nvs. Traversable f => Merge (f c) \u2013 do using Traversable\n\nsymbolic union a set of guarded values with diskoint guard.\n\nmerging union. at most one of any shape. bounded by number of possible shapes.\n\nputs some branching in rosette and some branch (on primitives) in SMT.\n\nsymbolic propfiling. Repair the encdoing.\n\ntools people have built.","date":"2019-11-16 01:54:32","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\": 31, \"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\": 0.6567146182060242, \"perplexity\": 1114.8343930826643}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-47\/segments\/1573496668716.69\/warc\/CC-MAIN-20191116005339-20191116033339-00476.warc.gz\"}"}
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{"url":"https:\/\/zenodo.org\/record\/5565648\/export\/xd","text":"Journal article Open Access\n\n# Brain Tumor Classification and Segmentation Based on Morphological Operations using Image Processing Techniques\n\nKotha Tirumala Naga Sriveni; Madala Vani Pujitha\n\n### Dublin Core Export\n\n<?xml version='1.0' encoding='utf-8'?>\n<oai_dc:dc xmlns:dc=\"http:\/\/purl.org\/dc\/elements\/1.1\/\" xmlns:oai_dc=\"http:\/\/www.openarchives.org\/OAI\/2.0\/oai_dc\/\" xmlns:xsi=\"http:\/\/www.w3.org\/2001\/XMLSchema-instance\" xsi:schemaLocation=\"http:\/\/www.openarchives.org\/OAI\/2.0\/oai_dc\/ http:\/\/www.openarchives.org\/OAI\/2.0\/oai_dc.xsd\">\n<dc:contributor>Blue Eyes Intelligence Engineering & Sciences Publication (BEIESP)<\/dc:contributor>\n<dc:creator>Kotha Tirumala Naga Sriveni<\/dc:creator>\n<dc:date>2020-04-30<\/dc:date>\n<dc:description>Brain Tumour is the solitary cause for the assassination of many individuals. A brain tumour is an accretion or widening of isolated cells in your brain. It can be identified by several tests like MRI (Magnetic Resonance Imaging), CT (Computer Tomography) scan along with several tests like biopsy, spinal tap etc. Classification and Segmentation activity take part a significant role in interpretation of brain tumours. In this paper the images should be taken in the form of jpeg format. The images are processed using data mining and machine learning classification methods. Previous research studies are intended as long as identifying brain tumours using dissimilar classification and segmentation approaches. The initiated system consists of certain process for recognition of the tumour. The first step is about Pre-processing and the next is about segmentation, Feature extraction is the third step in this process and Classification is used to detect the tumour. Morphological Operations are performed in this process based on the tumour size, shape and colour. Neural Network is used for classification along with -Support Vector Machine (SVM) classifiers are worn for structured recognition. Due to this we can reduce the inappropriate or false diagnosis error rate of brain tumour identification for the patients and also, we can get faster and accurate results.<\/dc:description>\n<dc:identifier>https:\/\/zenodo.org\/record\/5565648<\/dc:identifier>\n<dc:identifier>10.35940\/ijeat.D8319.049420<\/dc:identifier>\n<dc:identifier>oai:zenodo.org:5565648<\/dc:identifier>\n<dc:language>eng<\/dc:language>\n<dc:relation>issn:2249-8958<\/dc:relation>\n<dc:rights>info:eu-repo\/semantics\/openAccess<\/dc:rights>\n<dc:source>International Journal of Engineering and Advanced Technology (IJEAT) 9(4) 8384-2388<\/dc:source>\n<dc:subject>Brain Tumor, Computer Tomography, Diagnosis, Magnetic Resonance Imaging, Neural Network.<\/dc:subject>\n<dc:subject>ISSN<\/dc:subject>\n<dc:subject>Retrieval Number<\/dc:subject>\n<dc:title>Brain Tumor Classification and Segmentation Based on Morphological Operations using Image Processing Techniques<\/dc:title>\n<dc:type>info:eu-repo\/semantics\/article<\/dc:type>\n<dc:type>publication-article<\/dc:type>\n<\/oai_dc:dc>\n\n13\n13\nviews","date":"2022-05-20 06:56:53","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\": 0.2483660876750946, \"perplexity\": 4786.731824130464}, \"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\/1652662531762.30\/warc\/CC-MAIN-20220520061824-20220520091824-00007.warc.gz\"}"}
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A wide selection of elegant fine bone china teacups and saucers available in large and small sizes. Treat yourself to the perfect cup of tea out of one of our fine bone china tea cups. They make a lovely gift for a friend or a treat for yourself. The tea cup comes in two sizes. The small size has a capacity of 275ml and stands 7.8cm high. The large Teacup size has a capacity of 450ml and stands 8.7cm high. Perfect for a truly indulgent cup of tea or coffee! Create a smart tea set with a matching Sophie Allport Teapot.
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The Nicholas Effect
Nicholas' story
Places for Nicholas
Category Archives: Book: 87 and Still Wandering About
Children, Once Too Ill to Walk Across a Room, Take to the Ski Slopes
High in the Swiss Alps, in the little town of Anzere, 34 children from around the world, aged 6 to 17, were preparing to ski down a 45 degree slope in a revered competition that at one time none of them could have dreamed of being in.
It was a perfect day for the climax of the World Winter Transplant Games: the Nicholas Cup.
The weather was calm and clear, the sun dazzling on the pure white snow. The course was treacherous, however, hard ice in places, difficult to dig in the edges of the skis to cut the angles round the gates and more difficult than for the usual run of skiers because, a week earlier, none of these children had ever been on skis. Until then, some – such as those from Tunisia, Hong Kong and Israel – had never seen snow. "I falled over a few times at first," one small face said proudly. "But I'm alright now."
Day 1: First hesitant steps.
But the real challenge was of an order of magnitude greater than all that. All of them had once been so ill that their only cure was an organ transplant: a new heart or liver, kidneys or lungs to replace the ones that were dying inside them.
Some had been desperately sick at birth – yellow or blue or a lurid shade of green. One had kidneys the size of peas. A third had to be fed through a tube and, says his mother, "for the first two years he never laughed." Some could not walk across a room without stopping for breath. Others had lived normal lives, until felled by a virus that at first seemed no more severe than a headache. The first that one father knew of a problem was a scream in the night as one of his daughters heard her younger sister collapse on the floor and then kept her alive for forty minutes as the ambulance crew talked him through the CPR procedure.
For many of these children any form of exercise, let alone a competition mixing risk with athletic agility, was physically impossible. On top of that the years of dependence could have eaten away fatally at their self-confidence. Yet, on the day of the race, one by one the little figures appeared at the starting gate, high on the mountainside. Some came down with what the commentator charitably called "a racing snowplow" style and one or two held on to the instructors. But most tackled the course with assurance and a few with insouciance.
Day 7: "What's the problem?"
The triumph, however, was collective: these are not sickly lives prolonged by an experimental medical procedure but children who, if anything, perform better than other kids because they exercise and eat more healthily and, having learned at close quarters how precious life is, are determined to make the most of it.
The competition was started by a liver recipient, Liz Schick, a British-born mother of two living in Switzerland who, like so many recipients, wanted to say 'thank you' to the world and has done it in an unforgettable way. As one 15-year old girl, who had a transplant when she was 2, and has been shunted between homes to wherever the appropriate medical treatment could be obtained, said afterward to her mother, "This was the best thing I ever did."
From Reg Green's book "87 And Still Wandering About." 2016. www.authorhouse.com.
Filed under Book: 87 and Still Wandering About, Events, Nicholas' Cup, Nicholas' story, Stories
Organ Donation Leaps Over the World's Biggest Barrier
I have just spent a week in the company of a man whose experiences throw a fresh light on the Israeli-Palestine conflict. He is Ismael Khatib, the 46-year-old father of Ahmed, a 10- year old boy who was shot six years ago, in the tense West bank city of Jenin, by an Israeli soldier who, on a day of rioting, saw him among a group of other boys holding what looked like an automatic rifle. It turned out to be a plastic model.
Ahmed was taken to the Rambam hospital in Haifi where he was declared brain dead. The doctors then did what their counterparts in hospitals all over the world now do routinely. They asked Ismael and his wife, Abla, if they would donate their son's organs to whoever was at the top of the waiting list, which is compiled regardless of race or religion. The Khatibs consulted their religious leaders — who signaled their agreement – and their donation leapt what is probably the most bitterly-divisive barrier in the world, Ahmed's organs going to six Israelis, all of them small children, four of them Jews. I met Ismael when we were together on a tour of Eastern Canada which included talks with Muslim, Jewish and Christian communities. It was arranged by George Marcello of Toronto, who has had two liver transplants and has walked across Canada carrying a torch – subsequently blessed by Pope John Paul II — to tell everyone who will listen that tens of thousands of people around the world die every year because of the shortage of donated organs. George, lion-hearted in determination and achievement, is one of those remarkable recipients who cannot rest until they have paid back everything they can think of to a world that has shown them such unexpected selflessness.
In the hate-filled atmosphere of the Palestinian question, where every action is weighed by the committed on both sides to see what propaganda can be wrested from it, the implications of saying 'yes' to organ donation are profoundly ambivalent. Some Palestinians are embittered about Ahmed's organs going to Jews. Many others are using the donation quite cynically as a way of claiming a moral ascendancy over their enemies and advancing their cause in its wake. Given the intensity of the conflict, everyone involved can be presumed to have mixed emotions.
But what is perfectly clear is that to take the organs of a dead person, put them in the bodies of several others who are dying and out of that produce a crop of healthy lives is a triumph for humanity.
Yael Gladstone, seen here at Niagara Falls, is the sister of Yoni Jesner, a Jewish pre-medical student from Glasgow who was killed when a Palestinian suicide bomber blew up the bus he was traveling on when visiting Tel Aviv. Next to her is Khaled Khatib from the Palestinian town of Jenin, whose ten-year old brother, Ahmed, was shot by an Israeli soldier who thought the plastic replica of an assault gun he was holding was real. Both families donated their son's organs. One of Yoni's kidneys went to a seven-year old Palestinian girl. Six of Ahmed's organs went to young Israeli children, four of them Jews. Yael and Khaled are holding the Torch of Life that George Marcello, a Canadian who has had two liver transplants, has single-handedly made an international symbol of the power of organ donation to bridge even the world's most bitter divisions. He has walked across Canada carrying it, showing it in hundreds of towns and villages, and took it to Rome, where Pope John Paul II blessed it.
We can hope too that transplantation, with its ability to scrupulously avoid discrimination, will also be a stepping stone in bringing the whole world a little closer together. Since meeting Ismael I often think of Yoni Jesner, a 19-year-old Scottish Jew, who was killed by a suicide bomber in Tel Aviv in 2002 and one of whose kidneys went to a seven-year-old Palestinian girl.
The closing event on our tour added one more dimension, a talk to the governing council of an aboriginal community, the kind of society that from time immemorial has believed that tampering with the body is taboo. Now, it turns out, almost all of them have signed donor cards. For them also a medical miracle has modified the beliefs of all those accumulated generations and life has trumped death.
(From "87 And Still Wandering About" )
Filed under Book: 87 and Still Wandering About, Stories
April 13, 2016 · 11:31 am
Blind for 48 Years, He Can See Again
On the day after Christmas 1944, in a corner of what became one of the most fiercely fought battles of World War II, a German mine blew up in Sergeant Harold Urick's face. It left him totally blind and he stayed that way for 48 years.
Harold's unit, the 303rd Engineers, had just crossed the redoubtable German defensive barrier, the Siegfried Line, when they were ordered to dig up and defuse mines.
He remembers every detail. "It was a bitterly cold day and the ground was frozen hard. There was a man on each side of me as we moved forward. I saw the mine – it was one of the small ones they used, just about a quarter pound — and began digging it up very carefully with my bayonet. Suddenly I slipped on the icy ground. There was an explosion and everything went dark. I put my hands on my face. 'My God, I thought, what am I going to do now?'
"Most of all in those early days, I worried about Jean. I was 21 and we'd been married just over a year. I thought of it over and over. Instead of the life we'd dreamed of when the war was over, I was going to be a burden to her all her life."
He was flown to a military hospital in Valley Forge and then back home to Cleveland. One eye was so badly damaged that it to be taken out and a prosthetic one put in its place. With the other he could see just a patch of light.
He spent two years in a therapy school and then, with the dogged courage that has defined his life, started a physical therapy business of his own. "But people weren't as affluent then and it didn't take," he says. He worked for several years at the Cleveland Clinic and then for another 15 at a snack bar managed by the Cleveland Sight Center.
In the meantime, he and Jean had five children and seven grandchildren, none of whom he had ever seen. The family was central to his life. He went to almost every high school and college football game his son, Jeff, played in. "My wife would tell me what was going on. I just wanted to be there."
But his sight didn't improve. "I went to three or four ophthalmologists over the years but all of them said they couldn't do anything for me. Then one day in 1992 I was listening to a television program and I heard a doctor talking about transplanting corneas. I didn't know what to think but I went back to the eye doctors. They weren't encouraging until one of them said, 'I know a doctor who does these. I think you should go to him.'
"That's how I met Dr. Philip Shands at Kaiser Permanente. 'Yes,' he told me, 'I do these. Do you want to try?' 'You bet,' I said. 'What do I have to lose?'"
Shands had then been in practice for only a year or two and was unsure himself about how much he could help. "The prosthetic eye we could do nothing about, of course. But when I examined the other one, I could see a small bit of the iris which, when we shone a light on it, constricted a little. Then, using ultrasound and other tests, it appeared as though the retina and other structures inside the eye were intact."
With this encouragement, Harold was put on the waiting list and told it would probably take three or four months before they had a cornea for him. "You might think I'd be on pins and needles all that time but I wasn't. Most of the time I didn't think about it, probably because he exuded so much confidence," he recalls.
Just before Thanksgiving, he was called in and, with great care, Shands removed the badly damaged cornea and other scarred tissue, implanted an artificial lens to focus the light and sewed in the donated cornea. In about an hour it was all over, Harold remembers. "'Are you done?' I asked him. 'Yep,' he said 'but you'll have to wait until tomorrow morning when we remove the bandages.'
"The next day, when he began to take them off, I was lying face down on the bed and the first thing I saw were his shoes – the first things I'd seen in 48 years – then his pants. I looked up and saw he was wearing glasses. It was still a bit fuzzy, but they'd warned me it would take a while.
"Then I looked down the bed and there was Jean, looking as pretty as she did when I first met her. Then I looked at Yvonne, my oldest daughter. It was the first time I'd ever seen her face. And she was beautiful, too."
He had some shocks too, such as how big airplanes had become and how fast cars went. In a few months his sight had improved so that he could pass the driver's test and read just about anything he wanted. "Since then we've only had to fine-tune the prescriptions for his glasses, just like any normal aging person," Shands says. "With them on he has 20/25 vision. Like all corneal recipients, he takes small amounts of immune-suppressants but has never had a period of rejection."
The other patients Shands treats have much less dramatic stories. "This was a once-in-a-career case," he says. "But vision is the faculty people fear losing most and, with success rates of over 90 percent for those who are legally blind, cornea transplants reopen a world they thought they had lost forever."
All his life Harold has treasured the little things. Now it's being able to walk through a restaurant to find a table or waving at friends across the street. He can still see with only one eye but goes to baseball games regularly and doesn't need a running commentary. And at 86, he still bowls and plays golf.
"But best of all is being able to see the whole family," he says. "That was the hardest thing all those years. Now I have everything I want."
From "The Gift that Heals," by Reg Green, published by AuthorHouse, 2007, (www.authorhouse.com).
Child Killed at Random Gives Sight to Others
Roxanna Green is the mother of Christina-Taylor Green, the 9-year-old girl who was killed when a gunman fired into the crowd at an outdoor meeting for Congresswoman Gabrielle Giffords in Tucson in 2011. She remembers, as in a nightmare, her daughter covered with a sheet and she, beside her, kissing her face and stroking her feet, willing her to live.
But, even as she and her husband, John, grappled with the enormity of their loss, they found the strength to donate her corneas, restoring the sight of two people, for whom there was no other cure. The child, born on one day of indiscriminate killing, September 11, 2001 – '9/11' – and dying on another, gave the nation a reason to believe that, even in the most heart-wrenching circumstances, selflessness can overcome senselessness.
Shot at random: Christina-Taylor Green with her mother, Roxanna.
(Courtesy: the Green family)
Filed under Book: 87 and Still Wandering About, Stories, Uncategorized
The Seven-Year Old Policeman
Six-year old Noah Michael Davis of Shawnee, Kansas. wanted to be a policeman so he could make sure "everyone was safe." He didn't make it. Instead, he drowned in the family swimming pool and was declared brain dead. Although he couldn't help everyone, his family did donate his kidneys, giving two very sick people their lives back. On what would have been his seventh birthday, he was sworn in as an honorary police officer.
Noah Davis, Honorary Police Officer
(Courtesy: the Davis family)
Nicholas is remembered… in every Bioethics class
In the news: "Transplants, that gift from Nicholas' and Rolly's parents that saved lives" (from 'Il Corriere della Sera')
Organ Donations Set a Record at India's Biggest Hospital
Maria Pia, Dying at 19, Is Now a Radiant 47-Year Old
Twenty-eight Years Later: Where Are Nicholas' Killers?
From "La Stampa" Italian newspaper
Organ Donation Group Comforts Families Who Didn't Donate
"For 27 years, organ donation has been boosted by 'the Nicholas effect'"
Indian girl (6) shot, parents donate organs
Tel U on "For 27 years, organ don…
Michele San Pietro on Twenty-eight Years Later: Wher…
Shirley Sinclair on If I have a transplant, will I…
alice giovanninetti on A Letter to the Italian People…
હરીશ દવે (Harish Dav… on My son died in 1994 but his he…
American Heart Association (AHA)
Book: 87 and Still Wandering About
Nicholas' Cup
Nicholas' Gift movie
Nicholas' story
Places named for Nicholas
The Gift That Heals
View NicholasGreenFoundation?fref=ts's profile on Facebook
View UCMptQvk7qrLp9Z_YiQWpYPQ's profile on YouTube
Follow The Nicholas Effect on WordPress.com
Reg Green
Reg Green was the chief business writer for the London Daily Telegraph and a freelance commentator for the BBC. Although he specialized in economics, he wrote in his spare time for almost every section of the newspaper, including being the newspaper's jazz critic, writing travel articles, obituaries, book reviews and soccer. After emigrating to the United States he founded and edited Mutual Fund News Service, an investment newsletter. He is the father of Nicholas Green, a seven-year old California boy who was shot in an attempted car jacking while on a family vacation in Italy in 1994. The killing became a worldwide news event when Reg and his wife, Maggie, donated their son's organs to seven very sick Italians, four of them teenagers. They went on to found the Nicholas Green Foundation (https://www.nicholasgreen.org) to promote organ donation to save some of the tens of thousands of deaths around the world caused every year by the failure of one organ that could have been replaced by a donated one.
The Children's Bell Tower (1996) – Sculptor: Bruce Hasson. Location: Bodega Bay
The Nicholas Effect · A Boy's Gift to the world
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\section{Introduction}\label{sec_intro}
It is now generally believed that super-massive black holes reside
in the center of active galactic nuclei (AGNs; Lynden-Bell 1969).
Through accretion of gas, AGNs release vast radiant energy,
including high-energy ionizing photons, from an accretion disk
around the black hole (Rees et al. 1984). The radiation
photoionizes and heats surrounding gas so that it is able to leave
its imprint, for example broad emission line (BEL) and broad
absorption line (BAL), on the emergent continuum spectra emitted
by accretion disk (Davidson \& Netzer 1979; Osterbrock 1989;
Weymann et al. 1991). The observed properties of these lines, such
as strength, width, and profile, are determined by the combined
effects of various physical processes. Hence, studies of these
line features can reveal the physical conditions and processes in
the central region of AGNs, and further shed light on the
accretion and radiation mechanisms, and the co-evolution of black
holes and their host galaxies.
The broad emission line region (BELR) is the most studied
structure of AGNs. Extensive efforts had been devoted to probing
its structure and kinematics, which are important for estimation
of black hole masses and understanding of line formation.
Velocity-resolved reverberation mapping of several local AGNs
shows that there is no significant difference in the temporal
response of the blue and red parts of the BELs to variations in the
continuum (Gaskell 1988; Koratkar \& Gaskell 1991; Korista et al.
1995; Done \& Krolik, 1996; O'brien et al. 1998). These studies demonstrate
that the predominant motion of the BELR is either Keplerian or
virial motion, both driven by the gravity of the central black
hole (see Gaskell 2009, for a review). Further robust evidence
supporting this view is given by the correlation between the BELR
size and line width in the form $r \propto \sigma^{-2}$ for
various emission lines found in a few well-studied AGNs (Krolik et
al 1991; Peterson \& Wandel 1999; 2000; Onken \& Peterson 2002).
This correlation is readily expected for gravitation dominated
kinematics. Particularly, these works showed that the emitting
regions of both high- and low-ionization lines (e.g. \civ\ and
\hb) are gravitationally bound.
However, studies of luminous AGNs at high redshifts uncover quite
different behaviors of the BELR, especially the high-ionization
line (e.g. \civ) region. Gaskell (1982; see also Wilkes 1984;
Marziani et al. 1996) found that the peak of the \civ\ line tends
to be blueshifted with respect to the peak of low-ionization lines
in a small sample of high-redshift AGNs. This was confirmed by
Richards et al. (2002; also Vanden Berk et al. 2001) using a large
sample of AGNs selected from the Sloan Digital Sky Survey (SDSS;
York et al. 2000). Subsequently, the \civ\ blueshift was detected
in several low-luminosity AGNs (e.g. Leighly \& Moore 2004).
The blueshift is difficult to
reconcile with gravitationally bound BELR models, but is
considered as a signature of outflowing gas (Gaskell 1982;
Marziani et al. 1996; Leighly 2004). Outflow models based on
dynamical and photoionization calculations have been put forward
to reproduce the observed line profiles, equivalent widths and
line ratios, and further imposing constraints on the density,
ionization state and geometry of the line emitting gas (e.g.
Murray \& Chiang 1997; Leighly 2004; Wang et al. 2009b). In fact,
the frequent occurrences of blueshifted narrow absorption lines
and BALs in AGN spectra have proved that outflow is ubiquitous in
AGN (Weymann et al .1991; Crenshaw, Kraemer \& George 2003).
Outflow is therefore a natural interpretation of blueshift of
high-ionization lines.
Although there have been a few attempts to tune one single model,
i.e. outflow or gravitationally bound BELR, to simultaneously
account for the contradictory observational results in
reverberation-mapped objects and blueshifted \civ\ AGNs (e.g.
Chiang \& Murray 1996; Gaskell \& Goosmann 2008), the dramatic
inconsistency may indeed manifest fundamental differences in the
structure and kinematics of these two line emitting regions. If
this is the case, it would be interesting to find out what causes
such differences. Previous studies have already provided some
meaningful observational constraints on the underlying processes.
For example, it is well known that the blueshift of the \civ\
emission line in radio quiet AGNs is, on average, stronger than in
radio loud AGNs (Marziani et al. 1996; Sulentic et al. 2000a;
Richards et al. 2002; 2011). Recently, several studies found that
the \civ\ blueshift decreases with the increase of the X-ray to UV
flux ratio (Gibson, Brandt \& Schneider 2008; Richards et al.
2011). In addition, Sulentic et al. (2007) found that the
correlation between the width and equivalent width of the \civ\
BEL varies dramatically with the width of the \hb\ BEL. Richards
et al. (2011) found that \civ\ blueshift varies with the ionizing
spectral energy distribution. All these facts point towards that
BELR structure is related to the accretion process of the central
engine.
It is worthwhile to note that the low-ionization lines, such as
\mgii\ and \hb, are fairly close to the systemic redshift
(Marziani et al. 1996; Sulentic et al. 2000a; Richards et al.
2002). Apparently different from the high-ionization lines, the
low-ionization line region is gravitationally bound, and outflow
model is unlikely. This is supported by the fact that local AGNs
follow the same luminosity-BELR size relationship for the \hb\
line as for those well-studied AGNs, whose BELR have been
demonstrated to be governed by gravity (Kaspi et al. 2005; Bentz
et al. 2006). In particular, the power-law slope of this
relationship is about 0.5, indicating that all of these AGNs have
roughly the same ionization state and gas density in the
low-ionization lines region. The \hb\ and \mgii\ lines are
therefore widely adopted to estimate the black hole masses, \mbh,
of AGNs (Kaspi et al. 2000; Collin et al. 2006; Vestergaard \&
Peterson 2006; Mclure \& Jarvis 2002; Onken \& Kollmeier 2008;
Wang et al. 2009a). The \mbh\ estimate is plagued by many
uncertainties in, for example, the geometry, kinematics and
inclination of the BELR, the measurement of line with, the
influence from other forces (such as radiation pressure), the
validity of extrapolating the small-sample results to a large
sample (Krolik 2001; Collin et al. 2006; Marconi et al. 2008;
Richards et al. 2011). Although the \mbh\ estimate can be
calibrated using the correlation between \mbh\ and bulge/spheroid
stellar velocity dispersion (e.g. Onken et al. 2004), it is
accurate only from a statistical point of view.
In this paper, we probe the structure and kinematics of the
high-ionization line emitting region via a comparison with the
low-ionization lines. We use the \civ\ line, the most prominent
metal line, to represent high-ionization lines, while we adopt \mgii\
as a representation of low-ionization lines. Both lines are
observable in SDSS AGNs at redshift $z\sim2$, from which a
sufficiently large sample can be obtained for our purpose. Please
see Section \ref{sec_sam} for the sample selection. We present in
Section \ref{sec_c4b} the correlations between the properties of
\civ\ line, and the composite spectra. In Section \ref{sec_mc}, we
examine whether the \civ\ and \mgii\ line properties follow the same
correlations. Similarity in the correlations indicates that two
lines come from regions with similar kinematics, while opposite
results mean that the structures are different. Our method differs
from earlier investigations, in which the authors directly
compared the properties of the two lines. Then, in Section
\ref{sec_dis}, we analyze the geometry and kinematics of the \civ\
region and discuss the candidate models. We also present a
comprehensive comparison between BAL and the blueshifted \civ\ BEL.
Finally, we summarize our results in Section \ref{sec_sum}.
\section{Sample and Data Analysis}\label{sec_sam}
We select AGNs in the redshift range $1.7<z<2.2$ from the Fifth
Data Release (DR5) of SDSS spectroscopic database (Schneider et
al. 2007). The redshift range is chosen in such a way that both the \civ\ and
\mgii\ lines fall in the wavelength coverage of the SDSS
spectrograph. To ensure reliable measurements of emission line
parameters, we only select objects with median signal-to-noise
ratio (S/N)$\geq$ 7 per pixel in both the \civ\ (1450-1700 \A) and
the \mgii\ (2700-2900 \A) spectral regions. We further discard the
broad absorption line AGNs as cataloged by Scaringi et al. (2009).
6009 AGNs meet these criteria. The SDSS spectra are corrected for
the Galactic extinction using the extinction map of Schlegel et
al. (1998) and the reddening curve of Fitzpatrick (1999), and
transformed to the rest frame using the improved redshifts for
SDSS AGNs as computed by Hewett \& Wild (2010, hereafter HW10). To measure the
broad lines, we perform continuum and emission-line fitting using
Interactive Data Language (IDL) code based on MPFIT (Markwardt
2009), which performs $\chi^2$-minimization by the
Levenberg-Marquardt technique.
The \mgii\ broad lines are fitted using the exactly same method
as Wang et al. (2009a). Here we only present a brief
description of the procedures. First, we simultaneously fit the
featureless continuum (assumed to be a power law) and the \feii\
multiplet emission, which together constitute the so-called
pseudocontinuum. \feii\ is modelled with the tabulated
semi-empirical template generated by Tsuzuki et al. (2006) based
on their measurements of I ZW1; in the wavelength region covered
by the \mgii\ emission, this template uses the calculation with
the CLOUDY photoionization code (Ferland et al. 1998). After
subtracting the fitted pseudocontinuum, the broad components of
the \mgii\ $\lambda\lambda$2796, 2803 doublet lines are each
modelled with a truncated five-parameter ($p_i$, i=0 to 4) Gauss-Hermite series
profile (van der Marel \& Franx 1993). The expression for a Gauss-Hermite function is
\begin{eqnarray}
&{\rm G_h}(x)=p_0e^{-x^2/2}[1+p_3h_3(x)+p_4h_4(x)],\nonumber\\
&h_3(x)=\frac{1}{\sqrt{6}}(2\sqrt{2}x^3-3\sqrt{2}x),\nonumber\\
&h_4(x)=\frac{1}{\sqrt{24}}(4x^4-12x^2+3).\nonumber
\end{eqnarray}
where $x=(\lambda-p_1)/p_2$. The narrow component of each line is fitted with a single Gaussian. The full width at half
maximum (FWHM) is measured from the Gauss-Hermite model of \mgii\
$\lambda$2796, and rest equivalent width (EW) is the sum of the
broad doublet lines.
To measure the \civ\ broad lines, we first fit the local
continuum with a power-law in two wavelength windows near 1450\A\
and 1700\A, that have little or no contamination from
emission-lines. After subtracting the continuum, we fit the
residual spectrum around \civ\ with two Gaussians. Since the red
wing of \civ\ is contaminated by \heii, only the spectral region
of 1450-1580\A\ is considered in fitting the \civ\ line. We also
attempted to fit the residual spectrum with three Gaussians, which
results in little or no significant improvements.
We thus adopt the two-Gaussian model here.
In this work we introduce a blueshift and asymmetry index (BAI) to
measure the deviation of the \civ\ line from an unshifted and
symmetric profile. BAI is defined as the flux ratio of the blue
part to the total profile, where the blue part is the part of
\civ\ line at wavelengths short of 1549.06\A, the laboratory
rest-frame wavelength of \civ\ doublets. The line parameters, BAI,
FWHM and EW, of \civ\ are measured from the composite profiles of
the two-Gaussian model (in the wavelength range of 1450-1700\A).
The BAI estimation may be affected by the accuracy of the
redshifts which we use to transform the observed spectra to the
rest frame. To reduce possible uncertainty of BAI thus introduced,
we adopt the redshifts provided by HW10\footnote{More recently,
Richards et al. (2011) also used these redshifts to compute the
\civ\ line shift. They found that the resultant line-shift is
consistent with the shift with respect to the low-ionization line
\mgii, which is often used in the literature.}, which were derived
by cross correlation of observed spectra with a
carefully-constructed template. In particular, they corrected for
the dependence of emission-line shift on luminosity and redshift,
which is relevant to our investigation. BAI measures the combined
effects of the asymmetry and shift of a line profile, which are
generally treated separately in the literature (e.g. Sulentic et
al. 2000a). In the Appendix we consider line shift and asymmetry
separately and conclude that using BAI is a robust choice for our
purposes. We use blueshift and BAI alternately in this paper.
The fitting results for most of the objects are reasonable
according to our subsequent visual inspection. However, a small
fraction of objects display strong narrow absorption in the
emission lines regions, especially \civ\ spectral region, and cannot
be well fitted by our automated processing. To minimize
outliers left by the procedures, we eliminate objects with
unacceptable fitting, i.e. $\chi^2/$d.o.f$>1.5$. This restriction
leads to a final working sample of 4963 AGNs. We note that the last selection
has little or no effect on the results obtained in this paper.
\section{Blueshift of \civ\ Emission Line}\label{sec_c4b}
We show the distribution of BAI for the entire sample in Fig.
\ref{fig_udis}. This parameter distributes in a wide range, from
about 0.4 to more than 0.9, with a median value of 0.63. According
to our definition of BAI, a blueshifted line has a BAI parameter
larger than 0.5. Obviously, most of the AGNs in our sample display
blueshifted \civ\ emission lines with respect to their
systemic redshifts, in agreement with previous findings (Gaskell
1982; Richards et al. 2002). Only 7.2\% of the AGNs are
redshifted outliers. This fraction is the same as that found in
Richards et al. (2011), in spite of that we adopt a different method to
denote the blueshift. Since the blueshifted \civ\ line has been
suggested to be emitted from outflows (e.g. Gaskell 1982; Murray
\& Chiang 1997; Leighly 2004), the BAI distribution suggests that
outflows are common in AGNs.
We then show the equivalent width of \civ\ as a function of BAI
and FWHM(\civ) in the two upper panels of Fig. \ref{fig_uwe}. The
\civ\ emission line is weaker for AGNs with larger blueshifts or
line widths. Both two trends are consistent with previous results.
Richards et al. (2011) found an anti-correlation between blueshift
and equivalent width (see also Marziani et al. 1996; Leighly \&
Moore 2004), and Wills et al. (1993) reported an anti-correlation
of FWHM with EW. The left panel of Fig. \ref{fig_uf} shows
FWHM(\civ) against BAI. Our result confirms the finding of
Richards (2006) that the line width of \civ\ is, on average,
slightly larger for AGNs with larger blueshifts. Inspecting the
scatter plot in detail, one can find that the trend is complex and
there appears to exist a `V'-shaped lower envelope. It implies a
mixture of origins of the \civ\ emission. We will come back to
this issue later.
Composite spectra can provide a wealth of diagnostic information.
We show the composite spectra as a function of BAI in Fig.
\ref{fig_cs1}. Our composites are constructed through the
arithmetic mean method. We first sort the AGN sample according to
their BAI then sub-divide it into four equally-sized subsamples
(each subsample contains about 1241 AGNs). For each AGN, we use
the redshift from HW10 to deredshift the
spectrum. The spectrum is then normalized at 1450\A, rebinned into
the same wavelength grids. The composite spectra are created by
combining these normalized spectra in each of these subsamples.
Only four major emission line regions, \siiv, \civ, \ciii\ and
\mgii, are presented. The spectra are normalized in the
local continuum regions: (1355,1450),
(1450,1700), (1830,1975), (2695,2955) (in units of \A) for \siiv,
\civ, \ciii\ and \mgii.
As expected, the \civ\ emission line in our composites shifts
significantly towards shorter wavelength as BAI increases. The
equivalent width of \civ\ decreases with increasing BAI,
consistent with Fig. \ref{fig_uwe}. The blueshift is also
remarkable for \heii\ and moderate for \siiv, but seems to be
absent in lower-ionization lines, such as \mgii\ and \aliii, in
good agreement with Richards et al. (2002). We also create
composites as a function of EW(\civ) and BAI, following Richards
et al. (2011). The composites are very similar to that shown in
Richards et al. This is not surprising since we use the same AGN
redshifts provided by HW10. Our composites reveal a significant
excess flux in the blue wing of \civ\ (around 1500 \A), the
strength of which increases with BAI (Fig. \ref{fig_uwe}). We then
take the difference between the largest-BAI and smallest-BAI
composite spectra and show the difference as a function of
velocity with respect to \civ\ in Fig. \ref{fig_ex} (thick line).
The blue excess wing peaks at 8000\kms, ranging between
$\sim4000$\kms and 11000\kms.
Two additional phenomena are worth noting. First, the mean width
of \mgii\ tends to be narrower for AGNs with larger \civ\
blueshifts. We will address this issue in next section. Second,
the equivalent width of \aliii\ is dramatically boosted at large
BAI, different from other lines. Richards et al. (2011) paid
particular attention to the unusual property of the \aliii\ line.
They suggested that the strong \aliii, together with the large
\siiii/\ciii\ ratio, is indicative of an X-ray weak spectrum for
these AGNs. Although this explanation is reasonable, it might
simply be that \aliii\ is contaminated by other lines. One
possible contamination comes from the UV \feiii\ complexes. The
\feiii\ complexes are usually more prominent on the
long-wavelength side of \ciii (Laor et al. 1997). However, we do
not find the expected excess at the corresponding wavelength and
thus rule out this probability. Another promising explanation is
that this excess flux is the \ciii\ emission of the outflow. To
demonstrate this, we show the difference spectra of the
largest-BAI and smallest-BAI composites as a function of velocity
with respect to \ciii\ in Fig. \ref{fig_ex}(thin line). One can
find the average velocity of the `excess of \aliii' is about
8000\kms. This velocity is very similar to that of the blue wing
excess of \civ\, and thus supports our interpretation. Difference
spectra are usually sensitive to the normalization. To investigate
into this, we also try to use other local continuum regions. The
velocity ranges of the excess flux for both \civ\ and \ciii\
change only slightly.
The blueshifted \ciii\ component suggests that the number density
of the large-velocity part of the \civ\ BELR cannot be much larger
than $3\times10^{9}{\rm cm}^{-3}$, which is the critical density
of the intercombination line \ciii\ (Osterbrock 1989). This value
is consistent with that estimated by Wang et al.(2009b), but much
lower than that estimated by Ferland et al. (1992), about
$10^{11}{\rm cm}^{-3}$ (see also Kuraszkiewicz et al. 2000). The
discrepancy can be understood if there exist two kinds of \civ\
emitting region: a normal gravitationally bound BELR and an
outflow, as we will discuss in this paper. In fact, studies of
blueshifted absorption lines revealed quite low densities in
outflows (see Crenshaw et al. 2003 for a review). Moreover, the
column density of outflow can be constrained based on the absence
of blueshifted component in low-ionization line. For example,
Leighly (2004) performed photoionization calculation to model the
outflow components of various UV lines in two narrow-line Seyfert
1 galaxies and derived a rather low column density: $\log \colnh
\simeq 21.4$ for outflow gas. Leighly (2004) did not consider the
blueshifted \ciii\ component. If taking into account this
component, one may get a slightly larger column density. The lower
density and column density than the typical values of normal
emitting gas may be due to the expansion of outflow.
\section{Comparison of Kinematics of \mgii\ and \civ}\label{sec_mc}
In this section, we examine whether the \mgii\ and \civ\ line
properties follow the same correlations. Since \mgii\ is thought
to be emitted from a gravitationally bound BELR, the comparison
may offer insight into the kinematics and geometry of the \civ\
emitting region. Note that our method differs from earlier
investigations, in which the authors directly compared the
properties of the two lines.
\subsection{Correlations for \mgii\ and Fundamental Driver of \civ\ Blueshift}
We show the rest equivalent width of \mgii\ against BAI and
FWHM(\mgii) in the lower panels of Fig. \ref{fig_uwe}. Note that
the BAI presented here is calculated using \civ\ line. One can see
that EW(\mgii) declines with increasing BAI. The trend is similar
to but slightly weaker than \civ. Of particular interest is the
positive correlation between EW(\mgii) and FWHM(\mgii), which is
in contrast to \civ (Fig. \ref{fig_uwe}). We also found such a
correlation in a low-redshift AGN sample (Dong et al. 2009). The
opposite behaviors indicates that the properties of \mgii\ and
\civ\ emitting regions are essentially different.
The scatter plot of FWHM(\mgii) versus \civ\ blueshift is shown in
the right panel of Fig. \ref{fig_uf}. Here again, we find a
different correlation from \civ. AGNs with narrow \mgii\ BEL have
a strong tendency to exhibit \civ\ emission with prominent
blueshift. This trend is appreciable in previous work based on
small low-redshift samples. For instance, Bachev et al. (2004)
found the \civ\ blueshift can only be found in objects with
FWHM(\hb) less than 4000\kms. Baskin \& Laor (2005) found an
marginal correlation between \civ\ blueshift and FWHM(\hb) in 81
PG QSOs. Sulentic et al. (2007) used the centroid at half maximum
of \civ\ profile as a surrogate of line shift. Their Figure 2
clearly shows a somewhat weak correlation between the blueshift
and FWHM(\hb) (see also Sulentic et al. 2000b). Since FWHM(\mgii)
is closely correlated with FWHM(\hb)(e.g. Wang et al. 2009a),
their results broadly agree with ours.
This correlation hints that the \civ\ blueshift is
driven by some primary physical parameters, such as
black hole mass and the Eddington ratio\footnote{\lbol\ is the
bolometric luminosity and \ledd\ is the luminosity required for
radiation pressure arising from electron scattering to balance the
gravity of the central black hole.} (\lr). We calculate black hole
masses based on the FWHM(\mgii) and the monochromatic luminosity
$L_{\rm 3000}=\lambda L(3000 {\rm \AA})$ using the formula of Wang
et al. (2009a)\footnote{Our tests show that the results presented
below do not change if we adopt other \mgii\ black hole mass
formulae.}. We then compute the Eddington ratio assuming a
constant bolometric correction, $L_{\rm bol}\simeq 5.9 L_{\rm
3000}$ (McLure \& Dunlop 2004). To give a quantitative analysis,
we perform Spearman rank correlation tests over the correlations
of BAI with \lr, \mbh\ and FWHM(\mgii), but note that these
properties are degenerate, with \lr$\propto$FWHM$^{-2}$, and
\mbh$\propto$FWHM$^{2}$. The correlations with \lr\ and
FWHM(\mgii) are comparable in strength, with Spearman correlation
coefficients $r_s$ of 0.54 and -0.50 respectively (the
probabilities for null hypothesis are less than $10^{-100}$), and
are both significantly stronger than the dependence on \mbh ($r_s$
= -0.39). Eddington ratio is therefore a more fundamental driver
of the \civ\ blueshift than black hole mass. In Fig. \ref{fig_uledd},
we show BAI as a function of \lr. As \lr\
increases from 0.1 to 1, the median value of BAI significantly
increases from $\sim$0.5 to $\sim$0.75. A commonly accepted view
for this correlation is that outflow is driven by radiation
pressure (e.g. Murray et al. 1995; Boroson 2002), and therefore
prominent for high \lr\ AGNs. If outflow carries away a significant amount of
the angular momentum (e.g. Wang et al. 2007), it can serve as a driver
of the accretion process, and consequently strengthen this
correlation.
The correlation of BAI with FWHM(\mgii) is as strong as that with
the Eddington ratio. It would be interesting to know which
physical property dominates the correlations involving BAI.
However, given the tight correlation between FWHM(\mgii) and the
Eddington ratio ($r_s$=-0.93) in our sample, that is flux limited,
it is impossible to disentangle these dependencies. A sample of
AGNs covering a wide range in luminosity is required for this
purpose. Recently, Richards et al. (2011) reported that the
reverberation mapped AGNs occupy only part of the \civ\ line
parameter space, and suggested that these objects have different
ionizing spectral energy distribution (SED) from the mean SED of
AGNs. It is unclear whether applying the scaling relation to the
whole sample would lead to systematic error in determining \mbh\
and \lr. If yes, the origin of the correlation between BAI and the
inferred \lr\ would be more complex than that we discussed above,
because the ionizing SED also correlates with the \civ\ blueshift
(Richards et al. 2011). Even so, it doesn't necessarily mean the
relationship between real \lr\ and BAI is weaker than that shown
in Fig. \ref{fig_uledd}. In fact, the correlation between SED,
characterized by the ratio of X-ray flux to UV flux
($\alpha_{ox}$), and the inferred \lr\ and line width is weak or
absent (Vasudevan \& Fabian 2007; Shemmer et al. 2008). These
results doesn't favor that the estimates of \lr\ and \mbh\ are
significantly affected by the assumption of a single mean SED.
However, $\alpha_{ox}$ cannot fully characterize the ionizing SED,
further work is needed. Moreover, the constant bolometric
correction may introduce systemic bias in the dependence of BAI on
\lr. But it is not important here because the bolometric
corrections differ between objects by a factor of 2 (e.g. Richards
et al. 2006), much less than the \lr\ range of our sample.
\subsection{\civ\ in High and Low \lr\ AGNs}
When considering the correlations involving FWHM, we can see very
different or even opposite behaviors between \civ\ and \mgii. FWHM
may be a key to understanding the difference between \civ\ and
\mgii\ emitting regions. The width of an emission line reflects
the motion of the corresponding emitting gas. \mgii\ gas is
thought to be gravitationally bound, whereas \civ\ line is
generally blueshifted and the corresponding emitting gas may be
impacted or driven by the radiation field. Thus, FWHM(\mgii) is a
measure of the gravity, while FWHM(\civ) is more likely the result
of the competition between gravity and radiation pressure. It is
therefore not surprising to find inconsistent trends. In order to
understand the detailed effect of radiation pressure on \civ\ gas,
it is necessary to explore more differences between \mgii\ and
\civ, and to examine whether these trends for \civ\ hold for AGNs
of different Eddington ratio.
To do so, we select two extreme subsamples which comprise the 25\%
highest \lr\ and 25\% lowest \lr\ AGNs, designated as sample A and
B respectively. We first show the FWHM(\civ) as a function of BAI
for these two subsamples in the left panels of Fig. \ref{fig_fb}.
There is a clear trend that \civ\ line width increases with BAI in
sample A, but this trend disappears in sample B. An evidence for
this discrepancy can also be found in the entire sample (left
panel of Fig. \ref{fig_uf}). For comparison, we also show
FWHM(\mgii) versus BAI for the \emph{entire} sample in the same
two panels (black points) as background. The \civ\ line of AGNs in
sample A reveals an opposite tendency compared to the
low-ionization line \mgii, while the \civ\ distribution of sample
B is well consistent with the upper half of the \mgii\
distribution. We then make the same analysis of the FWHM-EW
correlations for both lines and obtain similar results (see the
right panels of Fig. \ref{fig_fb}). On one hand, AGNs in sample A
exhibit a strong anti-correlation between FWHM(\civ) and EW(\civ),
which is completely opposite to the correlation for \mgii. This
correlation also exists in the whole sample, albeit weaker. On the
other hand, for sample B AGNs, the correlation becomes marginal
and the discrepancy between \civ\ and \mgii\ become tiny compared
to sample A.
We note that the results shown above do not change if we select
subsamples based on FWHM(\mgii) rather than \lr. That is again due to the fact that
FWHM(\mgii) is strongly correlated with Eddington ratio in our
flux limited sample. Using 130 low-redshift AGNs with HST
ultraviolet-band spectroscopic observation, Sulentic et al.(2007)
found FWHM(\civ) increases with the blueshift \emph{only} in AGNs
with FWHM(\hb) $\leq$4000\kms. Their results are consistent with
ours based on a much larger sample and \mgii, supporting that the
kinematics of \hb\ and \mgii\ regions are similar. They found AGNs
with FWHM(\hb) less and greater than 4000\kms\ exhibit different
FeII and radio properties and further suggested that there is
apparent dichotomy between these two populations(see also Sulentic
et al. 2000a;2000b; Bachev et al. 2004; Zamfir, Sulentic \&
Marziani 2008). We also find similar differences between sample A
and B AGNs in the parameter space defined by BAI, FWHM and EW (and
the same differences between the small and large FWHM(\mgii)
subsamples). \emph{More importantly, we find that the \civ\
emission of sample A is totally different from the low-ionization
line \mgii, while the \civ\ emission of sample B is similar to
\mgii}. In addition, Fig. \ref{fig_uf} and \ref{fig_uledd} show
clearly that the \civ\ blueshift varies continuously and smoothly
with FWHM(\mgii) and \lr. This implies that the corresponding
variation in the properties of the \civ\ emitting region is
smooth, rather than abrupt.
\section{Discussion}\label{sec_dis}
In this section, we analyze the kinematics and geometry of the
\civ\ region on the basis of the results presented above. Then we
discuss candidate BELR models that can account for the specific
behavior of \civ. To get more insight into the origin of the \civ\
blueshift, we finally present a comprehensive comparison between
the \civ\ blueshift and BAL.
\subsection{Gravitationally Bound and Radiation Driven Emission
Line Regions}
The \civ\ emission of the AGNs in sample\,A is strongly
blueshifted, and it also displays an opposite tendency compared to
\mgii\ in the parameter space defined by BAI, FWHM and EW. It is
very likely dominated by outflow, whose velocity range can be
roughly measured by FWHM(\civ). Further evidence for the outflow
origin of the \civ\ blueshift is given by comparison of the
blueshifted \civ\ and BAL (see Sect. \ref{sec_cbo}), that is
believed to be produced by outflows.
The correlation between FWHM(\civ) and BAI found from sample A can
be easily understood in terms of outflows. In general, an outflow
with a large terminal velocity tends to produce emission with a
large blueshift and FWHM(\civ). However, not all outflow models
can successfully reproduce such a relationship. One of the
commonly proposed models is disk-like equatorial outflows with a
small opening angle. In this model, outflows on the far and near
sides emit redshifted and blueshifted \civ\ photons, respectively,
at comparable amounts (see, e.g. Figure 7 of Murray \& Chiang
1997). Only when viewed along the pole, the emission line is
significantly blueshifted. Meanwhile, we will see a very narrow
line because the line of sight is nearly perpendicular to the
outflow velocity. It is inconsistent with our finding here. One
solution is that, in the case of disk-like outflows, a large
opening angle is required. Alternatively, the outflow is funnel
like (see the geometry shown in Elvis 2000 and Wang et al. 2007),
even close to the polar direction in some cases (e.g. Zhou et al.
2006; Wang et al. 2008). For a funnel-like outflow, the projected
velocity of the far-side along the line of sight is so small that
it contributes only little to the red side of the \civ\
emission\footnote{The emission from an counter outflow on the
other side of a presumed optically thick accretion disk is
blocked.}.
The strong anti-correlation between FWHM(\civ) and EW(\civ) in
sample A suggests that the \civ\ emission is suppressed in
outflows at high velocities. This can possibly be ascribed to
that, with expansion, the density of high velocity outflow gets
lower, in agreement with our finding that the blueshifted
component of the \ciii\ emission is possibly enhanced in AGNs with
large BAI (see section \ref{sec_c4b} and Fig. \ref{fig_cs1}).
However, as a major coolant of BELR, \civ\ may be insensitive to
the change of the density. Alternatively, Murray \& Chiang (1997)
suggested that this correlation is related to the distribution of
the launching radius of outflows. Detailed dynamical and
photoionization model is needed to understand the underlying
process.
Different from the case of sample A, the \civ\ emission of the
AGNs in sample B nearly overlaps with \mgii\ in the parameter
space. In particular, the two lines have similar widths. To
demonstrate this more clearly, we show the probability
distribution of $\log({\rm FWHM(\mgii)/FWHM(\civ)})$ in the left
panel of Fig. \ref{fig_fr}, which peaks at zero, albeit a large
scatter of 0.16 dex. For comparison, we also plot the result for
sample A, show that \civ\ is much broader than \mgii. The
similarity between the widths of \civ\ and \mgii\ suggests that
they largely come from the same emitting gas, which should be
optically thick to ionizing radiation. Considering that radiation
pressure is not important for optically-thick clouds (e.g. Fabian
et al. 2006; Marconi et al. 2008) and that \mgii\ is a reasonable
indicator of black hole mass, our results suggest that the
kinematics of the \civ\ emission-line gas in these AGNs is
primarily governed by gravity rather than by radiation field. This
argument is also consistent with the facts that sample B AGNs have
small blueshifts of \civ\ and weak radiation field compared to
gravity for their low \lr.
The most convincing evidence to date for the gravitationally
dominated kinematics of the \civ\ regions, from reverberation
mapping observations of local AGNs, includes similar response
timescales of the blue and red wings of \civ, the correlation
between the BELR size and line width (Gaskell 1988; Koratkar \&
Gaskell 1991; Korista et al. 1995; Peterson \& Wandel 1999; 2000;
Onken \& Peterson 2002). We examine the Eddington ratio of these
reverberation mapped objects listed in Koratkar \& Gaskell (1991),
Peterson \& Wandel (2000), and Onken \& Peterson (2002) by
collecting data from the literature, and find that almost all of
these have quite low Eddington ratio, generally less than 0.1 (see
Wang et al. 2009a for black hole mass and luminosity data).
Moreover, radio-loud AGNs have averagely lower Eddington ratios
(e.g. Boroson 2002; Zamfir et al. 2008) and weaker \civ\
blueshifts in comparison with radio-quiet AGNs. Both results are
in agreement with our conclusion that the \civ\ region tends to be
gravitationally bound at low \lr.
Therefore, our finding reconciles naturally previous contradictory
results. The \civ\ region tends to be dominated by outflows in
high Eddington ratio AGNs, and dominated by normal gravitationally
bound BELR in low Eddington ratio AGNs. The emission strength from
these two regions varies with \lr\ in opposite directions, and
BAI is a measure of their radio. For low-BAI AGNs, in which the
outflow component is trivial, \civ\ is emitted primarily from the
gravitationally bound region and is expected have a similar line
width to \mgii. This is supported by the probability distribution
of $\log({\rm FWHM(\mgii)/FWHM(\civ)})$ for the 25\% lowest-BAI
AGNs, as shown in the right panel of Fig. \ref{fig_fr}.
Interestingly, we find that the distributions of high- and
low-\lr\ AGNs (sample A and B) on the FWHM-BAI plane join at
BAI$\sim0.6$ (Fig. \ref{fig_fb}). At this value the emission from
the two regions may be comparable, and also the distributions of
BAI for all the AGNs peak (Fig. \ref{fig_udis}). We thus conclude
that the gravitationally bound and radiation driven \civ\ emitting
regions coexist in most of the AGNs (see also Richards et al
2011), and there is no abrupt transition from one type to the
other.
\subsection{Models for Two \civ\ Regions}
Extensive efforts have already been devoted to understanding how
an outflow is launched from an accretion disk (e.g. Arav et al.
1994; Murray et al. 1995; Proga, Stone \& Kallman 2000; Everett
2005). These studies showed that the radiation force arising from
line absorption of the central UV continuum can accelerate
outflows to velocities up to 10000-20000\kms. In particular,
Murray et al. (1995) derived an approximate mass loss rate carried
by outflow (their equation 9), that is equivalent to the strength
of outflow, and found that it increases with the Eddington ratio
(see also Proga et al. 2000). This is consistent with our finding
here in observation. Another important parameter that also has
impact on outflows is the strength of the X-ray emission relative
to the UV (denoted as $\alpha_{\rm ox}$). A hard ionizing
continuum can over-ionize outflows so that the acceleration
efficiency of line absorption is suppressed; whereas a soft
ionizing continuum would allow the launch of a strong wind (see
e.g. Murray et al. 1995). Recently, Richards et al. (2011) found
that AGNs with larger \civ\ blueshifts are apparently weaker in
X-ray relative to UV (see also Gibson et al. 2008), consistent
with the theoretical expectation. Both the above facts strongly
favor the line driven outflow model.
If $\alpha_{\rm ox}$ decreases with increasing \lr\, the
dependencies of the \civ\ blueshift on \lr\ and $\alpha_{\rm ox}$
are possibly induced by the same underlying causal process. Recent
studies have revealed a complicated relationship between the two
parameters. Kelly et al. (2008) found that $\alpha_{\rm ox}$
decreases with $L_{\rm UV}$/\ledd, but increases with $L_{\rm
X}$/\ledd, where $L_{\rm UV}$ and $L_{\rm X}$ are the UV and X-ray
luminosity, respectively. Such a difference might be ascribed to
the bolometric corrections of these two bands, that change with
\lr\ in different ways (Vasudevan \& Fabian 2007). Vasudevan \&
Fabian (2007) directly calculated \lbol\ by fitting the broad
spectral energy distributions and didn't find any relationship,
while they pointed out that $\alpha_{\rm ox}$ cannot characterize
the full ionizing continuum. Shemmer et al. (2008) also found that
the dependence of $\alpha_{\rm ox}$ on \lr\ is rather weak. They
suggested that this correlation is probably a secondary effect of
the correlations of $L_{\rm UV}$ with \lr\ and $\alpha_{\rm ox}$.
Thus the outflow strength might be affected by least two
`independent' quantities: the Eddington ratio and the relative
strength of the ionizing continuum.
One prediction of the line-driven outflow model is that the
correlation between the outflow strength and \lr\ depends on the
ionizing continuum. In Fig. \ref{fig_uledd}, we show BAI against
\lr\ for the two subsamples that comprise the 25\% largest
EW(\civ) and 25\% smallest EW(\civ) AGNs respectively. One can
find that the correlation between BAI and \lr\ is apparently
stronger in the small EW sample than in the large EW sample. Since
EW(\civ) is strongly correlated with $\alpha_{\rm ox}$ (e.g. Wang
et al. 1998; Wu et al. 2009), it is reasonable to expect that the
small-EW AGNs are relatively X-ray weak compared to the large-EW
ones. The result shown here thus provides another piece of
possible evidence to support the model.
A viable model for the \civ\ emitting region must also account for
the weakening of the normal \civ\ BELs in high-\lr\ AGNs. One
possible mechanism is the change of the ionization state of BEL
clouds, as discussed in Leighly (2004). In that model, the
ionizing continuum is filtered through an outflow before reaching
the normal BELR. The outflow absorbs the photons that can produce
highly ionized ions, such as C$^{+3}$ and He$^{+2}$. As the
outflow becomes stronger, the continuum filtering is more severe
and high-ionization lines from the normal BELR become weaker. A
shortcoming of this model is that it cannot explain the weakness
of the low-ionization line \mgii\ in large BAI (strong outflow) or
high \lr\ AGNs (Fig. \ref{fig_uwe}). Because the ionization state
of the outflow is high, it can only absorb photons in the helium
continuum, but is transparent to low-energy ionizing photons
(Leighly 2004). Note that a high ionization state is required for
the outflow as there is no significantly blueshifted component in
low-ionization lines. Nevertheless, the ionization state-SED
scenario cannot be ruled out. The low-energy ionizing continuum
may be just intrinsically weak when a strong outflow is launched.
Another possible mechanism is that the amount of BEL clouds varies
with \lr. If radiation pressure can expel BEL clouds out of the
BELR (Dong et al. 2009; 2011, see also Ferland et al. 2009), the
suppression of the normal BEL in high-\lr\ AGNs can be easily
explained. Since BEL clouds are usually dust free, the radiation
pressure arises mainly from three processes: Thomson scattering,
resonance scattering and ionization absorption. Thomson scattering
is not favored since it is only important in AGNs with supper
Eddington luminosities. Resonance scattering is neither able to
drive clouds, because the internal velocity dispersion of a cloud
is generally small and only tiny fraction of photons can be
scattered. Recently, Fabian et al. (2006; see also Marconi et al.
2008) found that the radiation pressure arising from absorption of
ionizing photons cannot be neglected. Assuming the fraction,
$f_{\rm a}$, of ionizing flux is absorbed by a cloud with column
density $N_{\rm H}$, we can derive the ratio of the radiation
force (due to ionization absorption) to the gravitational force on
the cloud:
\begin{equation}
R_f=\frac{F_r}{F_g}=\frac{\frac{L_{\rm ion}f_{\rm a}}{4\pi r^2
c}}{\frac{G \mbh \colnh m_p}{r^2}} =\frac{b f_{\rm a}}{\st
\colnh}\frac{L_{\rm bol}}{L_{\rm Edd}}
\end{equation}
where $G$, $c$ and \st\ are gravitational constant, light speed
and Thomson cross section, $L_{\rm ion}$ the luminosity of
ionizing continuum, $b=L_{\rm ion}/L_{\rm bol}$, and $r$ the
distance from the cloud to the central source. When $R_f>1$,
the radiation force overcomes the gravity of the
central black hole, and the clouds can escape from the BELR. It
sets a lower limit of the column density of clouds that can
survive: $f_{\rm a}N_t\lr$, where $N_t=b/\st$.
There are two parameters, $f_{\rm a}$ and $N_t$, to be determined.
$f_{\rm a}$ is dependent on ionization degree and column density.
For the typical normal BELR, when $N_{\rm H}>
1.2\times10^{21}$cm$^{-2}$, that is the column density at the
hydrogen ionization front, the cloud is optically thick to the
ionizing continuum and $f_{\rm a} \approx 1$ (Ferland 1999;
Marconi et al. 2008). For $N_{\rm H}< 1.2\times10^{21}$cm$^{-2}$,
ionization absorption becomes ineffective, i.e. $f_{\rm a} \approx
0$. We then give a rough estimate of $N_t$ assuming the ionizing
continuum seen by the cloud is the same as what we observe.
Approximating the continuum at wavelength short of 1200\A\ as a
power law with an index $\alpha_{\nu}=-1.57$ (Zheng et al. 1997;
Telfer et al. 2000), $L_{\rm ion}$ is given by integrating over
all ionizing frequencies(i.e. above the frequency of Lyman edge):
$L_{\rm ion}\simeq 1.5\lambda L_{\lambda}(1200\A)$. Then
approximating the UV continuum between 1200\A\ and 3000\A\ as a
power law with an index $\alpha_{\lambda}=-1.54$ (Vanden Berk et
al. 2001), $\lambda L_{\lambda}(1200\A) \simeq 1.64 \lambda
L_{\lambda}(3000\A)$. Adopting $L_{\rm bol}\simeq 5.9 \lambda
L_{\lambda}(3000\A)$ (McLure \& Dunlop 2004), we obtain $b\approx
0.41$ and $N_t\approx 6\times10^{23}$cm$^{-2}$.
As long as $\lr \gs 1.2\times10^{21}/6\times10^{23}=
2\times10^{-3}$, clouds with column density in the range between
$1.2\times10^{21}$cm$^{-2}$ and $N_t\lr$ can be blown away from
the BELR. That is to say, the amount of BEL clouds that can
survive near the central engine drops with increasing \lr.
Increasing \lr\ up to 0.1, the upper limit of the column density
of expelled clouds increases to $6\times 10^{22}$cm$^{-2}$; where
clouds can effectively emit the low-ionization line \mgii. Note
that the estimation of $N_t$ is inexact, since it depends on
whether the ionizing emission is isotropic, or is blocked by other
BEL clouds (Gaskell 2009) and/or other structures (such as
outflows, Leighly 2004). Nevertheless, the mechanism proposed here
gives a promising explanation to the suppression of both the \civ\
and \mgii\ emission from the normal BELR in high-\lr\ AGNs.
\subsection{Connection Between \civ\ Blueshift and BAL}\label{sec_cbo}
One of the most prominent spectral features imprinted by outflows
is the broad absorption line. We refer to outflows associated with
BAL as BAL outflow, while that associated with blueshifted BEL as
BEL outflow. The comparison below suggests that BAL and BEL
outflows may represent the same physical component.
Richards et al. (2002) found that the emission line features, such
as the \ciii\ line complex\footnote{\ciii\ line complex is composed of
\ciii, \siiii\ and \aliii.}, \heii\ and the red wing of \civ, are
very similar between the composites of BAL AGNs and non-BAL AGNs
with large \civ\ blueshift. The broad band SED also displays
a similar trend. For a given UV luminosity, non-BAL AGNs with large
blueshifts tend to be X-ray weak compared to those with small
blueshifts (Richards et al. 2011). The X-ray emission of BAL AGNs
is usually severely absorbed, and thus cannot be directly used for a
comparison. After correction for absorption, Fan et al.
(2009) found that the intrinsic X-ray emission of BAL AGNs is on
average weaker than that of non-BAL AGNs of the same UV
luminosity. In particular, they found that the intrinsic X-ray strength
is anti-correlated with the absorption strength of the \civ\ BAL for
BAL AGNs. It is consistent with the correlation for the \civ\ BEL.
More similarities can be found when looking at the correlations of
the outflow properties with \lr. In this work, we find that the
BEL outflow is stronger at a higher \lr\ (Fig. \ref{fig_uledd}).
Similar correlations between the BAL properties and \lr\ have been
reported previously. Boroson (2002) has shown that BAL AGNs tend
to occupy the extreme end of the Boroson \& Green (1992)
Eigenvector 1, that is thought to be driven by the Eddington
ratio. Recently, Ganguly et al. (2007) found the fraction of BAL
AGNs, an indicator of the average covering factor of outflow,
increases with the Eddington ratio(see also Zhang et al. 2010).
They also found there appears to exist an overall upper-envelope
of increasing $v_{\rm max}$ of BALs with increasing Eddington
ratio. The correlations for the BAL outflows are consistent with
but weaker than those for the BEL outflows. There may be a simple
reason for this: BAL troughs hold only the information of outflow
along the line of sight, and thus may be sensitive to the local
structure; while BEL is an integral of emission over entire volume
of the outflow and represents the overall properties.
The similarity between the BEL and BAL outflows can also be found
directly from their own properties. The first is the
maximal velocity, $v_{\rm max}$. Gibson et al. (2009) have obtained
the distribution of $v_{\rm max}$ for BAL AGNs, which
ranges from $<$5000\kms\ to $>$20000\kms, with a mean value of
$\sim$12000\kms. The maximal velocity of a BEL outflow for individual AGN
is hard to estimate. We estimate the average $v_{\rm max}$ of the
BEL outflow from the difference spectra of the largest-BAI and
smallest-BAI composites (Fig. \ref{fig_ex}). It is about
11000\kms, similar to the BAL outflow.
We then compare their ionization states. As discussed above, the absence of
blueshifted \mgii\ suggests that the BEL outflows contain very
few Mg$^+$ ions. The same condition also appears in the BAL outflows.
About only 10\% of the BAL AGNs exhibit \mgii\ BAL (e.g Trump et al. 2006;
Zhang et al. 2010), suggesting the absence of Mg$^+$ ions in
most of the BAL outflows.
Given the similarities shown above, the BAL outflows may also be
responsible for producing the observed blueshifted BEL, at least
for the strongest blueshifted BEL. When the line of sight to the
continuum source intersects the outflow, BALs are produced in the
AGN spectrum; otherwise, the AGN appears as a non-BAL AGN with
blueshifted \civ. The frequency of occurrence of BAL in AGN
spectra, the strength of BAL trough, and the blueshift of \civ\
are all enhanced as the outflow is boosted with increasing \lr\
and/or decreasing the intrinsic X-ray emission. A viable outflow
model must simultaneously account for both, the absorption and
emission of \civ. Future studies on AGN outflows can be proceed
from these two different approaches. For example, it is possible
to use reverberation mapping results of the blueshifted \civ\ line
to estimate the distance of the BAL outflow to the central source,
an important parameter for understanding the launch of the outflow
(the difficulty lies in how one separates variation of the outflow
component from that of the normal BEL). One may also use the X-ray
emission of AGNs with strongly blueshifted \civ, rather than the
entire sample, to characterize the intrinsic X-ray emission of BAL
AGNs; the latter is generally strongly absorbed and hard to study
directly. In addition, we note that resonance scattering of the
continuum and emission lines by ions, such as C$^{3+}$ and
N$^{4+}$, in outflows may also contribute to the observed emission
(e.g. Wang et al. 2010). That is to say, for proper modeling of
the emission lines, especially \civ\ and \nv\ with large
blueshifts (a strong outflow and a weak normal BELR), the
scattering emission must be taken into consideration.
\section{Summary}\label{sec_sum}
There are two kinds of models proposed to describe the kinematics
and structure of the BELR of high-ionization lines (e.g. \civ) in
AGNs, namely, the outflow and gravitationally bound BELR,
that are apparently mutually contradictory. In this paper we attempt to uncover the
underlying physical process responsible for this difference, using
4963 AGNs in the redshift range $1.7<z<2.2$ selected from SDSS
DR5.
We introduce a blueshift and asymmetry index (BAI) to measure the
deviation of the \civ\ line from an unshifted and symmetric
profile. BAI is defined as the flux ratio of the blue part to the
total profile, where the blue part is the part of the \civ\ line
at wavelengths short of 1549.06\A, the laboratory rest-frame
wavelength of the \civ\ doublets. BAI actually measures the
combined effect of asymmetry and shift of a line profile, which is
generally treated separately in the literature. Since both
asymmetry and line shift may be caused by the same physical
process, BAI is the best choice for our purpose.
We confirm previous findings that the \civ\ BEL is generally
blueshifted with respect to the systemic redshift, and there exist
significant correlations among the BAI, the line width (FWHM) and
the rest equivalent width (EW) of \civ. For comparison, we
investigate the same relationships among the BAI of \civ, the FWHM
and EW of the low-ionization line \mgii. Dramatic differences are
found between these two lines. For the \mgii\ line, FWHM is
positively correlated with EW, and inversely correlated with BAI.
While for \civ, FWHM is anti-correlated with EW, and the
correlation between FWHM and BAI is complex and significantly
different from that for \mgii. Given that line profile reflects
the kinematic properties of the emitting gas, our results
demonstrate clearly that, in general, the \civ\ line comes from a
region with the structure and kinematics fundamentally different
from those of \mgii, which is thought to be gravitationally bound.
We find a prominent correlation between BAI and the Eddington
ratio, that is consistent with theoretical expectation. This
correlation, together with the previously known correlation
between \civ\ blueshift and the X-ray to UV flux ratio, advocates
strongly the view that outflows are driven by resonance line
absorption. Interestingly, there exist a number of similarities
between blueshifted emission lines and broad absorption lines in
AGNs in, for instance, the maximal velocity, ionization state and
the correlations with the Eddington ratio and with the X-ray to UV
flux ratio. These suggest that the same outflow produces these two
different phenomena observed.
We select two subsamples, one composed of the 25\% highest and one
of the 25\% lowest Eddington ratio AGNs. In the high Eddington
ratio subsample, FWHM(\civ) is positively correlated with BAI and
anti-correlated with EW(\civ). Both correlations are opposite to
those for \mgii\ and can be understood in terms of outflow.
Whereas, for the low Eddington ratio subsample, these two
correlations for \civ\ become marginal or absent. \civ\ overlaps
almost completely with \mgii\ in the parameter space. In
particular, the line width of \civ\ is, on average, the same as
that of \mgii. We thus conclude that the \civ\ line in this
subsample is emitted by optically-thick gas driven by gravity,
similar to the \mgii\ line.
Our results further suggest that the two \civ\ emitting regions,
gravitationally bound and radiation driven, coexist in most of the
AGNs. The emission strengths of these two regions vary smoothly
with \lr\ in opposite directions. The \civ\ emission is generally
dominated by outflows at high Eddington ratios, while it is
primarily emitted from the normal gravitationally bound BELRs at
low Eddington ratios. This explanation naturally reconciles the
contradictory views proposed in previous studies. Viable models
are also discussed that can account for both, the enhancement of
outflow emission and the suppression of the normal BEL, in AGNs
with high Eddington ratios.
\acknowledgements We thank the referee, Gordon Richards, for his
helpful suggestions that improved the paper. This work is
supported by NSFC (11073017, 11033007, 10973013, 10973012,
11073019), 973 program (2007CB815405, 2009CB824800) and the
Fundamental Research Funds for the Central Universities. Funding
for the SDSS and SDSS-II has been provided by the Alfred P. Sloan
Foundation, the Participating Institutions, the National Science
Foundation, the U.S. Department of Energy, the National
Aeronautics and Space Administration, the Japanese Monbukagakusho,
the Max Planck Society, and the Higher Education Funding Council
for England. The SDSS Web site is http://www.sdss.org/.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,528
|
{"url":"https:\/\/www.physicsforums.com\/threads\/misconceptions-about-gravity.878468\/","text":"Tags:\n1. Jul 11, 2016\n\n### Figaro\n\nFrom the weak EP, inertial mass is equivalent to the gravitational mass. The weak EP implies the universality of gravitation. Some implications of the EP are:\n1) Gravity is inescapable - there is no such thing as gravitationally neutral object with respect to which we can measure the acceleration due to gravity so acceleration due to gravity is not something that can be reliably defined.\n2) Gravity is not a force, a force is something that leads to acceleration, and the definition of zero acceleration is moving freely in the presence of whatever gravitational field happens to be around.\n\n1) If acceleration due to gravity is not something that can be reliably defined, what about 9.8m\/s^2?\n\n2) I know that gravity is not a force but how do we resolve the usual way of calculating the \"force due to gravity\" and \"acceleration due to gravity\" as in some general physics books? I know that these are due to the equivalence of inertial mass and gravitational mass but can someone expound on it?\n\nReference: Spacetime and Geometry by Carroll\n\n2. Jul 11, 2016\n\n### vanhees71\n\nIn the (1+3)-formulation of the motion of particles in a gravitational field you have clearly the usual notion of \"force\", \"acceleration\", etc., and there's also a non-relativistic limit, valid for weak gravitational fields and slow motion (speeds much less the the speed of light). In the non-relativistic limit you are back at Newton's law, and the value $g=9.81 \\; \\mathrm{m\/s}$ is determined by Newton's Law,\n$$g=\\frac{G M_{\\text{Earth}}}{r_{\\text{Earth}}^2}.$$\nThere's nothing mysterious about this. As any good theory also GR provides the correct limit to the successful predecessor theory of gravity, i.e., Newton's gravitational law.\n\nIn my opinion, it is misleading to teach students that \"gravity is no force\". Of course the motion of particles, when described in 4D space time is determined by the geodesics of space-time, but the emphasis is that it is on space-time not space! Space is, of course, an observer (i.e., frame) dependent concept as is the concept of force, acceleration, etc. However, measurements and observations are made by observers (a tautology in fact!) and thus require the introuction of a reference frame.\n\n3. Jul 11, 2016\n\n### A.T.\n\nGravity doesn\u2019t cause proper acceleration (that an accelerometer measures), but one aspect of it can be quantified as coordinate acceleration (dv\/dt, e.g. 9.8m\/s^2).\n\nThese are different models which give approximately the same results in most everyday applications. Even in GR gravity can locally be interpreted as an \"inertial froce\", or more geometrically like in the animation below.\n\n4. Jul 11, 2016\n\n### Staff: Mentor\n\nThat number tells us how the distance between the surface of the earth and a nearby object changes. If we were in a sealed windowless box we would be unable to measure it - there would be no problem determining that a dropped object accelerated towards the floor at 9.8m\/s^2, but no way of knowing how much of that is \"gravitational acceleration\" caused by the nearby earth and how much is due to the box being accelerated upwards.\nClassical physics does treat gravity as a force, and classical physics is still widely used because it works well enough in most problems. You can calculate the behavior of an object near the surface of the earth either by assuming that the earth exerts a gravitational force on the object or that the mass of the earth curves spacetime in such a way that the natural free-falling path of the object will bring it ever closer to the surface of the earth. The second way produces more exact results, but it is a lot more work and we often don't need that umpteenth decimal point of accuracy. There's an essay by Isaac Asimov that's worth reading: http:\/\/chem.tufts.edu\/answersinscience\/relativityofwrong.htm\n\n5. Jul 11, 2016\n\n### MeJennifer\n\nThe difference between an object moving by force and by gravity is that the prior undergoes proper acceleration while the latter does not.\n\n6. Jul 11, 2016\n\n### FactChecker\n\nNice video. Epstein also wrote a book, \"Relativity Visualized\" that I think is very enjoyable reading.\n\n7. Jul 11, 2016\n\n### Staff: Mentor\n\nYou are assuming that introducing a \"reference frame\" requires introducing a particular split of spacetime into space and time. That is only true if you interpret \"reference frame\" to mean \"coordinate chart\"--and then only if you pick a particular kind of coordinate chart, roughly speaking, one that has one timelike and three spacelike coordinates everywhere. (And this choice can be very non-intuitive--for example, in Schwarzschild spacetime, if you are dealing with a black hole, the only such choice known is Kruskal coordinates, whose \"space\" and \"time\" don't correspond to anything physically intuitive.)\n\nBut there is another interpretation of \"reference frame\" which actually models measurements and observations better and does not require introducing a particular split of spacetime into space and time, at least not globally. This interpretation takes \"reference frame\" to mean \"frame field\"--roughly speaking, an assignment of an orthonormal tetrad to every event in spacetime, subject to some constraints like continuity. The reason this models measurements and observations better than a coordinate chart is that an orthonormal tetrad, by definition, specifies a \"unit clock\", \"unit ruler\", and \"three perpendicular spatial directions\", i.e., it realizes our intuitive sense of a \"reference frame\" at a given event, whereas a coordinate chart does not.\n\nSuch an orthonormal tetrad, at a given event, implies a particular local split of spacetime into space and time at that event--roughly speaking, the split that is \"natural\" to an observer whose 4-velocity at that event is the timelike vector in the tetrad (but even this is not unique, since there will be multiple such observers with differing proper accelerations). But there is no requirement that all of the local splits must fit together into a single global split, and in fact in many cases they won't, even in flat spacetime (consider, for example, the frame field of Langevin observers).\n\n8. Jul 12, 2016\n\n### vanhees71\n\nSure, I've tacitly assumed that observers are local observers. A physical theory does not only consist of the mathematical framework but also needs to make contact with observations, and I don't see, how you can make sense of GR if not defining such local reference frames as you describe in the previous posting. Of course, there are infinitely many local reference frames, and the experimental setup (defining the \"observer\") determines which one is convenient to describe the outcomes.\n\nConcerning the question here, I find it ridiculus to answer it by saying that there are no gravitational forces and no acceleration. It depends on the physical setup, whether this is true. Of course, if you define everything covariant and work with invariant quantities, there's no proper acceleration and in this sense no force, but here the question was specific to how the $g=9.81 \\mathrm{m\/s}$ has to be interpreted, and for me the clear answer is that it refers to an observer who is at rest relative to the Earth and thus is not in a locally free falling reference frame and thus feels the force of the Earth counterbalancing the gravitational force. An object, initially at rest with respect to such an observer won't stay at rest but fall down to Earth. Thus there's a gravitational force acting on it from the point of view of this observer, and the acceleration is independent of the mass of the object in accordance with the (weak) equivalence principle. It is also clear that you get the value $g=9.81 \\mathrm{m\/s}$ from GR, e.g., by assuming approximately the Earth to be a spherical object and plug in the corresponding Schwarzschild solution to calculate the gravitational force with respect to the observer at rest relative to the Earth. Since in this case the non-relativistic limit for sure is valid, you are lead back to Newton's law of gravity and get the said value of the acceleration.\n\nIt's clear that one must be careful when interpreting frame dependent quantities, and physically it's always save to work with covariant quantities. Nevertheless one should not say that GR is counterintuitively claiming that gravity is no force.","date":"2017-12-16 07:50:50","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\": 0.8128361701965332, \"perplexity\": 378.19663880452856}, \"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-2017-51\/segments\/1512948585297.58\/warc\/CC-MAIN-20171216065121-20171216091121-00209.warc.gz\"}"}
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\section{Introduction}
Irrespective of their different optical properties and classification, the energy source
of active galactic nuclei (AGN) is strongly suggested to be intrinsically the same (e.g.
Antonucci \& Miller 1985). When broad lines are lacking, a direct view of central engine
would be prevented by a dusty absorber, covering a substantial, yet not complete fraction
of the solid angle, and thus commonly envisaged as a toroidal structure (Krolik \& Begelman
1988). The orientation-based idea that underlies AGN unification models (Antonucci 1993,
and references therein) is still broadly accepted. While it was argued early on that the
torus might well consist of individual \textit{clouds}, the multiple pieces of observational
evidence accumulated in the last decade imply that the circumnuclear environment in AGN is
characterized by a large degree of clumpiness and inhomogeneity on various physical scales,
from tens of pc down to a few hundreds of gravitational radii ($r_\rmn{g} = GM_\rmn{BH}/c^2$)
from the supermassive black hole (see Bianchi, Maiolino \& Risaliti 2012; Netzer 2015 for
recent overviews).
The nearby Seyfert galaxy NGC\,1365 ($z \simeq 0.0055$) is an ideal object to probe the
complexity of nuclear obscuration in AGN. Optically classified as a type 1.8 (Maiolino
\& Rieke 1995), NGC\,1365 has been extensively studied in the X-rays for its exceptional
variability, which makes it the most striking example of a changing-look AGN (Matt,
Guainazzi \& Maiolino 2003). Apparently due to a favourable line of sight, the inner
accretion disc/X-ray corona system is seen through an erratic absorbing medium, whose
marked column density gradients are betrayed by the random alternation of Compton-thin
($N_\rmn{H} < 10^{23}$ cm$^{-2}$) and Compton-thick ($N_\rmn{H} > 10^{24}$ cm$^{-2}$)
states. The switch from transmission- to reflection-dominated spectra (and back) can
take less than two days, involving the transit of a single cloud (Risaliti et al. 2007).
This kind of eclipses not only sets a tight empirical limit to the size of the X-ray
source (no larger than a few tens of $r_\rmn{g}$), but also provides an implicit
measure of the distance and density of the intervening blobs (both indicative of the
gas in the Broad Line Region; BLR), and reveals unique details about their shape (e.g.
Maiolino et al. 2010). Besides this, in the Compton-thin regime NGC\,1365 regularly
exhibits four strong absorption lines in the $\sim$6.7--8.3 keV band. Their spacing
prompts an identification with the K$\alpha$ and K$\beta$ pairs from
Fe\,\textsc{xxv}--\textsc{xxvi}, blueshifted by reason of an outflow velocity of
$v_\rmn{out} \sim 1000$--5000 km s$^{-1}$, variable over timescales of weeks/months
(Risaliti et al. 2005; Nardini et al., in preparation). These lines could just trace
the high-ionization phase of a much more pervasive wind, possibly including all the
manifest absorption components (Connolly, McHardy \& Dwelly 2014; Braito et al. 2014).
Adding to the overall merit of NGC\,1365 is one of the largest infrared luminosities
($L_\rmn{IR} \sim 10^{11}\,L_{\sun}$) among nearby, non-interacting galaxies. This
mostly arises from the great number of star-forming clusters in the central $\sim$2--3
kpc, disposed in an elongated ring around the nucleus (Alonso-Herrero et al. 2012, and
references therein). The powerful starburst is also the main source of the observed soft
X-ray emission ($E < 3$ keV), which is found to be constant in flux and shape. Indeed,
the $\sim$500-ks high-resolution spectrum obtained by combining all the 2004 and 2007
data from the \textit{XMM--Newton} Reflection Grating Spectrometer (RGS) is rife with
collisionally ionized lines from the hot diffuse gas, at odds with a typical obscured
Seyfert (Guainazzi et al. 2009). In this paper we report on two \textit{Chandra}
observations of NGC\,1365 taken with the High-Energy Transmission Grating (HETG;
Canizares et al. 2005) over a span of four days, during which the AGN remained in
a heavily absorbed, Compton-thick state.
\section{Observations and Data Reduction}
NGC\,1365 was observed twice by \textit{Chandra} in 2012, on April 9 and three days
later (ObsIDs 13920/1), for a total exposure of $\sim$200 ks. After a series of six
15-ks snapshots in 2006 (Risaliti et al. 2007) and a previous one of the same length
in 2002, these were the first observations of NGC\,1365 at high spectral resolution
with \textit{Chandra}. The HETG consists of two sets of gratings, optimized for medium
(MEG; 0.5--7 keV) and high (HEG; 0.8--10 keV) energies, respectively, and was used in
combination with the Advanced CCD Imaging Spectrometer (ACIS-S) array. The data were
reprocessed with the \textsc{ciao} version 4.4 software package and the v4.4.9
Calibration Database (CALDB). For each observation, the MEG and HEG spectra were
extracted from first-order events in both ($\pm 1$) diffraction arms. Redistribution
matrices were created with the \textsc{ciao} tool \texttt{mkgrmf}, while effective
area files were obtained through the \texttt{fullgarf} script. The spectra and detector
responses from the $\pm 1$ orders were combined with the appropriate weights. Since the
background is negligible, no correction was performed, and no systematic uncertainty
was introduced.
\begin{figure}
\includegraphics[width=8.5cm]{sb_ring.pdf}
\caption{X-ray image of the central $1\arcmin \times 1\arcmin$ region of NGC\,1365
in the 0.3--3 keV energy range (from ObsIDs 13920/1), showing the extent of the diffuse
starburst emission and the aperture adopted (green circle, 10$\arcsec$ radius). An
adaptive smoothing has been applied following the same criteria of Wang et al. (2009).}
\label{im}
\end{figure}
After verifying that the two observations are consistent with each other, in order
to improve the data quality for the subsequent analysis we also merged the spectra
(and auxiliary files) from ObsIDs 13920/1 into a single one. It is worth noting that
we adopted a narrower extraction strip than the default one (20$\arcsec$ instead of
35$\arcsec$): this allowed us to exclude part of the diffuse X-ray emission associated
with the star-forming ring of $\sim$15$\arcsec$ diameter on kpc scale (1$\arcsec \sim 90$
pc, Fig.~\ref{im}; see also Wang et al. 2009), and at the same time to extend the
final HEG spectrum up to $\sim$8 keV. In all the spectral fits (carried out with
\textsc{xspec} v12.8, with solar abundances from Wilms, Allen \& McCray 2000) we
considered the 0.5--5 keV (MEG) and 1.5--8 keV (HEG) energy ranges, over which a
total of $\sim$1580 and 1050 counts were collected, respectively. We initially binned
the data to 2048 channels, corresponding to a $\Delta\lambda$ of 20 (MEG) and
10 m\AA~(HEG), that is roughly the full width at half-maximum (FWHM) resolution.
However, due to the limited number of counts, we further imposed a minimum of four
counts per energy bin, and made use of the $C$-statistic (Cash 1979). Unless otherwise
stated, the lines' energies are given in the rest frame of NGC\,1365, and all the
uncertainties correspond to the 90\% confidence level for the single parameter of
interest ($\Delta C = 2.71$). For simplicity, throughout this work we assumed a
standard concordance cosmology with $H_0=70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_m=0.27$,
and $\Omega_\Lambda=0.73$, although the luminosity distance entailed for NGC\,1365
($\sim$21 Mpc) slightly differs from the one based on Cepheid variables of
$D = 18.6 \pm 1.9$ Mpc (Madore et al. 1998).
\begin{figure}
\includegraphics[width=8.5cm]{chandra_hetg.pdf}
\caption{\textit{Chandra} HETG spectra of NGC\,1365, plotted in black (MEG)
and red (HEG), respectively. The historical extremes of transmission- and
reflection-dominated states are also shown for comparison. The source has
the typical Compton-thick spectral shape at 2--10 keV, and is $\sim$15 times
dimmer than during the final part of the January 2013 \textit{XMM--Newton}
observation (blue), when the neutral column density dropped to $N_\rmn{H}
\sim 10^{22}$ cm$^{-2}$. Indeed, the flux lies above the minimum reached in
the 2007 \textit{XMM--Newton} monitoring (green) just by a factor of $\sim$1.8.
Note, however, that the narrower extraction region adopted for \textit{Chandra}
allowed us to disentangle the nuclear soft X-ray component from most of the
circumnuclear starburst emission. (All the data were rebinned for display
purposes).}
\label{xs}
\end{figure}
\section{Spectral Analysis}
The HETG spectra of NGC\,1365 are shown in Fig.~\ref{xs}, compared to the brightest flux
state ever reached by the source during an \textit{XMM--Newton} observation performed only
nine months later in January 2013, when the column density towards the AGN was just about
$N_\rmn{H} \sim 10^{22}$ cm$^{-2}$ (Braito et al. 2014; Rivers et al. 2015). \textit{Chandra}
clearly met a Compton-thick state, exhibiting a faint and very hard ($\Gamma = -1.5$)
continuum above 3 keV, which closely resembles the lowest reflection-dominated spectrum
of the first \textit{XMM--Newton} orbit in the 2007 five-day monitoring (Fig.~\ref{xs};
Risaliti et al. 2009a). In the following analysis, we first focus on the overall shape
of the continuum, and then take into account the rich emission-line spectrum in the soft
X-rays.
\subsection{Baseline continuum}
As a starting point we adopted a model that simply consists of three different AGN-related
components: the primary power-law continuum, attenuated by a foreground screen of cold gas
at rest in the source frame ($z = 0.005457$); reflection off the irradiated matter, described
as a \texttt{pexrav} template (Magdziarz \& Zdziarski 1995) with solar abundances, inclination
of 45$\degr$, and variable strength; and a soft X-ray power law, which is required by the modest
spectral rise below $\sim$1.5 keV and is intrepreted as the faint, scattered AGN continuum.
The latter component can be fitted in several alternative ways, for instance as a thermal
bremsstrahlung of $kT \sim 0.8$ keV, possibly associated with starburst-driven shocks. However,
due to its negligible impact on the final results and to the small ($\sim$1--2 per cent)
scattering efficiency implied, we retained for simplicity the link of this soft continuum
with the AGN, thus assuming a common photon index for the various forms of reprocessed AGN
emission (i.e. transmitted, reflected and scattered). This model (hereafter tagged as model
A for brevity) and all the subsequent ones also include the Galactic column density (fixed
to $N_\rmn{H} = 1.34 \times 10^{20}$ cm$^{-2}$; Kalberla et al. 2005) and the conspicuous
iron fluorescence line around 6.4 keV, whose properties remain consistent throughout the
fitting steps.
\begin{table*}
\caption{Best-fit continuum parameters for the different models (A--E) and components:
primary (1), scattered (2) and reflected (3) AGN emission, hot (4) and warm (5) thermal
emission. $N_\rmn{H}$: foreground column density. $\Gamma$: power-law photon index. $A$:
power-law normalization at 1 keV. $R$: reflection strength. $kT$: plasma temperature.
$Z$: elemental abundance. EM: emission measure. (f) and (t) denote fixed and tied
parameters. Each model also includes Galactic absorption and iron K$\alpha$ emission.}
\label{t1}
\begin{tabular}{l@{\hspace{30pt}}c@{\hspace{20pt}}c@{\hspace{20pt}}c@{\hspace{20pt}}c@{\hspace{20pt}}c}
\hline
Component & \multirow{2}{*}{Model A} & \multirow{2}{*}{Model B} & \multirow{2}{*}{Model C} &
\multirow{2}{*}{Model D} & \multirow{2}{*}{Model E}\\[-0.5ex]
~~~~~~~~~~Parameter & & & & & \\
\hline
(1)~~\texttt{powerlaw}$_1$ & & & & & \\[0.5ex]
~~~~~~~~~~$N_\rmn{H}$ (10$^{22}$\,cm$^{-2}$) & 200(f) & 200(f) & 200(f) & 200(f) & 140$^{+19}_{-12}$\\[0.5ex]
~~~~~~~~~~$\Gamma$ & 2.0(f) & 2.0(f) & 2.0(f) & 2.0(f) & 2.10$^{+0.05}_{-0.06}$ \\[0.5ex]
~~~~~~~~~~$A$ (10$^{-4}$\,cm$^{-2}$\,s$^{-1}$\,keV$^{-1}$) & 77$^{+22}_{-20}$ & 60$^{+21}_{-19}$ &
58$^{+21}_{-18}$ & 46$^{+20}_{-18}$ & 44$^{+3}_{-2}$ \\[1.0ex]
(2)~~\texttt{powerlaw}$_2$ & & & & & \\[0.5ex]
~~~~~~~~~~$\Gamma$ & 2.0(t) & 2.0(t) & 2.0(t) & $-$ & 2.10(t) \\[0.5ex]
~~~~~~~~~~$A$ (10$^{-4}$\,cm$^{-2}$\,s$^{-1}$\,keV$^{-1}$) & 1.01$\pm$0.06 & 0.71$\pm$0.08 &
0.68$^{+0.09}_{-0.08}$ & $-$ & 0.54$^{+0.06}_{-0.05}$ \\[1.0ex]
(3)~~\texttt{pexrav} & & & & & \\[0.5ex]
~~~~~~~~~~$\Gamma$ & 2.0(t) & 2.0(t) & 2.0(t) & 2.0(t) & 2.10(t) \\[0.5ex]
~~~~~~~~~~$R$ & 0.50$^{+0.20}_{-0.13}$ & 0.74$^{+0.38}_{-0.21}$ & 0.78$^{+0.41}_{-0.22}$ & 1.24$^{+0.88}_{-0.40}$ &
1.01$^{+0.16}_{-0.13}$ \\[1.0ex]
(4)~~\texttt{apec}$_1$ & & & & & \\[0.5ex]
~~~~~~~~~~$N_\rmn{H}$ (10$^{22}$\,cm$^{-2}$) & $-$ & $-$ & $-$ & $< 0.08$ & $-$ \\[0.5ex]
~~~~~~~~~~$kT$ (keV) & $-$ & 0.94$^{+0.07}_{-0.09}$ & 0.96$^{+0.07}_{-0.08}$ & 1.20$^{+0.10}_{-0.11}$ &
0.99$^{+0.08}_{-0.09}$ \\[0.5ex]
~~~~~~~~~~$Z_\rmn{O}$ ($Z_{\odot}$) & $-$ & 1.0(f) & 1.0(f) & 0.03$^{+0.04}_{-0.02}$ & 1.0(f) \\[0.5ex]
~~~~~~~~~~$Z_\rmn{Ne}$ ($Z_{\odot}$) & $-$ & 1.0(f) & 1.0(f) & 0.17$^{+0.33}_{-0.13}$ & 1.0(f) \\[0.5ex]
~~~~~~~~~~$Z_\rmn{Mg}$ ($Z_{\odot}$) & $-$ & 1.0(f) & 1.0(f) & 0.36$^{+0.22}_{-0.17}$ & 1.0(f) \\[0.5ex]
~~~~~~~~~~$Z_\rmn{Si}$ ($Z_{\odot}$) & $-$ & 1.0(f) & 1.0(f) & 0.49$^{+0.18}_{-0.15}$ & 1.0(f) \\[0.5ex]
~~~~~~~~~~$Z_\rmn{Fe}$ ($Z_{\odot}$) & $-$ & 1.0(f) & 1.0(f) & 0.05$^{+0.03}_{-0.05}$ & 1.0(f) \\[0.5ex]
~~~~~~~~~~EM (10$^{63}$\,cm$^{-3}$) & $-$ & 0.25$\pm$0.06 & 0.25$^{+0.06}_{-0.05}$ &
1.86$^{+0.23}_{-0.21}$ & 0.18$^{+0.05}_{-0.04}$ \\[1.0ex]
(5)~~\texttt{apec}$_2$ & & & & & \\[0.5ex]
~~~~~~~~~~$N_\rmn{H}$ (10$^{22}$\,cm$^{-2}$) & $-$ & $-$ & $-$ & $< 0.35$ & $-$ \\[0.5ex]
~~~~~~~~~~$kT$ (keV) & $-$ & $-$ & 0.14$^{+0.04}_{-0.03}$ & 0.15$^{+0.10}_{-0.05}$ & $-$ \\[0.5ex]
~~~~~~~~~~EM (10$^{63}$\,cm$^{-3}$) & $-$ & $-$ & 0.55$^{+0.46}_{-0.32}$ & $> 5.7^a$ & $-$ \\[1.0ex]
Fit statistic $C/\nu$ & 819/489 & 730/487 & 706/485 & 671/479 & 442/434 \\
\hline
\end{tabular}
\flushleft{Notes: $^a$Due to the fact that the peak temperature of this component falls
outside the fitting range, the emission measure is largely degenerate with the column density,
so that no sensible upper limit can be obtained.}
\end{table*}
\begin{figure}
\includegraphics[width=8.5cm]{fig_resid.pdf}
\caption{Fit residuals for the different models A--E (error bars are omitted for clarity).
Once the AGN-related continuum components (i.e. transmitted, reflected and scattered) and
the 6.4-keV iron K line are accounted for, a wealth of narrow emission features is left
below $\sim$4 keV (A). The addition of a thermal component from collisionally ionized gas
returns an appreciable improvement around 1 keV (B), but any further thermal contribution
is not strongly required (C,\,D). An adequate fit is obtained only after including
individual Gaussian profiles to describe the 22 remaining emission lines detected with
a statistical significance of at least 95 per cent (E).}
\label{mr}
\end{figure}
\begin{table*}
\caption{Statistically significant emission lines in the \textit{Chandra} HETG spectra, after
accounting for the collisional component. The most plausible identifications are also listed.
(f), (i), and (r) refer to forbidden, intercombination and resonance transitions for He-like
species. (u) stands for unresolved ($\sigma = 2$ eV is then assumed). Note that the equivalent
widths (EW) of broad features should not be taken at face value, since in most cases these are
blends of two (or more) narrow lines (see the text for a thorough discussion).}
\label{t2}
\begin{tabular}{r@{\hspace{5pt}}c@{\hspace{20pt}}ccc@{\hspace{20pt}}c@{\hspace{20pt}}c@{\hspace{10pt}}c}
\hline
\multicolumn{2}{c}{$E_\rmn{obs}$} & $\sigma$ & Flux & EW &
Transition & $E_\rmn{lab}$ & $\Delta C/\Delta\nu$ \\
\multicolumn{2}{c}{(eV)} & (eV) & (10$^{-6}$\,s$^{-1}$\,cm$^{-2}$) & (eV) & & (eV) & \\
\hline
1. & 555$^{+9}_{-8}$ & 21$^{+13}_{-7}$ & 93$^{+37}_{-32}$ & 410$^{+270}_{-220}$ &
O\,\textsc{v} K$\alpha$ & 554$^a$ & 54/3 \\[-0.5ex]
& & & & &
O\,\textsc{vii} He$\alpha$\,(f) & 561$^b$ & \\[1.0ex]
2. & 618$^{+3}_{-2}$ & 2(u) & 11$^{+11}_{-7}$ & 39$^{+39}_{-33}$ &
O\,\textsc{v} K$\beta$ & 621$^a$ & 10/2 \\[1.0ex]
3. & 655$^{+2}_{-3}$ & 2(u) & 7.0$^{+7.5}_{-5.3}$ & 37$\pm$34 &
O\,\textsc{viii} Ly$\alpha$ & 654$^b$ & 6/2 \\[1.0ex]
4. & 778$^{+3}_{-2}$ & 2(u) & 2.9$^{+2.8}_{-2.0}$ & 18$\pm$15 &
O\,\textsc{viii} Ly$\beta$ & 775$^b$ & 9/2 \\[-0.5ex]
& & & & &
Fe\,\textsc{xviii} $3s \rightarrow 2p$ & 775$^c$ & \\[1.0ex]
5. & 819$^{+1}_{-2}$ & 2(u) & 3.7$^{+2.8}_{-2.1}$ & 22$\pm$18 &
O\,\textsc{viii} Ly$\gamma$ & 817$^b$ & 15/2 \\[-0.5ex]
& & & & &
Fe\,\textsc{xix} $3s \rightarrow 2p$ & 822$^c$ & \\[1.0ex]
6. & 874$^{+6}_{-4}$ & 6$^{+9}_{-3}$ & 4.2$^{+2.8}_{-2.3}$ & 26$^{+23}_{-18}$ &
O\,\textsc{viii} RRC & 871$^b$ & 12/3 \\[0.5ex]
& & & & &
Fe\,\textsc{xviii} $3d \rightarrow 2p$ & 873$^c$ & \\[1.0ex]
7. & 1024$\pm$4 & 6$^{+7}_{-3}$ & 2.9$^{+1.8}_{-1.5}$ & 24$^{+22}_{-17}$ &
Ne\,\textsc{x} Ly$\alpha$ & 1022$^b$ & 14/3 \\[1.0ex]
8. & 1096$^{+2}_{-6}$ & 2(u) & 0.9$^{+1.0}_{-0.7}$ & 11$^{+10}_{-8}$ &
Ne\,\textsc{ix} He$\beta$\,(r) & 1074$^b$ & 6/2 \\[1.0ex]
9. & 1205$\pm$6 & 8$^{+7}_{-4}$ & 1.4$^{+1.0}_{-0.8}$ & 24$\pm$17 &
Ne\,\textsc{x} Ly$\beta$ & 1211$^b$ & 11/3 \\[1.0ex]
10. & 1334$^{+1}_{-2}$ & 2(u) & 1.4$^{+0.9}_{-0.6}$ & 26$\pm$15 &
Mg\,\textsc{xi} He$\alpha$\,(f) & 1331$^b$ & 24/2 \\[1.0ex]
11. & 1356$\pm$3 & 2(u) & 0.6$^{+0.6}_{-0.5}$ & 10$^{+12}_{-9}$ &
Mg\,\textsc{xi} He$\alpha$\,(r) & 1352$^b$ & 6/2 \\[1.0ex]
12. & 1476$\pm$1 & 2(u) & 1.2$^{+0.5}_{-0.4}$ & 29$^{+17}_{-14}$ &
Mg\,\textsc{xii} Ly$\alpha$ & 1473$^b$ & 42/2 \\[1.0ex]
13. & 1756$^{+7}_{-6}$ & 2(u) & 0.4$\pm$2 & 10$^{+10}_{-7}$ &
Mg\,\textsc{xii} Ly$\beta$ & 1745$^b$ & 9/2 \\[1.0ex]
14. & 1864$^{+8}_{-7}$ & 24$^{+9}_{-6}$ & 2.8$\pm$0.7 & 96$^{+67}_{-36}$ &
Si\,\textsc{xiii} He$\alpha$\,(r) & 1865$^b$ & 62/3 \\[1.0ex]
15. & 2006$^{+2}_{-3}$ & 2(u) & 0.5$\pm$0.3 & 19$^{+18}_{-15}$ &
Si\,\textsc{xiv} Ly$\alpha$ & 2006$^b$ & 10/2 \\[1.0ex]
16. & 2187$^{+7}_{-6}$ & 2(u) & 0.9$^{+0.5}_{-0.6}$ & 40$^{+49}_{-31}$ &
Si\,\textsc{xiii} He$\beta$\,(r) & 2183$^b$ & 9/2 \\[1.0ex]
17. & 2475$^{+8}_{-5}$ & 2(u) & 0.9$^{+0.7}_{-0.5}$ & 41$^{+53}_{-34}$ &
S\,\textsc{xv} He$\alpha$\,(r) & 2461$^b$ & 11/2 \\[1.0ex]
18. & 2630$\pm$20 & 27$^{+26}_{-19}$ & 2.0$^{+1.1}_{-1.0}$ & 100$^{+150}_{-80}$ &
S\,\textsc{xvi} Ly$\alpha$ & 2623$^b$ & 15/3 \\[1.0ex]
19. & 3138$^{+13}_{-11}$ & 19$^{+14}_{-10}$ & 1.7$^{+0.8}_{-0.7}$ & 83$^{+110}_{-42}$ &
Ar\,\textsc{xvii} He$\alpha$\,(r) & 3140$^b$ & 23/3 \\[1.0ex]
20. & 3310$^{+34}_{-31}$ & 54$^{+25}_{-14}$ & 2.0$^{+1.1}_{-0.9}$ & 105$^{+205}_{-75}$ &
Ar\,\textsc{xviii} Ly$\alpha$ & 3323$^b$ & 15/2 \\[1.0ex]
21. & 3873$^{+28}_{-30}$ & 83$^{+67}_{-22}$ & 2.8$^{+0.6}_{-0.9}$ & 160$^{+540}_{-140}$ &
Ca\,\textsc{xix} He$\alpha$\,(f) & 3861$^b$ & 17/3 \\[-0.5ex]
& & & & &
Ca\,\textsc{xix} He$\alpha$\,(i) & 3883$^b$ & \\[-0.5ex]
& & & & &
Ca\,\textsc{xix} He$\alpha$\,(r) & 3902$^b$ & \\[1.0ex]
22. & 6404$^{+13}_{-14}$ & 24$^{+17}_{-12}$ & 7.0$^{+2.8}_{-2.4}$ & 205$^{+80}_{-70}$ &
Fe\,\textsc{i} K$\alpha$ & 6403$^b$ & 38/3 \\
\hline
\multicolumn{8}{l}{References: $^a$Kaastra et al. (2004); $^b$NIST (\url{http://physics.nist.gov/asd});
$^c$CHIANTI (Landi et al. 2012).}
\end{tabular}
\end{table*}
Model A already provides a good representation of the observed continuum, while the intrinsic
power law is largely unconstrained at this stage, also because of the decreasing data quality
at higher energies; the photon index and absorbing column were then frozen to the reasonable
values of $\Gamma = 2$ and $N_\rmn{H} = 2 \times 10^{24}$ cm$^{-2}$. The overall statistics
of $C/\nu = 819/489$ are still rather poor without accounting for the emission lines (Fig.
\ref{mr}). To check whether some of these can be ascribed to optically-thin, collisionally
ionized plasma, which is indeed a major ingredient of the \textit{XMM--Newton}/RGS spectrum
(Guainazzi et al. 2009), we added an \texttt{apec} thermal component (Smith et al. 2001) with
solar abundances. In this scenario, the ionization is driven by the impact of free electrons
with a temperature comparable with the energy of the observed lines. The new fit (model B)
brings a substantial improvement, with $\Delta C = -89$ for the loss of two degrees of freedom
only, taken by the plasma temperature $kT \simeq 0.95$ keV and emission measure.\footnote{The
emission measure (in cm$^{-3}$) is defined as $\rmn{EM} = \int{n_e n_\rmn{H} \rmn{d}V}$, where
$n_e$ and $n_\rmn{H}$ are the electron and hydrogen densities.} The most affected is the
$\sim$0.6--1.2 keV (10--20\,\AA) range, where there are hints of iron L-shell emission, mainly
due to $3d \rightarrow 2p$ transitions from Fe\,\textsc{xviii}--\textsc{xxiii}. This hot gas
can be naturally identified with the residual contamination from the circumnuclear star formation
(Fig.~\ref{im}). The related continuum is much fainter than in the large-aperture RGS data
(see also Fig.~\ref{xs}), and the contribution to the most prominent features is no larger
than $\sim$30--40 per cent in the case of Ly$\alpha$ lines from O\,\textsc{viii},
Ne\,\textsc{x}, and Mg\,\textsc{xii}. We therefore introduced a second \texttt{apec}
component of different temperature, but this is remarkably cold ($kT \simeq 0.15$ keV;
Table~\ref{t1}) and simply imparts minor changes to the noisy lower end of the MEG
spectrum ($C/\nu = 706/485$; model C). Apparent structures compatible with the He-like
triplets from Mg\,\textsc{xi}, Si\,\textsc{xiii} and Ar\,\textsc{xvii} are left unexplained,
but no other zone of thermal emission is statistically required.
As an ultimate attempt to explore the significance of collisionally ionized plasma, we
also allowed for variable abundances (tied between the two components) for all the key
$\alpha$-elements (O, Ne, Mg and Si) plus Fe, and for the possible column density
enshrouding each star-forming region. The scattered AGN continuum was neglected to avoid
any degeneracies (model D). The same set of assumptions was successfully applied by Guainazzi
et al. (2009) in reproducing both the RGS and the previous \textit{Chandra}/ACIS spectra of
NGC\,1365. With respect to their description, in the HETG data the separation between the
plasma temperatures is much more pronounced, $\sim$0.15--1.2 keV against $\sim$0.3--0.7
keV, while absolute and relative abundances are rather similar (once the conversion
between the adopted solar standards is applied). In any case, the global statistics only
undergo a scarce decrease ($\Delta C = -35$ for $\Delta \nu = -6$), and the fit stays far
from being satisfactory ($C/\nu = 671/479$). The full details are listed in Table~\ref{t1}.
Equivalent results were achieved by letting vary a common $\alpha$-element metallicity
over the two regions ($Z_\alpha \sim 0.5$ and 0.03).
Incidentally, we note that model D actually delivers a fairly good fit ($C/\nu = 513/488$)
of the zeroth-order spectrum at CCD resolution,\footnote{A merged, low-resolution spectrum
was extracted from the undispersed images, but is not discussed any further in this work.}
although with slightly adjusted values ($kT \sim 0.9$ and 0.3 keV, $N_\rmn{H} \sim 1.5$ and
$< 0.2 \times 10^{22}$ cm$^{-2}$; abundances are poorly constrained but are consistent with
being solar). We conclude that the copious line emission revealed by the \textit{Chandra}/HETG
observations is dominated by photoionized gas directly exposed to the radiation field of the
AGN, which is clearly brought out for the first time.
\subsection{Emission lines}
While several star-forming regions are present within in the inner kpc, their weak soft
X-ray emission precludes an accurate determination of the full range of properties (e.g.
temperatures and abundances) of the hot diffuse gas. We therefore built on model B, with
a single thermal component of solar metallicity besides the transmitted, reflected and
scattered AGN continua. A Gaussian profile was then added for any residual emission line,
provided that each inclusion resulted in a $\Delta C = -6.0$ or $-7.8$, corresponding to
the 95 per cent confidence level for either two or three parameters of interest (model E).
Following this criterion, which is less stringent than usual but is more appropriate to
the signal to noise of the current data, 22 lines are detected (Table~\ref{t2}). At a
first glance, based on the most likely identifications, all the main transitions of
$\alpha$-elements from O to Ca appear to be present. Most lines are narrow, and some
of the broad ones are possible blends. Whenever the width turned out to be consistent
with zero at the 90 per cent level, $\sigma = 2$ eV was assumed. This does not automatically
imply that a line is unresolved, due to its low number of counts and significance. We will
address this point again in the next Section.
Interestingly, all the continuum components were left free to vary and returned very sensible
values (Table~\ref{t1}), leading to an excellent fit with $C/\nu = 442/434$. The photon index
of the intrinsic AGN power-law emission is $\Gamma \simeq 2.10$, and the gas column density is
$N_\rmn{H} \simeq 1.4 \times 10^{24}$ cm$^{-2}$;
the absorption-corrected 2--10 keV flux is of the order of $\sim$10$^{-11}$ erg s$^{-1}$
cm$^{-2}$, in keeping with the historical behaviour of NGC\,1365. The strength of the reflection
component is ordinary as well, $R \simeq 1$, and only $\sim$1 per cent of the primary AGN
continuum is scattered back into our line of sight. As for the collisionally ionized plasma,
its characteristic temperature converges to $kT \simeq 1$ keV, contributing to most of the
Fe L-shell forest and to some extent also to the Ly$\alpha$ lines from the main $\alpha$-elements
(see above). With this respect, the spectral parameters reported in Table~\ref{t2} only refer
to the photoionized component. Below we discuss in greater detail the properties of the various
lines and their implications on the physical conditions of the emitting gas.
\section{Discussion}
When seen at high resolution, the soft X-ray spectra of obscured active galaxies
display a wealth of narrow emission lines with little or no continuum, arising from
low-temperature ($T < 10^5$ K, or a few eV) gas photoionized and photoexcited by the
primary nuclear radiation (e.g. Sako et al. 2000; Kinkhabwala et al. 2002; Schurch
et al. 2004). \textit{Chandra} images have also revealed the substantial spatial
extension of the soft X-ray emission, and its striking correlation with the size
and morphology of the Narrow Line Region (NLR) as mapped by \textit{HST} in the
[O\,\textsc{iii}] $\lambda$5007 line (Ogle et al. 2000; Bianchi, Guainazzi \& Chiaberge
2006). This suggests that the same gas shines in both [O\,\textsc{iii}] and soft
X-rays. In general, the latter can also be a signature of mechanical and shock heating
in star-forming regions, yet the contribution from collisionally ionized plasma is
usually minor (Brinkman et al. 2002). Although detailed spectral diagnostics are
available for the handful of brightest sources only (e.g. Kallman et al. 2014),
this trend seems to apply to the entire population of local type 1.5--2 Seyfert
galaxies, with just a few exceptions (Guainazzi \& Bianchi 2007). NGC\,1365 stands
out among the peculiar objects by virtue of the foremost influence of thermal plasma
on its RGS spectrum. According to Guainazzi et al. (2009), evidence for photoionized
matter solely relies on excess emission in the forbidden (f) and intercombination (i)
components of O\,\textsc{vii} He$\alpha$, in N\,\textsc{vi} He$\alpha$\,(f), and in the
tentative O\,\textsc{vii} and O\,\textsc{viii} radiative recombination continua (RRC).
The new \textit{Chandra}/HETG observations take advantage of a much better angular
resolution, and allowed us to ignore the bulk of the circumnuclear starburst. The
resultant spectra cannot be explained through a multi-temperature gas in collisional
equilibrium, whose importance is conversely highly diminished. The emergence of the
diluted emission from a photoionized region closer to the hard X-ray source tends to
reconcile the nature of NGC\,1365 with the average properties of the local obscured
AGN. In order to move towards a self-consistent description of the whole sequence of
lines in Table~\ref{t2}, we removed all the Gaussian profiles from model E (except
for Fe\,\textsc{i} K$\alpha$) and generated several sets of photoionization grids
with \textsc{xstar} (Kallman \& Bautista 2001). We adopted an optical to X-ray spectral
energy distribution similar to the one used in Guainazzi et al. (2009), based on an
$\alpha_\rmn{ox} = 1.5$ energy index,\footnote{The spectral index $\alpha_\rmn{ox} =
-0.384 \log (L_\rmn{2\,keV}/L_\rmn{2500\,\text{\AA}})$ is the usual indicator of the
optical to X-ray luminosity ratio in AGN.} and on a 1--1000 Rydberg (13.6 eV to 13.6
keV) luminosity of $\sim$10$^{44}$ erg s$^{-1}$. For each turbulence velocity broadening
of 500, 1000, 1500 and 2000 km s$^{-1}$ (1$\sigma$), the grids cover five orders of
magnitude in both column density and ionization parameter,\footnote{The ionization
parameter is defined as $\xi = L_\rmn{ion}/nr^2$, where $n$ is the gas electron density
and $r$ is its distance from the source with 1--1000 Ry luminosity $L_\rmn{ion}$.} with
$5 \times 10^{19} < N_\rmn{H}/\rmn{cm^{-2}} < 5 \times 10^{24}$ and
$0 < \log\,(\xi/\rmn{erg\,cm\,s^{-1}}) < 5$, respectively. We also tested different
gas densities, typical of BLR and NLR clouds, with indistinguishable results.
The inclusion of any photoionized component was accepted as significant after a statistical
improvement of $\Delta C = -13.3$, corresponding to the 99 per cent confidence level for
four parameters of interest, i.e. $N_\rmn{H}$, $\xi$, normalization and outflow velocity.
As expected, no exhaustive solution was found in this effort, which should be merely taken
as a rudimentary proof of the existence of a fairly large range of ionization states. This
notwithstanding, a passable fit ($C/\nu = 605/479$) was achieved with three emission phases
with $\log\,(\xi/\rmn{erg\,cm\,s^{-1}}) > 4.1$, $\sim$3.1$\pm$0.3, and $< 0.6$. The other
gas properties are not well constrained (especially the column densities), so we refrain
from discussing their face values. Anyway, there is evidence for motions along the line
of sight: two \textsc{xstar} components have a modest outflow velocity of $v_\rmn{out} =
850^{+620}_{-330}$ km s$^{-1}$, while the third one prefers an inflow at $\sim$3500 km
s$^{-1}$ to a systemic velocity ($\Delta C = 7$). This is driven by the broad complex
centred at $E \sim 555$ eV (Table~\ref{t2}) and its identification with O\,\textsc{vii}
He$\alpha$, which is not fully reliable (see below). In this model, once the threefold
AGN continuum is excluded, the contribution from collisionally ionized plasma to the
0.5--4 keV flux is about 30 per cent. Overall, the main shortcoming is that the intensity
of many of the former Gaussian lines is slightly underpredicted, possibly due to higher
metallicity. A 3$\times$ solar Fe abundance in the nuclear region of NGC\,1365 is indeed
suggested by the X-ray reflection features (Risaliti et al. 2009b; Brenneman et al. 2013).
\begin{figure*}
\includegraphics[width=0.95\textwidth]{lines_zoom.pdf}
\caption{Enlarged view of the MEG (a--c) and HEG (d--f) spectra in the main emission bands.
The thermal and AGN continuum components were assumed from model E, while the lines were
refitted (red curve). The data were rebinned to 1024 channels, corresponding to $\sim$2 times
the native FWHM resolution. For the sake of a visual inspection, a 5-channel wide triangular
smoothing has been applied to the ungrouped spectra (turquoise curve). The vertical lines mark
the expected energy of the stronger transitions. (a) Due to the poor signal to noise, the sampling
in the oxygen band is further degraded to a factor of 8, with a smoothing window of 13 channels.
(b) Both Ne\,\textsc{x} Ly$\alpha$ and Ly$\beta$ are detected with a possible velocity broadening
($\rmn{FWHM} \sim 1300$ km s$^{-1}$). The thermal component is not able to fully account for all
the putative Fe lines. (c) Despite the triplet-like appearance of the emission complex at
$\sim$1.31--1.36 keV, the lower-energy line is not associated with Mg\,\textsc{xi} He$\alpha$
and is most likely due to Fe\,\textsc{xxi} $4d \rightarrow 2p$. (d) The broad resonance line
of Si\,\textsc{xiii} can be resolved into a blueshifted ($v_\rmn{out} \sim 1600$ km s$^{-1}$)
triplet. (e) The double peak across Ar\,\textsc{xviii} Ly$\alpha$ would imply inflows/outflows
at several thousands km s$^{-1}$, but the red horn is not confirmed in the MEG data. (f) Besides
the resolved Fe K$\alpha$ feature, both Fe K$\beta$ and Ni K$\alpha$ are clearly present although
statistically not significant due to the low effective area over this range. (See the text for
more details).}
\label{lz}
\end{figure*}
\subsection{Line properties}
For the sake of a qualitative assessment, we subsequently considered both the MEG and HEG
spectra at 1024 and 2048 channels, preserving the constant resolution in wavelength space
afforded by the gratings. This choice is not suitable for global statistical purposes, since
no photons are collected in several bins, especially at very low or high energies. Moreover,
because of the low number of counts, the aspect and position of some lines is contingent on
the binning criterion adopted. While some degree of speculation is admitted in this heuristic
approach, we always checked the raw data in wavelength units to avoid exotic interpretations,
sticking to the most conservative explanation. None the less, in many cases this helped us
extracting more detailed information on the properties of the emission lines, for instance
in terms of widths, velocity shifts and relative weight of the different components in He-like
triplets. To this aim, we also created smoothed spectral profiles by applying a triangular
moving average to the unbinned (2048 channels) data. For each band of interest, the results
of this procedure are shown in Fig.~\ref{lz}, where the baseline continuum is drawn from
model E and the key features have been fitted afresh. In the following we examine every
atomic species separately, and then try to infer a more general picture.
\subsubsection{Oxygen}
Unfortunately, at the energies of the O\,\textsc{vii}--\textsc{viii} emission the MEG spectrum
is extremely noisy, and perhaps also affected by some background. In this case, we had to rebin
down to 256 channels and perform a comparably heavy smoothing (Fig.~\ref{lz}a). Even so, it is
clear that the broad feature at $\sim$555 eV in model E (which could be blindly associated with
O\,\textsc{v} K$\alpha$ from its centroid) presents several substructures, and that the line at
$E \sim 618$ eV in Table~\ref{t2} (in formal agreement with O\,\textsc{v} K$\beta$) is actually
a blend (possibly including N\,\textsc{vii} Ly$\gamma$). We attempted at fitting the former
complex with a self-consistent O\,\textsc{vii} He$\alpha$ triplet, fixing the energy of the three
components and allowing for a common shift. As anticipated above, this selects a redshift with
velocity of $\sim$5500 km s$^{-1}$, which would be loosely supported by the identification of
the line at $E \simeq 581$ eV (falling just below our detection threshold) with N\,\textsc{vii}
Ly$\beta$ ($E \simeq 593$ eV at rest). Bearing in mind some claims in this sense (like for
Mrk\,110; Boller, Balestra \& Kollatschny 2007), such a fast inflow is not regarded as genuine
in this context, and the $\sim$555-eV blend remains ambiguous. We note that one of the spikes in
the smoothed spectrum has the right energy for the forbidden component of the oxygen He-like
triplet, but other species might be involved (for example, N\,\textsc{vi} RRC is found at 552 eV).
The statistics are seriously deficient, but the feature at $E \simeq 581$ eV can be tentatively
ascribed to outflowing O\,\textsc{vii}. Also the O\,\textsc{viii} Ly$\alpha$ line suggests a
$v_\rmn{out} \sim 500\pm200$ km s$^{-1}$, and the higher order Ly$\beta$, Ly$\gamma$ and RRC
transitions of this ion are consistent with this value,\footnote{In the O\,\textsc{viii} energy
range, the MEG absolute wavelength accuracy is equivalent to $\sim$200 km s$^{-1}$.} even if
suffering from contamination by the Fe L-shell array.
\subsubsection{Neon}
There is very little evidence for Ne\,\textsc{ix} emission, once the almost coincident
$3d \rightarrow 2p$ lines from Fe\,\textsc{xix} are attributed to collisionally ionized
gas. Ne\,\textsc{x} Ly$\alpha$ and Ly$\beta$, instead, are both obvious and definitely
interesting. They appear to be resolved ($\sigma = 1.9^{+0.7}_{-0.5}$ eV for $\Delta C
= 1$) and minimally blueshifted ($v_\rmn{out} < 400$ km s$^{-1}$; Table~\ref{t3}).
The intensity ratio Ly$\beta$/Ly$\alpha$ is quite large, $\sim$0.6$\pm$0.3. This is a hint
of photoexcitation, which boosts the higher order lines through radiative decay (e.g.
Kinkhabwala et al. 2002). Also Fe L-shell resonances would be enhanced (Sako et al. 2000),
and indeed the thermal component fails to reproduce their emission at $\sim$1.06--1.18 keV
(Fig.~\ref{lz}b). Notably, the strongest $3d \rightarrow 2p$ Fe lines, including
Fe\,\textsc{xx} (0.956 keV) and Fe\,\textsc{xxi} (1.009 keV), accept some blueshift at
$v_\rmn{out} \sim 900$ km s$^{-1}$. This is probably too high (e.g. Veilleux, Cecil \&
Bland-Hawthorn 2005) for any starburst superwind in NGC\,1365, favouring an origin from
matter photoionized and photoexcited by the AGN rather than shock-heated much farther out.
\subsubsection{Magnesium}
Three lines are seen in the Mg\,\textsc{xi} He$\alpha$ band (Fig.~\ref{lz}c), but the
low-energy one is actually due to Fe\,\textsc{xxi} $4d \rightarrow 2p$, again more
prominent than in a pure thermal scenario. The remaining pair are presumably the
forbidden and recombination components of the triplet. Together with the Mg\,\textsc{xii}
Ly$\alpha$ line, they share $\sigma = 1.6 \pm 0.6$ eV ($\Delta C = 1$) and $v_\rmn{out}
\sim 700\pm100$ km s$^{-1}$ (Table~\ref{t3}). The only other feature from these ions is
the possible Mg\,\textsc{xii} RRC, while the puzzling excess around the energy of the
Ly$\beta$ is formally incompatible with the shift of the parent series, and is eventually
unknown (Fig.~\ref{lz}d).
\begin{figure}
\includegraphics[width=8.5cm]{triplet.pdf}
\caption{Si\,\textsc{xiii} He$\alpha$ triplet in the HEG spectrum at 2048 channels
($\Delta\lambda \simeq 10~\rmn{m\AA}$, consistent with the FWHM resolution). The
blue and green dashed lines indicate the energy of the forbidden, intercombination,
and resonance transitions for $v_\rmn{out} = 0$ and 1600 km s$^{-1}$, respectively.
Both velocity components seem to be present within the energy/wavelength calibration
accuracy, the former possibly associated with the starburst and the latter to the
AGN. The continuum is drawn in red.}
\label{tr}
\end{figure}
\subsubsection{Silicon}
A broad line is detected in model E at the energy of Si\,\textsc{xiii} He$\alpha$, centred
around the resonance transition. Its width in the HEG spectrum at 1024 channels is $\sigma \sim
18$ eV, and a narrow core is noticeable (Fig.~\ref{lz}d). While the FWHM of $\sim$7000 km
s$^{-1}$ would dictate a BLR origin, we tried to disentangle the triplet components. The best
solution is found for unresolved profiles at $v_\rmn{out} \sim 1600\pm100$ km s$^{-1}$, with
the forbidden and resonance lines shifted to $\sim$1.850 and 1.875 keV (Fig.~\ref{tr}). This
outflow velocity is not confirmed by Si\,\textsc{xiv} Ly$\alpha$, which lies at the expected
rest-frame energy. Moreover, after the joint $\sim$10-eV shift, the intercombination line
becomes the stronger one at $\sim$1.865 keV, which is inconsistent with the weights of
Mg\,\textsc{xi} and practically unphysical. On the other hand, its intensity is naturally
explained by a contribution from resonant emission at rest, supported by the faint forbidden
companion and associated with either the AGN or the starburst. Two velocity components are
tentatively distinguished then. Only the properties of the blueshifted triplet are listed
in Table~\ref{t3}. Finally, there is an unidentified secondary peak at $E \sim 2.039$ keV.
The closer transition is Al\,\textsc{xiii} Ly$\beta$ ($E \simeq 2.048$ keV), but any Ly$\alpha$
counterpart would be much weaker. If due to H-like silicon, the sizable shift calls for
$v_\rmn{out} \sim 4700$ km s$^{-1}$.
\subsubsection{Argon}
While S\,\textsc{xv}--\textsc{xvi} is recognized but very faint, some basic constraints
can be put on Ar\,\textsc{xvii}--\textsc{xviii}. The broad ($\sigma \sim 17$ eV) He$\alpha$
line is found again at the resonance energy. The same considerations made above for the
Si triplet could apply, but here any fine structure cannot be appreciated since the
separation of the three components is commensurate with the FWHM. The same holds for
He$\beta$. Another double-peaked feature is visible across the Ar\,\textsc{xviii}
Ly$\alpha$ transition (Fig.~\ref{lz}e). The red horn is dubious, since the HEG and MEG
data are in conflict (the MEG resolution, however, is lower by a factor of 2). The blue
one would correspond to $v_\rmn{out} \sim 2700$ km s$^{-1}$. In any case, we can rule out
a contribution of the Ar\,\textsc{xviii} Ly$\beta$ line (3.936 keV at rest) to the blend
near $\sim$3.90 keV, which is the alleged combination of forbidden and resonant Ca\,\textsc{xix}
He$\alpha$ with modest blueshift.
\begin{table}
\caption{Summary of the best constrained lines. No errors are given for tied (or frozen)
parameters. Uncertainties are purely statistical at the 68 per cent confidence level
($\Delta C = 1$).}
\label{t3}
\begin{tabular}{l@{\hspace{20pt}}c@{\hspace{10pt}}c@{\hspace{10pt}}c@{\hspace{10pt}}c}
\hline
\multirow{2}{*}{Line} & $E_\rmn{lab}$ & $\sigma$ & FWHM & $v_\rmn{out}$ \\
& (keV) & (eV) & (km s$^{-1}$) & (km s$^{-1}$) \\
\hline
Ne\,\textsc{x} Ly$\alpha$ & 1.022 & 1.9$^{+0.7}_{-0.5}$ & 1280$^{+480}_{-510}$ & $< 400$ \\
Ne\,\textsc{x} Ly$\beta$ & 1.211 & 2.1 & 1280 & $< 400$ \\
Mg\,\textsc{xi} He$\alpha$\,(f) & 1.331 & 1.6$\pm$0.6 & 840$^{+300}_{-320}$ & 710$\pm$110 \\
Mg\,\textsc{xi} He$\alpha$\,(r) & 1.352 & 1.6 & 840 & 710 \\
Mg\,\textsc{xii} Ly$\alpha$ & 1.473 & 1.8 & 840 & 710 \\
Si\,\textsc{xiii} He$\alpha$\,(f) & 1.839 & $< 1.6$ & $< 600$ & 1590$^{+80}_{-60}$ \\
Si\,\textsc{xiii} He$\alpha$\,(r) & 1.865 & $< 1.6$ & $< 600$ & 1590 \\
Si\,\textsc{xiv} Ly$\alpha$ & 2.006 & $< 1.7$ & $< 600$ & $< 300$ \\
\hline
\end{tabular}
\end{table}
\subsubsection{Iron}
Above 4 keV, only the fluorescence K$\alpha$ line from neutral iron at
$E = 6.404^{+0.012}_{-0.015}$ is statistically significant, although the K$\beta$ is clear
as well, and there is a trace of Ni K$\alpha$ (Fig.~\ref{lz}f). All of these are signatures
of reflection of the AGN radiadion in cold, optically thick matter, arguably located at the
torus scale in the original unification scheme. We can assess the distance of this gas from
the width of the Fe K$\alpha$ line, which is nicely resolved thanks to its $\sim$35--40 counts
($\sigma = 27^{+17}_{-12}$ eV; Fig.~\ref{ka}). We assume that the broadening is due to the
virial motion in the emitting region, and that the velocity dispersion is related to the
FWHM through a factor $f = \sqrt{3}/2$, which corrects for the (unknown) geometry and
distribution of the gas (see also Netzer \& Marziani 2010). The predicted FWHM is
$\sim$760($M_8/r_\rmn{pc}$) km s$^{-1}$, where $M_8$ is the mass of the central black hole
in units of 10$^8 M_{\sun}$ and $r_\rmn{pc}$ is the radial distance in pc. This expression
agrees within a factor of $\sim$2 with the case of pure Keplerian motion with reasonable orbital
inclination ($i > 20\degr$). Far larger uncertainties are associated with the black hole mass.
No direct measurement (e.g. from reverberation mapping) is available for NGC\,1365, so that
the full range of $\log\,(M_\rmn{BH}/M_{\sun}) \sim 6$--8 is covered in the literature. The
higher values are based on the correlation of $M_\rmn{BH}$ with the bulge luminosity, and are
likely biased by the starburst contribution to the latter. The most sensible guess is then
of a few $\times$10$^6\,M_{\sun}$ (Risaliti et al. 2009b; Davis et al. 2014). With a conservative
$M_8 = 0.1$, and the observed K$\alpha$ FWHM of $\sim$3000$^{+1900}_{-1350}$ km s$^{-1}$, we
obtain that $r \sim 0.002$--0.02\ pc, which is within the BLR. Indeed, the width of the
K$\alpha$ line is consistent (at 90 per cent errors) with that of the broad nuclear component
of the H$\beta$ in the optical, whose FWHM is 1895 km s$^{-1}$ (Schulz et al. 1999). From the
K$\alpha$/H$\beta$ width ratio we can deduce that the relative size of the respective emission
regions is roughly the same. This is not surprising in a source like NGC\,1365, where BLR
clouds are responsible for variable X-ray obscuration up to the Fe-K band and beyond.
Regardless of the precise black hole mass, in terms of the gravitational radius the distance
of the Fe K$\alpha$ reflector perfectly agrees with the universal location of a few
$\times$10$^4\,r_{g}$ determined by Shu, Yaqoob \& Wang (2011).
\begin{figure}
\includegraphics[width=8.5cm]{fek_cont.pdf}
\caption{Confidence contours at the nominal 68, 90 and 99 per cent level for the Fe K$\alpha$
intensity versus velocity width, obtained from the unbinned HEG spectrum with all the AGN
continuum parameters free to vary. The vertical dashed line indicates the FWHM of the broad
H$\beta$ component in the optical, suggesting a common origin from BLR clouds.}
\label{ka}
\end{figure}
\subsection{Covering factor}
As established from the FWHM of Fe K$\alpha$ (3000 km s$^{-1}$) and, provisionally, from
those of Ne\,\textsc{x} ($\sim$1300 km s$^{-1}$) and Mg\,\textsc{xii} Ly$\alpha$ ($\sim$800
km s$^{-1}$), the gas probed by these \textit{Chandra}/HETG spectra is likely located across
the boundary between the classical BLR and NLR (see also Crenshaw \& Kraemer 2007). It is
therefore tempting to try to evaluate its covering fraction ($f_\rmn{cov}$) and to explore
its connection with the clumps responsible for the X-ray occultations of the source. To do
so, we applied an \textsc{xstar} grid to the 1.3--1.5 keV band, characterized by the intense
lines from Mg\,\textsc{xi}--\textsc{xii}. For given column density and amount of ionizing
radiation, the measured Mg luminosity of $L_\rmn{Mg} \sim 6 \times 10^{38}$ erg s$^{-1}$
depends on the fraction of solid angle occupied by the gas. The predicted luminosity for
a full covering of 4$\upi$ sr (i.e., $f_\rmn{cov} = 1$) is degenerate with the column
density, but becomes slowly responsive to its exact value at $N_\rmn{H} > 2 \times 10^{23}$
cm$^{-2}$, which is typical for BLR clouds in NGC\,1365 (Risaliti et al. 2009b). In that
range, the entailed $f_\rmn{cov}$ lies between $\sim$2--$7 \times 10^{-3}$. This is not far
from the NLR covering factor delivered by photoionization models, which, however, is
thought to be substantially underestimated (Netzer \& Laor 1993). Indeed, it should be
quite similar to the BLR one ($\sim$0.2--0.4; e.g. Korista, Ferland \& Baldwin 1997),
even if showing a stronger decreasing trend with luminosity (Stern \& Laor 2012). A
column of $\sim$10$^{21}$ cm$^{-2}$, still plausible for the NLR, would be needed to
match the expectations.
There are several caveats about this simple calculation, though. For instance, the nearly
equivalent intensity of the He$\alpha$\,(f) and Ly$\alpha$ lines requires a fine tuning of
$\log\,(\xi/\rmn{erg\,cm\,s^{-1}}) \sim 3.5$ in a single-zone model. If a wider range of
ionization states is involved, $f_\rmn{cov}$ can be considerably higher. Allowing for two
components with $N_\rmn{H} = 5 \times 10^{22}$ cm$^{-2}$ and $\log\,(\xi/\rmn{erg\,cm\,s^{-1}})
= 2.5$ and 4.5, respectively, returns a better fit and a covering fraction of $\sim$0.15.
Many other configurations are viable, and also a mild attenuation of $L_\rmn{Mg}$ by an
external absorption layer, maybe at host-galaxy scales, cannot be ruled out. Alternatively,
given the narrower profile of the Mg lines compared to Fe K$\alpha$, we can speculate that
the innermost clouds significantly reduce the ionizing flux seen by the emitting gas at
larger distance, thus producing an apparently low $f_\rmn{cov}$ for the NLR. For
$\log\,(\xi/\rmn{erg\,cm\,s^{-1}}) \sim 3.5$ and $n \sim 10^5$ cm$^{-3}$, Mg emission
would occur at $r \sim 0.2$ pc, at least an order of magnitude higher than what inferred
for Fe K$\alpha$ (remarkably proportional to the square of the FWHM ratio). This is the
most intriguing explanation, since it is consistent with the under-luminosity in the soft
X-ray oxygen lines noted by Guainazzi et al. (2009), despite the fact that the AGN in NGC\,1365
is not intrinsically weak. Unfortunately, the current data quality does not warrant any
conclusive answer.
\subsection{Temperature and density}
The presence of possible RRC from species like O\,\textsc{viii} or Mg\,\textsc{xii}
implies that the emitting gas has a low temperature and that the ionization state is
regulated by radiation rather than by collisional equilibrium. Radiative recombination,
in fact, is the emission of a photon following the capture of a free electron, mainly to
the ground state of an ion. The shape of the consequent feature is a powerful diagnostic
of the gas temperature. In a cold plasma, only the tail of high-energy electrons overcome
the recombination threshold, and the RRC have a narrow, line-like profile, whose width is
$\Delta E \sim kT$ (Hatchett, Buff \& McCray 1976; Liedahl \& Paerels 1996). Both detections
in proximity of O\,\textsc{viii} and Mg\,\textsc{xii} RRC rely on $\sim$6--7 line counts
only in the MEG and HEG data, respectively. Hence we cannot disentangle the putative
O\,\textsc{viii} RRC from the nearby Fe\,\textsc{xviii} L-shell transition, in particular
if the former is moderately blueshifted. No blend with other strong lines is instead
foreseen at the energy of Mg\,\textsc{xii} RRC, yet we remind that this feature is not
statistically significant, so we were only able to put an upper limit of 3 eV (or $3.5
\times 10^4$ K; $\Delta C = 1$) with a \texttt{redge} model.
More information can be potentially derived by the He-like triplets, consisting of
the resonance ($1s2p\ ^1\rmn{P}_1 \rightarrow 1s^2\ ^1\rmn{S}_0$), intercombination
($1s2p\ ^3\rmn{P}_{2,1} \rightarrow 1s^2\ ^1\rmn{S}_0$), and forbidden
($1s2s\ ^3\rmn{S}_1 \rightarrow 1s^2\ ^1\rmn{S}_0$) transitions. These provide an
effective measure of the physical conditions of the gas (Porquet \& Dubau 2000, and
references therein), since the intensity ratios $\mathcal{R} = \rmn{f/i}$ and
$\mathcal{G} = \rmn{(f+i)/r}$ are very sensitive to the electron density and
temperature, respectively. Given that O\,\textsc{vii} is too noisy, Ne\,\textsc{ix}
is formally undetected, and S\,\textsc{xvii}, Ar\,\textsc{xvii} and Ca\,\textsc{xix}
are too faint and/or unresolved, the only accessible species are Mg\,\textsc{xi}
and Si\,\textsc{xiii}. Even if the triplet decompositions proposed above (which
impose outflow velocities of $\sim$700 km s$^{-1}$ for Mg and $\sim$1600 km s$^{-1}$
for Si) are valid, only upper limits can be placed. The density can be anything below
the critical value ($n \sim 10^{13}$--10$^{14}$ cm$^{-3}$) beyond which the forbidden
components are collisionally suppressed, while temperature is constrained to be $T
< 3 \times 10^6$ K. This is barely meaningful in the light of the appearance of
narrow RRC features, but it is enough to exclude collisional ionization in a hot
($kT \sim 1$ keV) plasma as the dominant mechanism in these emission-line HETG
spectra of NGC\,1365.
\section{Summary and Conclusions}
In this paper we have presented the X-ray spectral analysis of the first
\textit{Chandra}/HETG observations of the prototypical changing-look Seyfert
galaxy NGC\,1365, which lingered in a Compton-thick state for the entire
span of four days. The soft X-ray spectrum was thus dominated by a wealth
of recombination lines belonging to He- and H-like ions of the most common
light elements from oxygen to calcium, plus iron L-shell transitions. Thanks
to the unrivaled spatial resolution offered by \textit{Chandra}, we were able
to zoom in on the close surroundings of the AGN, and unveil a photoionized gas
component that was largely diluted in previous observations. Indeed, the
spectra obtained with \textit{XMM--Newton}/RGS, whose large aperture also
encompasses all the diffuse emission from the inner 5 kpc, were heavily
contaminated by collisionally ionized plasma, shock-heated by the fierce
circumnuclear star-formation activity. The residual thermal contribution
to the overall emission-line intensity now amounts to $\sim$30 per cent only.
The emergence of a photoionized spectrum with properties analogous to those
reported in most of the nearby obscured Seyfert galaxies partly mitigates the
apparent anomaly of NGC\,1365. In spite of the modest statistical quality of
the data, whereby only a handful of lines have $> 10$ counts, the picture in
favour of cold ($kT \ll E$) gas exposed to the AGN radiation is corroborated
by the tentative presence of narrow RRC features (O\,\textsc{viii} and
Mg\,\textsc{xii}), and by the qualitative inspection of the He-like triplets
(mainly from Mg and Si). Photoexcitation might be important as well, as
indicated by the strength of some higher order transitions (e.g. Ne\,\textsc{x}
Ly$\beta$) and of the Fe L-shell forest around $\sim$1 keV. Possible outflow
velocities in the range $\sim$0--1600 km s$^{-1}$ are revealed, and a few lines
(Ne\,\textsc{x}, Mg\,\textsc{xi}--\textsc{xii}) show some evidence of broadening
($\sim$1000 km s$^{-1}$), signifying that the location of the gas is across the
virtual BLR/NLR boundary. The K$\alpha$ fluorescence feature from neutral iron
at $E = 6.404^{+0.012}_{-0.015}$ keV is resolved to a width of
$\sigma = 27^{+17}_{-12}$ eV, corresponding to a FWHM of
$\sim$3000$^{+1900}_{-1350}$ km s$^{-1}$. This is somewhat larger but fully consistent
with the optical H$\beta$ line, supporting a comparable size of the emitting regions.
With a preferential distance of few $\times$10$^4\,r_{g}$ from the black hole,
it is then very likely that Fe K$\alpha$ arises from the same Compton-thick
clouds that induce the recurrent column density jumps and the extreme variability
seen in this source.
Besides the main findings, there are also some unusual hints, such as of broad
(BLR-like) profiles in resonance lines, of double peaks, and of radial velocities of
several thousands km s$^{-1}$, even in inflow. If confirmed, these would be absolutely
exceptional traits, but caution is mandatory given the poor statistics. As opposed to
standard type-2 Seyferts like NGC\,1068, the erratic behaviour of NGC\,1365 below 10
keV makes it hard to amass strictly consistent information from different epochs, so
naively it could seem unfeasible to overcome this limitation with just a longer exposure.
However, even in a Compton-thin case, the column density is normally of the order of
$N_\rmn{H} \sim 10^{23}$ cm$^{-2}$, and the direct AGN continuum is almost completely
absorbed in the soft X-rays. The ample record of past observations suggests that a nearly
unobscured state such as the one sampled in January 2013 is a very rare occurrence for
NGC\,1365. The photoelectric cutoff is thus expected to fall beyond the main complexes
from O, Ne, Mg, and maybe also Si, leaving their aspect virtually constant with time
and allowing the build-up of a nuclear emission-line template. On the other hand, the
appearance of the transmitted AGN continuum at higher energies would enable the study
of the high-ionization absorption features originating from the accretion-disc/BLR wind,
from Fe\,\textsc{xxv}--\textsc{xxvi} down to Ca\,\textsc{xix}--\textsc{xx} and even
Ar\,\textsc{xvii}--\textsc{xviii}, depending on the exact value of $N_\rmn{H}$. For these
reasons, any prospective observation of NGC\,1365 at high spatial and spectral resolution
would provide further invaluable insights into the properties of the sub-pc scale
environment in active galaxies.
\section*{Acknowledgments}
We thank the anonymous referee for their useful comments. EN is supported
by STFC under grant ST/J001384/1. JNR acknowledges the financial support
provided through the \textit{Chandra} award GO2-13123A for this programme.
The scientific results reported in this article are based on observations
made by the \textit{Chandra} X-ray Observatory. This research has made use
of software provided by the \textit{Chandra} X-ray Center (CXC) in the
application package \textsc{ciao}. The figures were generated using
\texttt{matplotlib} (Hunter 2007), a \textsc{python} library for publication
of quality graphics.
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"redpajama_set_name": "RedPajamaArXiv"
}
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Q: Is it possible to write a function work for int and long (float, byte .etc) in F#? when use
let add a b = a + b
it works for int. and
let add2 a b:float = a + b
work for float.
Is it possible to write a function work for int and long (float, byte .etc) in F#?
i need a function whose "a" work for int and long like this:
let f a b = a >>> b
let f (a:int64) b = a >>> b
is it possible in F#?
A: When you want to write a function that can work with multiple different numeric types, you need to use inline and "static member constraints". The problem is that normal .NET generics cannot capture constraints like "supports the + operator".
To make your sample add function generic, you can use inline:
let inline add x y = x + y
When you look at the inferred type, you'll see something like this:
val inline add :
x: ^a -> y: ^b -> ^c
when ( ^a or ^b) : (static member ( + ) : ^a * ^b -> ^c)
This essentially says that the function can be called on any two arguments that support the + operator. Note that this only works because the function is inline and so the F# compiler does not have to rely on .NET to express the constraints. The same works for the >>> operator:
let inline f a b = a >>> b
The function can now be used with both int64 and int arguments:
f 1024L 2
f 1024 2
I wrote an article about writing generic numeric code in F# some time ago which you may find useful too.
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"redpajama_set_name": "RedPajamaStackExchange"
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\section{Introduction}
Electron paramagnetic resonance (EPR) is a central tool in the study
of open-shell electronic structure as found in many complex transition metal systems, such as in the active sites of
metalloenzymes.
The primary quantity measured is the transition energy between unpaired electron states
split by the external magnetic field. The proportionality between the effective magnetic moment
of the unpaired electron and its spin, namely the $g$-tensor, reports on the electronic environment of the electron.
The utility of EPR arises from the high sensitivity of the $g$-tensor,
which thus yields invaluable information on the nuclear geometry and electronic structure.
The most common route to compute EPR $g$-tensors is through density functional theory (DFT)~\cite{vLenthe,ziegler1,ziegler2,Malkina,Kaupp,Neese01_2,g_DKH,g_DKH2,Komorovsky,Repisky,Rinkevicius}.
\textit{Ab initio} wavefunction methods to compute $g$-tensors have also been explored, using multireference configuration interaction
\cite{Lushington1,Bundgen,Lushington2,Bruna,Neese03,Brownridge,Neese07,Neese01,gSOCI},
the complete active space self-consistent field \cite{Vahtras,Bolvin,Ganyushin, Lan},
multireference perturbation theory \cite{Neese03,Bolvin,Vancoillie}
and coupled-cluster theory \cite{Gauss, Bolvin}. A drawback of the electronic structure methods
listed above is that they are severely limited in terms of the number of open shells they can reliably handle,
restricting the kinds of transition metal complexes that can be studied.
Recently, in Ref.~\cite{roemelt}, Roemelt presented an approach to compute $g$-tensors using a
density matrix renormalization group (DMRG) description of the electronic structure, which is capable of
treating a significantly larger number of open shells than other techniques.
Here, we describe a related DMRG implementation to obtain $g$-tensors based
on a state interaction spin-orbit coupling DMRG formalism~\cite{roemelt, elviras, reiher}. The main
methodological difference between our approach and that of Roemelt that we use is a more flexible representation of the interacting states.
Both approaches include spin-orbit coupling in the determination of the zeroth order wavefunction (i.e. they are first order approaches)~\cite{Bolvin,Ganyushin,Chibotaru,Lan},
rather than treating it together with the magnetic field (second order approaches)~\cite{Malkina,Kaupp,Lushington1,Bundgen,Lushington2,Bruna,Neese03,Brownridge,Neese07,Vancoillie,ziegler1,ziegler2,Vahtras,Rinkevicius}.
Together with Ref.~\cite{roemelt}, our work is a step towards obtaining $g$-tensors in transition metal complexes including a
rigorous treatment of a large number of open shells. We first describe the formalism in section \ref{sec:theory},
then proceed to demonstrate the calculation of $g$-tensors at the DMRG level for the \ce{TiF_3} and \ce{CuCl4^2-} complexes,
a [2Fe-2S] model complex, and a \ce{Mn4CaO5} model of the S2 state of the oxygen evolving complex (OEC).
\section{Theory}
\label{sec:theory}
We first recapitulate how to extract $g$-tensors from the spin and ab initio electronic Hamiltonians
in sections \ref{sec:theory1} and \ref{sec:theory2}. Other useful presentations that we draw on can be found
in Refs.~\cite{Bolvin,Vancoillie,Lan,Chibotaru}. In Section \ref{sec:theory3} we summarize how to treat spin-orbit coupling within the spin-orbit mean-field approximation.
Section \ref{sec:theory3} also describes how to calculate all the required quantities with DMRG wavefunctions and a state-interaction formalism,
as used in our earlier work in Ref.~\cite{elviras}.
\subsection{The spin Hamiltonian and ab initio Hamiltonian}
\label{sec:theory1}
The relationship between theory and actual EPR spectra is provided by the effective spin Hamiltonian.
The $g$-tensor arises as a parameter of the effective spin Hamiltonian
and it describes the Zeeman interaction between an external magnetic field $\mathbf{B}$ and an
effective spin $\mathbf{S}_\text{eff}$ of the molecule.
Other parameters of the effective spin Hamiltonian, the zero-field splitting tensor $\mathbf{D}$ and the hyperfine coupling tensor $\mathbf{A}$,
define the splitting of energy levels in the absence of an external magnetic field .
Experimentally, the parameters $\mathbf{g}$, $\mathbf{D}$, $\mathbf{A}$ can all be extracted from EPR spectra.
To derive them from quantum chemistry calculations one should, first, assume
one-to-one correspondence between the spin-multiplet of an effective spin Hamiltonian
and ab initio many-electron wavefunctions, describing actual electronic spin states of the paramagnetic complex.
The effective spin Hamiltonian in a magnetic field $\mathbf{B}$ is
\begin{align}
\hat{H}_\mathrm{spin} &= \mu_B \mathbf{B} \cdot \mathbf{g} \cdot \hat{\mathbf{S}}_\text{eff}+\hat{\mathbf{S}}_\text{eff}\cdot \mathbf{D}\cdot \hat{\mathbf{S}}_\text{eff}+\sum_R \hat{\mathbf{S}}_\text{eff}\cdot \mathbf{A}\cdot\hat{\mathbf{I}}_R , \label{eq:Hspin}
\end{align}
where $\mu_B$ is the Bohr magneton, $\hat{\mathbf{S}}_\text{eff}$ is the effective spin operator, and $\hat{\mathbf{I}}_R$ is the
$R$th nuclear spin operator.
The parameters $\mathbf{g}$, $\mathbf{D}$, $\mathbf{A}$ can be obtained by fitting the spectrum of Eq.~\ref{eq:Hspin} to the
theoretical spectrum of an ab initio electronic Hamiltonian $\hat{H}$ in a magnetic field, which can be expressed as:
\begin{align}
\hat{H}&= \hat{H}_{0} +\hat{H}_\mathrm{Ze},
\end{align}
where $\hat{H}_{0}$ is the electronic Hamiltonian in the absence of the field and
$\hat{H}_\mathrm{Ze}$ (the Zeeman interaction) groups together all terms with
an explicit dependence on the field. The Zeeman interaction can be expressed as
\begin{align}
\hat{H}_{Ze} &= \mu_B(\hat{\mathbf{L}}+g_e \hat{\mathbf{S}}) \cdot \mathbf{B} \label{eq:zeeman}
\end{align}
where $\hat{\mathbf{L}}$ and $\hat{\mathbf{S}}$ are the total orbital and spin angular momentum operators,
and $g_e\approx 2.002319$ is the Land{\'e} factor for a free electron.
The electronic Hamiltonian $\hat{H}_{0}$ incorporates both spin-independent and spin-dependent relativitistic terms.
The latter include the spin-orbit coupling (SOC), spin-spin coupling and hyperfine interactions.
In this work, we determine $\mathbf{g}$ from an ab initio calculation.
The $g$-tensor is predominantly determined by the spin-orbit coupling, which changes the effective spin of the unpaired electrons.
Therefore we omit hyperfine interaction and spin-spin coupling (required for $\mathbf{D}$ and $\mathbf{A}$)
in the expression for $\hat{H}_{0}$ and write it in the form of:
\begin{align}
\hat{H}_{0} = \hat{H}_\mathrm{SR} + \hat{H}_\mathrm{SOC}. \label{eq:H0}
\end{align}
We discuss the treatment of spin-orbit coupling further in Sec.~\ref{sec:theory3}.
\subsection{Extracting the g-tensor}
\label{sec:theory2}
We next consider how to extract the $g$-tensor by relating the contributions of the Zeeman interaction (\ref{eq:zeeman}) in
the ab initio Hamiltonian to that of $\mu_B \mathbf{B} \cdot \mathbf{g} \cdot \hat{\mathbf{S}}_\text{eff}$ in the spin Hamiltonian (\ref{eq:Hspin}).
We follow the reasoning of Gerloch and McMeeking, first established within ligand field theory~\cite{gerloch}
and later generalized to ab initio Hamiltonians~\cite{Chibotaru2,Bolvin,Vancoillie}.
According to Kramers' theorem, in a molecular system with an odd number of electrons, i.e. with half-integer total spin, all states are at least
twofold degenerate in the absence of an external magnetic field;
such pairs of degenerate states are referred to as Kramers pairs, and are
related by time-reversal symmetry. The ground-state is then described by (at least one) Kramers pair $(\Phi, \bar{\Phi})$
at zero magnetic field. The first-order effect of an external magnetic field is
to split this degenerate Kramers pair. The corresponding first order energy can be computed
from the Zeeman interaction in the ab initio Hamiltonian as well as with the spin Hamiltonian, which gives the expression for the $g$-tensor.
Using degenerate first order perturbation theory, the splitting of the eigenvalue pair $(\Phi, \bar{\Phi})$ is obtained by diagonalizing the first order interaction.
Defining the symmetric quantity $G_{kl} =\sum_{n} g_{kn} g_{ln}$, or $\mathbf{G}=\mathbf{gg}^T$, one can then use the formula, proposed by Gerloch and McMeeking:
\begin{align}
\mathrm{G}_{kl} &=2 \sum_{u,v=\Phi, \bar{\Phi}} \langle u|\hat{L}_k+g_e\hat{S}_k|v \rangle \langle v|\hat{L}_l+g_e\hat{S}_l |u \rangle \label{eq:ggt},
\end{align}
Finally, diagonalizing $\mathbf{G}$ yields the principal axes for the $g$-tensor, and the positive square roots of the three eigenvalues are the $g$-factors $g_1, g_2, g_3$.
The primary ab initio task is thus to obtain the matrix elements of $\hat{L}_k$ and $\hat{S}_k$ between
the degenerate Kramers ground-state pair in Eq.~\ref{eq:ggt}. This requires
determining the eigenvalues of the electronic Hamiltonian $\hat{H}_{0}$, including the spin-orbit coupling,
and computing the specific matrix elements in Eq.~\ref{eq:ggt}, as discussed in the next section.
\subsection{Spin-orbit coupling and matrix elements with DMRG}
\label{sec:theory3}
We determine spin-orbit coupled wavefunctions using the state interaction spin-orbit coupled DMRG (DMRG-SISO) that we described in Ref.~\cite{elviras}.
In this approach, the spin orbit operator $\hat{H}_\text{SO}$ is evaluated in a basis of spin-adapted DMRG wavefunctions $\{ |\Psi_{I, S, M_S}\rangle \}$.
It is worth briefly mentioning the different choices of spin-adapted DMRG wavefunctions that can be used as the SISO basis.
For a set of $N$ orbitals (sites) the DMRG wavefunction amplitudes can be written in matrix product form. In
the so-called canonical form at site $i$, this is
\begin{align}
|\Psi\rangle = \sum_{\{n\} } \mathbf{L}^{n_1} \ldots \mathbf{L}^{n_{i-1}} \mathbf{C}^{n_i} R^{n_{i+1}} \ldots \mathbf R^{n_N} \ket{n_1 \ldots n_N} \label{eq:mps}
\end{align}
where for a given occupation string, $\mathbf{L}^n$, $\mathbf{C}^n$, $\mathbf{R}^n$ are $M \times M$ matrices,
and the leftmost and rightmost boundary matrices are $1\times M$ row and $M \times 1$ column vectors respectively.
There are different choices to optimize the matrices $\mathbf{L}^n$, $\mathbf{C}^n$, $\mathbf{R}^n$ in the DMRG sweeps.
In a so-called {\it state-averaged} DMRG calculation, a common renormalized basis (and thus a common set of $\mathbf{L}^n$, $\mathbf{R}^n$ matrices)
is optimized for all the electronic states, and only the $\mathbf{C}^n$ matrix is unique to each state.
The state-averaged DMRG representation was used in Ref.~\cite{roemelt} by Roemelt to represent all the states (including of different spin)
entering into the SISO procedure. An alternative, state-specific, approach is to have
different sets of $\mathbf{L}^n$, $\mathbf{C}^n$, $\mathbf{R}^n$ for different states in the calculations.
This was the approach in our previous work~\cite{elviras}, where we used a different set of $\mathbf{L}^n$, $\mathbf{C}^n$, $\mathbf{R}^n$ for states of different spin
(although we used a state-averaged representation for states of the same spin). For a given bond dimension $M$, the state-averaged approach
reduces the amount of computation, but results in a lower accuracy for each individual eigenstate compared to the state-specific approach. Finally, in this work we also consider
a cheaper approach, where in each spin-sector, we use the $\mathbf{L}^n$, $\mathbf{R}^n$ {\it optimized only for the lowest state} and represent
the excited states by different $\mathbf{C}^n$ matrices, determined at the middle of the sweep. We denote this choice as ``ground-state specific'', and it has the advantage of avoiding
the large number of Davidson steps required to solve for multiple states when optimizing the $\mathbf{L}^n$, $\mathbf{R}^n$ tensors. This allows us to compute
a larger number of DMRG states to use for the SISO basis.
For the spin-orbit operator $\hat{H}_\text{SO}$, we use the spin-orbit mean-field (SOMF) approximation. This has been shown
to approximate the effects of the full one and two electron Breit-Pauli SOC operator very accurately~\cite{Marian:SOC,Hess:AMFI,Tatchen,Neese:SOMF}.
In second quantization the one-electron SOMF Hamiltonian can be written as~\cite{Neese:SOMF,Malmqvist:RASSI_SO}:
\begin{align}
\hat{H}_\mathrm{SOMF} &= \sum_{ij}\left ({V}_{ij}^{x}\hat{T}_{ij}^{x} +{V}_{ij}^{y}\hat{T}_{ij}^{y}+{V}_{ij}^{z}\hat{T}_{ij}^{z} \right ) ,\label{eq:somf}
\end{align}
where
$\hat{T}_{ij}^{x,y,z}$ are the Cartesian triplet excitation operators \cite{helgaker:purplebook,MolProp}:
\begin{align}
\hat{T}_{ij}^{x}&=\frac{1}{2}\left ( a_{i\alpha}^{\dagger}a_{j\beta} + a_{i\beta}^{\dagger}a_{j\alpha}\right )
\\ \hat{T}_{ij}^{y}&=\frac{1}{2i}\left ( a_{i\alpha}^{\dagger}a_{j\beta} - a_{i\beta}^{\dagger}a_{j\alpha}\right )
\\ \hat{T}_{ij}^{z}&=\frac{1}{2}\left ( a_{i\alpha}^{\dagger}a_{j\alpha} - a_{i\beta}^{\dagger}a_{j\beta}\right ).
\end{align}
and $V_{ij}^{x,y,z}$ is an effective set of one-electron integrals, obtained as:
\begin{align}
\braket {i| \hat{\mathbf{V}}| j}&=\braket {i| \hat{\mathbf{h}}_{1} | j}+\sum_{kl}D_{kl}\left \{\braket {ik| \hat{\mathbf{g}}_{12} | jl} -\frac{3}{2}\braket{ ik| \hat{\mathbf{g}}_{12} | lj} -\frac{3}{2}\braket {ki| \hat{\mathbf{g}}_{12} | jl} \right \} \label{eq:Vint}
\end{align}
where $D_{kl}$ is the single-particle (not necessarily idempotent) density matrix element that takes into account single occupancy
due to unpaired spins;
the one- and two-electron operators are
\begin{align}
\hat{\mathbf{h}}_{i}&=\frac{\alpha ^{2}}{2}\sum_{A}Z_{A}r_{iA}^{-3}\hat{\mathbf{l}}_{iA}, \label{eq:bpterms1}
\\ \hat{\mathbf{g}}_{ij}&=-\frac{\alpha ^{2}}{2}\hat{\mathbf{l}}_{ij}r_{ij}^{-3}, \label{eq:bpterms2}
\end{align}
where $\alpha$ is the fine structure constant, $\hat{\mathbf{r}}_{i}$, $\hat{\mathbf{p}}_{i}$ are the position and momentum operators of the $i$th electron,
$r_{ij}= |\hat{\mathbf{r}}_{i}-\hat{\mathbf{r}}_{j} |$, $\hat{\mathbf{l}}_{ij} =\hat{\mathbf{r}}_{ij}\times\hat{\mathbf{p}}_{i}$ ,
$\hat{\mathbf{l}}_{iA} =\hat{\mathbf{r}}_{iA}\times\hat{\mathbf{p}}_{i}$, $r_{iA}= |\hat{\mathbf{r}}_{i}-\hat{\mathbf{R}}_{A}|$, and $Z_{A}$ denotes the nuclear charge of the $A$th nucleus.
Note that this form of the SOMF operator is only valid for doublet ground states;
for $S>1/2$ there is an additional correction $\frac{1}{2} \sum_{mn}D_{mn} \braket{ im| \hat{\mathbf{g}}_{12} | jn}$, where $m,n$ are the singly occupied orbitals \cite{Waroquier}. However, we have not considered this correction here as all our ground states are doublets.
As we work with a spin-adapted basis, internally we do not use the Cartesian triplet operators,
but rather the spherical tensor triplet operators. These are related to the Cartesian triplet operators through the linear transformation \cite{helgaker:purplebook}:
\begin{align}
\hat{T}_{ij}^{x}&=\frac{\hat{T}_{ij}^{1,-1}-\hat{T}_{ij}^{1,1}}{2} \\
\hat{T}_{ij}^{y}&=\frac{\hat{T}_{ij}^{1,-1}+\hat{T}_{ij}^{1,1}}{2i} \\
\hat{T}_{ij}^{z}&=\frac{1}{\sqrt{2}} \hat{T}_{ij}^{1,0}.
\end{align}
Using this form of the spin-orbit operator, we evaluate the Hamiltonian in Eq.~\ref{eq:H0} in the
basis of spin-adapted DMRG states using the transition density matrix algorithm described in Ref.~\cite{elviras}. Diagonalizing this yields the spin-coupled Kramers pairs wavefunctions and energies.
Additionally, to determine the $\mathbf{G}$ matrix and $g$-tensors following the procedure in the preceding section,
we need the matrix representations of the operators $\hat{L}_x, \hat{L}_y, \hat{L}_z$ and $\hat{S}_x, \hat{S}_y, \hat{S}_z$ for the ground-state Kramers pair.
We can obtain these from the matrix elements in the basis of spin-adapted DMRG wavefunctions $\{ |\Psi_{I,SM_S}\rangle\}$,
\begin{align}
\langle\Psi_{I, S' M'_{S}}| \hat{S}_{k} | \Psi_{J,SM_{S}}\rangle &= \sum_{p}\langle\Psi_{I, S' M'_{S}}| \hat{T}_{pp}^{k} | \Psi_{J,SM_{S}}\rangle, \qquad k=x,y,z \label{eq:Sk} \\
\langle\Psi_{I, S' M'_{S}}| \hat{L}_{k} | \Psi_{J,SM_{S}}\rangle &=\sum_{ij} \langle\Psi_{I, S' M'_{S}}| \hat{T}_{ij}^{0,0} | \Psi_{J,SM_{S}}\rangle \delta_{SS'} \delta_{M_SM'_{S}}L_{ij} \label{eq:Lk}
\end{align}
where $ \hat{T}_{ij}^{0,0}=\frac{1}{\sqrt{2}}\left ( a_{i\alpha}^{\dagger}a_{j\alpha} + a_{i\beta}^{\dagger}a_{j\beta}\right ) $ is the singlet operator,
and $L_{ij} =\langle i |(\hat{\mathbf{r}}-\hat{\mathbf{R}}_{0})\times\hat{\mathbf{p}}|j \rangle$ is the orbital angular momentum
integral between the molecular orbitals $i$ and $j$, calculated with respect to an arbitrary gauge origin $\mathbf{R}_{0}$, chosen here to be
the coordinates of the transition metal centers.
The singlet operator matrix element can be computed following Ref.~\cite{Sandeep:dmrg}. Once these matrix representations are obtained,
they are contracted with the expansions of the Kramers pairs in the spin-adapted basis $\{ |\Psi_{I,SM_S}\rangle\}$ to obtain representations in the Kramers basis.
\section{Results and Discussion}
\label{sec:results}
We implemented the above method as a stand-alone code and as a module within a development version of \textsc{PySCF}~\cite{pyscf}.
Spin-orbit integrals in Eq.~\ref{eq:bpterms1}, \ref{eq:bpterms2} were computed using \textsc{PySCF}. Additional CASSCF calculations
were carried out using the \textsc{Molpro} package and geometry optimization of the [2Fe-2S] complex was carried out using \textsc{ORCA}.
All three components of the ${g}$-tensor (transformed to the principal axes, denoted arbitrarily as $x,y,z$) can be
expressed as shifts from the Land\'{e} $g$-factor
\begin{align}
g_k=g_e + \Delta g_k, \qquad k=x,y,z
\end{align}
In systems with axial symmetry $g_x = g_y = g_{\perp}$ and $g_z = g_{\parallel}$.
For some systems, we present $\Delta g_k$ shifts instead of the full $g_k$-values.
\subsection*{A. \ce{TiF3}}
We begin by considering the \ce{TiF3} complex. This has been widely used as a benchmark system for $g$-tensor calculations.
We used ANO-RCC basis sets contracted as [4s3p2d1f] for F and [7s6p5d3f2g1h] for Ti, and a
$D_{3h}$ symmetric complex with a Ti--F bond distance of 1.774{\AA}, following Ref. \cite{Vancoillie};
the calculations employed the $C_{s}$ subgroup, with the
Ti atom at the origin, one F atom on the y axis and other two in the xy plane.
A minimal active space for this complex is formed by the $3d$ orbitals of Ti, giving a (1e,5o) active space. However,
there is no correlation within this space. To construct a larger active space,
we further included the $2s, 2p$ orbitals of each F atom, and the $3s, 3p, 4s, 4p$ orbitals of Ti. This gives a
(33e, 25o) active space that includes the dominant core-valence and valence-virtual correlation effects, both
for the energies and the density matrices.
The ground $^2A'_1$ state has one unpaired electron in the $3d_{z^2}$ orbital. The lowest excited states are
metal centred ligand-field states; charge-transfer states have been seen to give negligible contributions to the $g$-values
in previous studies~\cite{Vancoillie}.
Thus we choose the lowest 5 ligand-field states for the state-interaction basis. We first optimized $3d$ orbitals using state-averaged CASSCF in the (1e,5o) active space
using \textsc{Molpro}, with scalar relativistic effects included with the second-order Douglas-Kroll approximation~\cite{DKH1,DKH2,DKH3}. We then used DMRG in a larger (33e,25o) active space (using the (1e,5o) CASSCF orbitals).
The DMRG energy for each state was converged to better than $10^{-6} E_h$ with a bond-dimension of $M$ = 3000.
The 5 lowest electronic states, without SOC, are presented in Table \ref{tab:tab1}. The calculated and reference $g$-tensors from
the literature are summarized in Table \ref{tab:tab2}.
\begin{table}[h]
\begin{threeparttable}
\caption{The electronic states of \ce{TiF3} (cm$^{-1}$) from this work, experiment, and previous theoretical studies.}
\label{tab:tab1}
\begin{tabular}{c|c| c|c|c|c|c|c }
\hline \hline
State &CASSCF & DMRG& MRCISD+Q*\cite{solomonik}&CCSD(T)\cite{solomonik} &CCSD(T) \cite{Bolvin} &CASPT2 \cite{Bolvin} & CASPT2 \cite{Vancoillie} \\
&(1e,5o) & (33e,25o) & (1e, 5o)& & &(7e, 8o) & (17e,13o) \\
\hline
$X ^2A_1^{'}$ & & & & & & & \\
$1 ^2E'' $ & 3502 & 5785 &4414 &5181 & 5600 & 3700 & 4789 \\
$1 ^2E' $ & 20158 & 22538 &19379&19855& & & \\
\hline \hline
\end{tabular}
\end{threeparttable}
\end{table}
\begin{table}[h]
\begin{threeparttable}
\caption{ Calculated and experimental $\Delta g$ shifts for \ce{TiF3} (in ppt). }
\label{tab:tab2}
\begin{tabular}{ c|c|c|c|c|c|c|c|c|c}
\hline \hline
g-values & DMRG-SISO&CASPT2\cite{Bolvin}&CCSD(T) \cite{Bolvin} &CASPT2 \cite{Vancoillie} &MRCI \cite{Brownridge}& SORCI \cite{Neese03} &ZORA\cite{vLenthe}&BP86 & Exp.\cite{deVore}\\
& (33e,25o) &(7e, 8o) & &(17e,13o) & \\
\hline
$\Delta g_{\perp}$ & -113.7 & -125.3 & -118 & -143.5 (I) & -115.3 &-75.5 &-79.7 & -30.7\cite{Neese01} &-111.3$^a$ \\
& & & &-147.6 (II) & & & & -36.0\cite{Kaupp} & -123.7$^b$\\
& & & & & & & &-26.6\cite{Malkina} & \\
$\Delta g_{\parallel} $ &-1.6 & -2.4 & -1.6 & 0.0 (I) & -0.9 &-0.1 &-1.1 & -0.9 \cite{Neese01} & -11.1$^a$ \\
& & & & -2.5 (II) & & & &-1.3\cite{Kaupp} & -3.7$^b$ \\
& & & & & & & &-1.1 \cite{Malkina} & \\
\hline \hline
\end{tabular}
\begin{tablenotes}
\item [a] From the EPR spectrum of \ce{TiF3} in solid neon at 4K.
\item [b] From the EPR spectrum of \ce{TiF3} in solid argon at 4K.
\end{tablenotes}
\end{threeparttable}
\end{table}
The (1e,5o) CASSCF calculation underestimates the energy of the lowest excited $1 ^2E''$ state compared to larger active space calculations. The CASPT2 energies from Ref.\cite{Bolvin}, obtained with the (7e, 8o) active space (obtained from the (1e,5o) active space
by including three additional occupied ligand orbitals) confirms this observation.
The DMRG (33e,25o) energies are in good agreement with the literature CCSD(T) energies.
Including SOC removes the degeneracy of the $1 ^2E''$ and $1 ^2E'$ states and results in 144 cm$^{-1}$ and 228 cm$^{-1}$ splittings
at the DMRG level, respectively, giving two pairs of states with excitation energies 5719 cm$^{-1}$, 5863 cm$^{-1}$ and 22428 cm$^{-1}$, 22656 cm$^{-1}$.
For the $g$-tensor, the DFT-based approaches significantly underestimate $\Delta g_{\perp}$ \cite{Neese01, Kaupp,vLenthe,Malkina}.
The wavefunction-based $g$-shifts, including from the (33e,25o) DMRG-SISO calculation, are all in quite good agreement with experiment; there is
particularly close agreement between the DMRG-SISO $g$-values and those obtained from CCSD(T).
\subsection*{B. \ce{CuCl4^2-} }
We next consider the square planar \ce{CuCl4^2-} complex. This can be viewed as a model complex for copper sites in
blue copper proteins,
such as plastocyanin.
We used ANO-RCC basis sets contracted to [5s4p2d1f] for Cl and [7s6p5d3f2g1h] for Cu,
and a $D_{4h}$ symmetric complex with a Cu--Cl distance of 2.291{\AA} as in Ref. \cite{Vancoillie}.
For the active space, we considered a Cu $3d, 4s, 4d$ (9e, 11o) active space, a minimal active
space including double-shell effects. We also considered two larger active spaces: one with additional
$3s$, $3p$, $4p$ Cu orbitals and four $\sigma$-orbitals formed by the $3d$ orbitals of Cu and the $3p$ orbitals of Cl atoms,
giving a (25e, 22o) active space; and one that further incorporates the $3p$ orbitals of the Cl atoms, that
provide $\pi$-interactions with the metal, giving a (41e, 30o) active space.
We first optimized the $3d$ orbitals using state-averaged CASSCF with the (9e,11o) active space using \textsc{Molpro}~\cite{molpro}.
Scalar relativistic effects were included using the second-order Douglas-Kroll approximation~\cite{DKH1, DKH2,DKH3}.
DMRG calculations were then performed with the (25e, 22o) and (41e,30o) active spaces for the lowest 5 ligand-field excited states.
These 5 states were used as the SISO basis.
The DMRG energy for each state was converged to better than $10^{-6} E_h$ accuracy using a bond-dimension of $M$ = 3000.
The electronic states with and without SOC are presented in Table \ref{tab:tab3}. Calculated and reference g-tensors from the
literature are summarized in Table \ref{tab:tab4}.
\begin{table}[h]
\begin{threeparttable}
\caption{The electronic states of \ce{CuCl4^2-} (cm-1). The SOC-corrected energies from DMRG-SISO are given in parentheses. }
\label{tab:tab3}
\begin{tabular}{c|c|c|c|c|c|c|c }
\hline \hline
State & CASSCF& \multicolumn{2}{c|}{DMRG} & \multicolumn{2}{c|}{DMRG+NEVPT2} & CASPT2 \cite{Vancoillie} & Exp.* \\
&(9e,11o) & (25e, 22o) &(41e,30o)&(25e,22o)&(41e,30o) &(11e, 11o) & \\
\hline
$1 ^2B_{2g}$ &6735 & 9438 &9079 &10780 & 10459 & 11321 & 10500 \cite{Willet} , 12000\cite{Solomon1} \\
& &(9382) &(9025) &(10708)&(10392) & &\\
$1 ^2E_{g}$ &8925 & 11572&11274 &12884 &12673 &13379 &12800 \cite{Willet} , 13500\cite{Solomon1} \\
& &(11192,11480) &(11063,11179) &(12465,12778)&(12490,12561)& &\\
$1 ^2A_{1g}$ &9918 & 12226 &12369&13476 &13886 &14597 &16500\cite{Solomon1} \\
& &(13193) &(13164) &(14460)& (14632)& &\\
\hline \hline
\end{tabular}
\begin{tablenotes}
\item [*] Polarized absorption spectrum for a single-crystal $D_{4h}$ \ce{[CuCl4]^2-}.
\end{tablenotes}
\end{threeparttable}
\end{table}
\begin{table}[h]
\begin{threeparttable}
\caption{Calculated and experimental $\Delta g_{\perp}$ and $\Delta g_{\parallel} $ shifts of \ce{CuCl4^2-} (ppt). }.
\label{tab:tab4}
\begin{tabular}{ c|c|c|c|c|c|c|c }
\hline \hline
g-values & \multicolumn{2}{c|}{DMRG-SISO} & \multicolumn{2}{c|}{DMRG-SISO+NEVPT2} &LFT*\cite{Solomon2}& CASPT2 \cite{Vancoillie} & Exp. \\
&(25e,22o)&(41e,30o)&(25e,22o)&(41e,30o)& &(11e, 11o) & \\
\hline
$\Delta g_{\perp}$ & 100.6 &82.6 &92.3&77.1&117 & 96.1 (I); 77.7 (II) &47\cite{Chow} , 38\cite{Solomon1}\\
$\Delta g_{\parallel} $ & 517.9 &529.8&458.7&464.3&531 & 466.0 (I);437.7 (II) & 230\cite{Chow}, 219\cite{Solomon1}\\
\hline \hline
\end{tabular}
\begin{tablenotes}
\item [*] These are obtained by fitting the ligand field excited state energies, obtained from polarized single crystal electronic absorption spectroscopy, to the $g$-tensor expression in the ligand field approximation.
\end{tablenotes}
\end{threeparttable}
\end{table}
The (9e,11o) active space significantly underestimates the excitation energies of all the states.
Including the near-valence orbitals of Cu and the $3p$ orbitals of Cl atoms in the DMRG calculation
recovers an important piece of the dynamic electron correlation, shifting the
excitation energies upwards by $\approx$ 2300-2700 cm$^{-1}$.
To verify the effects of dynamic correlation, we have also carried out DMRG-NEVPT2 calculations for each state~\cite{dmrg:nevpt2};
for the corresponding $g$-tensor calculations, the energies were used to shift the SISO matrix elements by $\Delta \hat{H}_\mathrm{SR}^{IJ}=0.5(\Delta E^I_{PT2}+\Delta E^J_{PT2}) \langle \Psi_I|\Psi_J\rangle$~\cite{Malmqvist:RASSI_SO}.
The DMRG-NEVPT2 excitation energies are shifted further upwards, giving improved agreement with the experimental
excitation energies (see Table \ref{tab:tab4}). Including the SOC in the DMRG-SISO has a large effect on the $1^2A_{1g}$ excitation,
although it remains below the experimental number.
The $g$-values calculated with the different theoretical methods are roughly comparable. In the DMRG-SISO
calculations, the effect of increasing the active space size or including dynamic correlation is to lower $\Delta g_{\perp}$
but raise $\Delta g_{\parallel}$. However, the DMRG-SISO $g$-values remain too large when compared with experiment, almost by a factor of 2. This is consistent with earlier CASPT2 calculations~\cite{Vancoillie} which also found an overestimation by a factor of 2.
In Ref.~\cite{Vancoillie} it is argued that as the CASPT2 excitation energies are quite accurate for this compound, and that the error
must arise in the density matrices, which yield too large matrix elements for the spin-orbit coupling operator due to
too much ionic character in the Cu--Cl bond. Our results indicate that this remains true even when the density matrices are relaxed
in the larger active space treated by DMRG.
\subsection*{C. \ce{[2Fe-2S]^+}}
We now consider the \ce{[Fe2S2(SCH3)4]^3-} complex. This can be considered to be a model of the active site in certain iron-sulfur proteins,
such as the ferredoxins in their reduced form.
To assess geometrical effects we performed calculations at three different geometries: the relaxed geometry from Ref. \cite{sharma:FeS} (geometry I), which was optimized by the authors at the def2-SVP/BP86 level of theory, and two geometries, which we optimized
at the def2-TZVP/TPSSh level of theory with (geometry II) and without inclusion of solvation effects (geometry III), using \textsc{ORCA}~\cite{orca}. Solvation was included via the COnductor-like Screening Model (COSMO) with a dielectric constant 4.0, which crudely imitates a protein environment.
Table \ref{tab:tab5} summarizes the structural parameters for the three geometries used for the model \ce{[Fe2S2(SCH3)4]^3-} complex
as well as the geometries of two high-resolution X-ray structures of two reduced ferredoxin species: from the green alga \textit{Chlorella fusca} \cite{geom} and from the cyanobacterium \textit{Anabaena} PCC7119 \cite{geom2}.
As one can see, geometry II, obtained by including solvation effects, mimics the ferredoxin active centre
better than the other model geometries.
\begin{table}[h]
\begin{threeparttable}
\caption{Structural parameters for the reduced \ce{[2Fe-2S]} cluster, obtained from optimized geometries of a model compound \ce{[Fe2S2(SCH3)4]^3-} and high-resolution X-ray crystal structures of different reduced ferredoxins.}
\label{tab:tab5}
\begin{tabular}{c|c|c|c|c|c }
\hline \hline
Bond lengths& \multicolumn{3}{c|}{Optimized geometries}&\multicolumn{2}{c}{X-ray structures from} \\
angles & I & II& III & \textit{Chlorella fusca}\cite{geom}&\textit{Anabaena}PCC7119\cite{geom2}\\
\hline
Fe1-Fe2, {\AA} & 2.914 & 2.827 &2.775&2.733&2.749\\
Fe1-S1, {\AA} & 2.365 & 2.355 &2.326&2.230&2.293\\
Fe2-S1, {\AA} & 2.267 & 2.214 &2.222&2.196&2.235\\
Fe1-S2, {\AA} & 2.379 & 2.357 &2.336&2.224&2.261\\
Fe2-S2, {\AA} & 2.260 & 2.178 &2.213&2.157&2.178\\
Fe1-S1-Fe2, $^{\circ}$ & 77.9 & 76.4&75.2 &76.3&74.7\\
Fe1-S2-Fe2, $^{\circ}$ & 77.8 & 76.3 &75.1&77.2&76.5\\
S1-Fe1-S2, $^{\circ}$ & 98.8 & 99.2 &101.1&101.4&101.8\\
S1-Fe2-S2, $^{\circ}$ &105.5 & 108.1&108.5&104.8&106.4\\
\hline \hline
\end{tabular}
\end{threeparttable}
\end{table}
To determine a suitable active space at each geometry, we first carried out an unrestricted Kohn-Sham
(UKS) BP86/TZP-DKH calculation of the high spin state with $S = 9/2$. Scalar relativistic effects were included using the exact-two-component (X2C) approach \cite{x2c} implemented in \textsc{PySCF}.
From the alpha and beta UKS orbitals, we constructed unrestricted natural orbitals (UNOs).
From the UNO occupations, the orbitals were separated into three subspaces: doubly occupied, singly occupied and virtual molecular orbitals.
Next, localized orbitals were constructed by projecting atomic orbitals
into these 3 spaces (e.g. a localized core 1s orbital is obtained by projecting a 1s orbital into the doubly occupied space)
followed by a subsequent orthonormalization within the spaces. By population analysis and visualization of the projected AO's
we determined a suitable active space.
In this way we obtained a (31e,36o) active space including the (1) $3d$, $3d'$, $4s$ orbitals for Fe,
(2) three $3p$ and two lowest-energy $3d$ orbitals on each bridging S atom, (3) an additional $3p$ orbital on each ligand S atom.
\begin{table}[h]
\begin{threeparttable}
\caption{Dependence of $g$-values of the reduced \ce{[2Fe-2S]} complex on the number of electronic states included in the doublet and quartet manifolds (for geometry I).
The DMRG energies were converged using $M$=3000.}
\label{tab:tab6}
\begin{tabular}{ m{2cm}m{2cm} m{2cm}m{2cm} }
\hline \hline
$g$-values & \multicolumn{3}{c}{\# of doublet and quartet states in DMRG-SISO*} \\
&2 + 2&3 + 3&5 +5\\
\hline
$g_x$ & 1.989&1.888&1.807\\
$g_y $ & 2.004&1.989&1.931\\
$g_z$ & 2.006&2.004&1.969\\
\hline \hline
\end{tabular}
\end{threeparttable}
\end{table}
We carried out DMRG calculations for the doublet, quartet, and hextet states, i.e. with $S = 1/2, 3/2, 5/2$.
Note that sextet states and higher do not directly spin orbit couple with the ground doublet state,
however, they can contribute indirectly to the $g$-tensor via coupling with lower spin states, changing their energies.
Sharma et al~\cite{sharma:FeS} have shown that there are a large number of spin states at low energies in these systems,
thus we can expect a large number of states to contribute in the DMRG-SISO procedure.
Table \ref{tab:tab6} shows how $g$-values change with the number of doublet, quartet, and hextet states included in
the DMRG-SISO calculations for geometry I.
Table \ref{tab:tab7} presents the $g$-values obtained for all three geometries using the 5 lowest doublet and 5 lowest quartet states (10 states in total).
To include even more states in the DMRG-SISO, we used the ``ground-state specific'' procedure described in section \ref{sec:theory3}
to compute a large number of excited states without explicitly reoptimizing their renormalized bases.
Using this approach we were able to include up to 10 doublet and 10 quartet states. The effect
of including more states on the $g$-tensor for geometry II is presented in Table \ref{tab:tab8}. We see that after 10 doublet and 10 quartet states,
the $g$-tensor appears well converged; the remaining uncertainty is on the $O(0.01)$ level.
\begin{table}[h]
\begin{threeparttable}
\caption{Dependence of $g$-values of the reduced [2Fe-2S] complex on the number of electronic states included in the doublet and quartet manifolds (for geometry II).
The DMRG energies were converged to better than 10$^{-3} E_h$ accuracy using $M$=3000 for our standard state-specific procedure and using $M$=3200 for the cheap ground-state specific procedure.}
\label{tab:tab8}
\begin{tabular}{m{2cm}m{2cm}m{2cm}m{2cm}m{2cm}m{2cm}m{2cm}}
\hline \hline
$g$-values &\multicolumn{2}{c}{3 + 3}&\multicolumn{2}{c}{5 +5}&\multicolumn{2}{c}{10+10}\\
& state-specific & g.s. specific & state-specific & g.s. specific & state-specific & g.s. specific\\
\hline
$g_x$ & 1.909&1.907&1.834&1.831&N/A&1.831\\
$g_y $ & 1.959&1.953&1.945&1.935&N/A&1.935\\
$g_z$ & 2.004&2.004&1.957&1.962&N/A&1.961\\
\hline \hline
\end{tabular}
\end{threeparttable}
\end{table}
\begin{table}[h]
\begin{threeparttable}
\caption{$g$-values of the reduced \ce{[2Fe-2S]} complex from DMRG-SISO calculations for all geometries using the 5 lowest doublet and 5 lowest quartet states (10 states in total) and from experiment. The DMRG energies were converged using $M$=3000.}
\label{tab:tab7}
\begin{tabular}{ c|m{2cm}m{2cm}m{2cm}|cccc }
\hline \hline
$g$-values & \multicolumn{3}{c|}{Theory} & \multicolumn{4}{c}{Experiment}\\
& \multicolumn{3}{c|}{\ce{[Fe2S2(SCH3)4]^3-}}& &\multicolumn{3}{c}{reduced ferredoxin}\\
& I &II &III & \ce{[Fe2S2(SPh)4]^3-} &\textit{Anabaena} \cite{Cheng}&Spinach $^a$&\textit{Clostridium}$^b$\\
\hline
$g_x$ & 1.807&1.834 &1.852 &1.87-1.91&1.88&1.86-1.89&1.89-1.93\\
$g_y $ & 1.931&1.945 &1.936 &1.91-1.95& 1.96&1.94-1.96&1.95-1.96\\
$g_z$ & 1.969&1.957& 1.964 &2.00-2.01&2.05&2.04-2.05&2.00-2.01\\
\hline \hline
\end{tabular}
\begin{tablenotes}
\item [a] The range is given based on $g$-values for Spinach ferredoxin presented in Ref. \cite{fritz,Fe2S2_g, gayda3,Malkin,gibson,Mukai}.
\item [b] The range is given based on $g$-values for \textit{Clostridium pasteurianum} ferredoxin in Ref. \cite{Fe2S2_g,Palmer_g}.
\end{tablenotes}
\end{threeparttable}
\end{table}
Comparing the $g$-tensors from the model DMRG-SISO calculations, and the experimental $g$-tensors in biological complexes in Table~\ref{tab:tab7}, we find that while the middle $g$-value
is in reasonable agreement with experiment, the other two $g$-values are significantly underestimated. As
we have argued, we do not think this is due to insufficient states in the DMRG-SISO procedure. Further, our earlier work has suggested that
the lowest spin state excitation energies are at least qualitatively reasonable in the active space.
We have computed the partial charges on the Fe and S atoms in the DMRG-SISO calculation as well as with the BP86 functional (see Table \ref{tab:chg}). As can be seen the DMRG predicts significantly more ionic Fe--S bonds than at the DFT level.
This suggests that the error in the $g$-values may once again arise from errors in the density and ionicity of the metal-ligand bonds, similar to the case of \ce{CuCl_4^2-} above.
\begin{table}[h!]
\caption{Selected L{\"{o}}wdin partial charges for the \ce{[Fe2S2(SCH3)4]^3-} complex.}
\label{tab:chg}
\begin{tabular}{ crrrr }
\hline \hline
Atom & \multicolumn{2}{c}{geometry I}& \multicolumn{2}{c}{geometry II}\\
& BP86&DMRG &BP86&DMRG\\
\hline
Fe1 &0.705&1.097&0.690&0.854\\
Fe2 &0.776&1.047&0.736&0.994\\
S1 &-0.782&-0.910&-0.790&-0.927\\
S2&-0.811&-0.942&-0.801&-0.936\\
\hline \hline
\end{tabular}
\end{table}
\subsection*{D. \ce{Mn4CaO5} model of the S2 state of OEC}
Here we consider a model of the S2 state of the oxygen evolving complex in photosystem II.
We use an oxygen-bridged tetramanganese calcium \ce{Mn4CaO5} complex using the geometry in
Ref. \cite{oec}, which was optimized for the S2 state using broken-symmetry DFT at the def2-TZVP(-f)/BP86-D3 level of theory,
and with the zeroth-order regular approximation (ZORA) to include scalar relativistic effects. This model has
previously been studied using DMRG in Ref.~\cite{kurashige2013entangled}.
We first carried out an unrestricted BP86/def2-TZVPP-DKH basis set calculation on the high spin state with $S$ = 13/2 and we included scalar-relativistic effects using the X2C method.
As in the previous example, from the alpha and beta UKS orbitals, we constructed UNOs,
which were further separated into three subspaces: doubly occupied, singly occupied and virtual molecular orbitals.
Next, we constructed localized orbitals by projecting atomic orbitals and
chose the $2p$ orbitals of the five bridging oxygens and $3d$ orbitals of
the four manganese centers
to comprise the active space.
With this (43e, 35o) active space, we calculated 7 doublet and 11 quartet states using DMRG-CI with $M$=1000.
(Previous studies in Ref.~\cite{kurashige2013entangled} showed that the DMRG energy can be converged
to beyond chemical accuracy at this bond dimension).
We obtained $g$-values of 2.0014484, 2.0014628, 2.0022972, giving (small) $g$-shifts relative to
the Land{\'e} factor of -870, -856 and -22 ppm.
We are not aware of other theoretical estimates for these $g$-values. However,
in the experimental EPR spectrum of the OEC S2 state with $S$=1/2, one observes
a multiline EPR signal centered at $g$=2.0 \cite{oec,oec2, oec3,oec4}.
There is evidence also that this signal is quite isotropic~\cite{oec,oec2},
and this is consistent with the nearly isotropic $g$-tensor that we compute.
\section{Conclusions}
In this work, we presented a method to calculate molecular $g$-tensors using
state-interaction spin-orbit coupling and density matrix renormalization group wavefunctions.
We have demonstrated this approach on two mononuclear transition
metal complexes and a binuclear and tetranuclear transition metal complexes.
Our results show that it is possible to converge the calculations with respect to the number
of states entering in the state-interaction picture. Remaining discrepancies often appear attributable
to the description of the ionic/covalent character of the metal ligand bond, which requires a careful
balance between static and dynamic correlation. Nonetheless, our work is a step towards truly
multireference calculations of $g$-tensors in complex systems, including in the study of larger active sites in metalloenzymes.
\section*{Acknowledgments}
We acknowledge the US National Science Foundation for funding this research through the award NSF:CHE-1657286.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,578
|
package net.bytebuddy.dynamic.scaffold;
import net.bytebuddy.description.method.MethodDescription;
import net.bytebuddy.description.type.TypeDescription;
import net.bytebuddy.test.utility.MockitoRule;
import net.bytebuddy.test.utility.ObjectPropertyAssertion;
import org.junit.Before;
import org.junit.Rule;
import org.junit.Test;
import org.junit.rules.TestRule;
import org.mockito.Mock;
import java.util.Collections;
import static org.hamcrest.CoreMatchers.is;
import static org.hamcrest.CoreMatchers.not;
import static org.hamcrest.MatcherAssert.assertThat;
import static org.mockito.Mockito.mock;
import static org.mockito.Mockito.when;
public class MethodGraphCompilerDefaultHarmonizerForJVMMethodTest {
@Rule
public TestRule mockitoRule = new MockitoRule(this);
@Mock
private TypeDescription first, second;
private MethodGraph.Compiler.Default.Harmonizer<MethodGraph.Compiler.Default.Harmonizer.ForJVMMethod.Token> harmonizer;
@Before
public void setUp() throws Exception {
harmonizer = MethodGraph.Compiler.Default.Harmonizer.ForJVMMethod.INSTANCE;
}
@Test
public void testMethodEqualityHashCode() throws Exception {
assertThat(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first))).hashCode(),
is(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first))).hashCode()));
}
@Test
public void testMethodEquality() throws Exception {
assertThat(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first))),
is(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first)))));
}
@Test
public void testMethodReturnTypeInequalityHashCode() throws Exception {
assertThat(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first))).hashCode(),
not(harmonizer.harmonize(new MethodDescription.TypeToken(second, Collections.singletonList(first))).hashCode()));
}
@Test
public void testMethodReturnTypeInequality() throws Exception {
assertThat(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first))),
not(harmonizer.harmonize(new MethodDescription.TypeToken(second, Collections.singletonList(first)))));
}
@Test
public void testMethodParameterTypesHashCode() throws Exception {
assertThat(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first))).hashCode(),
not(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(second))).hashCode()));
}
@Test
public void testMethodParameterTypesEquality() throws Exception {
assertThat(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(first))),
not(harmonizer.harmonize(new MethodDescription.TypeToken(first, Collections.singletonList(second)))));
}
@Test
public void testFactory() throws Exception {
assertThat(MethodGraph.Compiler.Default.forJVMHierarchy(), is((MethodGraph.Compiler) new MethodGraph.Compiler
.Default<MethodGraph.Compiler.Default.Harmonizer.ForJVMMethod.Token>(MethodGraph.Compiler.Default.Harmonizer.ForJVMMethod.INSTANCE,
MethodGraph.Compiler.Default.Merger.Directional.LEFT, TypeDescription.Generic.Visitor.Reifying.INITIATING)));
}
@Test
public void testObjectProperties() throws Exception {
ObjectPropertyAssertion.of(MethodGraph.Compiler.Default.Harmonizer.ForJVMMethod.class).apply();
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,087
|
Combine flour, sugar, baking powder and cinnamon. Cut into butter to coarse crumb stage. Stir in berries. Combine egg and milk. Add to flour mixture. Stir until just moistened (will be sticky).
Shape dough in a 7" circle on floured surface. Cut into 12 wedges. Place on baking sheet. Brush with milk or cream. Sprinkle with sugar if desired. Bake at 400° until lightly browned (10-12 min).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,731
|
\section{Introduction}
\IEEEPARstart{D}{rawing} a sketch is may be the easiest way for amateurs to describe an object or scene quickly. Compared with photographs or portraits, it does not require technical capture devices or professional painting skills. Generating photo-realistic images from free-hand sketch enables a novice to create images from their imagination, making reality a face or scene otherwise only existing in their dreams. However, the sketches drawn by non-artists are usually simple and imperfect. They are sparse, lack of necessary details, and strokes do not precisely align to the original images or actual objects. It is hence challenging to synthesize natural and realistic images from such poorly-drawn sketches.
\begin{figure*}[t]
\centering
\centerline {\includegraphics[width=\textwidth]{images/pipeline}}
\caption{ The overall architecture of our method. Stroke Calibration Network first calibrates unreasonable strokes and adds necessary details. The modified sketches are then fed into Image Synthesis Network to produce photo-realistic face images.}
\label{fig:pipeline}
\end{figure*}
Recent progress on image-to-image translation \cite{isola2017image,CycleGAN2017, Zhou2019BranchGAN,StarGAN2018,wang2018pix2pixHD,Chen2019Quality,XuKW19} has shown that an end-to-end generative adversarial network (GAN) architecture could produce high quality results. A few of them are capable of synthesizing facial photos from sketches, but it requires sketches with precisely and strictly aligned boundary to produce plausible results. Building such an exquisite large-scale dataset with thousands of image pairs (i.e, face photo and its corresponding sketch drawn by professional portraitists) would be quite time-consuming and expensive. It is much easier to build a dataset of face photos and their corresponding free-hand sketches drawn by amateurs. Technically, given such poorly-drawn sketches and photos, the networks proposed for cross-domain translation \cite{isola2017image,CycleGAN2017,huang2018munit,DRIT} would learn both stroke modification and image generation simultaneously. However, the remarkable stroke and appearance differences between sketches and photos diminish the effectiveness of these networks, thus leading to unpleasant results.
There are some interactive face image modification methods under the framework of image inpainting \cite{jo2019sc,yu2018generative,nazeri2019edgeconnect,liu2019homography}. Given a partially-and-irregularly masked image, they refill the erased regions with strokes provided by the user as guidance. The refilled regions are consistent with input reference strokes and compatible with the whole image. Recent work \cite{jo2019sc} can obtain a realistic synthetic face photo even though the user conducts some modifications and the network tolerates minor error or mismatching. However, to generate an appropriately edited and restored result, a plausible sketch of the original image is still needed by them. When poorly-drawn sketches are fed into the model, the results can be unacceptable. Moreover, synthesizing an image from a total sketch is much harder than from a regionally-erased image, since in the latter case the rest edges and colors can significantly help the reconstruction.
Some methods \cite{Chen2018CVPR, lu2017sketch} consider the case of casual free-hand frontal face sketches, where the generated images do not have to strictly align with the input sketches and present more freedom in appearance. But their methods produce blurry and artifactual results. What's more, crucial components and drawing intention of the original sketches such as facial contours and hairstyles are not preserved in the synthesized images.
To address those above issues, we propose a novel two-stage generative adversarial network called ``Cali-Sketch``, to realize face photo synthesis from poorly-drawn sketches in a unified framework. It explicitly models stroke calibration and image generation using two constituent GANs: a Stroke Calibration Network ({\it SCN}), which calibrates and completes strokes of facial features and enriches facial details while preserving the original intent features of the painter, and an Image Synthesis Network ({\it ISN}), which transfers the calibrated and completed sketches to face photos. Two GANs are first separately trained for each stage, and then trained jointly.
We focus on image generation from ``poorly-drawn sketches", which is less discussed but appears more in real applications. Compared with the aforementioned methods in \cite{isola2017image, jo2019sc,wang2018pix2pixHD}, ours doesn't necessarily desire a sketch well aligned to the original image to generate an appropriately edited and restored result while those methods might produce unacceptable results given such poorly-drawn sketches as input.
To preserve facial features and drawing intention, we propose both global contour loss and local detail loss to accomplish necessary stroke modifications and detail improvements. To eliminate artifacts, we also incorporate a perceptual loss and a reconstruction loss in the overall objective function. In this way, we manage to make the final appearance of generated images photo-realistic, while keeping the determinant attributes and drawing intention of input sketch. Experiments confirms that face images synthesized by our proposed method are natural-looking and visually pleasant without observable artifacts.
To sum up, our key contributions are three-fold:
\begin{itemize}
\item We present the first two-stage poorly-drawn face sketch to photo translation. It achieves stroke calibration and image synthesis with two consecutive GANs: SCN and ISN.
\item We propose SCN for necessary stroke calibration and detail completion. To preserve identity and drawing intention during the reconstruction of fine-grained face sketches, we design novel calibration loss functions. Furthermore, when given a free-hand drawn sketch, this network can act as a pre-processing modification module for other tasks using reference sketches such as interactive face image modification.
\item We propose ISN for face sketch-to-image generation. The synthesized face images are both identity-consistent and appearance-realistic.
\end{itemize}
The rest of this paper is organized as follows.
Section \ref{sec:related works} provides an overview of the previous methods and related techniques. Section presents the proposed Cali-Sketch method.
Section \ref{sec:experiments} reports the qualitative and quantitative performance of sketch-based image synthesis experiments using the proposed method, and Section \ref{sec:conclusion} summarizes and concludes the paper.
\section{Related Work}
\label{sec:related works}
\subsection{Photo-Realistic Image Synthesis}
Photo-realistic image synthesis methods have progressed rapidly during the last few years. The goal of image synthesis is to generate photo-realistic and faithful images from sketches or abstract semantic label maps, refer to as label-based image synthesis and sketch-based image synthesis, respectively.
Label-based image synthesis methods \cite{wang2018pix2pixHD, ChenK17Photographic,QiCJK18Synthesis} synthesize image semantically from abstract label maps, such as sparse landmarks or pixel-wise segmentation maps.
\cite{wang2018pix2pixHD} proposes a framework for instance-level image synthesis with conditional GANs. \cite{ChenK17Photographic} proposes a cascade framework to synthesis high-resolution images from pixel-wise labeling maps.
Facial sketch-based image synthesis approaches have been widely developed during the last few years. Those existing studies can be broadly classified into two categories: image retrieval based approaches \cite{chen2009sketch2photo,eitz2011photosketcher,chen2013poseshop} and deep learning based methods \cite{isola2017image,CycleGAN2017,Chen2018CVPR,lu2017sketch,wang2018high,gao2017ca-gan}. The former mainly has three basic steps: retrieve, select and composite. Given a sketch plus overlaid text labels as input, Sketch2Photo \cite{chen2009sketch2photo} and Photo-Sketcher \cite{eitz2011photosketcher} automatically synthesize realistic pictures by seamlessly composing objects and backgrounds based on sketch searching and image compositing. PoseShop \cite{chen2013poseshop} constructs a large segmented character database for human synthesis, where people in pictures are segmented and annotated by actions and appearance attributes. Then human images are composed by feeding given sketches with text labels into the query. Those methods often suffer from heavily blurred effects and tedious inference process.
Deep learning based methods learn the mapping between sketches and photos. The pix2pix \cite{isola2017image} translates precise edge maps to pleasing shoe pictures using conditional GANs. CycleGAN \cite{CycleGAN2017} proposes cycle-consistent loss to handle the paired training data limitation of pix2pix.
SketchyGAN \cite{Chen2018CVPR} synthesizes plausible images of objects from 50 classes. It aims to synthesis results both photo-realistic and faithful to the intention of given sketches. In this case, intention was defined as generated images sharing similar poses with input sketches since it's hard to learn human intention.
PhotoSketchMAN \cite{wang2018high} generates face photos iteratively from low resolution to high resolution by multi-adversarial networks. CA-GAN \cite{gao2017ca-gan} proposes to use pixel-wise labelling facial composition information to help face sketch-photo synthesis. Contextual-GAN \cite{lu2017sketch} formulates the task of sketch-image synthesis as the joint image completion. Sketches provide contextual information for completion.
\begin{figure*}[th]
\centering
\centerline {\includegraphics[width=\textwidth]{images/results.png}}
\caption{Qualitative comparison with baselines. We compare our methods with pix2pix \cite{isola2017image}, CycleGAN \cite{CycleGAN2017}, DRIT \cite{DRIT}, MUNIT \cite{huang2018munit}. Our approach generates more photo-realistic images. The corresponding image can be recognised easily from a batch of mixed sketches, which means crucial components and drawing intention of original sketches such as facial contours and hair styles are well-preserved in the synthesized images.}
\label{fig:qualitative comparison with baselines}
\end{figure*}
\subsection{Generative Adversarial Networks}
In recent years, Generative Adversarial Networks (GANs) \cite{Goodfellow2014Generative} have been successfully applied in many computer vision tasks to improve realism of generated images, such as domain adaption \cite{murez2018image,deng2018image,long2018conditional}, super-resolution \cite{Yan2019Quality,jiang2017SRLSP,Shi2019face,xie2019depth,wang2018esrgan,xue18Review}. They are composed of a generator $G$ and a discriminator $D$. Discriminators try to distinguish the generated fake images, while generators aim to fool discriminators from identifying real images from fake ones. The ideal solution is the Nash equilibrium where $G$ and $D$ couldn't improve their cost unilaterally.
Despite of great success, there are still several challenges in GANs including generalization \cite{arora2017generalization,mescheder2017numerics} and training stability \cite{arjovsky2017wasserstein,salimans2016improved}. To alleviate those problems, technologies are proposed to improve GANs. For example, Arjovsky et al. \cite{arjovsky2017wasserstein,Gulrajani2017Improved} propose to minimize the Wasserstein distance between model and data distributions. Berthelot et al. \cite{berthelot2017began} try to optimize a lower bound of the Wasserstein distances between auto-encoder loss distributions on real and fake data distributions. Mao et al. \cite{mao2017least} proposes a least squares loss for the discriminator, which implicitly minimizes Pearson $\chi^2$ divergence, leading to stable training, high image quality and considerable diversity.
\subsection{Image-to-Image Translation with GANs}
General image-to-image translation methods aim to learn a mapping from the source domain to the target domain. Isola et al. \cite{isola2017image} propose a pix2pix framework trained with image pairs and achieve convincing synthetic images on many translation tasks. To handle the limitation of paired images for training, CycleGAN \cite{CycleGAN2017}, DualGAN \cite{yi2017dualgan}, DiscoGAN \cite{kim2017learning} present cycle consistency loss to constrain the translation between inputs and translated images.
CSGAN \cite{kancharagunta2019csgan} extends \cite{CycleGAN2017} with additive cyclic-synthesized loss between the synthesized image of one domain and the cycled image of another domain.
InstaGAN \cite{mo2018instagan} incorporates instance attribute information for multi-instance transfiguration.
MUNIT \cite{huang2018munit} and DRIT \cite{DRIT} are proposed for one-to-many diverse image translation. ComboGAN \cite{anoosheh2018combogan} also proposes a multi-component translation method without being constrained to two domains.
\section{Method}
\label{sec:method}
\subsection{Overview}
Our goal is to realize face photo synthesis from a poorly-drawn sketch. Consider two data collections from different domains, $\textbf{S}\subset {{I}^{H\times W\times1} } $ referring to input sketch domain and $\textbf{P}\subset {{I}^{H\times W\times3}}$ referring to output photo domain. $I^{H\times W\times N}$ represents an image of height $H$, width $W$ and channel $N$. Converting a face sketch from source domain $\textbf{S}$ to an image in the target photo domain $\textbf{P}$ can be referred to as ${G: \textbf{S} \to \textbf{P}}$ . This is a typical cross-domain image translation problem but we could not directly learn the mapping by existing image-to-image translation methods. Instead, we decompose this translation into two stages: 1) Stroke Calibration Network named {\it SCN}, and 2) Image Synthesis Network named {\it ISN}. Let $G_1$ and $D_1$ be the generator and discriminator of SCN, $G_2$ and $D_2$ be the generator and discriminator of ISN, respectively. As shown in Figure \ref{fig:pipeline}, the input sketch $\textbf{S}$ is first put into SCN to get the refined sketch $\textbf{R}$ after stroke calibration and detail completion, which is then fed into ISN to generate a photo-realistic face image $\textbf{P}$. We first train Stroke Calibration Network and Image Synthesis Network separately until the losses plateau, and then train them jointly in an end-to-end way until convergence. Qualitative comparison with baselines is demonstrated in Figure \ref{fig:qualitative comparison with baselines}. Illustrations of SCN and ISN are shown in Figure \ref{fig:Illustration of SCN} and \ref{fig:Illustration of ISN}, respectively. Training details and network architecture can be found in Section \ref{sec:experiment settings}.
\subsection{Stroke Calibration Network}
\label{sec:SCN}
Stroke Calibration Network aims to modify inconsequent strokes and enrich necessary details of input sketch. Let $\mathbf{S}$ be input sketches. Ground truth face photos and their edge counterparts will be denoted as $\mathbf{I}_{gt}$ and $\mathbf{E}_{gt}$. The mapping from poorly-drawn sketches $\mathbf{S}$ to the modified ones $\mathbf{R}$ can be denoted as ${G_{1}: \mathbf{S} \to \mathbf{R}}$:
\begin{equation}
\mathbf{R}=G_{1}\left(\mathbf{S}, \mathbf{E}_{gt}\right)
\end{equation}
where $\mathbf{E}_{gt}$ are composed of two components: global contours $\mathbf{E}_{gc}$ and local details $\mathbf{E}_{ld}$.
To modify inconsequent strokes and enrich necessary details, we introduce a novel calibration loss $\mathcal{L}_{CL}$ which consists of global contour loss and local detail loss. Global contour loss aims to modify inconsequent strokes and local detail loss enriches necessary details.
We define both losses based on the feature matching loss \cite{wang2018pix2pixHD}. Feature representations of real and synthesized images extracted from multiple layers of discriminator are then used to calculate the feature matching loss as
\begin{equation}
\mathcal{L}_{CL}=\mathbb{E}\left[\sum_{i=1}^{T} \frac{1}{N_{i}}\left\|D_{1}^{(i)}\left(\mathbf{E}_{gt}[j]\right)-D_{1}^{(i)}\left(\mathbf{R}\right)\right\|_{1}\right],
\end{equation}
where $\mathbf{E}_{gt}[j], j\in\{ 0,1\}$ represents global contour and local detail respectively, $D_{1}^{(i)}$ represents intermediate representations from $i$th-layer feature extractor of discriminator. In our experiments, global contour and local detail are implemented by HED \cite{xie15hed} and Canny \cite{canny1987computational} edge map, respectively. This calibration loss can stabilize training by forcing the generator to produce natural statistics at different scales \cite{wang2018pix2pixHD}.
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{images/SCN}
\caption{Illustration of Stroke Calibration Network (SCN): (a) reference; (b) input sketch; (c) Canny result; (d) modified sketch by our SCN.}
\label{fig:Illustration of SCN}
\end{figure}
For stable training, high image quality and considerable diversity as discussed in Section \ref{sec:related works}, we use the least-squares GAN \cite{mao2017least} in our experiment. Thus, $\mathcal{L}_{adv, SCN}$ can be formulated as
\begin{equation}
\begin{aligned}
\min _{D_{1}} L_{\mathrm{adv}, \mathrm{SCN}}\left(D_{1}\right)=&\frac{1}{2} \mathbb{E}_{\boldsymbol{x} \sim p{\mathrm(\boldsymbol{x})}}\left[\left(D_{1}(\boldsymbol{x})-b\right)^{2}\right] +\\
& \frac{1}{2} \mathbb{E}_{\boldsymbol{z} \sim p_{\boldsymbol{z}}(\boldsymbol{z})}\left[\left(D_{1}\left(G_{1}(\boldsymbol{z})\right)-a\right)^{2}\right] \\
\min _{G_{1}} L_{\mathrm{adv}, \mathrm{SCN}}\left(G_{1}\right)= &\frac{1}{2} \mathbb{E}_{\boldsymbol{z} \sim p_{z}(\boldsymbol{z})}\left[\left(D_{1}\left(G_{1}(\boldsymbol{z})\right)-c\right)^{2}\right],
\end{aligned}
\end{equation}
where a, b, c denotes the labels for fake data and real data and the value that G wants D to believe for fake data respectively. In our experiment, $x$ are ground truth images and $z$ are input sketches sampled from distribution $p{\mathrm(\boldsymbol{z})}$.
The total loss of Stroke Calibration Network combines an improved adversarial loss and calibration loss as
\begin{equation}
\min \limits_{G_{1}} \max \limits_{D_{1}} \mathcal{L}_{G_{1}}=\min \limits_{G_{1}}\left(\max \limits_{D_{1}}\left(\mathcal{L}_{adv, SCN}\right)+\lambda \mathcal{L}_{CL}\right),
\end{equation}
where $\lambda$ is regularization parameters controlling the importance of two terms.
\subsection{Image Synthesis Network}
\label{sec:ISN}
After stroke calibration and detail completion, the refined sketch $\textbf{R}$ is then fed into Image Synthesis Network to generate photo-realistic face photo $P$. This translation process from the refined sketch $\textbf{R}$ to the photo-realistic face image $\textbf{P}$ can be defined as ${G_{2}: \textbf{R} \to \textbf{P}}$.
The output image should yield both high sketch identification similarity and favourable perceptual quality, while sharing the same resolution with the input sketch:
\begin{equation}
\mathbf{P}=G_{2}\left(\mathbf{R},\mathbf{I}_{gt}\right)
\end{equation}
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{images/ISN}
\caption{Illustration of Image Synthesis Network (ISN): (a) reference; (b) original input sketch; (c) input sketch modified by our SCN. (d) generated image by our ISN.}
\label{fig:Illustration of ISN}
\end{figure}
We train this image synthesis network with a joint loss, which consists of five terms: an $\ell_{1}$ reconstruction loss $\mathcal{L}_{\ell_{1}}$, adversarial loss $\mathcal{L}_{adv, 2}$ , perceptual loss $\mathcal{L}_{\text{percep}}$, style loss $\mathcal{L}_{\text{style}}$ and total variation loss $\mathcal{L}_{\text{tv}}$:
\begin{equation}
\mathcal{L}_{G_{2}}=\lambda_{1} \mathcal{L}_{\ell_{1}}+\lambda_{ 2} \mathcal{L}_{adv, ISN}+\lambda_{3} \mathcal{L}_{\text{percep}}+\lambda_{4} \mathcal{L}_{\text{style}}+\mathcal{L}_{\text{tv}}
\end{equation}
Reconstruction loss $\mathcal{L}_{\ell_{1}}$ minimizes the differences between reference and generated images:
\begin{equation}
\mathcal{L}_{\ell_{1}}=\mathbb{E}\left[\sum_{i} \frac{1}{N_{i}}\left\|\mathbf{I}_{gt}-\mathbf{P}\right\|_{1}\right]
\end{equation}
Perceptual loss is proposed by Johnson et al. \cite{Johnson2016Perceptual} based on perceptual similarity. It is originally defined as the distance between two activated features of a pre-trained deep neural network. Here we adopt a more effective perceptual loss which uses features before activation layers \cite{wang2018esrgan}. These features are more dense and thus provide relatively stronger supervision, leading to better performance:
\begin{equation}
\mathcal{L}_{\text {percep}}=\mathbb{E}\left[\sum_{i} \frac{1}{N_{i}}\left\|\phi_{i}\left(\mathbf{I}_{gt}\right)-\phi_{i}\left(\mathbf{P}\right)\right\|_{1}\right]
\end{equation}
where $\phi_{i}$ donates the feature maps before activation of the VGG-19 network pre-trained for image classification.
Style loss \cite{Johnson2016Perceptual} is adopted in the same form as in the original work, which aims to measure differences between covariance of activation features:
\begin{equation}
\mathcal{L}_{\text {style}}=\mathbb{E}_{j}\left[\left\|G_{j}^{\phi}\left(\mathbf{I}_{gt}\right)-G_{j}^{\phi}\left(\mathbf{P}\right)\right\|_{1}\right]
\end{equation}
where $G_{j}^{\phi}$ represents the Gram matrix constructed from feature maps $\phi_{j}$.
Total variation loss is based the principle that images with unrestrained and possibly spurious detail have high total variation. According to this, reducing total variation of an image subject to it being a close match to the original image, removes unwanted noises while enforcing spatial smoothness and preserving important details such as edges.It is defined on the basis of the absolute gradient of generated images:
\begin{equation}
\mathcal{L}_{\text {tv}}=\left\|{\nabla_x \mathbf{P}}-{\nabla_y \mathbf{P}}\right\|_{1}
\end{equation}
\section{Experiments}
\label{sec:experiments}
\subsection{Training Data}
Appropriate and adequate training data is important for network performance. Since it is infeasible to collect large-scale paired images and sketches, most existing free-hand sketch based image synthesis methods generate sketches automatically from images.
To exhibit different styles of free-hand sketches and to improve the network generality, we augment training data by adopting multiple different styles of input sketches. Specifically, we generate four different free-hand sketch styles in total. We use the XDoG edge detector \cite{WinnemollerKO12}, Photocopy effect \cite{photocopy} in Photoshop to generate two styles. To better resemble hand-drawn sketches, we simplified the edge images using \cite{Simo-SerraISI16} as in \cite{LuWTT18}. We also use photo-sketch \cite{LIPS2019} to generate the desired face sketches. This recent method generates imperfect alignment contour sketches of input images.
The poorly-drawn sketches should be sparse and contain wrong edges. That's why the Canny algorithm \cite{canny1987computational} shouldn't be chosen to get input sketches. Those edges generated by Canny are solid and well-aligned with input images.
To show effectiveness and efficiency of our approach, the CUHK Face Sketch Database \cite{wang2009face} is used in our experiment for its appropriateness and popularity. We use its $256\times256\times3$ resized and cropped version.
\begin{figure}[th]
\centering
\includegraphics[width=\linewidth]{images/well-drawn-sketch}
\caption{Illustration of well-drawn sketches from \cite{wang2009face}. Best viewed in color.}
\label{fig:well-drawn-sketch}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{images/sketch_style}
\caption{Illustration of four different free-hand sketch styles: photo-sketch \cite{LIPS2019}, XDoG \cite{Simo-SerraISI16}, Photocopy\cite{photocopy} and FDoG\cite{WinnemollerKO12}.}
\label{fig:sketch_style}
\end{figure}
Figure \ref{fig:well-drawn-sketch} are illustration of well-drawn sketches from \cite{wang2009face}. These sketches are drawn by the artist. Compared with poorly-drawn sketches in Figure \ref{fig:sketch_style}, the well-depicted sketches capture the most distinctive characteristics of human faces and are faithful to the original face images. We often can easily recognize a person from corresponding sketch. The free-hand sketches are often sparse, deformed, lack of necessary strikes or details and lines don't precisely align to the real face images, sometimes even lack of necessary lines in the area of mouth or jaw as illustrated in Figure \ref{fig:sketch_style}.
The ground truth sketches for Stroke Calibration Network are generated using Canny algorithm \cite{canny1987computational} and Holistically-nested Edge Detection (HED) edge detector \cite{xie15hed}. Specifically, we extract HED from images after histogram equalization to avoid the interference of light. Thus, we generate a desired new dataset consisted of high-quality face photos and corresponding poorly-drawn face sketches, Canny together with HED edges.
\subsection{Experiment Settings}
\label{sec:experiment settings}
\textbf{Network architecture.}
Inspired by recent image translation studies, our generators follow an encoder-decoder architecture similar to the method proposed by Johnson et al. \cite{Johnson2016Perceptual}. Each of the generators consists of two down-sampling encode layers, followed by eight residual blocks\cite{He2016Deep} and two up-sampling decoders. Skip connections are added to concatenate previous layers with the same spatial resolution. We replace regular convolutions in the residual blocks with dilated convolutions with dilation factor two to obtain large receptive fields. Our discriminators are based on the SN-PatchGAN \cite{yu2018free} architecture, which determines whether or not overlapping image patches of certain size are real. Spectral normalization \cite{miyato2018spectral} is introduced for rapid and stable training and helps produce high-quality results.
Notice that here we didn't deliberately design the structure of Image Synthesis Network (SCN). In fact, we adopt a quite simple structure of SCN to show that it's easy to generate satisfactory results from the calibrated sketches even the sktech2image synthesis network is not deliberately designed. For more details about the indispensability of Stroke Calibration Network and scalability of Image Synthesis Network, refer to Section \ref{sec:impact of SCN} and \ref{sec:scalability of ISN} respectively.
\textbf{Training strategy.}
The training strategy is demonstrated in Algorithm \ref{alg:Training strategy}. Forward and backward in Algorithm \ref{alg:Training strategy} represent forward propagation and back propagation respectively. The forward process includes steps of passing the input through the network layers and calculating the actual output and losses of the model. The backward process back-propagates errors and updates weights of the network. We refer corresponding operations to as forward and backward for simplicity and emphasize that our method is an end-to-end method with three-stage training. $N_1, N_2, N_3$ are iteration numbers which are large enough to guarantee convergence.
Firstly, we train our Stroke Calibration Network $G_1$ using the Canny and HED edges as supervision with a $10^{-4}$ learning rate. Meanwhile, we train Image Synthesis Network $G_2$ using Canny $\odot$ HED as input refined sketches and ground truth face images as supervision with the same $10^{-4}$ learning rate. Here, $\odot$ denotes the Hadamard product. We then decrease the learning rate to $10^{-5}$ and jointly train both $G_1$ and $G_2$ in an end-to-end way until convergence. Discriminators are trained with a learning rate one tenth of the generators' according to different training stages. Both networks are trained with resized $256 \times 256$ images with a batch of $8$.
\begin{algorithm}[t]
\DontPrintSemicolon
\textbf{Stage 1: SCN training}
\KwIn{$\mathbf{S}$, free-hand sketch. }
\KwOut{$\mathbf{R}$, Refined sketch }
\While{$n \leq N_1$ }{
$\mathbf{R}$, $\mathcal{L}_{G_{1}}$, $\mathcal{L}_{D_{1}}$ = $G_1$.forward$ (\left(\mathbf{S}, {\mathbf{E}}_{gt}\right))$\;
$G_1$.backward
}
\textbf{Stage 2: ISN training}
\KwIn{$\mathbf{R}$, Canny$\odot$ HED.}
\KwOut{$\mathbf{P}$, Generated face image. }
\While{$n \leq N_2$}{
$\mathbf{P}$, $\mathcal{L}_{G_{2}}$, $\mathcal{L}_{D_{2}}$ = $G_2$.forward$ (\left(\mathbf{R}, {\mathbf{I}}_{gt}\right))$\;
$G_2$.backward
}
\textbf{Stage 3: Joint training}
\KwIn{$\mathbf{S}$, free-hand sketch.}
\KwOut{$\mathbf{P}$, Generated face image. }
\While{$n \leq N_3$}{
$\mathbf{R}$, $\mathcal{L}_{G_{1}}$, $\mathcal{L}_{D_{1}}$ = $G_1$.forward$ (\left(\mathbf{S}, {\mathbf{E}}_{gt}\right))$\;
$\mathbf{P}$, $\mathcal{L}_{G_{2}}$, $\mathcal{L}_{D_{2}}$.forward$ (\left(\mathbf{R}, {\mathbf{I}}_{gt}\right))$\;
$G_1$.backward
$G_2$.backward
}
\caption{{\sc Training strategy}}
\label{alg:Training strategy}
\end{algorithm}
\textbf{Evaluation metrics.} For our task of face image synthesis from poorly-drawn sketches, we use two kinds of evaluation metrics: similarity metrics and perceptual scores.
We apply the widely used full reference image quality assessment metrics such as PSNR, SSIM as similarity metrics. Given two images $I, I^{\prime}\subset I^{H \times W \times C}$, the peak signal-to-noise ratio (PSNR) are defined as
\begin{equation}
PSNR=10 \log _{10}^{\left(\frac{L^{2}}{MSE}\right)},
\end{equation}
where L is usually 255, $\|\cdot\|_{F}^{2}$ is the Frobenius norm and $MSE=\frac{1}{HWC}\|I-I^{\prime}\|_{F}^{2}$. The structural similarity index (SSIM) is defined as
\begin{equation}
SSIM(I, I^{\prime})=\frac{2 \mu_{I} \mu_{I^{\prime}}+k_{1}}{\mu_{I}^{2}+\mu_{I^{\prime}}^{2}+k_{1}} \cdot \frac{\sigma_{I I^{\prime}}+k_{2}}{\sigma_{I}^{2}+\sigma_{I^{\prime}}^{2}+k_{2}},
\end{equation}
where $\mu_{I}$ and $\sigma_{I}^{2}$ is the mean and variance of $I, \sigma_{I \hat{I}}$ is the
covariance between $I$ and $\hat{I},$ and $k_{1}$ and $k_{2}$ are constant
relaxation terms. A highest score indicates a more structurally similar face for a given sketch.
For perceptual scores, we use Fr$\acute{e}$chet Inception distance (FID) \cite{heusel2017gans}. The FID is defined using the Fr$\acute{e}$chet distance between two multivariate Gaussians:
\begin{equation}
\mathrm{FID}=\left\|\mu_{r}-\mu_{g}\right\|^{2}+\operatorname{Tr}\left(\Sigma_{r}+\Sigma_{g}-2\left(\Sigma_{r} \Sigma_{g}\right)^{1 / 2}\right),
\end{equation}
where $X_{r} \sim \mathcal{N}\left(\mu_{r}, \Sigma_{r}\right)$ and $X_{g} \sim \mathcal{N}\left(\mu_{g}, \Sigma_{g}\right)$ are the 2048-dimensional activations of the Inception-v3 pool3 layer for real and generated samples respectively
The lowest FID means it achieves the most perceptual results.
\subsection{Baselines}
We perform the evaluation on the following baseline approaches:
\textbf{Pix2pix} \cite{isola2017image} is an early work of image-to-image translation. It achieves good photo results on edge-to-photo generation, and the models trained on automatically detected edges can generalize to human drawings.
\textbf{CycleGAN} \cite{CycleGAN2017} achieves unsupervised image-to-image translation via cycle-consistent loss.
\textbf{DRIT} \cite{DRIT} is a recent work, which realizes diverse image-to-image translation via disentangled content and attribute representations of different domains. Experiment on the edge-to-shoes dataset shows it can produce both realistic and diverse images.
\textbf{MUNIT} \cite{huang2018munit} is the state-of-the-art unsupervised multi-domain image-to-image translation framework. It achieves quality and diversity comparable to the state-of-the-art supervised algorithms on the task of edge-to-shoes/handbags.
We implement all baselines using default architecture and details.
\subsection{Comparison Against Baselines}
\label{sec:comparison against baselines}
\textbf{Qualitative evaluation.} Qualitative comparison with baselines are demonstrated in Figure \ref{fig:qualitative comparison with baselines}. The results produced by pix2pix \cite{isola2017image} all have obvious artifacts. Facial features are all suffer from shape distortion to a degree, especially the facial and ear contours on the first and fifth rows. CycleGAN \cite{CycleGAN2017} produces the most similar face with the reference, but its results are blurry and unpleasing. There are two or more visible spots in the area of hair. The contours of face images generated by DRIT \cite{DRIT} are aligned with the ir lines of the input sketches, which notably deteriorate the image quality. MUNIT \cite{huang2018munit} could produces relatively visually realistic and qualitatively consistent results. however, they are more like oil paintings rather than photos.
Compared with baseline methods, our approach generates high-quality images. The generated human face images are more photo-realistic. The corresponding image can be recognised easily from a batch of mixed sketches, which means crucial components and drawing intention of original sketches like facial contours, hair styles are well-preserved in the synthesized images.
\textbf{Quantitative comparison.} Quantitative evaluation with baselines are shown in Table \ref{Quantitative comparison}. For PSNR and SSIM, CycleGAN \cite{CycleGAN2017} achieves the highest structural similarity, and our method ranks the second. For the task of sketch-to-image generation, similarity is not that important, since for most free-hand drawn sketches, there are no corresponding real face images as reference. What really matters is whether generated images are photo-realistic or not.
Fr$\acute{e}$chet Inception Distance (FID) is calculated by computing the Fr$\acute{e}$chet distance between two Gaussians of feature representations extracted from the pre-trained inception network \cite{szegedy2016rethinking}. It is not only a measure of similarity between two datasets of images, but also shown to correlate well with human visual judgement of image quality. Due to above advantages, FID \cite{heusel2017gans} is most often used to evaluate the quality of images generated by Generative Adversarial Networks. As shown in Table \ref{Quantitative comparison}, our method achieves the lowest FID score, which means that our method produces the best results in both perceptual judgement and high-level similarity.
\begin{table}
\centering
\caption{Perfomance as PSNR, SSIM and FID on the CUHK dataset. The \textbf{best} and \underline{second} best results are highlighted in each column. For details refer to Section \ref{sec:comparison against baselines}}
\label{Quantitative comparison}
\begin{tabular}{cccl}
\toprule
Method &PSNR & SSIM & FID\\
\midrule
pix2pix &18.83 &0.7554 &\underline{76.90} \\
CycleGAN &\textbf{ 24.21} &\textbf{0.8508} &80.17 \\
MUNIT & 17.23 & 0.7515 &78.57 \\
DRIT & 16.14 & 0.7047 &97.36 \\
Ours &\underline{20.25} &\underline{0.8006} &\textbf{58.43} \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Component Analysis of Cali-Sketch}
\subsubsection{The choice of contour and detail}
There are many choices of contour and detail for our methods such as edges, boundaries and contours. These are a few differences between them. Edge maps are precisely aligned to object boundaries, and they usually contain more information about details and backgrounds. Boundaries pay more attention to external lines. Contours contain object boundaries, salient internal and background edges. Contours can be obtained by the boundary contour edge extractors like HED \cite{xie15hed}, COB \cite{Man+16a,ManinisPAG18}, RCF \cite{liu2017richer,liu2019richer}, or similar to pix2pixHD \cite{wang2018pix2pixHD}, simplified from the face parsing semantic labels. For a face image, contours are more like facial feature boundaries.
Since sketches are the approximate outline of the objects with spatial transformations and deformed strokes, we need to modify its strokes and add more details before synthesis. Contours and edges are respectively responsible for stroke calibration and detail completion. We will illustrate the reasons in the next part.
In our experiment, we choose HED as global contour and Canny as ground truth local detail for simplicity.
\subsubsection{The impact of Stroke Calibration Network}
\label{sec:impact of SCN}
We have tested directly applying the pix2pix to generate face images from poorly-drawn sketches, but found the training unstable and the quality of results unsatisfactory. The original sketches are deformed and sometimes lack of necessary lines in the area of mouth or jaw, as shown in Figure \ref{fig:Illustration of SCN} and Figure \ref{fig:impact_scn}. It inspires us to modify strokes and add essential details before image synthesis. Edges like the Canny detector can act as ground truth for the training of this process. The refined sketches are more visually favourable and consistent with the original identity, as shown in the third column of Figure \ref{fig:impact_scn}.
\begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{images/impact_scn}
\caption{The impact of Stroke Calibration Network and with or without global contour. (a) input sketch. (b) canny edge. (c) result with only local detail loss. (d) result with both local detail loss and global contour loss. }
\label{fig:impact_scn}
\end{figure}
However, it also demonstrates that only being supervised by Canny is not enough. It results in unwanted strokes at the area of eyebrow mouth or jaw, and even changes the shape of eyes. Stroke calibration should be superior to detail enrichment. We want the Stroke Calibration Network to modify strokes without changing holistic properties like facial contours and hair styles. So we add both the contours as the global constraint and the edges as local constraint. As shows in the fourth column of Figure \ref{fig:impact_scn}, it calibrates unreasonable strokes and preserves original properties.
Table \ref{tab:impact of SCN} shows the accuracy of our Stroke Calibration Network. We measure precision and recall with Canny for ablation study of local detail loss and global contour loss. For each setting, we convert the refined sketch and corresponding Canny to binary with a constant threshold value (\textit{i.e.}, each pixel is either zero or one). Precision means how many ones in the refined sketch are actual ones in the ground truth Canny, and recall means how many ones in the the ground truth Canny are contained in the refined sketch. The high precision and relative low recall are in line with expectations. The original purpose of Stroke Calibration Network is to modify unreasonable strokes and add essential details. The low accuracy of using local detail loss only is consistent with results in Figure \ref{fig:impact_scn}. Since HED and Canny are different, it is not surprising that the accuracy of using global contour loss only is low.
\begin{table}[t]
\centering
\caption{Quantitative performance of our Stroke Calibration Network trained on only local detail loss(detail only), global contour loss(contour only) and local detail loss together with global contour loss(detail and contour).}
\label{tab:impact of SCN}
\begin{tabular}{ccl}
\toprule
Components &Precision & Recall \\
\midrule
detail only & 0.1559 & 0.1475 \\
contour only & 0.1713 & 0.1564 \\
detail and contour & \textbf{0.9962} &\textbf{0.4772} \\
\bottomrule
\end{tabular}
\end{table}
\subsubsection{The scalability of Image Synthesis Network}
\label{sec:scalability of ISN}
Notice that in Section \ref{sec:ISN} we didn't deliberately design the structure of Image Synthesis Network (SCN). In fact, we adopt a quite simple structure of SCN to show that it's easy to generate satisfactory results from the calibrated sketches even the sktech2image synthesis network is not deliberately designed. Since there are many methods \cite{jo2019sc,yu2018generative} for "well-drawn" sktech2image problem, we argue that such stroke calibration is indispensable for these methods to be well applied in some real applications, such as cultural relics or digital sketch generation for suspects, to produce realistic images. Therefore, it is a useful application and a new solution to synthesize a high-quality image from poorly-drawn sketches. The results in Section \ref{sec:comparison against baselines} have shown that our proposed stroke calibration network is a simple yet effective. The calibrated sketches can be directly fed into other existing "well-drawn" sktech2image methods \cite{jo2019sc,yu2018generative} to produce more diverse and more photo-realistic results. Our two-stage Algorithm \ref{alg:Training strategy} provides end-to-end scalability for improving SCN by designing novel architecture or combining with existing "well-drawn" sktech2image methods.
For example, we can improve SCN by simply doubling the numbers of residual blocks (refer to as Improved-1). Or building our generator based on U-Net and using Masked Residual Unit (MRU) module proposed in \cite{Chen2018CVPR} (refer to as Improved-2). MRU is shown to be more effective than ResNet, Cascaded Refinement Network (CRN) or DCGAN structure in image synthesis task according to \cite{Chen2018CVPR}. We compare images generated by different structures of SCN on the CUHK dataset using PSNR, SSIM and FID as metrics. The results are shown in Table \ref{tab:scalability of ISN}.
\begin{table}[t]
\centering
\caption{The scalability of Image Synthesis Network. We compare results generated by different structures of SCN on the CUHK dataset using PSNR, SSIM and FID as metrics. For details refer to Section \ref{sec:comparison against baselines} and Section \ref{sec:scalability of ISN}.}
\label{tab:scalability of ISN}
\begin{tabular}{cccl}
\toprule
Method &PSNR & SSIM & FID\\
\midrule
Original &{20.25} &{0.8006} &{58.43} \\
Improved-1 &{20.34} &{0.8092} &{57.09} \\
Improved-2 &{21.09} &{0.8137} &{55.12} \\
\bottomrule
\end{tabular}
\end{table}
\section{Conclusion and Discussion}
\label{sec:conclusion}
We propose a poorly-drawn sketch based face image synthesis method named Cali-Sketch.
Our method can generate pleasing results even when the input sketches are not plausible. To achieve this, we introduce a two-stage sketch-to-image translation method consisting of two GANs. Stroke Calibration Network first calibrates unreasonable strokes and adds necessary details. The refined sketches are then fed into Image Synthesis Network to produce photo-realistic face images. Given poorly-drawn sketches, Cali-Sketch can generate identity-consistent and appearance-realistic face images.
Experimental results shows effectiveness and efficiency of the proposed Cali-Sketch, showing superior performance than the state-of-the-art methods.
\subsection{Extended Application}
Our Stroke Calibration Network can act as a pre-processing module for real-world sketches. For interactive face image manipulation like \cite{jo2019sc}, a plausible input sketch is necessary. When free-hand drawn sketches are directly fed into those models, the results may be unacceptable. In this case, our Stroke Calibration Network can also act as pre-processing modification module. \cite{jo2019sc} is a recent facial image editing method. Users draw sketch $S$ and color as guidance on incomplete image $I\odot M$ erased by mask $M$. To show effectiveness and efficiency of our approach in this case, we first directly use original poorly-drawn sketch $S$ as input sketch for \cite{jo2019sc} to get an edited image. Then we feed the refined sketch $R$ pre-processed by our Stroke Calibration Network to produce another edited image. As demonstrated in Figure \ref{fig:pre-processing_for_SCFEGAN}, when the input sketch is sparse and contains wrong strokes and directly fed into \cite{jo2019sc}, the generated facial features are distorted and deformed. Our Stroke Calibration Network can calibrates unreason strokes and add necessary details. When this refined sketch is fed into \cite{jo2019sc}, the result is improved significantly.
\begin{figure}[th]
\centering
\includegraphics[width=\linewidth]{images/pre-processing_for_SCFEGAN}
\caption{Stroke Calibration Network as a pre-processing module for real-world sketches. (a) original image. (b) masked image and input sketch. (c) masked image and modified sketch. (d) editing result of original sketch. (e) editing result of modified sketch. }
\label{fig:pre-processing_for_SCFEGAN}
\end{figure}
Our method also show its potentialities for sketch-based object search \cite{yuan2018query,he2019triangles} and image retrieval \cite{huang2019content,Ioannakis2019Retrieval,Choi2019SketchHelper}. Various works have been proposed to efficiently support automatic annotation of multimedia contents and help content-based retrieval, and obtaining precise image sample sufficing the user specification may not be always handy in every instance. In such cases, sketch can be an alternative solution to initialize the search, \textit{i.e.}, sketch based image retrieval \cite{yuan2018query,Zhang2019retrieval}. Our method can complete necessary object information that would be critical for a reliable search performance.
\subsection{Limitation and Future Work}
Compared with image inpainting or image-to-sketch synthesis, generate photo-realistic image from poorly-drawn sketch is more challenging since there is less information in sketches.
Thus, we temporarily experiment on frontal faces without large rotation and translation. The dataset limitations provide strong motivation for future work to improve performance by expanding the datasets into faces with various angles or expressions, and further into all classes, \textit{e.g.}, the Google QuickDraw Dataset. In addition, the category of a sketch is also critical for image generation. Sketches are far from being complete in terms of the object information that would be transformed into a totally different object during generation. For example, as illustrated in Figure \ref{fig:pyramid}, if a user is intent on generating a pyramid image by simply drawing a `triangle', it is not sufficiently discriminative to uniquely resemble the pyramids. Thus incorporating category information of poorly-drawn sketches is critical. We will develop our Cali-Sketch into a drawing assistance that creates photographic self-portraits or user's favorite cartoon characters.
\begin{figure}[th]
\centering
\includegraphics[width=\linewidth]{images/pyramid}
\caption{Sketch samples of `triangle'. It is not sufficiently discriminative to uniquely resemble the pyramids by simply drawing a `triangle'. Incorporating category information is critical for image generation from poorly-drawn sketches.}
\label{fig:pyramid}
\end{figure}
\bibliographystyle{IEEEtran}
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"redpajama_set_name": "RedPajamaArXiv"
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Q: Julia 1.5.2 Suppressing Gurobi academic license in parallel I am attempting to suppress the academic license output from Gurobi. I have to solve an LP several times in my code and the print statement is slow and annoying to look at. I have created a working example. I wish to be able to execute the LP in parallel in Julia to increase performance. To suppress the output I use the package Suppressor. This seems to work well when running only using a single processor. However if I wrap the LP in a function and insert this into a loop and attempt to run the model in parallel I get an error:
TaskFailedException: SystemError: dup: bad file descriptor
Running the code works fine when using Windows 7 and an i5 processor.
Running the code on MAC OS 10.13.6 with an 2.66 GHz Intel core 2 duo does not work.
I am capable of running the code in parallel on MAC when it is not suppressed. Is it just because the hardware in ancient (the cores might not be able to communicate correctly to share information)? or is there a fix to this issue?
Additional information:
Julia: 1.5.2
Gurobi License version: 9.0.1
JuMP: 0.21.5
Suppressor: 0.2.0
clearconsole()
using Gurobi
using JuMP
using Suppressor
using BenchmarkTools
# Create LP frunction
function runlp()
@suppress begin
global primal = Model(Gurobi.Optimizer)
set_optimizer_attributes(primal, "OutputFlag" => 0)
set_optimizer_attributes(primal, "Threads" => 1)
end
# Declare variables with lower bound 0
@variable(primal, x1 >= 0)
@variable(primal, x2 >= 0)
@variable(primal, -Inf <= x3 <= Inf)
# Declare minimization of costs objective function
@objective(primal, Min, -5*x1+4*x2-3*x3)
# Declare constraint for minimum of lubricant 1
@constraint(primal, Cons_1,2*x1-3*x2-x3 <= 5)
@constraint(primal, Cons_2,4*x1-x2+2*x3 >= 11)
@constraint(primal, Cons_3,-3*x1+4*x2+2*x3 <= 8)
@constraint(primal, Cons_4,6*x1-5*x2+x3 == 1)
# Optimize model
optimize!(primal)
end
# Create function to ru LP multiple times
function testing()
for i in 1:100
runlp()
end
end
testing()
@btime testing()
function testing_par()
@sync Threads.@threads for i in 1:100
runlp()
end
end
@btime testing_par()
A: I'm not sure how Supressor works, but the way to resolve this with Gurobi.jl is to re-use an environment for multiple solves:
https://github.com/jump-dev/Gurobi.jl#reusing-the-same-gurobi-environment-for-multiple-solves
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,443
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Mohawk Dam, located in Jefferson Township, Coshocton County, Ohio northwest of Nellie, is a dry dam constructed by the United States Army Corps of Engineers (USACE) in the mid-1930s for the purpose of flood control on the Walhonding River. The dam is part of the larger 18-county Muskingum Watershed Conservancy District (MWCD). The dam has been in service for 70 years and was recently placed on the USACE's "Urgent" dam safety classification list and plans are currently being drafted that would allocate funds for dam stabilization.
History
Construction of the Mohawk Dam was started in April 1935 and was completed in September 1937. The dam was authorized by the Flood Control Act of 1938 and was built as a dry dam along with 13 other dams in the Muskingum River Watershed for flood control and water conservation. The dam was built right across the right-of-way of the Walhonding Canal, which ran from Coshocton to Cavallo.
The dam has always operated as a dry dam, holding back water only during a flood and releasing it slowly downstream. The highest water level ever recorded at the Mohawk Dam was during the flood of January 2005, where the water reached a height of above its normal level.
Future
The dam has been in service for 70 years but was only built with the expectation that it would function for around 50 years before sedimentation and erosion weakened the dam. The dam has weakened and several safety issues have arisen, which is why the USACE has placed it on its list of the nation's most at-risk dams, where it ranked seventh most at-risk in 2006. In 2007, the dam was classified as "Urgent", which is the second-highest classification level of the dam safety rating system used by the USACE. This classification indicates that the dam is a high federal priority for repairs since failure of the dam during a flood is moderately uncertain. The MWCD estimates that if the Mohawk Dam were to fail during a flood, the water normally held back could cost 307 people their lives and up to $449 million in property damage.
According to the MWCD, the dam's greatest problem is the inherent downstream seepage that occurs with most earthen dams. In the case of the Mohawk Dam, this condition is exacerbated by the fact that it was built on highly permeable land, which could cause instability if too much water were to seep through the lower part of the dam. A rehabilitation and repair plan to stabilize the structure has not yet been established, nor has an official cost-estimate been prepared. Funds were set aside by Congress in 2006 and 2007 to analyze the current state of the dam and gather data for a rehabilitation report. The MWCD serves as the local sponsor of the rehabilitation projects and must pay 3.45 percent of the costs. The remainder will be paid by the federal government. In order to pay for their share, the MWCD will levy an assessment of the properties in its 18-county district, requiring those property owners to pay for the dam improvements throughout the entire watershed. The total local-share cost to be paid by the MWCD for the work on four of the dams, including the Mohawk Dam, is estimated to be between $95 million and $135 million.
Gallery
References
Buildings and structures in Coshocton County, Ohio
Dams in Ohio
Muskingum Watershed Conservancy District
United States Army Corps of Engineers dams
Dams completed in 1937
1935 establishments in Ohio
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
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# perth & west coast australia
# Contents
## Plan Your Trip
### Region Map
### Welcome to Perth & West Coast Australia
### Perth & West Coast Australia's Top 12
### Need to Know
### What's New
### If You Like...
### Month by Month
### Itineraries
### Discover Margaret River & the Southwest Coast
### West Coast Australia Outdoors
### Travel with Children
### Regions at a Glance
## ON THE ROAD
### Perth & Fremantle
#### Perth & Fremantle Highlights
#### Perth
#### Fremantle
#### City Centre
#### Fishing Boat Harbour
#### East & North Fremantle
#### South Fremantle
### Around Perth
#### Around Perth Highlights
#### Rottnest Island (Wadjemup)
#### Rockingham
#### Peel Region
#### Mandurah
#### Yalgorup National Park
#### Pinjarra
#### Dwellingup
#### Jarrahdale & Serpentine National Park
#### Dryandra to Hyden
#### Hyden & Wave Rock
#### Darling Range
#### Kalamunda
#### Mundaring
#### Walyunga National Park
#### Swan Valley & Guildford
#### Avon Valley
#### York
#### Northam
#### Toodyay
#### Avon Valley National Park
#### New Norcia
#### Wildflower Way
#### Moora
#### Wongan Hills
#### Perenjori
#### Morawa, Mingenew & Mullewa
#### Sunset Coast
#### Yanchep
#### Guilderton
#### Lancelin
#### Turquoise Coast
#### Cervantes & Pinnacles Desert
#### Jurien Bay
#### Green Head & Leeman
### Margaret River & the Southwest Coast
#### Margaret River & the Southwest Coast Highlights
#### Geographe Bay
#### Bunbury
#### Tuart Forest National Park
#### Busselton
#### Dunsborough
#### Cape Naturaliste
#### Margaret River Wine Region
#### Yallingup & Around
#### Cowaramup & Wilyabrup
#### Margaret River
#### Around Margaret River
#### Augusta & Around
#### Southern Forests
#### Nannup
#### Balingup & Greenbushes
#### Bridgetown
#### Manjimup
#### Pemberton
#### Shannon National Park
### South Coast
#### South Coast Highlights
#### Walpole & Nornalup
#### Denmark
#### Albany
#### Around Albany
#### Mt Barker
#### Porongurup National Park
#### Stirling Range National Park
#### Bremer Bay
#### Fitzgerald River National Park
#### Hopetoun
#### Esperance
#### Around Esperance
### Monkey Mia & the Central West
#### Monkey Mia & the Central West Highlights
#### Batavia Coast
#### Dongara-Port Denison
#### Geraldton
#### Kalbarri
#### Shark Bay
#### Overlander Roadhouse to Denham
#### Denham
#### François Peron National Park
#### Monkey Mia
#### Gascoyne Coast
#### Carnarvon
#### Point Quobba to Gnaraloo Bay
### Coral Coast & the Pilbara
#### Coral Coast & the Pilbara Highlights
#### Coral Coast
#### Coral Bay
#### Exmouth
#### Around Exmouth
#### Ningaloo Marine Park
#### Cape Range National Park
#### The Pilbara
#### Dampier to Roebourne
#### Millstream-Chichester National Park
#### Karijini National Park
#### Port Hedland
### Broome & the Kimberley
#### Broome & the Kimberley Highlights
#### Broome Region
#### Port Hedland to Broome
#### Broome
#### Around Broome
#### Dampier Peninsula
#### The Kimberley
#### Derby
#### Gibb River Road
#### Derby to Wyndham & Kununurra
#### Devonian Reef National Parks
#### Fitzroy Crossing to Halls Creek
#### Wyndham
#### Kununurra
## Understand Perth & West Coast Australia
### Understand Perth & West Coast Australia
### Perth & West Coast Australia Today
### History
### Local Produce & Wineries
### Boom Town: Mining & the Environment
### Indigenous Art in Western Australia
## Survival Guide
### Directory A–Z
### Transport
### Map Legend
## Special Features
### Itineraries
### Off the Beaten Track
### Discover Margaret River & the Southwest Coast
### West Coast Australia Outdoors
Welcome to Perth & West Coast Australia
_If you subscribe to the 'life's a beach' school of thought, you'll fall in love with Western Australia (WA) and its 12,500km of spectacular coastline._
### An Immense, Sparsely Populated Land
If the huge expanses of WA were a separate nation, it would be the planet's 10th-largest country. Most of the state's population clings to the coast, yet you can wander along a beach for hours without seeing another footprint, or be one of a handful of campers stargazing in a national park.
The south is a playground of white-sand beaches, expanses of springtime wildflowers and lush green forests teeming with life. Up north in the Kimberley, you'll encounter wide open spaces that conceal striking gorges, waterfalls and ancient rock formations.
### Action Stations
WA has plenty for the active traveller. Traverse the 963km Bibbulmun Track (or focus on a few spectacular day walks), or mountain bike the 1000km Munda Biddi Trail. Shorter but equally interesting walks include wandering amid the wildflowers of the Stirling Range National Park and negotiating Porongurup's granite formations. Dive and snorkel in stunning marine parks and around fascinating shipwrecks, or surf around Margaret River and kiteboard and windsurf off Lancelin's expansive beaches.
### All Creatures Great & Small
WA's fauna includes kangaroos, emus and colourful parrots, and there is also the chance to get acquainted with lesser-known local critters like quokkas, bilbies and potoroos. The WA coast's lengthy dalliance with the Indian and Southern Oceans means opportunities to spot marine wildlife also abound. Each year about 30,000 whales cruise the coast-hugging 'Humpback Hwy'. At Ningaloo Marine Park you can dive with the world's largest fish, the whale shark, and at Rockingham, Bunbury and Monkey Mia you can interact with wild dolphins.
### The Finer Things in Life
Perth and neighbouring Fremantle are cosmopolitan cities, yet both retain a laid-back feel courtesy of their fantastic beaches and parks. The mining boom continues to add a glitzy sheen to everything in the shadow of its skyscrapers, and earlier boom times have left grand architectural legacies in Fremantle, Albany, Guildford and York.
Around Margaret River and the southwest, vignerons and brewers craft world-class wines and beers, complemented by the inventive menus of the region's restaurants. Truffles are grown down south, and WA's seafood is consistently sublime.
Greens Pool, William Bay National Park (Click here)
ORIEN HARVEY/GETTY IMAGES ©
Why I Love Perth & West Coast Australia
By Brett Atkinson, Author
Despite being very familiar with Australia's eastern states, I always find the country's far west a compellingly different destination. Perth's pride at being the world's most remote capital is reflected in the verve and independence of the locals, and I love exploring the state's emerging culinary scene, which combines great wine and local produce. Fremantle's historic townscape – and excellent pubs serving great craft beer – is worth multiple leisurely explorations, and the state's combination of the outback's elemental red-dirt expanses and cliff-studded coastline is truly like nowhere else I've been.
See authors for much more.
Perth & West Coast Australia's Top 12
Ningaloo Marine Park
AUSCAPE / UIG/GETTY IMAGES ©
1 Swim alongside 'gentle giant' whale sharks, snorkel among pristine coral, surf off seldom-visited reefs and dive at one of the world's premier locations at this World Heritage–listed marine park (Click here), which sits off the North West Cape on the Coral Coast. Rivalling the Great Barrier Reef for beauty, Ningaloo has more easily accessible wonders: shallow, turquoise lagoons are entered straight from the beach for excellent snorkelling. Development is very low-key, so be prepared to camp, or take day trips from the access towns of Exmouth and Coral Bay.
## Perth & West Coast Australia's Top 12
Margaret River Wine Region
JON ARNOLD IMAGES LTD/ALAMY ©
2 The joy of drifting from winery to winery along country roads shaded by tall gum trees is just one of the delights of Australia's most beautiful wine region (Click here). Right on its doorstep are the white sands of Geographe Bay, and even closer to the vines are the world-famous surf breaks of Yallingup and Margaret River Mouth. And then there are the caves – magical subterranean palaces of limestone, scattered along the main wine-tasting route. Sup, swim, surf, descend – the only difficulty is picking the order.
## Perth & West Coast Australia's Top 12
Shark Bay & Monkey Mia
Dolphins, Monkey Mia
PHOTO BY MARTIN COHEN WILD ABOUT AUSTRALIA/GETTY IMAGES ©
3 The aquamarine waters of World Heritage–listed Shark Bay (Click here) teem with an incredible diversity of marine life, from Monkey Mia's world-famous dolphins to Hamelin Pool's ancient stromatolites. Enjoy simple coastal camping; excellent indigenous cultural tours explain how to care for and understand the country. Explore remote Edel Land, with its towering limestone cliffs, cross over to historically rich Dirk Hartog Island or relax, lie back and sail after the elusive, sea-grass-munching dugong.
## Perth & West Coast Australia's Top 12
Pinnacles Desert
CHERYL FORBES/GETTY IMAGES ©
4 It could be mistaken for the surface of Mars: scattered among Nambung National Park's dunes, thousands of ghostly limestone pillars rise like a vast, petrified alien army. One of the West's most bizarre landscapes, the Pinnacles (Click here) attract thousands of visitors each year. It's easily enjoyed as a day trip from Perth, but staying overnight in nearby Cervantes allows for multiple visits to experience the full spectrum of colour changes at dawn, sunset and full moon, when most tourists are back in their hotels.
## Perth & West Coast Australia's Top 12
Perth & Fremantle
City skyline, Perth
JOHN W BANAGAN/GETTY IMAGES ©
5 Perth (Click here) may be isolated, but it's far from being a backwater. Scattered across the city are sophisticated restaurants showcasing modern Australian cuisine, while chic cocktail bars bubble away in unlikely laneways and restored heritage buildings. In contrast to the flashy face that Perth presents to the river, charmingly grungy inner suburbs echo with the hum of guitars and turntables, and the sizzle of woks. Just downstream, the lively port of Fremantle has a pub on just about every corner, most pouring craft brews from around Western Australia and the world.
## Perth & West Coast Australia's Top 12
Karijini National Park
Fern Pool, Dales Gorge
PETER PTSCHELINZEW/GETTY IMAGES ©
6 Hidden deep in the heart of the Pilbara, the shady pools and plunging waterfalls of Karijini (Click here) offer cool respite from the oppressive heat of the surrounding ironstone country. While most are content to explore the open gorges, booking an adventure trip will take you beyond the public areas as you abseil, swim, dive, climb and paddle through deep water-worn passages. Up top, witness the amazing spring transformation as wildflowers carpet the plains, and get some altitude on the state's highest peaks, including Mt Bruce (1235m).
## Perth & West Coast Australia's Top 12
Broome
DAVID WALL PHOTO/GETTY IMAGES ©
7 You can bitch and moan about the price of beer or how long your twice-cooked pork belly takes to arrive, but one thing is for certain: when that boiling crimson sun starts sinking slowly behind a conga-line of camels into a languid Indian Ocean at Cable Beach, you'll realise there's no other place like it in the world. Broome (Click here) is a melting pot of travellers, one of the world's great crossroads, and you'll find everything you need (though perhaps not everything you want) in the back streets, bars and markets, and on the noticeboards.
## Perth & West Coast Australia's Top 12
Water Adventures
DOUGLAS PEARSON/GETTY IMAGES ©
8 If you can't catch a wave on WA's 12,000km of coastline, mate, you're doing it wrong. In which case, head straight to one of Perth's surf schools (Click here) and leave Margaret River and Gnaraloo to the pros, where breaks with nicknames like 'suicides' and 'tombstones' beckon the fearless. Diving and snorkelling are excellent in many spots, and WA is the place to swim with your favourite marine animal. Windsurfers breeze off to gusty Lancelin (Click here) and Gnaraloo Bay (Click here), while paddlers splash their way along the many rivers.
## Perth & West Coast Australia's Top 12
Bushwalking
Valley of the Giants
ANDREW WATSON/GETTY IMAGES ©
9 Western Australia has 96 national parks, not counting dozens of other nature reserves and regional parks. These special places present oodles of opportunities to go walkabout on the many waymarked trails, and camp in isolated spots. The Bibbulmun Track (Click here) , the mother of them all, starts on the outskirts of Perth and heads nearly 1000km to Albany on the south coast, sheltered by the cooling giant eucalypts of the southern forests. At the Valley of the Giants (Click here) you can walk through the canopy on the 40m-high Tree Top Walk.
## Perth & West Coast Australia's Top 12
Gibb River Road
TONY WHEELER/GETTY IMAGES ©
10 Launch yourself into Australia's last frontier on a wild drive down this old cattle road (Click here) into the heart of the Kimberley. This is not for the faint-hearted; you'll need a serious 4WD, good planning and plenty of fuel, spares, food and water. Bring big doses of self-reliance, flexibility and humour. The rewards are fantastic gorges, hidden waterholes, incredible rock art and amazing wildlife, and you'll gain a first-hand insight into life in the outback. Did we mention there are also flies, dust and relentless heat?
## Perth & West Coast Australia's Top 12
Wildlife
Numbat
AUSCAPE / UIG/GETTY IMAGES ©
11 Welcome to an idiosyncratic menagerie of species: endangered numbats, woylies, bilbies and boodies in the Dryandra Woodland (Click here), quokkas on Rottnest Island (Click here), freshwater crocodiles in Windjana Gorge National Park (Click here), migratory shorebirds at Parry Lagoons Nature Reserve (Click here), beautiful red-tailed tropicbirds of the southwest coast, migrating humpback whales, dolphins at Monkey Mia (Click here) and whale sharks in Ningaloo Reef (Click here).
## Perth & West Coast Australia's Top 12
Indigenous Art
Wandjina figures, Mitchell Plateau
RICHARD I'ANSON/GETTY IMAGES ©
12 From urban galleries featuring contemporary art to centuries-old rock carvings, the culture and spirit of indigenous WA infuses this land. In Perth and Fremantle, visit excellent Indigenart (Click here) and Japingka (Click here) galleries; in the Kimberley, visit Short Street Gallery (Click here), before looking back across the eons at Wandjina and Gwion Gwion rock-art sites (Click here). Near spectacular Wave Rock (Click here) to the south, visit the 450 stencils and hand prints of the nearby Mulkas Cave.
Need to Know
#### For more information, see Survival Guide
Currency
Australian dollar ($)
Language
English
Money
ATMs widely available. Credit cards accepted in most hotels and restaurants.
Visas
All visitors require a visa, although New Zealanders receive one on arrival. Residents of Canada, the US, and many European and some Asian countries can apply online.
Mobile Phones
Australia's network is compatible with most European phones, but generally not with the US or Japanese systems. The main service providers offer prepaid SIMs.
Time
Western Standard Time (GMT/UTC plus eight hours). Daylight saving does not operate in WA.
### When to Go
High Season (Dec–Mar)
» In the south the weather is at its hottest and driest.
» The season peaks from Christmas to the end of the school holidays in January.
» In the north, this is the wet (low) season.
Shoulder (Apr, May & Sep–Nov)
» Wildflowers are in bloom from September.
» Also the months to visit the north.
» Humpback whales from September to November, whale sharks from April to June. Monkey Mia's dolphins are seen throughout the year.
Low Season (Jun–Aug)
» Wettest and coolest time in Perth and the south.
» Lows in the south are usually over 10°C.
» High season for the Coral Coast, the Pilbara, Broome and the Kimberley; dry and usually above 30°C.
### Websites
Lonely Planet (www.lonelyplanet.com/australia) Destination information, traveller forum and more.
Tourism Western Australia (www.westernaustralia.com) Official tourist site.
Tourism Australia (www.australia.com) Transport, event and destination information.
West Australian (www.thewest.com.au) Online version of the newspaper.
Department of Environment and Conservation (www.dec.wa.gov.au) Details on national parks. Some camp sites can be prebooked.
### Important Numbers
Drop the zero from the area code if calling from outside Australia ( 61-8). If calling a WA number while in WA, drop the 08 prefix.
International access code | 0011
---|---
Australia's country code | 61
WA area code | 08
Emergency (police, fire, ambulance) | 000
Directory assistance | 12455
### Exchange Rates
Canada | C$1 | $0.97
---|---|---
Euro | €1 | $1.23
Japan | ¥100 | $1.20
New Zealand | NZ$1 | $0.79
UK | £1 | $1.54
USA | US$1 | $0.96
For current exchange rates see www.xe.com.
### Your Daily Costs
##### Budget: Up to $150
» Campsite (two people): $14–45
» Dorm bed: $24–48
» Private room in hostel: $80–120
» Mainly self-catering but having an occasional budget meal out: $25
##### Midrange: $150–275
» Double room in a midrange hotel: $120–220
» Lunch and dinner in cafes and pubs: $60
» Car hire: $40–50 per day
##### Top End: Over $275
» Mains in top restaurants: over $35
» Double room in a top hotel: from $250
### Opening Hours
Note that, outside Perth, shops may not be open on weekends. Vineyard restaurants are usually only open for lunch, and many cafes also open later for dinner. Sunday shopping was introduced to the Perth CBD in August 2012, and most central-city stores now open seven days a week.
Banks 9.30am to 4pm Monday to Friday
Restaurants noon to midnight
Cafes 7am to 4pm
Pubs 11am to midnight
Shops 9am to 5pm Monday to Saturday, 11am to 5pm Sunday
### Arriving in Perth & West Coast Australia
Perth Airport (Click here ) The Connect Shuttle runs every 50 minutes to Perth ($18), less frequently to Fremantle ($33). A taxi is about $40 to central Perth and $60 to Fremantle. Buses run every 10 to 30 minutes to the city, hourly after 7pm; journey time is 44 minutes.
### Getting Around
Rental Car The most flexible way to get around, especially in attraction-packed areas like Margaret River. Distances are huge in other parts of the state, though, so investigate combining a one-way hire and a flight back to your starting point. See Click here for more information.
Airlines A good option to cover WA's huge distances quickly. Consider flying from Perth to Esperance, Exmouth or Broome, and then renting a car locally if your focus is only around those areas.
Train A good option for day trips south of Perth to Mandurah and Rockingham. Regular trains make Fremantle a worthwhile base for exploring Perth.
Bus Extensive coverage and relatively good frequency throughout the state. Good links from Perth to Margaret River and the southwest, and north to Geraldton and Exmouth.
Public Transport Both Perth and Fremantle have excellent urban bus and train networks. Be sure to use the free CAT bus services.
See transport for much more.
What's New
#### Brookfield Place
A precinct of heritage buildings along St Georges Terrace in central Perth has been lovingly restored to house the city's coolest new opportunities for eating and drinking.
#### The Terrace Hotel
Another careful heritage makeover in central Perth, this time transforming an expansive 19th-century terrace house into the city's newest and most luxurious boutique hotel.
#### The Rise (& Rise) of Craft Beer
Western Australia has always been a craft-beer hot spot, but new microbreweries in the Swan Valley and Margaret River now make it an essential destination for travelling beer buffs.
#### Jewel Cave & Moondyne Cave
Experience the stunning new Jewel Cave Preservation Centre before donning a hard hat and overalls to explore the adjacent and recently opened Moonydne Cave.
#### Margaret River Gourmet Escape
Some of the planet's truly great chefs celebrate a four-day food-and-wine adventure amid Margaret River's verdant vineyards.
#### Cooking Schools
Harness WA's fine natural produce by cooking up a storm at Wildwood Valley near Yallingup Click here and Foragers Field Kitchen Click here in Pemberton.
#### Castle Rock Granite Skywalk
Negotiate this newly opened walkway for spectacular views of the idiosyncratic rocky landscapes and karri forests of the Porongurup National Park.
#### Broome's Short Street Gallery
Broome's oldest gallery throws open its stock room, containing incredible canvases from indigenous artists scattered across the Kimberley and beyond.
#### Yarliyil Gallery
A new initiative from Halls Creek Shire provides local indigenous artists with a commercial outlet.
#### Duncan Road
Hauntingly beautiful and remote, this historic Kimberley route sees little tourist traffic yet is no more technical than its more famous cousin the Gibb River Road.
For up-to-date tips and suggestions from travellers, see lonelyplanet.com/australia/western-australia
If You Like...
Beaches
You're in luck. Western Australia (WA) has some of Australia's finest, which makes them among the best in the world. And you'll have many of them completely to yourself.
Cottesloe Perth's most iconic beach, with cafes and bars close at hand. (Click here )
Bunker Bay Brilliant white sand edged by bushland; you'll have to look hard to spot the few houses scattered about. (Click here )
Hellfire Bay Sand like talcum powder in the middle of Cape Le Grand National Park (Click here ), which is precisely in the middle of nowhere.
Shark Bay 1500km of remote beaches and towering limestone cliffs. (Click here )
Turquoise Bay A beautiful bay in Ningaloo Marine Park, with wonderful snorkelling. (Click here )
Eighty Mile Beach You're guaranteed at least 79 miles of solitude on this remote, white-sand beach. (Click here )
William Bay National Park Sheltered swimming around the granite boulders of Greens Pool and Elephant Rocks. (Click here )
Cable Beach Surely the most famous, camel-strewn, sunset-photographed beach in WA. (Click here )
### IF YOU LIKE... FINE FOOD
Foodies shouldn't resist a visit to the Wine & Truffle Co ( Click here ) in Manjimup, where you can take part in a truffle hunt.
Diving & Snorkelling
Reefs and wrecks are plentiful around WA and the marine life is lush, providing a smorgasbord of options for geared-up diving pros or gung-ho first-time snorkellers.
Mettams Pool Excellent snorkelling within Perth's city limits. (Click here )
Rottnest Island Over a dozen wrecks and two underwater snorkelling trails make this an excellent option. (Click here )
Busselton Lots to see around the southern hemisphere's longest timber jetty, plus the wreck of a decommissioned Navy destroyer not far away. (Click here )
Albany Look for sea dragons among the coral reefs and the wreck of the HMAS _Perth_ . ( Click here )
Ningaloo Marine Park Australia's largest fringing reef, where you can snorkel and dive with the world's largest fish, the whale shark, along with turtles, dolphins and dugongs. (Click here )
Houtman Abrolhos Islands Dive, snorkel, bushwalk or fish around these historic islands that rarely see tourists. (Click here )
Surfing & Windsurfing
Wax the board and fire up the Kombi van: WA's surfing is legendary.
Trigg Beach Perth's surfers come here straight from work to catch a few waves. (Click here )
Lancelin A mecca for windsurfers and kiteboarders, a great spot to learn to surf. (Click here )
Yallingup/Margaret River 'Yals' and 'Margs' are the hub of the WA surf scene – with a major pro competition held there every year. (Click here ) ( Click here )
Ocean Beach, Denmark You might find yourself sharing this beautiful bay with whales. (Click here )
Geraldton The surrounding beaches are thrilling for both wind- and wave-powered surfers. (Click here )
Gnaraloo Surfers flock here in winter to try their luck at the famous Tombstones break; in summer the windsurfers take their place. (Click here )
North West Cape Big swells hit the west of the cape from July to October. (Click here )
Forests & Bushwalking
You might be forgiven for thinking that WA was all about white sand and red dirt. There is an awful lot of both, but the state's arboreal delights are also worthy of exploration.
Lesueur National Park A huge diversity of flora with many rare and endemic trees. (Click here )
Karri Forest Explorer This shady circuit passes through three national parks surrounding Pemberton. (Click here )
Valley of the Giants Tree Top Walk A wobbly walkway arches through the lofty canopy of the tingle forest. (Click here )
Bibbulmun Track The big one – stretching nearly 1000km from the edge of Perth through the southern forests to Albany. (Click here )
Cape to Cape Track Enjoy Indian Ocean views on this 135km trail from Cape Naturaliste to Cape Leeuwin. (Click here )
Walyunga National Park Explore the trails in this beautiful park, where the Avon River cuts through the Darling Range. (Click here )
Derby With its bloated trunk and often bare, scrawny branches, the alien-looking boab tree is emblematic of this Kimberley town. (Click here )
Stirling Range National Park This rugged range is known for its flora and chameleon-like ability to change colour. (Click here )
Marine Mammals
It's extraordinarily easy to come close to the great creatures of the deep along WA's coast.
Perth & Fremantle Thirty thousand whales cruise past between mid-September and early December, and boat trips will take you out to cheer them on. (Click here )
Rottnest Island The sharp-of-eye may spot New Zealand fur seals, dolphins and whales. (Click here )
Rockingham Wild Encounters Cruise out to swim with dolphins and spot seals. (Click here )
Sea Lion Charters, Green Head Splash with sea lions in the shallows. (Click here )
Dolphin Discovery Centre, Bunbury Wade next to the wild dolphins that regularly drop by, or take a boat trip to swim with them. (Click here )
Albany Between July and mid-October the bay turns into a whale nursery, with mothers and calves easily spotted from the beach, and cruises to take you a little closer. (Click here )
Monkey Mia Watch dolphins feeding in the shallows and take a dugong-spotting cruise. (Click here )
Beer, Wine & Food
WA's wine industry is now being complemented by innovative craft breweries, and vineyard restaurants and provedores also abound.
Swan Valley Within Perth's eastern reaches, this semirural area's cosy wineries and bustling microbreweries are packed with city folk at the weekend. (Click here )
Fremantle The traditional home of WA craft beer, from mighty Little Creatures to the marvellous Sail & Anchor (43 taps and counting). (Click here )
Margaret River Known for its Bordeaux-style varietals, chardonnay and sauvignon blanc, and a growing number of craft breweries. (Click here )
Pemberton Another esteemed wine area, producing extremely good pinot noir, chardonnay and sauvignon blanc. (Click here )
Denmark Notable wineries and craft breweries dot this picturesque area of the cool-climate Great Southern region. (Click here )
Mt Barker & Porongurup Considered the most significant part of the Great Southern, with cool climes suiting riesling, pinot noir and cabernet sauvignon. (Click here )
Little Creatures brewery (Click here), Fremantle
ANDREW WATSON/GETTY IMAGES ©
Aboriginal Art & Culture
Around 59,000 Aboriginal people still call WA home, comprising many different Indigenous groups, speaking distinct languages.
Art Gallery of Western Australia A treasure trove of indigenous art. (Click here )
Yanchep National Park Didgeridoo and dance performances, and history and cultural tours with Noongar guides. (Click here )
Wardan Aboriginal Centre Learn about Wardandi beliefs and way of life; try your hand at stone-tool making, and boomerang and spear throwing. (Click here )
Kepa Kurl Eco Cultural Discovery Tours Day tours to visit rock art and waterholes, sample bush food and hear ancient stories. (Click here )
Wula Guda Nyinda Aboriginal Cultural Tours Offers bushwalks and kayak tours, where you'll learn some of the local Malgana language, and how to identify bush tucker. (Click here )
Dampier Peninsula Interact with remote communities and learn how to spear fish and catch mud crabs. (Click here )
The Kimberley View artists' cooperatives, visit ancient rock art, and get to know 'country' on a cultural tour. (Click here )
Getting Off the Beaten Path
In a destination so varied and expansive, there are plenty of spectacular opportunities to craft your own journey of discovery.
Mornington Wilderness Camp The 95km stretch from the Gibb River Road to this riverside oasis is some of WA's most exquisite and loneliest country. (Click here )
Dryandra Woodland Less than two hours from Perth, but a world away, with endangered populations of endemic wildlife. (Click here )
Gnaraloo Station Come for a night and stay for a month as your skills are put to work on this sustainable marvel. (Click here )
Middle Lagoon Life doesn't get much more laid-back than at this Dampier Peninsula beachside campground far from anywhere. (Click here )
Mt Augustus Uluru is a mere pup compared to this art-adorned monolith five hours from the closest asphalt. (Click here )
Duncan Road A real outback adventure without the masses, Duncan Rd is both a destination itself and a 'long-cut' to the Northern Territory. (Click here )
Marble Bar Burnt into the Australian psyche by the sun's rays, the Iron Clad Hotel is surrounded by incredibly scenic and empty landscapes. (Click here )
Kayaking near Mornington Wilderness Camp (Click here)
STEVE WATERS/GETTY IMAGES ©
Month by Month
### Top Events
Southbound Festival , January
Perth International Arts Festival , February
West Coast Blues 'n' Roots Festival , April
Broome Opera Under the Stars , August
Margaret River Gourmet Escape , November
## January
The peak of the summer school holidays sees families head to the beach en masse. Days are hot and dry, except in the far north, where the wet season is in full force.
3 Busselton's Big Music Festival
The Southbound Festival starts off the new year with three days of alternative music and camping in Busselton. Featuring big-name international artists, it's Western Australia's Glastonbury, but with less mud. ( Click here )
2 Lancelin's Windsurfing Challenge
In early January, tiny Lancelin's renowned blustery conditions attract thousands for its world-famous windsurfing event, the Lancelin Ocean Classic. Held over four days, the event starts with wave sailing on the Thursday and Friday, followed by the marathon on Saturday and the Sunday slalom. ( Click here )
## February
The kids head back to school, freeing up some room at the beach and taking some of the pressure off coastal accommodation. It's still hot and dry (and soggy in the north).
3 Alternative Music Festival, Perth
The Big Day Out is Australia's biggest touring music festival, attracting leading alternative artists and lots of local up-and-comers. It comes to Claremont Showground in early February. ( Click here )
z Perth International Arts Festival
Held over 25 days from mid-February, Perth's festival attracts an international line-up, spanning theatre, classical music, jazz, visual arts, dance, film, literature – the whole gamut. It's worth scheduling your trip around. ( Click here )
3 Leeuwin Concert Series
Leeuwin Estate winery in Margaret River hosts world-class performers of popular music, opera and the stage (Roxy Music, kd lang, Sting) during its annual event in mid-February; other concerts run from January to April. ( Click here )
z Boyup Brook Country Music Festival
Good ol' boys and gals descend on a tiny southern forest town for five days of country music, bush poetry, markets and the annual 'Ute & Truck Muster'. Recent acts have included Kasey Chambers. ( Click here )
## March
It's still beach weather, but it's not quite as swelteringly hot in the south. It's hot and steamy in the north, however, with rain still bucketing down. Prices shoot up at Easter.
2 Margaret River Surfing Pro
Officially called the Drug Aware Pro, this World Qualifying Series (WQS) event, held over six days in mid-March, sees the world's best up-and-coming surfers battle it out in the epic surf at Margaret River. ( Click here )
## April
Another pleasant month in Perth, with the temperatures dropping to the mid-20s and a little more rainfall. Up north, it's finally starting to dry out and a great time for a Kimberley flyover.
5 Margaret River Wine Festival
This five-day festival titillates the taste buds with the best of the southwest's wine, food, art, music and outdoor adventures. It includes carnivals, master classes, the Slow Food Long Table Feast and a cricket match at Cowaramup Oval. ( Click here )
3 Blues 'n' Roots Festival
Held in Fremantle Park, this festival interprets its remit widely: the 2012 line-up featured Crosby, Stills and Nash, My Morning Jacket and The Specials. Its 10th anniversary was held in 2013. ( Click here )
## May
Temperatures creep down and Broome and Exmouth both finally drop below the 30s, making them particularly appealing – especially now the box jellyfish have retreated. Autumn showers are more common in the south.
2 Ord Valley Muster
For two weeks Kununurra hits overdrive during this annual collection of sporting, charity and cultural events, leading up to a large outdoor concert under a full moon on the banks of the Ord River. ( Click here )
## June
Winter hits Perth, with plenty of rain and possibly some snow on the Stirling Range further south. The warm, dry north, however, heads into peak season. Whale watching commences in Augusta.
5 Avon Valley Food & Wine
Gourmet food from around the world, tasty goodies from more local producers, and the best of the expanding Avon Valley wine scene are all showcased at this welcome winter festival in Northam. ( Click here )
z Derby Boab Festival
Derby strings out its party season from late May to early July with concerts, mud footy, horse and mudcrab races, film festivals, poetry readings, art exhibitions, street parades and a dinner out on the mudflats.
3 Denmark Festival of Voice
Rousing choruses blow away the cobwebs from the south-coast town of Denmark during the Festival of Voice held over the June long weekend. The town is flooded with soloists, duos, choristers and their admirers. It's accompanied by a workshop program. ( Click here )
## July
It's still wet and cold in the south and beautiful in the north – sparking a winter-break exodus from Perth. Whales congregate in the bays around Albany.
z Indigenous Cultural Celebrations
Indigenous art exhibitions and performances take place throughout WA during National Aboriginal & Islander Day Observance Committee week, which celebrates the history, culture and achievements of indigenous people. ( Click here )
## August
Much the same as July climate-wise, although temperatures start to edge up. Manjimup truffles come into season, to the delight of Perth's chefs and their customers; whales continue to hang out on the south coast.
z Avon River Festivities
Northam and Toodyay both turn on festivals the day before the Avon Descent, a gruelling 133km white-water rafting event for powerboats, kayaks and canoes between the two towns. Northam hosts the Avon River Festival, while Toodyay has a Festival of Food. ( Click here )
z Broome Race Round
Local fillies and stallions frock up and get slaughtered as the Broome Race Round heads towards a frenzied climax with the Kimberley Cup, Ladies Day and the Broome Cup, all in early August. There's also some horse racing. ( Click here )
3 Opera Under the Stars, Broome
World-class opera performers sing under clear Kimberley night skies at the Cable Beach Amphitheatre, their vocal pyrotechnics accompanied by a fireworks display. The event (www.operaunderthestars.com.au) is now preceded by the Oper-Arte fundraising art auction.
## September
Spring brings a flurry of excitement, with wildflowers blooming and whales heading up the west coast. Broome pops back into the 30s and the tourists start to head south again.
3 Red Earth Arts Festival, Pilbara
Spread across the Pilbara's coastal mining towns during most of September, the Red Earth Arts Festival is an eclectic mix of live music (all genres), theatre, comedy, visual arts (including film, photography and sculpture) and storytelling. ( Click here )
z Festival of the Pearl
Starting either in late August or early September, Broome's Shinju Matsuri celebrates its pearl industry and multicultural heritage with a carnival of nations, a film festival, art exhibitions, food, concerts, fireworks and dragon-boat races. ( Click here )
z Perth's Wildflower Festival
In September and early October, Kings Park and the Botanic Garden are filled with colourful wildflower displays for the annual Kings Park Festival, which celebrates WA's unique, spectacular flora. Includes guided walks, talks and live music every Sunday. ( Click here )
## October
The last of the whales depart the south coast and hit the west-coast leg of the Humpback Hwy. The weather's warmer and drier, and the wildflowers are still wonderful.
z Geraldton Greenough Sunshine Festival
It started in 1959 as a tomato festival, but now Geraldton's solar celebrations (www.sunshinefestival.com.au) include dragon-boat races, parades, sand sculptures and parties, held over nine days in early October. Sunshine guaranteed.
## November
A great time to be in Fremantle, with temperatures in the mid-20s, very little rain and a convoy of whales passing by. In the far north, box-jellyfish season begins.
5 Margaret River Gourmet Escape
The culinary world's heavy hitters – David Chang and AA Gill attended the inaugural event in 2012 – descend on Margaret River for four days of culinary inspiration (www.gourmetescape.com.au). Australia's growing crew of celebrity chefs usually attend as well.
z Fremantle Festival
Ten days of parades, performances, music, dance, comedy, visual arts, street theatre and workshops. Founded in 1905, it's Australia's longest-running festival (www.fremantle.wa.gov.au). Highlights: the Kite Extravaganza on South Beach and the Wardarnji Indigenous Festival.
z Broome Mango Festival
Broome celebrates its mango harvest with four days of mango-themed everything (www.broome.wa.au/events/broome-mango-festival). So how exactly do you celebrate mangos? With a quiz night, a fashion parade and a Great Chefs of Broome Cook-Off, apparently. If you don't end up with sweet, sticky fingers, you're doing it wrong.
Itineraries
1 WEEK
A Southwest Short Circuit
If you've got limited time, this itinerary offers a taste of the best of the state – city life, colonial history, beaches, wildlife, wine, forests and rural roads. Base yourself in either Perth (Click here) or Fremantle (Click here) and spend three days exploring the conjoined cities and one day on Rottnest Island (Click here). Hire a car and head south, stopping first at Bunbury (Click here) for lunch and a visit to the Dolphin Discovery Centre. Continue on to Geographe Bay ( Click here), basing yourself in either Busselton (Click here) or Dunsborough ( Click here), and use the rest of the day to explore the beaches. Pick up a wine-region map and spend day six checking out the wineries, surf beaches and caves, all of which are close by. Base yourself in the Margaret River (Click here) township that night and head to Settlers Tavern, the local pub. The next morning, head to Augusta via Caves Rd and take the scenic detour through the karri forest along unsealed Borunup Drive (Click here). Visit Cape Leeuwin (Click here), where the Indian and Southern Oceans meet, before heading back to Bunbury on a picturesque rural drive through Nannup (Click here) and Balingup (Click here). From here it's a two-hour drive back to Perth.
## Itineraries
3 WEEKS
The Southwest Uncut
Australia's southwest is a magical part of the continent and this itinerary covers its main highlights. Bump it up by another week to really relax into it. Start by following the previous itinerary as far as Cape Leeuwin (Click here), but spend a second night in Margaret River (Click here) for more winery, brewery and beach time.
Continue to Pemberton (Click here), amid three forested national parks, for more wineries and the Karri Forest Explorer scenic drive. The next day, continue through Walpole (Click here) to the extraordinary Valley of the Giants Tree Top Walk (Click here), then press on to Denmark (Click here). Check out the beaches, wineries and breweries before making the short hop to Albany (Click here) the next day. Spend two days here swimming (in summer), whale watching (in winter) and exploring the nearby coastal national parks.
Head north for more wineries at Mt Barker (Click here) before scuttling east to spend the night at Porongurup National Park (Click here). Spend the next day (or two) tackling the mountainous tracks here or at Stirling Range National Park (Click here) further north.
From here the driving distances get longer. Continue through Ongerup and Jerramungup to the South Coast Hwy and at Ravensthorpe hop down to Hopetoun (Click here ) to spend the night. This will take about three hours from the Stirling Range, so you can spend the afternoon at the beach. The following day, head back to the South Coast Hwy and continue east to Esperance (Click here), a drive of around 2½ hours. Stay there for at least two days, spending one exploring gorgeous Cape Le Grand National Park (Click here).
Head back on the South Coast Hwy and turn north just past Ravensthorpe for the road to Hyden (Click here) and extraordinary Wave Rock (Click here); allow four hours' driving. The following day, head west on Hwy 40 to Brookton and then turn north on the Great Southern Hwy and follow the Avon Valley to quaintly colonial York (Click here); allow 3½ hours. For your last day, take a leisurely drive back to Perth via Mundaring (Click here), stopping at the Swan Valley (Click here) wineries en route.
To make this itinerary shorter, head straight to Hyden from the Stirling Range, or take the Albany Hwy directly to Perth from Mt Barker.
Mitchell Falls (Click here)
FEARGUS COONEY/GETTY IMAGES ©
Swan River, Perth
FRANCES ANDRIJICH/GETTY IMAGES ©
## Itineraries
1 Month
The Gibb River Road & Kimberley Outback
The biggest adventure in the west leaves Broome (Click here) during the Dry and traverses the heart of the rugged Kimberley by 4WD. First stop is the Dampier Peninsula ( Click here), with its Aboriginal communities, beautiful beaches and mud crabs, and your last saltwater swim. Take the back road to Derby (Click here), with its boabs, then on to the Gibb River Road (Click here), where Lennard River (Click here) is the first of many inviting gorges. Explore wildlife and gorges at Mt Hart (Click here) and remote Mornington Wilderness Camp (Click here) and look for Wandjina at Galvans Gorge (Click here) and Mt Elizabeth Station (Click here). Turn off onto the Kalumburu Road (Click here), check the road conditions at Drysdale River (Click here) and drive on to the Mitchell Plateau (Click here), with its forests of Livistona and mind-blowing falls. Marvel at the area's rock art before hitting the northern coast and excellent fishing at Honeymoon Bay (Click here), just beyond the mission community of Kalumburu (Click here).
It's all downhill from here as you retrace your route back to the Gibb, then turn left for wonderful Home Valley Station (Click here), where someone else can do the cooking and the soft beds make a pleasant change from camping. Nearby El Questro (Click here) has gorges aplenty, none more beautiful than Emma Gorge (Click here). Soon you're back on asphalt, but not for long as you take in the amazing bird life of Parry Lagoons Nature Reserve (Click here). Let Wyndham's Five Rivers Lookout (Click here) blow your mind with its view of Cambridge Gulf, before heading for the civility of Kununurra ( Click here), with its excellent food and supplies. Look for fruit-picking work, ride a canoe down the mighty Ord River, or jump back behind the wheel for the wonders of Purnululu National Park (Click here), home to the orange-domed Bungle Bungle Range (Click here). Darwin and the Northern Territory are beckoning, or you can follow the Great Northern Hwy back to Broome, stopping in at beautiful Geikie Gorge (Click here) for a relaxing boat cruise where you might spot freshwater crocs. If you don't see any, don't worry, as nearby Windjana Gorge (Click here) has loads sunning on the river banks. Grab your torch and head for a cold wade through the icy waters of Tunnel Creek (Click here), with its bats and rock art, before planting the pedal back to Broome, where you won't care how much that beer costs any more.
## Itineraries
2 Weeks
Indian Ocean Dreaming
Beautiful beaches, spectacular sunsets and diverse wildlife are constants on this coastal cruise. Take Indian Ocean Dr north from Perth (Click here) to Cervantes for sunset on the otherwordly Pinnacles Desert (Click here). Cruise the wildflower-laden Kwongan back roads and marvel at Lesueur National Park's (Click here) flora before snorkelling with sea lions at Green Head (Click here). Follow the flowers out to Perenjori (Click here), then hit the cafes and museums of Geraldton (Click here). Have a surf on a kiteboard, then move on to the wonderful Kalbarri (Click here) coastline. Enjoy a canoe in the gorges before sampling the outback on the long drive to World Heritage–listed Shark Bay (Click here). Watch dolphins at Monkey Mia (Click here), go sailing with dugongs, and learn about country on an indigenous cultural tour. Check out the stromatolites of Hamelin Pool (Click here), before putting in more road time on the stretch to Carnarvon (Click here). Drop into Gnaraloo (Click here) for world-class waves before arriving at tiny Coral Bay (Click here) and Exmouth (Click here), where whale sharks, manta rays and turtles inhabit the exquisite Ningaloo Marine Park (Click here). You can fly out of Exmouth, drive back to Perth in two days, overnighting in historic Greenough (Click here), or push on to the gorges of Karijini ( Click here).
## Itineraries
1 Week
Pilbara Jewels
You'll camp most of the way on this link between Ningaloo and Broome, with long empty beaches, shady pools and surprisingly good food. From Exmouth (Click here), take Burkett Rd back to the highway, and head north, turning off at Nanutarra for the long, scenic haul up to Tom Price (Click here). After stocking up, spend the next few days camped in Karijini National Park (Click here), exploring the sublime gorges and indulging in a spot of peak bagging among the state's highest mountains. Don't miss a swim at Hamersley Gorge en route to restful, shady Crossing Pool in Millstream-Chichester National Park (Click here). Admire the mesas and breakaways of the Chichester Range before dropping down to the coast and some snorkelling at lovely Point Samson ( Click here). Take the North West Coastal Hwy directly to Port Hedland (Click here), and scoff some wonderful coffee and cake in the Silver Star railcar, before camping at remote 80 Mile Beach (Click here), where you might spot nesting turtles. Your last leg is a long stretch of nothing as you skirt the Great Sandy Desert to arrive in tropical Broome (Click here). You can bail out here or tool up for the Kimberley. Alternatively, skip the country on a direct Bali flight from Port Hedland.
Contos Beach, Leeuwin-Naturaliste National Park (Click here)
ORIEN HARVEY/GETTY IMAGES ©
## Plan Your Trip
Discover Margaret River & the Southwest Coast
Margaret River features family-friendly beaches, brilliant surfing, labyrinthine caves studded with limestone formations, and a world-class gourmet scene – all in a relatively compact area. Vineyards producing excellent chardonnays and Bordeaux-style reds segue to rural backroads punctuated with craft breweries, providores, cheese shops, chocolate shops, and art galleries.
Best of the Region
#### Best Wineries
Vasse Felix ( 08-9756 5000; www.vassefelix.com.au; cnr Caves & Harmans Rds) Regional pioneer leading the way with its Heytesbury Cabernet blend and Heytesbury Chardonnay.
Cullen Wines (Click here ) Another Margaret River pioneer, with the 2009 Diana Madeline cabernet sauvignon merlot awarded Wine of the Year in the _Australian Wine Annual 2012_ .
Leeuwin Estate (Click here ) Wonderful wines, especially its Art Series chardonnay and sauvignon blanc.
Watershed Premium Wines (Click here ) One of WA's best vineyard restaurants and renowned for its Awakening cabernet sauvignon.
Ashbrook (Click here ) Great quality, good value; try the cabernet merlot.
#### Four Things You Wouldn't Expect
Artworks by Arthur Boyd and Sidney Nolan in the Bunbury Regional Art Gallery (Click here ).
A highly rated French-Australian film festival, CinéfestOZ (Click here ), is held annually in beachy Busselton.
A colony of red-tailed tropicbirds roosts off Cape Naturaliste.
Most of the best restaurants aren't open in the evenings.
## Plan Your Attack
### What's the Layout?
The sheltered white sands of Geographe Bay arch from south of Bunbury to Cape Naturaliste, with Busselton and Dunsborough its main towns. At Cape Naturaliste the coastline pirouettes and runs nearly due south to Cape Leeuwin. The wine region runs parallel to this coast with Margaret River cutting roughly east to west through the centre, passing through its namesake town. Wineries are scattered around, but most are north of the river.
### Where to Stay
» For a beach holiday Busselton or Dunsborough
» For surfing Yallingup, Prevelly or Margaret River
» For wineries Yallingup, Margaret River or anywhere in between
» For caves Anywhere between Yallingup and Augusta
» For peace and quiet Augusta
### When to Go
» For a beach holiday December to March
» For surfing Anytime, but the big surf pro is in March
» For wineries, breweries and caves All year
» For whale watching June to September from Augusta, September to December from Dunsborough
» For French films August
### When to Avoid
» January in Busselton, unless you're going to the Southbound music festival or have booked well in advance
» November in Dunsborough, when the place is overrun by end-of-school revellers
» Weekends in Margaret River, accommodation prices are higher and there are loads of people – but at least everything will be open
### What to Do
##### Surfing the Wineries
The two main north–south routes are the Bussell Hwy (passing through Cowaramup, Margaret River and Augusta) and leafy Caves Rd (running south from Dunsborough). Numerous bucolic back roads link the two. Pick up one of the excellent free maps, squabble over who's going to be the nondrinking driver, and dive right in. The other alternative is to take a tour – public transport is not a workable option.
Most of the wineries offer tastings between 10am and 5pm daily. At busy times (this includes every weekend), consider booking ahead for lunch before you set out.
##### Tasting the Waves
Known to surfers as 'Yals' (around Yallingup) and 'Margs' (around the mouth of the Margaret River), the beaches between Capes Naturaliste and Leeuwin offer powerful reef breaks, mainly left-handers (the direction you take after catching a wave). The surf at Margs has been described by surfing supremo Nat Young as 'epic', and by world surfing champ Mark Richards as 'one of the world's finest'.
As is the way with such hot spots, surfers can be quite territorial, so respect the etiquette and defer to locals if you're unsure. If you're planning on spending a lot of time on the breaks, call into the surf shops and get to know some locals.
Around Dunsborough, the better locations include Rocky Point (short left-hander) and the Farm and Bone Yards (right-handers), which are between Eagle and Bunker Bays. Near Yallingup there are the Three Bears (Papa, Mama and Baby, of course), Rabbits (a beach break towards the north of Yallingup Beach), Yallingup (reef with breaks left and right), and Injidup Car Park and Injidup Point (right-hand tube on a heavy swell; left-hander). You'll need a 4WD to access Guillotine/Gallows (right-hander), north of Gracetown. Also around Gracetown are Huzza's (an easy break within the beach), South Point (popular break) and Lefthanders (the name says it all). The annual surfer pro is held around Margaret River Mouth and Southside ('Suicides') in March.
Pick up a surfing map from one of the visitor centres.
Surfing is never without its risks. Two people have been killed by sharks in the vicinity of Gracetown in the last six years.
### BEST FAMILY ACTIVITIES
» Dolphin Discovery Centre ( Click here ), Bunbury
» Bunbury Wildlife Park ( Click here )
» Busselton Drive-in Outdoor Cinema ( Click here )
» Busselton Jetty ( Click here )
» Margaret River Chocolate Company (Click here )
##### Going Underground
The main cave complexes are spread, perhaps unsurprisingly, along Caves Rd. Ngilgi Cave sits by itself near Yallingup, but the other main complexes are between Margaret River township and Augusta, and are split between those run by the Department of Environment and Conservation (Calgardup Cave and Giants Caves) and the more commercialised CaveWorks caves (Lake Cave, Jewel Cave and Mammoth Cave). Caveworks offers a combined ticket for its three caves. If you're feeling adventurous, don overalls and a hard hat and explore the recently reopened Moondyne Cave on a guided tour.
##### Getting Crafty
The hoppy wave of craft beer that's sweeping many countries has also washed up on WA shores, and an innovative generation of brewers is proving there's more to beer than innocuous Euro lagers. Look forward to a global array of beer styles including India Pale Ales, Belgian Ales and Chocolate Porters, and decide on a designated driver or join a tour. See Click here for our picks of the best of Margaret River's craft brewing scene. Most are open for drinks and food from around 11am to 5pm.
Lake Cave (Click here)
LUCA TROVATO/GETTY IMAGES ©
##### Other Attractions
» Beaches – and lots of them; they're particularly beautiful between Dunsborough and Cape Naturaliste.
» Walking – there are excellent tracks around Cape Naturaliste and between the capes.
» Diving – trips leave from Busselton and Dunsborough to explore local wrecks and reefs.
» Whale watching – cruises leave from Augusta (starting in June) and Dunsborough (starting in September).
» Lighthouses – both capes have them and both can be visited. From Cape Leeuwin you can watch the Indian and Southern Oceans collide.
» Adventure sports – from mountain biking to climbing and kayaking. See Click here .
Leeuwin Estate (Click here)
CLAVER CARROLL/GETTY IMAGES ©
Quokka (Click here), Rottnest Island (Wadjemup)
KATY CLEMMANS/GETTY IMAGES ©
## Plan Your Trip
West Coast Australia Outdoors
With incredible landscapes and seascapes, intriguing wildlife, and all that brilliant sunshine, Western Australia (WA) is the perfect playground for outdoor enthusiasts, with numerous tracks to follow, waves to surf and reefs to explore.
Best Outdoors
#### Best for Daredevils
Karijini National Park Scramble, abseil, slide and dive through the gorges
Horizontal waterfalls, Derby Ride the surge in a speedboat
#### Best Wildlife Encounters
Whales Whale-watching boats leave from Perth, Fremantle, Dunsborough, Augusta, Albany, Coral Bay, Exmouth, Kalbarri, Broome and the Dampier Peninsula
Whale sharks and manta rays Ningaloo Marine Park
Dolphins Rockingham, Bunbury, Monkey Mia
Sea lions Rockingham, Green Head
Seals Rottnest Island
Dugongs Monkey Mia
Little marsupials Rottnest Island, Dryandra Woodland
Huge lizards Anywhere in the Kimberley
Kangaroos and parrots Everywhere
## Bushwalking
WA's excellent bushwalking terrain includes the southwest's cool forests, the expansive Bibbulmun Track and the north's rugged national parks.
See www.bushwalkingwa.org.au for details of local bushwalking clubs, and to contact potential walking buddies, or buy and sell gear, see the forums on www.bushwalk.com.
For responsible-bushwalking tips, see the camping and bushwalking guidelines online at www.dec.wa.gov.au.
### THE BIBBULMUN TRACK
Taking around eight weeks to walk, the 963km Bibbulmun Track (www.bibbulmuntrack.org.au) goes from Kalamunda, 20km east of Perth, through mainly natural environment to Walpole and Albany.
Terrain includes jarrah and marri forests, wildflowers, granite outcrops, coastal heath country and spectacular coastlines.
Comfortable camp sites are spaced regularly, and the best time to do it is from August to October.
### Perth & Surrounds
With hiking and camping facilities, John Forrest National Park has an easy 15km walk to waterfalls, and the rugged Wal-yunga National Park features a medium-to-hard 18km walk that fords the Avon River and has excellent wildlife viewing. The Yanchep National Park has short strolls and challenging full-day walks. The Yaberoo Budjara trail follows an Aboriginal walking trail.
### Down South
Serious walkers gravitate to the ruggedly beautiful Stirling Range National Park. Popular are the Bluff Knoll climb (6km, three to four hours), and the park's 1500 species of wildflower. Visit from September to November for the park's flowering glory, and be prepared for wind chill and rain (and sometimes snow) in winter.
North of Albany is the smaller Porongurup National Park, with spectacular granite rocks and dense karri forest. Trails include the 10-minute Tree in the Rock stroll, the medium-grade Hayward and Nancy Peaks (three hours) and the challenging three-hour Marmabup Rock hike. Wildflowers and bird activity make springtime the peak season for Porongurup, but it can be visited year-round.
Spectacular coastal hghlights are walks through Walpole, Fitzgerald River and Cape Le Grand National Parks. The Cape to Cape Track ( Click here ) follows the coastline 135km from Cape Naturaliste to Cape Leeuwin, taking five to seven days, and featuring wild camp sites en route.
### BEST WILDFLOWER SPOTS
» Kings Park, Perth, especially the Botanic Garden
» Fitzgerald River National Park, between Albany and Esperance
» Porongorup National Park, north of Albany
» Stirling Range National Park, also north of Albany
» Mulleaw, in the central midlands, especially at August's annual flower show
» Kalbarri National Park, on the Batavia Coast
» Wongan Hills and Morawa in the central midlands
### Up North
Summer's no picnic in the sweltering, remote national parks of the north, and high season for many bushwalkers is from April to October. The arid terrain can be treacherous, so research carefully, be prepared with water and supplies, and check in with rangers before setting out.
Kalbarri National Park showcases scenic gorges, thick bushland and rugged coastal cliffs. The popular six-hour loop features dramatic seascapes, including spectacular Nature's Window.
Rugged, sometimes hazardous treks can be taken into the dramatic gorges of Karijini National Park. The walk to the Mt Bruce summit (9km, five hours) is popular with experienced bushwalkers.
Visitors to the Kimberley's Purnululu National Park come to see the striped beehive-shaped domes of the World Heritage–listed Bungle Bungles. Walks include the easy Cathedral Gorge walk, and the more difficult overnight trek to Piccaninny Gorge. The park is only open from April to December.
## Camping
It's very easy to 'get away from it all' in WA, and in the state's national parks, sleeping in a swag under the stars is almost obligatory. The weather is a factor, though: it can be uncomfortable in the north during summer due to heat and flash flooding, and cold down south during winter. School holidays can be very busy.
Bungle Bungle Range, Purnululu National Park (Click here)
KIRKLANDPHOTOS/GETTY IMAGES ©
## Surfing & Windsurfing
Beginners, intermediates, wannabe pros and adventure surfers will all find excellent conditions to suit their skill levels. WA gets huge swells (often over 3m), so it's critical to align the surf and the location with your ability. Look out for strong currents, sharks and territorial local surfers.
WA's traditional surfing home is the southwest, particularly from Yallingup to Margaret River. This stretch has many different breaks to explore.
Around Perth the surf is smaller, but there are often good conditions at bodyboard-infested Trigg and Scarborough. If the waves are small, head to Rottnest Island for (usually) bigger and better waves. Check out Strickland Bay.
Heading north, there are countless reef breaks waiting to be discovered (hint: take a 4WD). Best known are the left-hand point breaks of Jakes Point near Kalbarri; Gnaraloo Station, 150km north of Carnarvon, and Surfers Beach at Exmouth. Buy the locals a beer and they might share a few more secret world-class locations.
Windsurfers and kitesurfers have plenty of choices with excellent flat-water and wave sailing. Kitesurfers appreciate the long, empty beaches and offshore reefs.
After Perth's city beaches, head to Lancelin, home to a large summertime population of surfers. Flat-water and wave sailing are excellent here. Further north, Geraldton has the renowned Coronation Beach. The Shark Bay area has excellent flat-water sailing and Gnaraloo Station is also a world-renowned wave-sailing spot.
Salmon Holes, Torndirrup National Park (Click here)
ORIEN HARVEY/GETTY IMAGES ©
## Wildlife Watching
### Whales
Because so many southern right and humpback whales (upwards of 30,000) cruise along the WA coast, it has become known as the Humpback Hwy. From June onwards their annual pilgrimage begins from Antarctica to the warm tropical waters of the northwest coast, and mothers with calves seek out the shallower bays and coves of King George Sound in Albany from July to October. In whale-watching season, whales can be spotted from coastal clifftops, and often from the beach as well.
### NATIONAL PARK PASSES
Thirty of WA's 96 national parks charge vehicle entry fees (per car/motorcycle $11/5), which are valid for any park visited that day. If you're camping within the park, the entry fee is only payable on the first day (camping fees are additional). If you plan to visit more than three WA parks with entry fees – which is quite likely if you're travelling outside Perth – get the four-week Holiday Pass ($40). All DEC offices sell them, and if you've already paid a day-entry fee in the last week (and have the voucher to prove it), you can subtract it from the cost of the pass.
### Dolphins
Dolphins can be seen up close at the Dolphin Discovery Centre in Bunbury, around Rockingham, and at Monkey Mia. Monkey Mia also has 10% of the world's dugong population.
### Birds
The Broome Bird Observatory attracts a staggering 800,000 birds each year, and the Yalgorup National Park near Mandurah is another important waterbird habitat. The Lesueur National Park is home to the endangered Carnaby's cockatoo, and migratory shorebirds flock to Parry Lagoons Nature Reserve in the Kimberley.
Longreach Bay (Click here), Rottnest Island (Wadjemup)
GILLIANNE TEDDER/GETTY IMAGES ©
## Cycling
WA's southwest is good for cycle touring, and while there are thousands of kilometres of flat, virtually traffic-free roads elsewhere in the state, the distances between towns makes it difficult to plan.
Perth is a relatively bike-friendly city, with good recreational bike paths, including routes that run along the Swan River to Fremantle, and paths overlooking the city through Kings Park.
Cyclists rule on virtually car-free Rottnest Island, with long stretches of empty roads circumnavigating the island and its beaches. Geraldton also has great cycle paths.
The most exciting route for mountain bikers is the Munda Biddi Trail (www.mundabiddi.org.au) , meaning 'path through the forest' in the Noongar Aboriginal language. The 1000km mountain-biking equivalent of the Bibbulmun Track, all the way from Mundaring on Perth's outskirts to Albany on the south coast, was projected to be completed around April 2013. Camp sites are situated a day's easy ride apart, and maps are available online and at visitor centres.
## Diving & Snorkelling
WA's fascinating diving and snorkelling locations include stunning marine parks and shipwrecks.
Close to Perth, divers can explore wrecks and marine life off the beaches of Rottnest Island, or explore the submerged reefs and historic shipwrecks of the West Coast Dive Park within Shoalwater Islands Marine Park, near Rockingham. You can take a dive course in Geographe Bay with companies based in Dunsborough or Busselton; the bay offers excellent dives under the Busselton jetty, on Four Mile Reef (a 40km limestone ledge about 6.5km off the coast) and the scuttled HMAS _Swan_ .
Other wrecks include the HMAS _Perth_ (at 36m), deliberately sunk in 2001 in King George Sound near Albany; and the _Sanko Harvest,_ near Esperance. Both teem with marine life on the wrecks' artificial reefs.
Divers seeking warmer water should head north. Staggering marine life can be found just 100m offshore within the Ningaloo Marine Park, fantastic for both diving and snorkelling. In Turquoise Bay, underwater action is equally accessible, and one of the planet's most amazing underwater experiences is diving or snorkelling alongside the incredible whale shark, the world's largest fish. Tours leave from Exmouth and Coral Bay.
There's also excellent diving and snorkelling around the Houtman Abrolhos Islands.
### REDUCING THE RISK OF SHARK ATTACK
This list of shark safety guidelines is from WA's Department of Fisheries. After a spate of fatal shark attacks in 2012, the WA government also announced a $20- million safety program including a system to track, catch and potentially kill any sharks posing an imminent threat. See www.fish.wa.gov.au.
» Swim between the flags at patrolled beaches.
» Swim close to shore.
» Swim, dive or surf with other people.
» Avoid areas close to bird rookeries or where there are large schools of fish, dolphins, seals or sea lions.
» Avoid areas where animal, human or fish waste enter the water.
» Avoid deep channels or areas with deep drop-offs nearby.
» Do not remain in the water with bleeding wounds.
» Look carefully before jumping into the water from a boat or jetty.
» If spearing fish, don't carry dead or bleeding fish attached to you and remove all speared fish from the water as quickly as possible.
» If schooling fish or other wildlife start to behave erratically or congregate in large numbers, leave the water.
» If you see a shark, leave the water as quickly and calmly as possible – avoid excessive splashing or noise.
## Fishing
From sailfish in the north to trout in the south, all types of fishing are on offer along WA's immense coastline. Fishing is the state's largest recreational activity, with many locals catching dinner nearly every time.
Close to Perth, Rottnest Island has plentiful schools of wrasse and Western Australian dhufish (previously called jewfish).
South of Perth, popular fishing hot spots include Mandurah, with options for deep-sea fishing, catching tailor from the beach or nabbing Mandurah's famed blue manna crabs and king prawns in the estuaries. In Augusta you can chase salmon in the Blackwood River or whiting in the bay, or drop a line from the Busselton Jetty.
Sunny Geraldton's popular spots include Sunset Beach and Drummond Cove, and fishing charters go to the nearby Houtman Abrolhos Islands. There's great fishing all along the coast, and lots of charters in the hotter, steamier northwest. There's a good chance to hook a monster fish at Exmouth, the Dampier Archipelago and the game-fishing nirvana of Broome. The northern Kimberley is good for barramundi.
Snorkelling off Busselton (Click here)
SHELDON LEVIS/GETTY IMAGES ©
Buy a recreational fishing licence (RFL; $40) if you intend to catch marron (freshwater crayfish) or rock lobsters, use a fishing net or go freshwater angling in the southwest. If you're fishing from a motorised boat, someone on the boat will need to have a Recreational Fishing from Boat Licence (RFBL; $30). Licences can be obtained online (www.fish.wa.gov.au) or from Australia Post offices. Note that there are strict licence, bag and size limits – see the Fisheries website for specific details.
Corellas, Yalgorup National Park (Click here)
AUSCAPE / UIG/GETTY IMAGES ©
## Plan Your Trip
Travel with Children
With lots of sunshine, beaches and big open spaces, Western Australia (WA) is a wonderful destination for children of all ages. Australians are famously laid-back and their generally tolerant, 'no worries' attitude extends to children having a good time and perhaps being a little raucous.
Best Regions for Kids
#### Perth & Fremantle
See Click here and Click here .
#### Margaret River & the Southwest
Geographe Bay features family-friendly beaches, Yallingup has a surf school, and Bunbury has the Dolphin Discovery Centre and Bunbury Wildlife Park. The region also features whale watching.
#### Monkey Mia & the Central West
Beaches, and lots of marine wildlife, especially Monkey Mia's dolphins and dugongs, Kalbarri's pelicans, and Denham's Ocean Park aquarium.
#### Coral Coast & the Pilbara
Coral Bay has plenty of safe-water options and like-minded families.
#### Broome & the Kimberley
While there's plenty of wildlife interaction such as camel rides and crocodile-park tours, it's the camping experiences, gorge swimming and Indigenous culture the Kimberley offers that kids will find most memorable, particularly in the Dampier Peninsula and along the Gibb River Road.
## West Coast Australia for Kids
Interacting with Australia's native fauna, in either the wild or wildlife parks, will create lifetime memories for your kids. The wildlife can be dangerous, but in reality you're unlikely to strike any problems if you take sensible precautions.
The sun's harshness is more of a concern. Don't underestimate how quickly you and your kids can get sunburnt, even on overcast days. A standard routine for most Australian parents is to lather their kids in high-protection sunscreen (SPF 30-plus) before heading outside for the day. It's a habit worth adopting. Avoid going to the beach in the middle of the day. Head out in the morning or mid-afternoon instead.
On hot days, dehydration is a problem, especially for small children. Always carry fluids, especially on long car journeys.
## Babies & Toddlers
Perth and most major towns have public rooms where parents can nurse their baby or change nappies; check with the local visitor centre. While many Australians are relaxed about public breastfeeding or nappy changing, some aren't.
Many motels and larger caravan parks have playgrounds and swimming pools, and can supply cots and baby baths. Motels in touristy areas may have in-house children's videos and child-minding services. Top-end and midrange hotels usually welcome families with children, but some B&Bs market themselves as child-free havens.
Many eateries lack a specialised children's menu, but others do have kids' meals or will provide smaller servings. Some supply high chairs.
Medical services and facilities are of a high standard, and baby food, formula and disposable nappies are widely available. Major car-hire companies will supply and fit booster seats for a fee.
## School-Age Kids
The biggest challenge is a sudden attack of the 'are-we-there-yets?'. Adults – let alone kids – find the long drives tedious. Bring along books, computer games, iPads and child-friendly CDs. Consider hiring a car with a backseat screen for playing DVDs.
Snacks are essential for journeys where shops might be 200km or further apart, and toilet paper is also a blessing.
Have a word to the kids about insects, snakes and spiders, stressing the need for them to keep their distance, particularly for kids who like to prod things with sticks. While bushwalking, make sure they wear socks with shoes or boots.
## Children's Highlights
### Beaches
Beaches are a big part of the WA experience. Ensure the kids swim between the flags, and ask the locals about the safer beaches.
### Wildlife Parks & Zoos
There are wildlife parks throughout WA, especially in tourist areas. Many have walk-in aviaries, so prepare for a freak-out when an over-friendly parrot lands on little Jimmy's shoulder. Watch out for emus: those beady eyes and pointy beaks are even more intimidating when they're attached to something that's double your height.
### Whale Watching
If you're in the right part of the coast at the right time of year, you'll definitely see whales from the shore. Organised whale-watching boat trips depart from Perth, Fremantle, Dunsborough, Augusta, Albany, Coral Bay, Broome, Kalbarri, Exmouth and the Dampier Peninsula.
### Other Marine Mammals
» Rockingham Wild Encounters (Click here ) Swimming with wild dolphins for over-fives.
» Dolphin Discovery Centre (Click here ) Wade into the shallows alongside the dolphins in Bunbury.
» Monkey Mia (Click here ) Watch dolphins being fed in the bay or head out on a cruise to spot dolphins and dugongs.
» Sea Lion Charters (Click here ) Splash about with sea lions in the shallows.
### Surf Schools
» Surfschool, Perth and Lancelin Lessons for kids aged 11 and over.
» Yallingup Surf School (Click here ) 'Microgrom' lessons for the under 10s.
### Amusement Parks & Rides
» Adventure World ( Click here ) Perth's amusement park.
» Perth Royal Show ( Click here ) Annual event.
## Planning
When booking accommodation and rental cars, specify whether you need cots, high chairs and car booster seats. If travelling with an infant, bring a mosquito net to drape over the cot. Bring rash tops for the beach and warm clothes if travelling south in winter. Anything you forget can be easily purchased when you arrive.
## Discounts
Child concessions (or family rates) often apply for tours, admission fees (babies and infants are often free) and public transport. Note: a 'child' can vary from under 12 to under 18 years. Accommodation concessions usually apply to children under 12 years. On major airlines, infants travel free if they don't occupy a seat.
Regions at a Glance
Perth & Fremantle
#### Beaches
They may not offer the solitude and pristine natural surroundings of elsewhere in WA, but Perth and Fremantle's long beaches are popular playgrounds for city dwellers. Surfers, snorkellers and swimmers can all find a stretch of sand to suit.
#### Museums & Galleries
Perth's public institutions include the Art Gallery of Western Australia, housing traditional and contemporary art. Nearby is the edgy Perth Institute of Contemporary Art and the Western Australian Museum. Fremantle showcases the superb maritime museum and Shipwreck Galleries.
#### Historic Buildings
Relics of the colonial era and gold rushes abound. Fremantle has a frozen-in-time streetscape with a wonderful historic ambience. The drawcard is the old convict-built prison, its murky stories brought to life through fascinating guided tours.
**Click here**
## Regions at a Glance
Around Perth
#### Beaches
Rottnest Island is ringed by gorgeous beaches that are often deserted midweek. Mandurah, Rockingham and Yanchep are built-up beach 'burbs bustling with cafes and marinas. Guilderton sits on a picturesque lagoon, while Lancelin is windsurfing heaven.
#### Wildlife
Whales, dolphins, sea lions, seals, penguins, kangaroos, possums, quokkas, bilbies, boodies, woylies – it's quite amazing how much wildlife lives in such close proximity to the city.
#### Heritage Towns
The quaint townships in the forests, hills and river valleys surrounding Perth make perfect day trips. York has contiguous rows of historic buildings, preserving a gold-rush atmosphere.
**Click here**
## Regions at a Glance
Margaret River & the Southwest Coast
#### Beaches
The sandy beaches of Geographe Bay are perfect for a bucket-and-spade family holiday. The most beautiful spots are near Cape Naturaliste, and the state's primo surf breaks also roll ashore to the south.
#### Wineries
Australia's most beautiful wine region also produces some of the country's best wine. The cool-climate vineyards around Pemberton are worth exploring too.
#### Forests
Studded with tuart and karri, WA's forests of tall trees are an impressive sight. Some of the larger specimens are rigged with spikes, allowing the fit and fearless to climb up to 68m into the canopy.
**Click here**
## Regions at a Glance
South Coast
#### Beaches
Glorious, isolated bays of powdery white sand are spread all along this long stretch of coast. On many you'll be more likely to spot a whale than another person.
#### Wineries
The wineries of the Great Southern region are constantly growing in stature. Sup your way from Denmark to Mt Barker and on to Porongurup.
#### National Parks
This region's parks encompass the dramatic Tree Top Walk in Walpole-Nornalup and end with the silky sands of Cape Arid. Also, don't miss the rugged Porongurup and Stirling Range National Parks, or the vast wild heath of Fitzgerald River.
**Click here**
## Regions at a Glance
Monkey Mia & the Central West
#### Beaches
The white shell beaches of Shark Bay – with famous visitors, the Monkey Mia dolphins – are just part of a turquoise coastline stretching from family-friendly Port Denison to the wilds of Gnaraloo Station.
#### Adventure
Surfers and windsurfers flock to Geraldton and Gnaraloo for winter swells and summer winds; fisherfolk and explorers head west to Edel Land. Bushwalkers prefer Kalbarri in winter.
#### History
Historic artefacts, shipwrecks and 19th-century buildings stud this rugged coastline, including Green-ough's pioneer settlement and the 1629 _Batavia_ wreck off the Houtman Albrolhos Islands.
**Click here**
## Regions at a Glance
Coral Coast & the Pilbara
#### Beaches
Superb isolated beaches lead down to shallow lagoons hemmed by World Heritage–listed Ningaloo Marine Park. World-class snorkelling and diving are only a short wade from shore, and camping is right behind the dunes.
#### Adventure
Karijini National Park is the Pilbara's adventure playground, with deep, narrow gorges inviting exploration, and the state's highest peaks begging to be climbed.
#### Wildlife
Whale sharks, manta rays, turtles and migrating whales all visit Ningaloo, while inland birds flock to the oasis pools of Millstream-Chichester National Park, and pythons and rock wallabies hide in the shadows of Karijini.
**Click here**
## Regions at a Glance
Broome & the Kimberley
#### Beaches
Don't miss the sunset camel trains of iconic Cable Beach. Equally spectacular are the seldom-visited beaches of the Dampier Peninsula and Coloumb Nature Reserve.
#### Indigenous Culture
Learn traditional practices from the Aboriginal communities of the Dampier Peninsula. Follow Broome's Lurujarri Dreaming Trail, before exploring the Kimberley's amazing Wandjina and Gwion Gwion images.
#### Adventure
Drive the bone-shaking Gibb River Rd, detouring to Mitchell Falls and remote Kalumburu. Zip on a speedboat to the horizontal waterfalls, or negotiate a canoe down the mighty Ord River.
**Click here**
# Perth & Fremantle
#### Perth & Fremantle Highlights
#### Perth
#### Fremantle
#### City Centre
#### Fishing Boat Harbour
#### East & North Fremantle
#### South Fremantle
Perth & Fremantle
### Why Go?
Planted by a river and beneath an almost permanent canopy of blue sky, the city of Perth is a modern-day boom town, stoking Australia's economy from its glitzy central business district. Yet it remains as relaxed as the sleepy Swan River – black swans bobbing atop – which winds past the skyscrapers and out to the Indian Ocean.
Even in its boardrooms, Perth's heart is down at the beach, tossing around in clear ocean surf and stretching out on the sand. The city's beaches trace the western edge of Australia for some 40km, and you can have one to yourself on any given day – for a city this size, Perth is sparsely populated.
Perth has sprawled to enfold Fremantle within its suburbs, yet the port city maintains its own distinct personality – proud of its nautical ties, working-class roots, bohemian reputation and, especially, its football team.
### When to Go
Feb Perth's Arts Festival is on and school starts, so the beaches are less crowded.
Mar Warm and dry, so great weather for the beach, and not as swelteringly hot.
Sep Kings Park wildflowers, the Perth Royal Show and the Parklife festival.
### Best Places to Eat
» Duende ( Click here )
» Namh Thai ( Click here )
» Print Hall ( Click here )
» Il Lido ( Click here )
» Cantina 663 ( Click here )
### Best Places to Stay
» Eight Nicholson ( Click here )
» Wickham Retreat ( Click here )
» Durack House ( Click here )
» Above Bored ( Click here )
» Norfolk Hotel ( Click here )
## Perth & Fremantle Highlights
Stretching out on the lawn in Kings Park (Click here ) with the glittering river and city spread out below you
Doing time with the ghosts of convicts past in World Heritage–listed Fremantle Prison (Click here )
Experiencing Perth's emerging restaurant scene in the bustling eateries of Mt Lawley (Click here ), Northbridge (Click here ) and the city centre (Click here )
Exploring a wealth of local art, indigenous and otherwise, at the Art Gallery of Western Australia (Click here )
Soaking up the decaying gold-rush grandeur of Fremantle's historic streetscape (Click here )
Enjoying the sunset with a sundowner in hand after a hard day's beaching at Cottesloe (Click here )
Hitting Fremantle's pubs (Click here ) and letting the bands of Bon Scott's hometown shake you all night long
## Perth
pop 1.75 million
Laid-back, liveable Perth has wonderful weather, beautiful beaches and an easygoing character. About as close to Bali as to some of Australia's eastern state capitals, Perth's combination of big-city attractions with relaxed and informal surrounds offers an appealing lifestyle for locals and lots to do for visitors. It's a sophisticated, cosmopolitan city with myriad bars, restaurants and cultural activities all vying for attention. When you want to chill out, it's easy to do so. Perth's pristine parkland, nearby bush, and river and ocean beaches – along with a good public transport system – allow its inhabitants to spread out and enjoy what's on offer.
Relaxed doesn't mean static, though. The mining boom of Western Australia (WA) continues to see Perth blossom like the state's wildflowers in spring. Those on the gravy train are out eating, socialising, spending money and flexing their muscles in the sun.
The city of Perth lies along a wide sweep of the Swan River. The river borders the city centre to the south and east, and links Perth to its neighbouring port city, Fremantle. Follow the river north from the city and you'll reach prosperous nooks such as Claisebrook Cove, lined with ostentatious houses, cafes and public sculpture.
Train tracks divide the city centre from the Northbridge entertainment enclave, immediately to the north. Here's where you'll find Perth's cultural institutions, most of its hostels and the lively Little Asia restaurant strip.
Continue northeast along Beaufort St and you'll reach the sophisticated suburbs of Highgate and Mt Lawley. Heading west there's Mt Hawthorn and hip Leederville. To the west of the central city rises Kings Park, with well-heeled Subiaco beyond it. Go further west and you'll hit the beaches.
### PERTH & FREMANTLE IN...
#### Two Days
Book ahead for dinner in Highgate or Mt Lawley and then spend your first morning in the art galleries and museum of the Perth Cultural Centre . Grab lunch in Subiaco before exploring verdant and view-friendly Kings Park . For your second day, catch the train to Fremantle and spend the whole day there, prioritising the world-heritage prison, maritime museum and Shipwreck Galleries. Grab a bite in Fishing Boat Harbour and then head to a pub to catch a band or drink WA craft beer.
#### Four Days
Take the two-day itinerary but stretch it to a comfortable pace. Head to Rottnest Island for a day trip and spend any time left over on Perth's beaches. Allocate a night each to Leederville and the city's best new bars and restaurants.
#### One Week
As for the four-day itinerary, but spend a day in Guildford and the Swan Valley , take a whale-watching cruise and head out to Rockingham to view penguins and sea lions and to swim with dolphins. Spend one of the extra evenings in emerging Maylands and another in bohemian Northbridge .
History
The discovery of stone implements near the Swan River suggests that Mooro, the site on which the city of Perth now stands, has been occupied for around 40,000 years. The indigenous Wadjuk people, a subgroup of the Noongar, believed that the Swan River (Derbal Yaragan) and the landforms surrounding it were shaped by two Wargal (giant serpentlike creatures), which lived under present-day Kings Park.
In December 1696 three ships in the Dutch fleet commanded by Willem de Vlamingh anchored off Rottnest Island. On 5 January 1697 a well-armed party landed near present-day Cottesloe Beach and then marched eastward to a river near Freshwater Bay. They tried to make contact with the local people to enquire about survivors of the _Ridderschap van Hollant,_ lost in 1694, but were unsuccessful, so they sailed north. It was de Vlamingh who bestowed the name Swan on the river.
Modern Perth was founded in 1829 when a hopeful Captain James Stirling established the Swan River Colony, and named the main settlement after the Scottish hometown of the British Secretary of State for the Colonies. The original settlers paid for their own passage and that of their servants, and in return they received 200 acres for every labourer they brought with them.
At the time Mooro belonged to a Wadjuk leader called Yellagonga and his people, whose main camp was at Boorloo, near where the colony was founded. Relations were friendly at first, the Noongar believing the British to be the returned spirits of their dead, but competition for resources led to conflict. Yellagonga moved his camp first to Lake Monger and, by the time of his death in 1843, his people had been dispossessed of all of their lands around Perth's city centre and were forced to camp around the swamps and lakes to the city's north.
Midgegooroo, an elder from south of the Swan River, along with his son Yagan, led resistance to the British settlement. In 1833 Midgegooroo was caught and executed by firing squad, while Yagan was shot a few months later by teenage settlers whom he had befriended. Yagan's head was removed, smoked and sent to London where it was publicly displayed as an anthropological curiosity.
Life for the settlers was much harder than they had expected it to be. The early settlement grew very slowly until 1850, when convicts alleviated the labour shortage and boosted the population. Convict labour was also responsible for constructing the city's substantial buildings such as Government House and the Town Hall. Even then, Perth's development lagged behind that of the cities in the eastern colonies. That is, until the discovery of gold inland in the 1890s increased Perth's population fourfold in a decade and initiated a building bonanza.
The mineral wealth of WA has continued to drive Perth's growth. In the 1980s and '90s, though, the city's clean-cut, nouveau-riche image was tainted by a series of financial and political scandals. Today Perth is thriving once again, thanks to another mining boom throughout the state. Rumours of a slowdown by the Chinese and Indian economies continue to bubble away, but obviously no-one's told more than a few of the fiscally confident locals.
Largely excluded from this race to riches are the Noongar people. In 2006, the Perth Federal Court recognised native title over the city of Perth and its surrounds, but this was appealed by the WA and Commonwealth governments. In December 2009 an agreement was signed in WA's parliament, setting out a two-year time frame for negotiating settlement of native-title claims across the southwest.
1 Sights
Many of Perth's main attractions are within walking distance of the inner city, several in the Perth Cultural Centre precinct past the railway station in Northbridge. Most of the farther-flung sights, including the beaches, can be reached by public transport, although you'll find it easier to hop between them with a car. There are several easy day trips, including the Swan Valley, that can be reached from the city.
Central Perth
Top Sights
1 Art Gallery of Western Australia D2
Sights
2 Bell Tower C4
3 Perth Institute of Contemporary ArtsC2
4 Perth Mint E4
5 Western Australian Museum – PerthD2
Activities, Courses & Tours
6 Captain Cook Cruises C4
Captain Cook Cruises (see 10)
7 Cycle Centre E4
8 Golden Sun Cruises C4
9 Oceanic Cruises C4
10 Swan Jet C4
Sleeping
11 City Waters E4
12 Comfort Hotel Perth City F4
13 Emperor's Crown D2
14 Mantra on Hay F4
15 Medina Executive Barrack PlazaD3
16 Melbourne B2
17 Miss Maud D3
18 Mounts Bay Waters A3
19 Pensione Hotel D3
20 Perth City YHA D2
21 Regal Apartments G3
22 Riverview on Mount Street A3
23 The Sebel Residence G2
24 The Terrace Hotel A3
25 Travelodge Perth D3
26 Wickham Retreat G3
Eating
27 Annalakshmi C4
28 Balthazar C3
29 Bivouac Canteen & Bar C2
30 Cabin Fever D3
31 City Farm Organic Growers Market F2
32 Flipside C1
33 Good Fortune Roast Duck House D1
34 Greenhouse C3
35 Kakulas Bros C2
36 La Cholita C1
37 Little Willy's C1
38 Mama Tran B2
39 Matsuri A2
40 Print Hall B3
41 Restaurant Amusé F3
Secret Garden (see 43)
Taka (see 42)
42 Taka D2
The Trustee (see 40)
43 Tiger, Tiger B2
44 Tom's Kitchen B2
45 Venn Cafe & Bar C2
Viet Hoa (see 68)
Drinking & Nightlife
46 C2
47 Air C1
48 Ambar D3
49 Brass Monkey C1
Cheeky Sparrow (see 43)
Ezra Pound (see 35)
50 Geisha C1
Greenhouse (see 34)
51 Helvetica C3
52 Hula Bula Bar E4
Mechanics Institute (see 32)
53 Metro City B1
54 The Bird C2
55 The Court D2
56 The Grosvenor E4
Wolfe Lane (see 43)
Entertainment
57 Amplifier B2
58 Cinema Paradiso C1
59 Connections C2
60 Devilles Pad E2
61 Ellington Jazz Club D1
62 His Majesty's Theatre B3
63 NIB Stadium E1
64 Perth Arena B1
65 Perth Concert Hall D4
66 State Theatre Centre C2
67 The Bakery B1
68 The Moon C1
Universal (see 49)
69 WACA G4
Shopping
70 78 Records C2
71 Elizabeth's Bookshop B3
Perth Map Centre (see 70)
Pigeonhole (see 30)
Pigeonhole (see 44)
72 Wheels & Doll Baby B2
Information
73 i-City Information KioskC2
74 WA Visitor CentreC3
Transport
75Esplanade BusportB3
76Ferries to South Perth & FremantleC4
77 Integrity Coach LinesC2
Top of Chapter
1 City Centre
Bell Tower LANDMARK
OFFLINE MAP GOOGLE MAP
(www.thebelltower.com.au; adult/child $14/9; 10am-4pm, ringing noon-1pm Mon, Tue, Thu, Sat & Sun) This pointy glass spire fronted by copper sails contains the royal bells of London's St Martin's-in-the-Fields, the oldest of which dates to 1550. They were given to WA by the British government in 1988, and are the only set known to have left England. Clamber to the top for 360-degree views of Perth by the river.
The tower sits on land that was reclaimed in the 1920s and 1930s, and now forms a green strip between the river and the city. Long, thin Langley Park is still occasionally used as an airstrip for light aircraft demonstrations. Stirling Gardens and Supreme Court Gardens have lawns and formal gardens which fill up with city workers at lunchtime.
Perth Mint HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(www.perthmint.com.au; 310 Hay St; adult/child $15/5; 9am-5pm) Dating from 1899, the oddly compelling mint displays a collection of coins, nuggets and gold bars. You can fondle a bar worth over $200,000, mint your own coins and watch gold pours (on the hour, starting 10am).
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1 Northbridge
Art Gallery of Western Australia GALLERY
OFFLINE MAP GOOGLE MAP
(www.artgallery.wa.gov.au; Perth Cultural Centre; 10am-5pm Wed-Mon) F Founded in 1895, this excellent gallery houses the state's pre-eminent art collection. It contains important post-WWII works by Australian luminaries such as Arthur Boyd, Albert Tucker, Grace Cossington Smith, Russell Drysdale, Arthur Streeton and Sidney Nolan, but it's the Indigenous galleries that provide the highlight.
Work ranges from canvases to bark paintings and sculpture, and artists include Rover Thomas, Angilya Mitchell, Christopher Pease and Phyllis Thomas. The annual WA Indigenous Art Awards entries are displayed here from August to December. Free tours take place at 11am and 1pm on Sunday, Monday, Wednesday and Thursday, at 12.30pm and 2pm on Friday, and at 1pm on Saturday.
Perth Institute of Contemporary Arts GALLERY
OFFLINE MAP GOOGLE MAP
(PICA; www.pica.org.au; Perth Cultural Centre; 11am-6pm Tue-Sun) F Commonly referred to by its acronym, PICA (pee-kah) may have a traditional wrapping (it's housed in an elegant 1896 red-brick former school), but inside it's anything but, being one of Australia's principal platforms for cutting-edge contemporary art – installations, performance, sculpture, video works and the like. It actively promotes new and experimental art, and exhibits graduate works annually.
Western Australian Museum – Perth MUSEUM
OFFLINE MAP GOOGLE MAP
(www.museum.wa.gov.au; Perth Cultural Centre; 9.30am-5pm) F The state's museum is a six-headed beast, with branches also in Fremantle, Albany, Geraldton and Kalgoorlie. This one includes dinosaur, mammal, butterfly and bird galleries, a children's discovery centre, and an excellent WA Land and People display covering indigenous and colonial history.
In the courtyard, set in its own preservative bath, is Megamouth, a curious-looking species of shark with a soft, rounded head. Only about five of these benign creatures have ever been found; this one beached itself near Mandurah, south of Perth.
The museum complex includes Perth's original gaol, built in 1856 and used until 1888 – the site of many hangings.
### A CITY IN TRANSITION
With Perth's population increasing faster than that of any other Australian state capital, it's also a city rapidly transitioning from a relatively sleepy centre into an international hub with its commercial gaze resting as much on China, India and Indonesia as it does on Sydney and Melbourne.
Major civic works under consideration include an audacious light-rail plan and a new football stadium, and visitors to Perth can already witness ongoing work on two major reboots of the central city's urban landscape.
Historically, Northbridge's entertainment and cultural precinct has been awkwardly separated from the CBD by the labyrinth of train tracks around Perth railway station. The Perth City Link project is scheduled to take until 2016 to complete, and will transform the area between Northbridge and the CBD by installing train tracks and the Wellington St bus station underneath pedestrian malls. See www.pta.wa.gov.au/perthcitylink.
At the opposite end of the CBD, the Elizabeth Quay development will revamp around 10 hectares of riverfront land between Barrack and William Sts, and link the central city back to the Swan River. Public parks and retail and hospitality precincts are planned, and the development is also scheduled to be completed by 2016. See www.mra.wa.gov.au.
Come back in a few years, and there's a good chance you won't recognise the city.
Hyde Park PARK
OFFLINE MAP GOOGLE MAP
(William St) One of Perth's most beautiful parks, suburban Hyde Park is a top spot for a picnic or lazy book-reading session on the lawn. A path traces the small lake, and mature palms, firs and Moreton Bay figs provide plenty of shade. It's within walking distance of Northbridge; continue northeast along William St.
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1 Subiaco & Kings Park
o Kings Park & Botanic Garden PARK
OFFLINE MAP
(www.bgpa.wa.gov.au; Lotterywest Federation Walkway 9am-5pm, guided walks 10am, noon & 2pm) Rising above the Swan River on the western flank of the city, the 400-hectare bush-filled expanse of Kings Park is Perth's pride and joy. When the sun's shining (which isn't exactly a rare occurrence) it's a good spot for a picnic under the trees or to let the kids off the leash in one of the playgrounds. Its numerous tracks are popular with walkers and joggers all year round, with an ascent of the steep stairs from the river rewarded with wonderful views from the top.
The Noongar people knew this area as Kaarta Gar-up and used it for thousands of years for hunting, food gathering, ceremonies, teaching and tool-making. A freshwater spring at the base of the escarpment, now known as Kennedy Fountain but before that as Goonininup, was a home of the Wargal, mystical snake-like creatures that created the Swan River and other waterways.
At the park's heart is the 17-hectare Botanic Garden, containing over 2000 plant species indigenous to WA. In spring there's an impressive display of the state's famed wildflowers. A highlight is the Lotterywest Federation Walkway , a 620m path through the gardens that includes a beautifully designed, 222m-long, glass-and-steel bridge that passes through the canopy of a stand of eucalypts.
The main road leading into the park, Fraser Ave, is lined with towering lemon-scented gums that are dramatically lit at night. At its culmination are the State War Memorial, a cafe, a gift shop, Frasers restaurant and the Kings Park Visitor Centre. Free guided walks leave from here.
To get here take bus 37 (39 on weekends), heading west along St Georges Tce (S-stand), to the visitor centre. You can also walk up (steep) Mount St from the city or climb Jacob's Ladder from Mounts Bay Rd, near the Adelphi Hotel
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1 Beaches
When the mercury rises the only sensible decision is to head west to cool down on one of Perth's many clean, sandy beaches. Most of them are comparatively undeveloped, which is just how the locals like it. The most famous of them, Cottesloe, gets by quite well with a beachside pavilion, a couple of giant pubs and a scattering of other businesses delineating the edge of suburbia.
Run by the Surf Life Saving Club of WA, the website www.mybeach.com.au has a profile of all the city beaches, including weather forecasts and information about buses, amenities and beach patrolling. Note that many can be rough, with strong undertows and rips – swim between the flags.
The following are the main beaches, listed from south to north.
Port & Leighton Beaches BEACH
Popular for surfing; the Port (south) end is slightly better for swimming, and has some eateries. Leighton Beach is a short walk from North Fremantle station.
Hamersley Pool, North,
Watermans & Sorrento Beaches BEACH
Excellent swimming, picnic areas, BBQs, bike path through scrub.
Cottesloe Beach BEACH
The safest swimming with cafes, pubs, pine trees and fantastic sunsets. From Cottesloe station (on the Fremantle line) it's 1km to the beach. Bus 102 (William St) goes there.
Swanbourne Beach BEACH
Safe swimming, and an unofficial nudist and gay beach. From Grant St station it's a 1.5km walk to the beach (2km from Swanbourne station). Catch bus 102 from William St.
City Beach BEACH
Swimming, surfing, lawn and amenities. Take bus 84 (85 on weekends) from Wellington St (40 minutes, hourly).
Floreat Beach BEACH
Less crowded but sometimes windy, with swimming, surfing, cafes and playground. Bus to City Beach and walk north 800m.
Scarborough Beach BEACH
Popular young surfers' spot. Swim between flags as it can be dangerous. Has lots of shops and eateries. Bus 400 from Wellington St.
Trigg Beach BEACH
Better surf and a more hardcore group of locals who come out when the surf's up; dangerous when rough and prone to rips – always swim between the flags.
Mettams Pool BEACH
This beach is like a turquoise paddle pool – good for snorkelling.
Aquarium of Western Australia AQUARIUM
(AQWA; 08-9447 7500; www.aqwa.com.au; Hillarys Boat Harbour; adult/child $28/16; 10am-5pm) Dividing WA's vast coastline into five distinct zones (Far North, Coral Coast, Shipwreck Coast, Perth and Great Southern), AQWA offers the chance to enjoy its underwater treasures without getting wet. Or eaten, stung or otherwise poisoned (the displays of WA's most poisonous fish, octopi, shells and sea snakes is particularly interesting).
Wander through a 98m underwater tunnel as gargantuan stingrays, turtles, fish and sharks stealthily glide over the top of you. Moon jellyfish billow iridescently through a giant cylinder lit up like a school disco, while sea horses and sea dragons drift on delicate underwater currents.
The daring can snorkel or dive with the sharks in the giant aquarium with the help of the in-house dive master; book in advance ($159 with your own gear; hire snorkel/dive gear $20/40; 1pm and 3pm). Another interactive option is donning a wetsuit and breathing tube and negotiating an underwater seascape as a Reefwalker ($20). You can also simply dip your hands into the touch pool and get to know harmless guys like the Port Jackson shark, sea stars, sea cucumbers and the Western stingaree.
To get here on weekdays, take the Joondalup train to Warwick station and then transfer to bus 423. By car, take the Mitchell Fwy north and exit at Hepburn Ave, or take the coastal road north from Scarborough Beach. AQWA is by the water at Hillarys Boat Harbour, behind Hillarys shopping centre.
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1 Other Areas
Perth Zoo ZOO
(www.perthzoo.wa.gov.au; 20 Labouchere Rd; adult/child $28/14; 9am-5pm) Part of the fun of a day at the zoo is getting there – taking the ferry across the Swan River from Barrack Street Jetty to Mends Street Jetty (every half-hour) and walking up the hill. Zoo zones include Reptile Encounter, African Savannah (rhinos, cheetahs, zebras, giraffes and lions), Asian Rainforest (elephants, tigers, sun bears, orangutans) and, of course, Australian Bushwalk (kangaroos, emus, koalas, dingos).
If you don't fancy the ferry ride, catch bus 30 or 31 from the Esplanade Busport.
Lake Monger PARK
(Lake Monger Dr) In spring, black swans and their cygnets plod about the grounds – something of a meeting place for the local bird life – nonplussed by the joggers circling the lake on the flat 3.5km path. There's plenty of grass for cricket, football and picnics. It's walking distance from Leederville train station; exit on the side opposite the shops, turn right onto Southport St and veer left onto Lake Monger Dr.
2 Activities
Whale Watching
The whale-watching season runs from mid-September to early December, when 30,000 of them take the 'Humpback Highway' up the coast. Tour operators offer either a refund or a repeat trip in the unlikely event that whales aren't spotted. Tour boats are also fitted with underwater hydrophones, so you can to listen to the whales singing.
Mills Charters WHALE WATCHING
( 08-9246 5334; www.millscharters.com.au; adult/child $80/65) Informative three- to four-hour trips departing from Hillarys Boat Harbour at 9am on Wednesday.
Oceanic Cruises WHALE WATCHING
OFFLINE MAP GOOGLE MAP
( 08-9325 1191; www.whalewatching.com.au; adult/child $77/34) Departs Barrack Street Jetty at 8.30am, returning at 5.45pm after spending the afternoon in Fremantle. Daily departures during the school holidays, otherwise Wednesday and Friday to Sunday only.
Cycling
Cycling is an excellent way to explore Perth. Kings Park has some good bike tracks and there are cycling routes along the Swan River, running all the way to Fremantle, and along the coast. Bikes can be taken free of charge on ferries at any time and on trains outside of weekday peak hours (7am to 9am and 4pm to 6.30pm) – with a bit of planning you can pedal as far as you like in one direction and return via public transport. Bikes can't be taken on buses at any time, except some regional coaches (for a small charge). For route maps, see www.transport.wa.gov.au/cycling/ or call into a bike shop.
About Bike Hire BICYCLE RENTAL
( 08-9221 2665; www.aboutbikehire.com.au; 1-7 Riverside Dr, Causeway Carpark; per day/week from $36/80; 9am-5pm) Also hires kayaks (per hour/day $16/65).
Cycle Centre BICYCLE RENTAL
OFFLINE MAP GOOGLE MAP
( 08-9325 1176; www.cyclecentre.com.au; 313 Hay St; per day/week $25/65; 9am-5.30pm Mon-Fri, 9am-3pm Sat, 1-4pm Sun) See the website for recommended rides.
Gecko Bike Hire BICYCLE RENTAL
( 0439 989 610; www.geckobikehire.com.au) Excellent company with four locations around the city. See the website for route maps.
Other Activities
Surf Sail Australia WINDSURFING, KITESURFING
OFFLINE MAP GOOGLE MAP
( 1800 686 089; www.surfsailaustralia.com.au; 260 Railway Pde; 10am-5pm Mon-Sat) When the afternoon sea breeze blusters in, windsurfers take to the Swan River, Leighton and beaches north of Perth. Here's where you can hire or buy your gear.
Australasian Diving Academy DIVING
( 08-9389 5018; www.ausdiving.com.au; 142 Stirling Hwy) Hires diving gear (full set per day/week $75/200) and offers diving courses (four-day open-water $495). There are a variety of sites in the vicinity, including several around Rottnest Island and four wrecks.
Funcats SAILING
( 0408 926 003; www.funcats.com.au; Coode Street Jetty; per hr $40; Oct-Apr) These easy-to-sail catamarans are for hire on the South Perth foreshore. Each boat holds up to three people.
Surfschool SURFING
( 08-9447 5637; www.surfschool.com; Scarborough Beach; adult/child $55/50) Two-hour lessons at Scarborough Beach (at the end of Manning St), including boards and wetsuits.
Beatty Park Leisure Centre SWIMMING
OFFLINE MAP GOOGLE MAP
( 08-9273 6080; www.beattypark.com.au; 220 Vincent St; swimming adult/child $5.70/4.30; 5.30am-8.30pm Mon-Fri & 8am-4pm Sat & Sun) Originally built for the 1962 Commonwealth Games, this recently expanded complex has indoor and outdoor pools, water slides and a gym. Turn left at the top of William St and continue on Vincent St to just past Charles St.
### PERTH FOR CHILDREN
With a usually clement climate and plenty of open spaces and beaches to run around in, Perth is a great place to bring children. Of the beaches, Cottesloe is the safest and a family favourite. With older kids, arrange two-wheeled family expeditions along Perth's riverside and coastal bike paths. Kings Park has playgrounds and walking tracks.
The Perth Royal Show ( Click here ), held late September, is an ever-popular family outing – all sideshow rides, showbags and proudly displayed poultry. Many of Perth's big attractions cater well for young audiences, especially the Aquarium of Western Australia ( Click here ), Perth Zoo ( Click here ), the Western Australian Museum – Perth ( Click here ) and the Art Gallery of Western Australia ( Click here ).
Scitech OFFLINE MAP GOOGLE MAP (www.scitech.org.au; Sutherland St, City West Centre; adult/child $14/9; 10am-4pm) is another rainy-day option, with over 160 hands-on, large-scale science and technology exhibits.
Adventure World (www.adventureworld.net.au) has exciting rides such as 'Bounty's Revenge', a giant swinging pirate boat, as well as pools, water slides and a castle. From Perth, come off the Kwinana Fwy at Farrington Rd, turn right and follow the signs.
Look for the LetsGoKids (www.letsgokids.com.au) booklet at the WA Visitor Centre (Click here ) for loads more kid-friendly information.
WA Skydiving Academy SKYDIVING
OFFLINE MAP GOOGLE MAP
( 1300 137 855; www.waskydiving.com.au; 458 William St; Mon-Thu) Tandem jumps from 8000/10,000/12,000ft from $300/340/380.
T Tours
Indigenous Tours WA INDIGENOUS CULTURE
(www.indigenouswa.com) See Perth through the eyes of the local Wadjuk people. Options include the Indigenous Heritage Tour ( 08-9483 1106; adult/child $25/15; 1.30pm) – a 90-minute guided walk around Kings Park – and an indigenous-themed stroll (Click here ) around Fremantle.
City Sightseeing Perth Tour BUS TOUR
( 08-9203 8882; www.citysightseeingperth.com; adult/child $28/10) Hop-on, hop-off double-decker bus tour, with loop routes taking in the central city, Kings Park and the Burswood Entertainment Complex. Tickets are valid for two days. The Kings Park section can be purchased separately (adult/child $6/3).
Two Feet & A Heartbeat WALKING TOUR
( 1800 459 388; www.twofeet.com.au; per person $40-50) Daytime walking tours of Perth, and a popular after-dark Small Bar Tour. Tight Arse Tuesdays are just $20 for the Perth tour.
Rockingham Wild Encounters WILDLIFE INTERACTION
( 08-9591 1333; www.rockinghamwildencounters.com.au; cnr Arcadia Dr & Penguin Rd) S Long-standing and laden with ecotourism awards, these guys are the only operator licensed to take people to Penguin Island, and they also run a variety of low-impact tours. The most popular is the dolphin swim tour (departs Val Street Jetty; tours $205-225; 8am Sep-May) , which lets you interact with some of the 200 wild bottlenose dolphins in the marine park. If you don't fancy getting wet, there are two-hour dolphin-watch tours (departs Mersey Street Jetty, Shoalwater; adult/child $85/50; 10.45am Sep-May) . Pickups can also be arranged from Perth hotels.
There's also a 45-minute penguin and sea lion cruise (departs Penguin Island; adult/child $36.50/27.50; 10.15am, 11.15am & 1.15pm Sep-May) , which heads around the islands in a glass-bottomed boat.
Swan Jet BOAT TOUR
OFFLINE MAP GOOGLE MAP
( 1300 554 026; www.swanjet.com.au; Barrack Street Jetty; adult/child $55/25) Exciting jetboat blasts on the Swan River.
Captain Cook Cruises CRUISE
OFFLINE MAP GOOGLE MAP
( 08-9325 3341; www.captaincookcruises.com.au) Cruises to the Swan Valley or Fremantle, with an array of add-ons such as meals, wine tastings and tram rides.
Golden Sun Cruises CRUISE
OFFLINE MAP GOOGLE MAP
( 08-9325 9916; www.goldensuncruises.com.au) Cheaper and with fewer frills than Captain Cook Cruises.
Beer Nuts BREWERY
( 08-9295 0605; www.beernuts.com.au) Visits five Swan Valley microbreweries and a rum distillery.
Out & About WINE TASTING
( 08-9377 3376; www.outandabouttours.com.au) Wine-focused tours of the Swan Valley and historic Guildford. Some include river cruises, cheese and chocolate stops, or the opportunity to make your own wine blend.
Swan Valley Tours FOOD, WINE TASTING
( 03-9274 1199; www.svtours.com.au) Food- and wine-driven tours that cruise up to and/or drive through the Swan Valley.
Rottnest Air Taxi SCENIC FLIGHTS
( 08-9292 5027; www.rottnest.de) Thirty-minute joy flights over the city, Kings Park and Fremantle ($88 to $115), leaving from Jandakot airport.
z Festivals & Events
Perth Cup HORSE RACING
(www.perthracing.org.au) New Year's Day sees Perth's biggest day at the races, with the party people heading to 'Tentland' for DJs and daiquiris.
Summadayze MUSIC
(www.summadayze.com) Electronic beeps and beats get booties shaking at Paterson's Stadium in Subiaco in early January.
Australia Day Skyworks NATIONAL
(www.perth.wa.gov.au/skyworks; 26 Jan) Around 250,000 people come down to the riverside for a whole day of family entertainment, culminating in a 30-minute fireworks display at 8pm.
Big Day Out MUSIC
(www.bigdayout.com; Claremont Showgrounds; early Feb) Australia's biggest music festival, attracting big-name alternative bands and lots of local up-and-comers.
Laneways MUSIC
(http://perth.lanewayfestival.com.au; early Feb) Perth's skinny-jean and floppy-fringe hipsters party to the planet's up-and-coming indie acts. The über-cool festival takes place in early February around the Perth Cultural Centre in Northbridge.
Perth International Arts Festival ARTS
(www.perthfestival.com.au; mid-Feb) Artists like Laurie Anderson, Dead Can Dance and Philip Glass perform alongside top local talent. Held over 25 days, it spans theatre, classical music, jazz, visual arts, dance, film and literature. Worth scheduling a trip around, especially for nocturnal types.
Kings Park Festival WILDFLOWERS
(www.kingsparkfestival.com.au; Sep) Festival held throughout September to coincide with the wildflower displays, it includes live music every Sunday, guided walks and talks.
Perth Royal Show AGRICULTURE FESTIVAL
(www.perthroyalshow.com.au; Claremont Showground; late Sep-early Oct) A week of fun-fair rides, spun sugar and showbags full of plastic junk. Oh, and farm animals.
Parklife MUSIC
(www.parklife.com.au; Wellington Sq; late Sep) A one-day festival of international indie bands of a more danceable bent.
Awesome International Festival for
Bright Young Things CHILDREN
(www.awesomearts.com; school holidays Oct) This 13-day contemporary-arts festival celebrates young creativity with exhibitions, film, theatre, dance and wacky instruments. It strikes a balance between international performers and participation.
4 Sleeping
Perth is very spread out, so choose your location carefully. Northbridge is backpacker/boozer central, and can be noisy. The CBD and Northbridge are close to public transport, making hopping out to inner-city suburbs such as Leederville and Mt Lawley straightforward.
If you care most for the beach, consider staying there, as public transport to this part of town can be time-consuming.
Fuelled by the ongoing mining boom, Perth is an expensive town for accommodation. Book as early as you can, and see our other tips to maximise your Perth travel budget (see boxed text, Click here ).
Top of Chapter
4 City Centre
Perth City YHA HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9287 3333; www.yha.com.au; 300 Wellington St; dm $39, r with/without bathroom $120/95; ) Occupying an impressive 1940s art-deco building by the train tracks, the centrally located YHA has a slight boarding-school feel in the corridors, but the rooms are clean and there are good facilities including a gym. Like many Perth hostels, it's popular with FIFO ('fly-in, fly-out') mine workers, so the traditional YHA's travellers' vibe has been diminished.
Riverview on Mount Street APARTMENT $$
OFFLINE MAP GOOGLE MAP
( 08-9321 8963; www.riverviewperth.com.au; 42 Mount St; apt from $140; ) There's a lot of brash new money up here on Mount St, but character-filled Riverview stands out as the best personality on the block. Its refurbished 1960s bachelor pads sit neatly atop a modern foyer and a relaxed cafe. Rooms are sunny and simple; the front ones have river views, while the back ones are quieter.
Medina Executive Barrack Plaza APARTMENT $$
OFFLINE MAP GOOGLE MAP
( 08-9267 0000; www.medina.com.au; 138 Barrack St; apt from $229; ) The meticulously decorated apartment-sized hotel rooms of the Medina are minimalist yet welcoming. All one-bedrooms have balconies, and rooms on Barrack St tend to have more natural light (not always easy to obtain in central Perth).
Pensione Hotel BOUTIQUE HOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9325 2133; www.pensione.com.au; 70 Pier St; d from $155; ) Formerly the budget-oriented Aarons, this central-city 98-room property has recently had a shiny boutique sheen applied to become the Pensione Hotel. The standard rooms definitely veer to cosy and (very) compact, but classy decor and a good location are two definite pluses in an expensive city.
Miss Maud HOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9325 3900; www.missmaud.com.au; 97 Murray St; s/d $189/239; ) Anyone with a love of Scandinavia, kitsch or _The_ _Sound_ _of_ _Music_ will find a few of their favourite things in the alpine murals and dainty rooms. The Scandinavian rooms are best, as they're bigger and well maintained. The smorgasbords (lunch/dinner $34/45) are enough to feed a goat herd.
City Waters MOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9325 1566; www.citywaters.com.au; 118 Terrace Rd; s/d $130/150; ) Apricot-hued City Waters is one of a dying breed of old-fashioned Perth waterfront motels. Rooms are small and simple and face onto the car park, but they're clean and airy, and the waterfront location is top-notch. Top-floor rooms are best; river views exist but are difficult to secure.
Melbourne HOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9320 3333; www.melbournehotel.com.au; cnr Hay & Milligan Sts; r $190-330; ) Classic country charm wafts through this heritage-listed hotel. Built in the gold-rush era, its facade – particularly the deep corrugated-iron balcony that wraps around the building – recalls a mining-town pub perched on the edges of the red-dust desert. Rooms are unpretentious and comfortable, though 1st-floor rooms facing Milligan St can be noisy.
Travelodge Perth HOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9238 1888; www.travelodge.com.au; 417 Hay St; r from $189; ) No surprises here, just unassuming well-kept rooms, some with views. Occasional online deals are good value in an expensive city.
Mantra on Hay APARTMENT $$$
OFFLINE MAP GOOGLE MAP
( 1300 987 604; www.mantra.com.au; 201 Hay St; apt from $239; ) Low-key but classy, Mantra's roomy apartments have laundries, dishwashers, good-sized benches and all the utensils you'll need.
Comfort Hotel Perth City HOTEL $$
OFFLINE MAP GOOGLE MAP
( 9220 7000; www.comforthotelperthcity.com.au; 200 Hay St; r from $170; ) Generic and outmoded, but rooms are large, the staff friendly and the breakfast spread excellent.
Mounts Bay Waters APARTMENT $$$
OFFLINE MAP GOOGLE MAP
( 08-9213 5333; www.mounts-bay.com.au; 112 Mounts Bay Rd; apt from $290; ) Giant apartment complex, where 165 out of 440 units are available for short-term lease.
The Terrace Hotel BOUTIQUE HOTEL $$$
OFFLINE MAP GOOGLE MAP
( 08-9214 4444; www.terracehotelperth.com.au; 237 St Georges Tce; d from $432; ) Opened in late 2012, the Terrace Hotel fills a heritage-listed terrace house in Perth's historic West End. There are just 15 deluxe rooms and suites, all with a clubby and luxurious ambience. Modern accoutrements include huge flat-screen TVs, Apple TV and iPads, and king-size four-poster beds with Egyptian-cotton linen.
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4 Northbridge
Most of Perth's hostels are in Northbridge, and it's possible to walk around and inspect rooms before putting your money down. We've only listed the better ones, and note that many hostels have long-term residents working in Perth, and this can alter the ambience for short-term visitors and travellers.
Emperor's Crown HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9227 1400; www.emperorscrown.com.au; 85 Stirling St; dm $36, r with/without bathroom from $130/110; ) One of Perth's best hostels has a great position (close to the Northbridge scene without being in the thick of it), friendly staff and high housekeeping standards. Granted, it's a bit pricier than most, but it's worth it.
Witch's Hat HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9228 4228; www.witchs-hat.com; 148 Palmerston St; dm/tw/d $34/88/99; ) Witch's Hat is like something out of a fairy tale. The 1897 building itself could be mistaken for a gingerbread house, and the witch's hat (an Edwardian turret) stands proudly out the front, beckoning the curious to step inside. Dorms are light and uncommonly spacious, and there's a red-brick BBQ area out the back.
One World Backpackers HOSTEL $
( 08-9228 8206; www.oneworldbackpackers.com.au; 162 Aberdeen St; dm $28-30, d $80; ) S Polished floorboards beam brightly in all the rooms of this nicely restored old house, and the dorms are big and sunny, if a little messy sometimes. The kitchen is large and functional, with everything provided, and the hostel tends to be quieter on weeknights. Like most Perth hostels, though, it can get noisy.
Coolibah Lodge HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9328 9958; www.coolibahlodge.com.au; 194 Brisbane St; dm $32, r $80; ) Built from two big old houses, Coolibah Lodge is comfortable and homely but nothing fancy. Dorms are tidy if a bit poky, and doubles are of a good standard. Expect a mix of travellers and longer-term guests. Breakfast is included. Brisbane St runs off William St, north of Northbridge.
Pension of Perth B&B $$
OFFLINE MAP GOOGLE MAP
( 08-9228 9049; www.pensionperth.com.au; 3 Throssell St; s/d from $150/165; ) Pension of Perth's French belle époque style lays luxury on thick: chaise lounges, rich floral rugs, heavy brocade curtains, open fireplaces and gold-framed mirrors. Two doubles with bay windows (and small bathrooms) look out onto the park, and there are two rooms with spa baths. Location wise, it's just across the road from gorgeous Hyde Park.
Hotel Northbridge HOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9328 5254; www.hotelnorthbridge.com.au; 210 Lake St; r from $160; ) Hotel Northbridge isn't the hippest kid in town, but there's a spa bath in every room, and it's a quieter part of a sometimes noisy neighbourhood.. The classic pub rooms in the budget wing ($65) face onto a broad verandah but share shabby toilets.
### 8 HOW TO MAXIMISE YOUR PERTH TRAVEL BUDGET
Everything you've heard is true. Compared to other Australian state capitals, Perth is expensive. Central city hotels especially are in high demand, and prices can be significantly higher than in east-coast Australia. Follow these tips to make the most of your dollars when visiting the city.
» Book accommodation as far ahead as possible.
» Accommodation can be significantly cheaper from Friday to Sunday.
» Consider a self-contained apartment with full cooking facilities.
» Perth B&Bs are usually good value.
» Consider Fremantle, especially for B&B accommodation, as a base while visiting Perth.
» Use Perth and Fremantle's free-of-charge Central Area Transit (CAT) bus services.
» Look out for good-value lunch deals at central city pubs and cafes.
» Cheaper ethnic restaurants dot the streets around Northbridge.
» Visit markets and other specialist stores for self-catering supplies (see boxed text, Click here ).
» Free Perth attractions include the Art Gallery of Western Australia, the Perth Institute of Contemporary Arts and the Western Australian Museum.
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4 East Perth
o Wickham Retreat HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9325 6398; www.facebook.com/WickhamRetreatBackpackers; 25-27 Wickham St; dm $35-40, d $70-100; ) Located in a residential neighbourhood east of the city centre, Wickham Retreat has a quieter vibe compared to other hostels around town. Most of the guests are international travellers, drawn by the colourful rooms and dorms, and a funky AstroTurf garden. Free food (including rice, fresh bread and vegies) stretches travel budgets eroded by Perth's high prices.
Regal Apartments APARTMENT $$
OFFLINE MAP GOOGLE MAP
( 08-9221 8614; www.regalapartments.com.au; 11 Regal Pl; apt from $230; ) Tucked in behind good-value Asian restaurants east of the city centre, these recently redecorated one- and two-bedroom apartments are spacious and modern. Fully-equipped kitchens and private laundry facilities make them ideal for families watching their dollars. Pretty Claisebrook Cove is just a short walk away.
The Sebel Residence APARTMENT $$$
OFFLINE MAP GOOGLE MAP
( 08-9223 2500; www.mirvachotels.com/perth; 60 Royal St; apt from $315; ) Modern and chic apartments with self-contained kitchenettes and a classy hotel vibe. Adjacent Claisebrook Cove Promenade has a few nights' worth of restaurants, cafes and bars.
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4 Highgate & Mt Lawley
o Durack House B&B $$
( 08-9370 4305; www.durackhouse.com.au; 7 Almondbury Rd; s $160, d $175-190; ) It's hard to avoid words like 'delightful', when describing this cottage, set on a peaceful suburban street behind a rose-adorned white picket fence. The three rooms have plenty of old-world charm, paired with thoroughly modern bathrooms. It's only 250m from Mt Lawley station; turn left onto Railway Pde and then first right onto Almondbury Rd.
Mt Lawley
Sights
1 Hyde Park B2
Activities, Courses & Tours
2 WA Skydiving Academy B4
Sleeping
3 Billabong Backpackers Resort C3
4 Coolibah Lodge A3
5 Hotel Northbridge A3
6 Pension of Perth A2
7 Witch's Hat A3
Eating
8 Cantina 663 D1
9 El Público C2
10 Jackson's C2
Must Winebar (see 9)
11 Namh Thai B3
12 Red Teapot A4
13 Sayers Sister A3
14 Source Foods B4
15 Tarts A3
16 The Beaufort St Merchant C3
17 Veggie Mama C2
Drinking & Nightlife
18 A4
19 Five Bar C2
20 Flying Scotsman D1
21 Luxe C3
Must Winebar (see 9)
22 Queens C2
23 The Brisbane B4
Velvet Lounge (see 20)
Entertainment
24 Astor D1
25 Lazy Susan's Comedy Den B4
26 Perth Steam Works A4
Shopping
27 Planet D1
Billabong Backpackers Resort HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9328 7720; www.billabongresort.com.au; 381 Beaufort St; dm $29-31, r $82; ) This large hostel (about 150 beds) has a busy poolside area. It's popular with longstay guests and can be noisy, but it's close to Mt Lawley's bars and cafes.
Above Bored B&B $$
( 08-9444 5455; www.abovebored.com.au; 14 Norham St; d $190-200; ) In a quiet residential neighbourhood, this 1927 Federation house is owned by a friendly TV scriptwriter. The two themed rooms in the main house have eclectic decor, and in the garden there's a cosy self-contained cottage with a kitchenette. In an expensive town for accommodation, Above Board is great value. Northbridge and Mt Lawley are a short drive away.
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4 Subiaco & Kings Park
o Eight Nicholson BOUTIQUE HOTEL $$$
( 08-9382 1881; www.8nicholson.com.au; 8 Nicholson Rd; r from $369; ) Concealed behind the whitewashed walls of this stylishly renovated heritage house is accommodation that's one-part luxury boutique hotel and one-part welcoming B&B. Hip but elegant decor and interesting artworks are evidence of the well-travelled owners' eclectic tastes, and it's just a short walk to Kings Park or Subiaco's cafes and restaurants.
Subiaco & Kings Park
Sights
1 Scitech F2
Activities, Courses & Tours
2 Beatty Park Leisure Centre G1
3 Surf Sail Australia E2
Sleeping
4 The Outram E3
5 The RichardsonE3
Eating
6 Boucla C4
7 Chez Jean-Claude Patisserie C4
8 Chutney Mary's C3
9 Duende F1
10 Green's & Co E1
11 Jus Burgers C3
12 Jus Burgers E1
13 Kailis Bros E1
14 New Norcia Bakery C4
15 Perugino E3
16 Sayers F1
Snags & Sons (see 12)
17 Station St Markets C2
18 Stimulatte C3
19 Subiaco Hotel C3
Drinking & Nightlife
20 Honey Lounge E1
Leederville Hotel (see 12)
Subiaco Hotel (see 19)
Entertainment
21 Ace Subiaco C3
22 Luna E1
23 Patersons Stadium D2
24 Regal Theatre C3
25 Subiaco Arts Centre B4
Shopping
Atlas Divine (see 10)
26 Indigenart D3
Richardson HOTEL $$$
OFFLINE MAP GOOGLE MAP
( 08-9217 8888; www.therichardson.com.au; 32 Richardson St; r from $520; ) Ship-shaped and shipshape, the Richardson offers luxurious, thoughtfully designed rooms – some with sliding doors to divide them into larger suites. The whole complex has a breezy, summery feel, with pale marble tiles, creamy walls and interesting art. There's an in-house spa centre if you require additional pampering.
The Outram HOTEL $$$
OFFLINE MAP GOOGLE MAP
( 08-9322 4888; www.wyndhamvrap.com.au; 32 Outram St; r $380-410; ) Discreet and understated, the Outram (aka the unwieldly Wyndham Vacation Resorts Asia Pacific Perth) is stylish, with compact open-plan rooms, a bathroom with a walk-through shower, king-size beds and flat-screen TVs.
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4 Beaches
Ocean Beach Backpackers HOSTEL $
( 08-9384 5111; www.oceanbeachbackpackers.com; 1 Eric St; dm/s/d $26/70/80; ) Offering (some) ocean views, this big, bright hostel in the heart of Cottesloe is just a short skip from the sand. Rooms are basic, but all have private bathrooms, and you'll probably just be here to sleep given the great location. Hire a bike to get around locally, or take advantage of the hostel's free bodyboards and surfboards.
Western Beach Lodge HOSTEL $
( 08-9245 1624; www.westernbeach.com; 6 Westborough St; dm $30-34, d with shared bathroom $75; ) A real surfer hang-out, this sociable, homely hostel has surfboards and boogie boards available, and a good, no-frills feel.
Trigg Retreat B&B $$
( 08-9447 6726; www.triggretreat.com; 59 Kitchener St; r $190; ) Quietly classy, this three-room B&B offers attractive and supremely comfortable queen bedrooms in a modern house a short drive from Trigg Beach. Each has fridge, TV, DVD player and tea- and coffee-making facilities. A full cooked breakfast is included in the rates. When we last dropped by, the beautiful jarrah floors were getting a makeover.
Sunmoon Boutique Resort HOTEL $$
( 08-9245 8000; www.sunmoon.com.au; 200 West Coast Hwy; r from $175; ) Separated from Scarborough Beach by a busy road and a petrol station, this Balinese-themed complex has wooden pathways leading to shady palm gardens and fishponds. Batik furnishings adorn large rooms with terracotta-tiled floors, and all rooms have been recently refurbished. Check online for good discounts.
Ocean Beach Hotel HOTEL $$
( 08-9384 2555; www.obh.com.au; cnr Marine Pde & Eric St; r $170-250; ) A good midrange option facing Cottesloe Beach, this accommodation is slightly removed from the raucously popular pub of the same name. Rooms are large and pretty good value, either in an older art-deco area, or in a towering new block. It's a good alternative to the pricey hotels of central Perth _and_ the Indian Ocean is just across the road.
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4 Other Areas
Discovery Holiday Parks – Perth CAMPGROUND $
( 08-9453 6877; www.discoveryholidayparks.com.au; 186 Hale Rd; powered sites for 2 people $38-45, units $125-187; ) This well-kept holiday park, 15km out of the city, has a wide range of cabins and smart-looking units, many with deck, TV and DVD player.
The Peninsula APARTMENT $$
( 08-9368 6688; www.thepeninsula.net; 53 South Perth Esplanade; apt from $205; ) While only the front few apartments have full-on views, the Peninsula's waterfront location lends itself to lazy ferry rides and sunset strolls along the river. It's a sprawling, older-style complex, but it's kept in good nick. The apartments all have kitchenettes and there's a communal laundry room.
### SELF-CATERING
These are the pick of the crop.
Boatshed Market (www.boatshedmarket.com.au; 40 Jarrad St, Cottesloe; 6.30am-8pm) Upmarket shed stacked with fresh produce, meat, fish, delicatessen goods, pastries and bread.
Chez Jean-Claude Patisserie OFFLINE MAP GOOGLE MAP (www.chezjeanclaudepatisserie.com.au; 333 Rokeby Rd, Subiaco; 6am-6.30pm Mon-Fri) Line up with the locals for brioche and baguettes.
City Farm Organic Growers Market OFFLINE MAP GOOGLE MAP (www.perthcityfarm.org.au; 1 City Farm Pl, East Perth; 8am-noon Sat) Local organic producers sell eggs, fruit, vegetables and bread.
Kailis Bros OFFLINE MAP GOOGLE MAP (www.kailisbrosleederville.com.au; 101 Oxford St, Leederville; 8am-6pm) Big, fresh seafood supplier with cafe attached.
Kakulas Bros OFFLINE MAP GOOGLE MAP (www.kakulasbros.com.au; 183 William St, Northbridge; ) Provisions store overflowing with sacks and vats of legumes, nuts and olives, plus a deli counter, well stocked with cheese. There's another branch, Kakulas Sister (Click here ), down in Fremantle.
Station St Markets OFFLINE MAP GOOGLE MAP (www.subiacomarkets.com; Station St, Subiaco; 7.30am-5.30pm Fri-Mon) Covered market selling fresh produce.
5 Eating
Where many of Australia's other state capitals might have a handful of top restaurants charging over $40 a main, in Perth those prices are fast becoming the norm for any establishment that considers itself above average. Unfortunately, the experience doesn't always match the outlay, and inferior and lax service is more prevalent than it should be.
It's still possible to eat cheaply, especially in the Little Asia section of William St, Northbridge. Many restaurants are BYO, meaning you can bring your own wine; check first. The better cafes are good places to go for a midrange meal, and good coffee and free wi-fi are becoming more prevalent. Some establishments listed under Drinking blur the line between bar, cafe and restaurant, and offer good dining as well.
The happening neighbourhoods for new cafes and restaurants are Northbridge, Mt Lawley and more recently Maylands, and the city centre has also seen many new options open around the Brookfield Pl precinct (www.brookfieldplace.com.au) on St George's Terrace.
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5 City Centre
Mama Tran VIETNAMESE $
OFFLINE MAP GOOGLE MAP
(www.mamatran.com.au; 36-40 Milligan St; snacks & mains $8-12; 7am-4pm) Now you don't have to truck across to Northbridge for a hearty bowl of _pho_ (Vietnamese noodle soup). The hip Mama Tran also does excellent coffee, fresh rice-paper rolls, and Asian salads. Grab a spot on one of the big shared tables and order up a storm including plump _banh mi ga_ (Vietnamese chicken baguettes).
Tiger, Tiger CAFE $
OFFLINE MAP GOOGLE MAP
( 08-9322 8055; www.tigertigercoffeebar.com; Murray Mews; mains $8-20; 7am-5pm Mon & Sat, to 8pm Tue-Thu, to midnight Fri; ) In a laneway off Murray St, Tiger, Tiger has a shabby-chic interior that isn't as popular as its outdoor setting. The free wi-fi's a drawcard, but the food is also excellent – all the regular breakfast favourites, along with pasta, curry, tarts, soups and baguettes on the lunch menu. Table service kicks in at lunchtime; before that you'll need to order at the counter.
Cabin Fever CAFE $
OFFLINE MAP GOOGLE MAP
(88 Barrack St, Bon Marche Arcade; snacks $5-10; 7am-5pm Mon-Fri, 10am-5pm Sat; ) Hidden away in a central Perth shopping arcade, Cabin Fever features quirky retro decor last seen at your aunt's place circa 1973. It's like bees to a heritage honeypot for Perth's cool kids, drawn also by free wi-fi, homestyle baking and excellent coffee. And just when you thought this part of town wasn't very interesting.
Annalakshmi INDIAN $
OFFLINE MAP GOOGLE MAP
( 08-9221 3003; www.annalakshmi.com.au; 1st fl, Western Pavilion; pay by donation; noon-2.30pm & 6.30-9pm Tue-Sun) While the 360- degree views of the Swan River are worth a million dollars, the food's literally priceless. Run by volunteers (formidable baby-boomers, in the main), this place asks for payment by donation. An eclectic mix of hippies, Hindus and the just plain hungry line up for spicy vegetarian curries and fragrant dhal. Chilled coconut-milk and cardamom desserts cleanse the palate.
Secret Garden CAFE $
OFFLINE MAP GOOGLE MAP
(www.secretgardencafe.com.au; Murray Mews; mains $10-19; 7am-3pm Mon-Fri; ) Tucked away down a boho laneway off Murray St, Secret Garden has good coffee, enticing counter food and all-day breakfasts for hangovers. Free wi-fi is the perfect partner for a robust espresso.
Taka JAPANESE $
OFFLINE MAP GOOGLE MAP
(www.takaskitchen.iinet.net.au; mains $7-10; 11am- 9pm Mon-Sat) This straightforward Japanese eatery whips out standards like teriyaki, udon and sushi. Great for a quick bite if you're out drinking. It has branches at Barrack St OFFLINE MAP (150-152 Barrack St) and Shafto Lane OFFLINE MAP (shops 5 & 6 Shafto Lane) .
Greenhouse TAPAS $$
OFFLINE MAP GOOGLE MAP
( 08-9481 8333; www.greenhouseperth.com; 100 St Georges Tce; tapas $10-19; 7am-midnight Mon-Sat) S Groundbreaking design – straw bales, plywood, corrugated iron and living exterior walls covered with 5000 individual pot plants – combines with excellent food at this hip tapas-style eatery. Asian and Middle Eastern influences inform a sustainably sourced menu including spiced lamb with yoghurt and quinoa, or lamb with pistachio and pomegranate.
Venn Cafe & Bar CAFE $$
OFFLINE MAP GOOGLE MAP
(www.venn.net; 16 Queen St; mains $13-28, pizza $15; 7am-5pm Mon-Tue, 7am-midnight Wed-Fri, 9am-midnight Sat) Equal parts design store, gallery, bar and cafe, and more proof that Perth is a foodie city on the rise. Breakfast and lunch team with good coffee – try the quinoa and banana pancakes or carpaccio of Margaret River Wagyu beef – and later at night pizza and charcuterie combine with a surprising wine list and craft beers from around Australia.
Tom's Kitchen CAFE $$
OFFLINE MAP GOOGLE MAP
( 08-9321 0345; www.tomskitchenwa.com.au; Shafto Lane; lunch 2/3 courses $21.50/28.50, dinner mains $30-35; 6.30am-9pm Mon-Fri, from 6pm Sat) Cafe by day, dining room by night, Tom's Kitchen is a standout amid the ethnic eateries and rambunctious pubs of Shafto Lane. Good-value multi-course lunches feature classy comfort food, and are a great way to battle the impact of Perth's expensive menus. Evenings showcase warming dishes like slow-cooked pork belly and crispy-skin salmon.
Matsuri JAPANESE $$
OFFLINE MAP GOOGLE MAP
(www.matsuri.com.au; 250 St Georges Tce; mains $18-23; noon-2.30pm Mon-Fri, 6-10pm Mon-Sat) You'll feel a bit like a carp in a fish tank here – floor-to-ceiling glass runs the perimeter of this large, long-standing Japanese restaurant. Excellent teriyaki, tempura and sashimi combine with slightly formal but friendly service.
Print Hall ASIAN, MODERN AUSTRALIAN $$$
OFFLINE MAP GOOGLE MAP
(www.printhall.com.au; 125 St Georges Tce; snacks $10-18, mains $25-45; noon-midnight Mon-Fri, 4pm-midnight Sat) Formerly the base of the _West Australian_ newspaper, this sprawling complex in the Brookfield Place precinct includes the Apple Daily, featuring Southeast Asian–style street food, and the expansive Print Hall Dining Room, with an oyster bar and grilled WA meat and seafood. Don't miss having a drink and Spanish tapas in the rooftop Bob's Bar, named after Australia's larrikin former prime minister, Bob Hawke.
Restaurant Amusé MODERN AUSTRALIAN $$$
OFFLINE MAP GOOGLE MAP
( 08-9325 4900; www.restaurantamuse.com.au; 64 Bronte St; degustation $125; 6.30pm-late Tue-Sat) The critics have certainly been amused by this degustation-only establishment, regularly rated as WA's finest. The latest gong was for Perth's Restaurant of the Year in the 2013 _Good Food Guide_ . Book well ahead and come prepared for a culinary adventure.
The Trustee BISTRO $$$
OFFLINE MAP GOOGLE MAP
(www.thetrustee.com.au; 133 St Georges Tce; bar snacks $13-25, mains $33-39; 11.45am-midnight Mon-Fri, from 5pm Sat) Just one of the new eateries and bars filling the heritage buildings around central Perth's Brookfield Place precinct, The Trustee channels a European bistro vibe with dishes like chicken black bean cassoulet and confit duck leg. A spectacular wine list draws Perth's movers and shakers, and the flash bar snacks are pricey but delicious.
Balthazar MODERN AUSTRALIAN $$$
OFFLINE MAP GOOGLE MAP
( 08-9421 1206; 6 The Esplanade; mains $30-45; noon-late Mon-Fri, 6pm-late Sat) Low lit, discreet and sophisticated, with a hipster soundtrack and charming staff, Balthazar's informal cool vibe is matched by exquisite food and a famously excellent wine list. The menu here is refreshingly original, combining European and Asian flavours with not-at-all-reckless abandon.
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5 Northbridge
Little Willy's CAFE $
OFFLINE MAP GOOGLE MAP
(267 William St; mains $5-14; 6am-6pm Mon-Fri, 8am-4pm Sat & Sun) It's tiny and it's on William St, and it's a go-to spot to grab a sidewalk table and tuck into robust treats like the city's best breakfast burrito and bircher museli. It's also a preferred coffee haunt for the hip Northbridge indie set. BYO skinny jeans.
Viet Hoa VIETNAMESE $
OFFLINE MAP GOOGLE MAP
(349 William St; mains $10-23; 10am-10pm) Don't be fooled by the bare-bones ambience of this corner Vietnamese restaurant – or you'll miss out on the fresh rice-paper rolls and top-notch _pho_ . Greenery creeping up the beams gives the place an offbeat feel.
Source Foods CAFE $
OFFLINE MAP GOOGLE MAP
(www.sourcefoods.com.au; 289 Beaufort St; mains $10-19; 7.30am-3pm; ) S Unassuming cafe committed to sustainable practices; free wi-fi also. Pop along for 'Burger Night' on a Friday – try the harissa steak burger ($16).
Flipside BURGERS $
OFFLINE MAP GOOGLE MAP
(www.flipsideburgerbar.com.au; 222 William St; burgers $10.50-14.50; 11.30am-10pm Tue-Sat, to 9pm Sun) Gourmet burgers with the option of takeout upstairs at Mechanics Institute bar (Click here ).
o Namh Thai THAI $$
OFFLINE MAP GOOGLE MAP
( 08-9328 7500; 223 Bulwer St; mains $22-40; 6-10pm Mon-Sat) Not your average Thai restaurant, Namh experiments with interesting taste combinations – duck with lychees is the speciality, but we love the soft-shell crab with watermelon – and serves them in an elegant candlelit dining room. Friday and Saturday are given over to banquet-style dining. Bulwer St intersects William St, north of Northbridge.
Bivouac Canteen & Bar CAFE $$
OFFLINE MAP GOOGLE MAP
(www.bivouac.com.au; 198 William St; mains $16-36, pizzas $21-24; noon-late Tue-Fri, 10am-late Sat) Bivouac is another of the cool recent openings on William St resurrecting the area as a hip destination. Mediterranean- style cuisine partners with a good wine list, and gourmet pizzas go well with boutique beers and artisan ciders. The coffee is excellent, and Bivouac's utilitarian decor is softened with a rotating roster of work from local artists.
Tarts CAFE $$
OFFLINE MAP GOOGLE MAP
(www.tartscafe.com.au; 212 Lake St; mains $14-33; 7am-10pm Tue-Fri, to 5pm Sat-Mon) Massive tarts piled with berries, apples or lime curd; rich scrambled eggs tumbling off thickly sliced sourdough; mini custard tarts stacked with glazed strawberries. Packed like a picnic hamper on weekends, and a worthy bistro-style dinner option during the week.
Good Fortune Roast Duck House CHINESE $$
OFFLINE MAP GOOGLE MAP
(www.goodfortuneduckhouse.com.au; 344 William St; mains $10-24; 10am-10pm Wed-Mon) This is the real thing – just like being in China. Locals charge in for family-sized feeds of barbecue pork, roast duck and noodles – the front window is crammed with options. A half-serve of boneless duck is $21, and seafood options include crispy soft-shell crab.
La Cholita MEXICAN $$
OFFLINE MAP GOOGLE MAP
(cnr Aberdeen & William Sts; snacks $6-12, mains $26-28; 5pm-late Wed-Sun) _Sí_ , the Mexican culinary wave has also washed up on Western Australian shores, and La Cholita's energetic combo of Mexican street food, ice-cold _cerveza_ and gutsy tequilas is _muchas_ fun. Don't come expecting a quiet romantic evening – you may have to share tables – and there are no reservations, so arrive early.
Sayers Sister CAFE $$
OFFLINE MAP GOOGLE MAP
(www.sayersfood.com.au; 236 Lake St; mains $10-27; 7am-5pm Tue-Sun) Top-notch breakfasts and lunches (including scrambled eggs with feta, truffle and smoked salmon) and a convenient Northbridge location.
Red Teapot CHINESE $$
OFFLINE MAP GOOGLE MAP
(www.redteapotrestaurant.com.au; 413 William St; mains $11-22; 11.30am-3pm & 5.30-10pm Mon-Sat) An intimate restaurant, always busy with diners enjoying stylishly executed Chinese favourites like fragrant prosperous chicken and chilli salt squid.
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5 Highgate & Mt Lawley
Veggie Mama VEGETARIAN $
OFFLINE MAP GOOGLE MAP
(www.veggiemma.com.au; cnr Beaufort & Vincent Sts; mains $10-20; 7am-5pm Mon-Fri, from 8am Sat & Sun; ) S Loads of vegan and gluten-free options shine at this cute corner cafe where flavour is definitely not compromised. The menu includes delicious salads, smoothies, vegie curries and burgers – try the polenta and butternut burger with mango salsa – and weekend breakfasts are very popular. There's free wi-fi, and it's all really well priced.
Cantina 663 MEDITERRANEAN $$
OFFLINE MAP GOOGLE MAP
( 08-9370 4883; www.cantina663.com; 663 Beaufort St; lunch $12-28, dinner $26-34; 8am-late Mon-Sat, to 3pm Sun) It's a mini culinary World Cup, featuring Spain, Portugal and Italy, at this cool but casual cantina with tables spilling into the arcade. Service can be a bit too cool for school, but it's worth waiting for dishes like Ortiz anchovies with lemon and charred bread, or braised baby goat with pearl barley and yoghurt.
The Beaufort St Merchant CAFE $$
OFFLINE MAP GOOGLE MAP
( 08-9328 6299; www.beaufortmerchant.com; 488 Beaufort St; breakfast $13-22, lunch & dinner $24-37; 7am-10pm) Our favourite cafe in Mt Lawley, and one of our favourites in Perth – especially for a leisurely breakfast over the papers and a couple of coffees. Go for the chorizo and manchego-cheese tortilla, and work out what you'd order if you came back for dinner. Maybe the lime-baked ocean trout or crab linguini, we reckon.
El Público MEXICAN $$
OFFLINE MAP GOOGLE MAP
( 0418 187 708; www.elpublico.com.au; snacks $9-16, mains $22-28; 5pm-midnight Wed-Fri, from noon Sat & Sun) El Público in Mt Lawley is one of Perth's hippest new eateries. Look forward to interesting and authentic spins on Mexican street food, all served as small plates that are perfect for sharing. Menu standouts include fish soft-shell tacos, and tequila-infused marshmallows for dessert. Bring along a few friends, and groove to the occasional DJs.
Jackson's MODERN AUSTRALIAN $$$
OFFLINE MAP GOOGLE MAP
( 08-9328 1177; www.jacksonsrestaurant.com.au; 483 Beaufort St; mains $41-49, degustation $125; 6pm-late Mon-Sat) The finest of fine dining is offered in this upmarket dining room, where the wait staff don white gloves to present you with wonderfully creative treats from the kitchen of Neal Jackson, one of Perth's most established chefs.
Must Winebar FRENCH $$$
OFFLINE MAP GOOGLE MAP
( 08-9328 8255; www.must.com.au; 519 Beaufort St; mains $39-46; noon-midnight) Not content with being Perth's best wine bar, Must is one of its best restaurants as well. The Gallic vibe is hip, slick and a little bit cheeky, and the menu marries classic French bistro flavours with the best local produce.
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5 Mt Hawthorn
New Norcia Bakery BAKERY, CAFE $
OFFLINE MAP GOOGLE MAP
(www.newnorciabaker.com.au; 163 Scarborough Beach Rd; mains $11-17; 7am-6pm) Perth's best bread, delicious pastries and a bright cafe as well. It gets crammed on the weekends. There's another more central branch Subiaco OFFLINE MAP (Bagot Rd, The Cloisters; 7.30am-6pm Mon-Sat, to 4pm Sun) for takeaway baked goodies.
Divido ITALIAN $$
( 08-9443 7373; www.divido.com.au; 170 Scarborough Beach Rd; mains $33-39, 6-course degustation $95; 6pm-late Mon-Sat) Italian but not rigidly so (the chef is of Croatian extraction, so delicious Dalmatian-style doughnuts make it onto the dessert menu), this romantic restaurant serves handmade pasta dishes and delicately flavoured mains. Good-value 'Champagne Mondays' feature three courses and a glass of bubbles for $65.
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5 Leederville
Snags & Sons FAST FOOD $
OFFLINE MAP GOOGLE MAP
(www.snagsandsons.com.au; 749 Newcastle St; sausages $5-10; 11am-10pm Tue-Sat, to 9pm Sun & Mon) S It's sausage heaven at Snags & Sons. Tasty spins on the humble snarler – often made from free range and organic produce – include smoked cheese kransky, Thai red curry or North African lamb. Sauces include tamarind chutney, harissa yoghurt and horseradish cream, and healthy single-serve salads are also on offer.
Green's & Co CAFE $
OFFLINE MAP GOOGLE MAP
(123 Oxford St; cakes $5-8; 8am- midnight) Dive into great coffee and a 'how-do-I-choose?' selection of cakes, and see if your favourite band is featured on the posters adorning the walls.
Jus Burgers BURGERS $
OFFLINE MAP GOOGLE MAP
(www.jusburgers.com.au; burgers $11-14; 11.30am- 10pm) S Carbon-neutral gourmet burgers; branches in Leederville OFFLINE MAP (743 Newcastle St) and Subiaco OFFLINE MAP (1 Rokeby Rd) .
o Duende TAPAS $$
OFFLINE MAP GOOGLE MAP
( 08-9228 0123; www.duende.com.au; 662 Newcastle St; tapas & mains $14-29; 7.30am-late) Sleek Duende occupies a corner site amid the comings and goings of Leederville. Stellar modern-accented tapas are served: make a meal of it or call in for a late-night glass of dessert wine and _churros_ (doughnuts served with hot chocolate sauce). We're also very partial to starting the day with an espresso and Duende's crab-and-chorizo omelette.
Kitsch ASIAN $$
(www.kitschbar.com.au; 229 Oxford St; small plates $5-19; 5pm-midnight Tue-Sat) Southeast Asian–style street food, Thai beers and an eclectic, slighty overgrown garden make Kitsch a great spot for a few laid-back hours of tasty grazing. Standout dishes include the son-in-law eggs with tamarind and pork crackling, or the five-spice pork with plums and ginger chilli caramel. Expect to stay (and eat) longer than you planned.
Sayers CAFE $$
OFFLINE MAP GOOGLE MAP
(www.sayersfood.com.au; 224 Carr Pl; mains $10-27; 7am-3pm) This classy cafe's counter groans under the weight of its alluring cakes. The breakfast menu includes eggy treats such as beetroot-cured salmon omelette, and lunch highlights include a zingy calamari, watermelon and fresh mint salad.
WORTH A TRIP
### MAYLANDS: THE NEXT BIG THING?
If the recent expansion of new bars, cafes and restaurants in Mt Lawley makes the suburb the 'new Subiaco', we reckon Maylands just to the east could be the 'new Mt Lawley'. It's early days, with just a few eating and drinking spots huddled on Whatley Cres, but there's a definite foodie buzz around the neighbourhood. It's also very easy to reach by train, just a short Zone 1 hop ($2.70) to the Maylands station on the Midland line.
Mrs S (178 Whatley Cres; mains $10-17; 7am-5pm Tue-Fri, 8am-4pm Sat & Sun) Mrs S has a quirky retro ambience, the perfect backdrop for excellent homestyle baking or a lazy brunch. Menus – presented in Little Golden children's books – feature loads of innovative variations on traditional dishes. Try the breakfast tortilla with poached eggs, spicy beans and a lime sour cream. Weekends are _wildly_ popular, so try to visit on a weekday.
Swallow (198 Whatley Cres; snacks $10-24; 4pm-late Mon-Sat. from noon Sun) Channeling an art deco ambience with funky lampshades and vintage French advertising, Swallow is the kind of place you'd love as your local. Wine and cocktails are exemplary, and the drinks list includes Spanish wheat beers and French ciders. DJs often play on Sunday afternoons in the courtyard, and bar snacks also come with a Euro accent.
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5 Subiaco & Kings Park
Stimulatte CAFE $
OFFLINE MAP GOOGLE MAP
(361 Hay St; brunch $7.50-12.50; 7am-3pm) It's worth taking the short stroll from central Subiaco to this cool neighbourhood cafe. Big-format photos of New York adorn the walls, providing a cosmopolitan backdrop for interesting brunches and serious coffee. The brekky wrap or the homemade baked beans with ciabatta toast are recommended.
Boucla CAFE $
OFFLINE MAP GOOGLE MAP
(www.boucla.com; 349 Rokeby Rd; mains $11-22; 7am-5pm Mon-Fri, to 3.30pm Sat) A locals' secret, this Greek- and Levantine-infused haven is pleasingly isolated from the thick of the Rokeby Rd action. Baklava and cakes tempt you from the corner, and huge tarts filled with blue-vein cheese and roast vegetables spill off plates. The salads are great too.
Subiaco Hotel GASTROPUB $$
OFFLINE MAP GOOGLE MAP
( 08-9381 3069; www.subiacohotel.com.au; 465 Hay St; mains $19-34; 7am-late) A legendary boozer with a makeover, the Subi's buzzy dining room is the suburb's main place to see and be seen. The menu ranges from lighter fare like Caesar salads and Asian-inspired pork belly to perfectly cooked steaks and excellent fish dishes. Around the corner, the main bar (Click here ) is still relatively old school.
Old Brewery STEAKHOUSE $$
( 08-9211 8910; www.theoldbrewery.com.au; 173 Mounts Bay Rd; mains $29-48; breakfast Sun, lunch & dinner daily) Even Perth's steakhouses are glamorous, evidenced by this designer joint in the historic Swan Brewery building (1838). There are river views across to the city, but hardcore carnivores will be more interested in the beef aging gracefully in glass display cabinets. Splash out on a 300g Wagyu scotch fillet ($79). Craft-beer fans won't go thirsty either.
Chutney Mary's INDIAN $$
OFFLINE MAP GOOGLE MAP
(www.chutneymarys.com.au; 67 Rokeby Rd; mains $15-28; noon-2.30pm Mon-Sat, 5.30pm-late daily) The feisty, authentic Indian food here is much loved and a sizeable chunk of the large menu is devoted to vegetarian favourites.
Perugino ITALIAN $$
OFFLINE MAP GOOGLE MAP
( 08-9321 5420; www.perugino.com.au; 77 Outram St; mains $27-41; noon-3pm Tue-Fri, 7pm-late Tue-Sat) Traditional, formal Italian restaurant with a three-course lunch for $52.
Fraser's MODERN AUSTRALIAN $$$
( 08-9481 7100; www.frasersrestaurant.com.au; Fraser Ave; mains $36-44; noon-late) Atop Kings Park, overlooking the city and the glittering Swan River, Fraser's is in a wonderful location. Thankfully, the food is also excellent, making it a popular spot for business lunches and romantic dinners on the terrace on balmy summer nights. Pair the turmeric, snapper and king prawn curry with a Leeuwin Estate riesling from Margaret River.
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5 Beaches
Dancing Goat CAFE $
(14 Railway St; mains $10-15; 6am-4pm Mon-Fri, 7.30am-12.30pm Sat) The hip and bohemian Dancing Goat is the best place in the beach suburbs for a coffee. It's near the Swanbourne train station.
John St Cafe CAFE $
(37 John St; mains $10-25; 7am-4pm) Tucked up a residential street, five minutes from the beach, John St is another fine Cottesloe breakfast spot.
Il Lido ITALIAN $$
(www.illido.com.au; 88 Marine Pde; mains $20-35; 7.30am-late) Il Lido's al fresco area is popular with Cotteslocals and their dogs, but we prefer the sunny interior of this self-styled 'Italian canteen'. Breakfast and coffee attract the early-bird swimmers, and throughout the day antipasto plates, pasta and risottos, and a good beer and wine list continue the culinary buzz. Maybe linger for cocktails and an Indian Ocean sunset.
Naked Fig CAFE $$
(www.thefig.com.au; 278 Marine Pde; breakfast & lunch $16-33, dinner $27-36; 7am-late, closed dinner Mon; ) S It's all about the location here, especially the sublime ocean-gazing deck near Swanbourne beach. Modern Australia and Mediterranean flavours make perfect sense given the stunning view, and the sustainable menu tends to free-range this and organic that.
6 Drinking & Nightlife
Once upon a time, licences to sell alcohol in WA were tightly restricted and massively expensive. Venues therefore had to be built on a grand scale in order to recoup the investment, and big booze barns became part of the culture.
A law change a few years back has given birth to a new breed of quirky little bars that are distinctly Melbourne-ish in their hipness and difficulty to locate. They're sprouting up all over the place, including in the formerly deserted-after-dark central city. Northbridge is also a happy-hunting ground for more idiosyncratic drinking establishements.
One of the by-products of the mining boom has been the rise of the Cashed-Up Bogan (CUB) – young men with plenty of cash to splash on muscle cars, beer and drugs. A spate of fights and glassings in bars has caused many venues, particularly around Northbridge, to step up security. Most pubs now have lockouts, so you'll need to be in before midnight in order to gain entry. You may need to present photo ID to obtain entry and it would pay to keep your wits about you in pubs and on the streets after dark.
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6 City Centre
Greenhouse COCKTAIL BAR
OFFLINE MAP GOOGLE MAP
(www.greenhouseperth.com; 100 St Georges Tce; 7am-midnight Mon-Sat) In a city so in love with the great outdoors, it's surprising that nobody's opened a rooftop bar in the central city before now. Hip, eco-conscious Greenhouse is leading the way, mixing up a storm amid the greenery with great cocktails and an interesting beer and wine list.
Helvetica BAR
OFFLINE MAP GOOGLE MAP
(www.helveticabar.com.au; rear 101 St Georges Tce; 3pm-midnight Tue-Thu, noon-midnight Fri, 6pm-midnight Sat) Clever artsy types tap their toes to delicious alternative pop in this bar named after a typeface and specialising in whisky and cocktails. The concealed entry is off Howard St: look for the chandelier in the lane behind Andaluz tapas bar.
Cheeky Sparrow BAR, CAFE
OFFLINE MAP GOOGLE MAP
(www.cheekysparrow.com.au; 1/317 Murray St; 11.30am-late Tue-Fri, from 4pm Sat) Cheeky Sparrow's multi-level labyrinth of leather banquettes and bentwood chairs is great for everything from brunch and coffee through to pizza and cheese and charcuterie plates. If you're feeling peckish later at night, pop in for robust bar snacks including chorizo croquettes and chickpea fritters. Cocktail fans certainly won't be disappointed. Access is via Wolfe Lane.
Hula Bula Bar COCKTAIL BAR
OFFLINE MAP GOOGLE MAP
(www.hulabulabar.com; 12 Victoria Ave; 4pm-midnight Wed-Fri, 6pm-1am Sat) You'll feel like you're on _Gilligan's Island_ in this tiny Polynesian-themed bar, decked out in bamboo, palm leaves and tikis. A cool but relaxed crowd jams in here on weekends to sip ostentatious cocktails out of ceramic monkey's heads.
Wolfe Lane COCKTAIL BAR
OFFLINE MAP GOOGLE MAP
(www.wolflane.com.au; Wolfe Lane; 4pm-midnight Tue-Sat) Exposed bricks, classic retro furniture and high ceilings create a pretty decent WA approximation of a New York loft. A serious approach to cocktails and wine combines with an eclectic beer selection, and bar snacks include share plates of cheese and chorizo. Here's where to come for the last drink(s) of the night.
The Grosvenor PUB
OFFLINE MAP GOOGLE MAP
(www.thegrosvenorperth.com.au; cnr Hay & Hill Sts; 11am-midnight) The perfect spot for a lazy afternoon drink. This classic corner pub – complete with wrought-iron balconies and one of Perth's best garden bars – draws a crowd of loyal locals, nearby desk jockeys and thirsty students.
1907 COCKTAIL BAR
OFFLINE MAP GOOGLE MAP
(www.1907.com.au; 26 Queen St; 4pm-midnight Wed-Sat) Hidden away down a lane, behind a gate and down the side of a building, this modern-day speakeasy has a back-lit bar and Rat Pack photos on the walls. Blue Note Thursdays feature $10 cocktails.
Metro City CLUB
OFFLINE MAP GOOGLE MAP
(www.metroconcertclub.com; 146 Roe St) Thumping super-club (capacity 2000), which doubles as a concert venue.
Ambar CLUB
OFFLINE MAP GOOGLE MAP
(www.boomtick.com.au/ambar; 104 Murray St) Perth's premier club for breakbeat, drum'n'bass and visiting international DJs.
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6 Northbridge
Northbridge is the rough-edged hub of Perth's nightlife, with dozens of pubs and clubs clustered around William and James Sts. It's so popular, it even has its own website (www.onwilliam.com.au). A few recent openings have lifted the tone of the area.
Mechanics Institute BAR
OFFLINE MAP GOOGLE MAP
(www.mechanicsinstitutebar.com.au; 222 William St; noon-midnight Tue-Sun) Negotiate the laneway entrance around the corner on James St to discover one of Perth's most down-to-earth small bars. Share one of the big tables on the deck or nab a stool by the bar. Craft beers from Two Birds Brewing are on tap, and you can even order in a gourmet burger from Flipside (Click here ) downstairs.
Ezra Pound BAR
OFFLINE MAP GOOGLE MAP
(www.epbar.com.au; 189 William St; 1pm-midnight Thu-Tue) Down a much-graffitied lane leading off William St, Ezra Pound is favoured by Northbridge's bohemian set. It's the kind of place where you can settle into a red velvet chair and sup a Tom Collins out of a jam jar. Earnest conversations about Kerouac and Kafka are strictly optional.
399 BAR
OFFLINE MAP GOOGLE MAP
(www.399bar.com; 399 William St; 10am-midnight Mon-Sat, to 10pm Sun; ) This friendly neighbourhood bar has booths along one side and a long bar down the other, making it easy to interact with the engaging bar staff. Cocktails are artfully crafted, and there's a serious approach to beer and wine. Good-value tapas are three for $19, and 399 is also a good espresso and wi-fi stop during the day.
The Brisbane PUB
OFFLINE MAP GOOGLE MAP
(www.thebrisbanehotel.com.au; 292 Beaufort St; 11.30am-late) It was a very clever architect indeed who converted this classic corner pub (1898) into a thoroughly modern venue, where each space seamlessly blends into the next. Best of all is the large courtyard where the phoenix palms and ponds provide a balmy holiday feel. Dining, shooting pool or lazing on a lounge are all options.
Brass Monkey PUB
OFFLINE MAP GOOGLE MAP
(www.thebrassmonkey.com.au; cnr James & William Sts; 11am-1am Wed-Sat, to 10pm Sun) A massive 1897 pub with several different component parts, each with its own vibe: sit up on a stool at the bar, lean back in the relaxed beer garden, or hunker down on a chesterfield by the fire (and sports screen). Semidetached GrapeSkin is the Monkey's (slightly) more upmarket wine and tapas bar.
The Bird BAR
OFFLINE MAP GOOGLE MAP
(http://williamstreetbird.com; 181 William St; 1pm-midnight) Grungy indie bar that's always worth a look for local bands and DJs. Upstairs there's a bricklined deck with city views.
Air CLUB
OFFLINE MAP GOOGLE MAP
(www.airclub.com.au; 139 James St; from 9pm Fri & Sat) Serious clubbers head here for nonstop house, techno and trance.
Geisha CLUB
OFFLINE MAP GOOGLE MAP
(www.geishabar.com.au; 135a James St; 11pm-6am Fri & Sat) A small-and-pumping DJ-driven, gay-friendly club; the vibe's usually music-focused and chilled out.
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6 Highgate & Mt Lawley
Five Bar CRAFT BEER, CAFE
OFFLINE MAP GOOGLE MAP
(www.fivebar.com.au; 560 Beaufort St; 11am-midnight) More than 50 international and Australian craft beers – and a few interesting ciders – make Mt Lawley's Five Bar worth seeking out by the discerning drinker. Wine lovers are also well catered for, and the menu leans towards classy comfort food _._
Must Winebar WINE BAR
OFFLINE MAP GOOGLE MAP
(www.must.com.au; 519 Beaufort St; noon-midnight) With cool French house music pulsing through the air and the perfect glass of wine in your hand (40 offerings by the glass, 500 on the list), Must is hard to beat. Upstairs is an exclusive, bookings-only Champagne bar.
Luxe COCKTAIL BAR
OFFLINE MAP GOOGLE MAP
(www.luxebar.com; 446 Beaufort St; 8pm-late Wed-Sun) With retro wood panelling, big, sexy lounge chairs and velvet curtains, Luxe is knowingly hip. It's also armed with turntables, and the gregarious bar staff are good for a chat while they shake their stuff.
Queens PUB
OFFLINE MAP GOOGLE MAP
(www.thequeens.com.au; 520 Beaufort St; 10am-midnight Mon-Sat, to 10pm Sun) Big, nicely renovated Federation-style pub, popular on Sunday. A cold beer in the dappled courtyard is the standard routine.
Flying Scotsman PUB
OFFLINE MAP GOOGLE MAP
(www.theflyingscotsman.com.au; 639 Beaufort St; 11am-midnight) Old-style pub that attracts the Beaufort St indie crowd. A good spot before a gig up the road at the Astor.
Velvet Lounge PUB
OFFLINE MAP GOOGLE MAP
(www.theflyingscotsman.com.au; 639 Beaufort St) Out the back of the Flying Scotsman is this small, red-velvet-clad lounge with ska, punk and indie beats. Upstairs, the Defectors bar channels cocktails and chilled dub and dance beats.
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6 Leederville
Leederville Hotel PUB
OFFLINE MAP GOOGLE MAP
(www.leedervillehotel.com; 742 Newcastle St; 11am-late) The good old Leederville has been turning out beers and Jägerbombs for many years. The something-for-everyone philosophy is etched out in the sports screens, dance floors and pool tables. Wednesday is big with the younger folk, and Retro Friday is the go for any lapsed 1980s New Romantics. Next door is the Garden, the Leederville's decent stab at a 21st-century gastropub.
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6 Subiaco & Kings Park
Subiaco Hotel PUB
(www.subiacohotel.com.au; 465 Hay St; 11am-late) The Subi's the locals' institution of choice for a morning coffee with the papers or a pre-footy beer. Middie-clutching men perch themselves for hours in the side bar, friends banter in lounges by the central bar and the Sunday sundowner crowd settle into the sun-speckled courtyard to squeeze the last drops out of the weekend.
Old Brewery MICROBREWERY
(www.theoldbrewery.com.au; 173 Mounts Bay Rd; noon-late) Cowhide stools gather around the bar, gazing towards the shiny copper vats making the magic (ales and wheat beers, actually), carrying on the tradition of the Swan Brewery, which opened on this site in 1879. It's the perfect place for a riverside sundowner. Check the website for regular seasonal brews.
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6 Beaches
Elba BAR
(www.elbacottesloe.com.au; 29 Napoleon St; 3pm-late Mon-Thu, noon-late Fri-Sun) In the swanky residential part of Cottesloe, not the chilled-out beach strip, Elba has taken its street name as inspiration and produced a slick Napoleonic bar complete with a gilt-framed portrait of the little man. Come dressed for cocktails, although perhaps in flat shoes out of deference. Small plates (obviously) complete the picture for a worthwhile evening assignation.
Cottesloe Beach Hotel PUB
(www.cottesloebeachhotel.com.au; 104 Marine Pde; 11am-midnight Mon-Sat, to 10pm Sun) Grab a spot on the lawn in the massive beer garden, or watch the sun set from the balcony. Sunday is big. A recent trendy makeover has installed a specialist craft-beer bar downstairs.
Ocean Beach Hotel PUB
(www.obh.com.au; cnr Marine Pde & Eric St; 11am-midnight Mon-Sat, to 10pm Sun) Backpackers and locals drink up the beer and soak up the sun at this rambling beachside pub, especially on Sunday.
3 Entertainment
Live Music
Ellington Jazz Club LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(www.ellingtonjazz.com.au; 191 Beaufort St; 7pm-1am Mon-Thu, to 3am Fri & Sat, 5pm-midnight Sun) There's live jazz nightly in this handsome, intimate venue. Standing-only admission is $10, or you can book a table (per person $15) for tapas and pizza.
Perth Arena LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(www.pertharena.com.au; 700 Wellington St) Opened in November 2012, and used for big concerts by major international acts like Elton John and Russell Brand. It's also used by the Perth Wildcats NBL basketball franchise.
The Bakery LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(www.nowbaking.com.au; 233 James St; 7pm-late) Run by Artrage, Perth's contemporary arts festival body, the Bakery draws an arty crowd. Popular indie gigs are held almost every weekend.
Amplifier LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(www.amplifiercapitol.com.au; rear 383 Murray St) The good old Amplifier is one of the best places for live (mainly indie) bands. Part of the same complex is Capitol, used mainly for DJ gigs.
The Moon LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(www.themoon.com.au; 323 William St; 6pm-late Mon-Tue, 11am-late Wed-Sun) Low-key, late-night cafe with singer-songwriters on Wednesday, jazz on Thursday, poetry slams on Saturday afternoon and '10 Minute Tuesday', when it's guaranteed that 10 minutes of oddness will occur.
Universal LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(www.universalbar.com.au; 221 William St; 7am-late) The unpretentious Universal is one of Perth's oldest bars and much-loved by jazz and blues enthusiasts.
Rosemount Hotel LIVE MUSIC
(www.rosemounthotel.com.au; cnr Angove & Fitzgerald Sts, North Perth; noon-late) Local and international bands play regularly in this spacious art-deco pub with a laid-back beer garden.
Charles Hotel LIVE MUSIC
(www.charleshotel.com.au; 509 Charles St, North Perth) Hosts lots of live music, including the Legendary Perth Blues Club on Tuesday.
Astor CONCERT VENUE
OFFLINE MAP GOOGLE MAP
(www.liveattheastor.com.au; 659 Beaufort St) The beautiful art-deco Astor still screens the odd film but is mainly used for concerts these days.
Cabaret & Comedy
Devilles Pad CABARET
OFFLINE MAP GOOGLE MAP
(www.devillespad.com; 3 Aberdeen St; 6pm-midnight Thu, to 2am Fri & Sat) The devil goes to Vegas disguised as a 1950s lounge lizard in this extremely kooky venue. Punters are encouraged to dress to match the camp interiors (complete with erupting volcano). Burlesque dancers, live bands and assorted sideshow freaks provide the entertainment, and good food is available. Thursday is rock 'n' roll karaoke night, so bring along your Elvis A-game.
Lazy Susan's Comedy Den COMEDY
OFFLINE MAP GOOGLE MAP
(www.lazysusans.com.au; 292 Beaufort St; 8.30pm Tue, Fri & Sat) Shapiro Tuesday offers a mix of first-timers, seasoned amateurs and pros trying out new shtick (for a very reasonable $5). Friday is for more grown-up stand-ups, including some interstaters. Saturday is the Big Hoohaa – a team-based comedy wrassle. The Den is at the Brisbane Hotel.
### GAY & LESBIAN PERTH
Perth is home to all of WA's gay and lesbian venues. Before you get excited, let's clarify matters: it has precisely two bars, one club and one men's sauna. Many other bars, especially around Highgate and Mt Lawley, are somewhat gay-friendly, but it's hardly what you'd call a bustling scene.
For a head's up on what's on, pick up the free monthly newspaper Out In Perth (www.outinperth.com) . Perth Pride (www.pridewa.asn.au) runs a three-week festival in October, starting with a fair day and culminating in the Pride Parade.
The Court OFFLINE MAP GOOGLE MAP (www.thecourt.com.au; 50 Beaufort St, Northbridge; noon-midnight Sun-Thu, to 2am Fri & Sat) A large, rambling complex consisting of an old corner pub and a big, partly covered courtyard with a clubby atmosphere. Wednesday is drag night, with kings and queens holding court in front of a young crowd.
Connections OFFLINE MAP GOOGLE MAP (www.connectionsnightclub.com; 81 James St, Northbridge; 10pm-late Wed, Fri & Sat) Reputedly the oldest surviving gay-and-lesbian venue in Australia, Connections keeps on keeping on, with DJs, drag shows and the occasional bit of lesbian mud wrestling.
Honey Lounge OFFLINE MAP GOOGLE MAP (663 Newcastle St, Leederville; Tue-Sun) Ladies only on Queen Bee nights, the first Thursday of every month.
Perth Steam Works OFFLINE MAP GOOGLE MAP (www.perthsteamworks.com.au; 369 William St, Northbridge; admission $21; noon-1am Sun-Thu, to 3am Fri & Sat) Gay men's sauna. Entry on Forbes St.
Theatre & Classical Music
Check the _West Australian_ for what's on. Book through www.ticketek.com.au.
His Majesty's Theatre THEATRE
OFFLINE MAP GOOGLE MAP
(www.hismajestystheatre.com.au; 825 Hay St) The majestic home to the West Australian Ballet (www.waballet.com.au) and West Australian Opera (www.waopera.asn.au) , as well as lots of theatre, comedy and cabaret.
Perth Concert Hall CONCERT HALL
OFFLINE MAP GOOGLE MAP
(www.perthconcerthall.com.au; 5 St Georges Tce) Home to the Western Australian Symphony Orchestra (WASO; www.waso.com.au) .
State Theatre Centre THEATRE
OFFLINE MAP GOOGLE MAP
(www.statetheatrecentrewa.com.au; 174 William St) Opened in 2011, this flash new complex includes the 575-seat Heath Ledger Theatre and the 234-seat Studio Underground. It's home to the Black Swan State Theatre Company and Perth Theatre Company.
Subiaco Arts Centre THEATRE
OFFLINE MAP GOOGLE MAP
(www.subiacoartscentre.com.au; 180 Hamersley Rd) Indoor and outdoor theatres used for drama and concerts; home to Barking Gecko young people's theatre (www.barkinggecko.com.au).
Regal Theatre THEATRE
OFFLINE MAP GOOGLE MAP
(www.regaltheatre.com.au; 474 Hay St) Popular musicals and stage shows.
Cinema
Somerville Auditorium CINEMA
(www.perthfestival.com.au; 35 Stirling Hwy; Dec-Mar) A quintessential Perth experience, the Perth Festival's film program is held here on the University of WA's beautiful grounds surrounded by pines. Picnicking before the film is a must.
Luna CINEMA
OFFLINE MAP GOOGLE MAP
(www.lunapalace.com.au; 155 Oxford St) Art-house cinema with Monday double features and a bar. Screens outdoor movies in summer.
Cinema Paradiso CINEMA
OFFLINE MAP GOOGLE MAP
(www.lunapalace.com.au; 164 James St) Art-house cinema in the Galleria complex.
Ace Subiaco CINEMA
OFFLINE MAP GOOGLE MAP
(www.moviemasters.com.au; 500 Hay St) Four-screen multiplex screening Hollywood fare.
Moonlight Cinema CINEMA
(www.moonlight.com.au; Synergy Parklands, Kings Park) Bring a picnic and blanket and enjoy a romantic moonlit movie; summer only.
Camelot Outdoor Cinema CINEMA
(www.lunapalace.com.au; 16 Lochee St, Memorial Hall; Dec-Easter) Seated open-air cinema in Mosman Park.
Sport
In WA 'football' means Aussie Rules and during the Australian Football League (AFL) season it's hard to get locals to talk about anything but the two local teams – the West Coast Eagles (www.westcoasteagles.com.au) and the Fremantle Dockers (www.fremantlefc.com.au) – and the joy of beating 'the Vics' (any Victorian team is considered an arch-enemy). Rugby League (considered an east-coast game) doesn't get a look in, even during the finals season.
Patersons Stadium FOOTBALL
OFFLINE MAP GOOGLE MAP
(Subiaco Oval; 08-9381 2187; www.patersonsstadium.com.au; 250 Roberts Rd) The home of Aussie Rules and huge concerts; you're guaranteed a great atmosphere.
WACA CRICKET
OFFLINE MAP GOOGLE MAP
(Western Australian Cricket Association; 9265 7222; www.waca.com.au; Nelson Cres) In summer, cricket fans while away lazy afternoons here watching a test or state match.
NIB Stadium SOCCER, RUGBY
OFFLINE MAP GOOGLE MAP
(Perth Oval; www.nibstadium.com.au; Lord St) Both the Perth Glory (www.perthglory.com.au) soccer (football) team and the Western Force (www.westernforce.com.au) Super 15 rugby union team play here, and it's the home of WA rugby league.
Challenge Stadium NETBALL
(www.venueswest.wa.gov.au; Stephenson Ave, Mt Claremont) Home to the West Coast Fever (www.westcoastfever.com.au) netball team.
7 Shopping
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7 City Centre
Murray St and Hay St Malls are the city's shopping heartland, while King St is the place for swanky boutiques. London Court arcade has opals and souvenirs.
Wheels & Doll Baby CLOTHING
OFFLINE MAP GOOGLE MAP
(www.wheelsanddollbaby.com; 26 King St; 10am-6pm Mon-Sat, 11am-5pm Sun) Punky rock-chick chic with a bit of baby doll mixed in. Perhaps Perth fashion's coolest export, and worn by Courtney Love, Katy Perry and Debbie Harry.
Pigeonhole CLOTHING, ACCESSORIES
OFFLINE MAP GOOGLE MAP
(www.pigeonhole.com.au; Shop 16, Bon Marche Arcade, 80 Barrack St; 10am-5.30pm Mon-Sun) Hip clothing, and stylish retro accessories and gifts. There are five stores around the city – the main store is adjacent to the associated Cabin Fever (Click here ) cafe in Bon Marche Arcade – and Pigeonhole's Shop 9 OFFLINE MAP (Shop 9; 9 Shafto Lane; 10am-6pm Mon-Sun, to 9pm Fri) features local and international fashion.
78 Records MUSIC
OFFLINE MAP GOOGLE MAP
(www.78records.com.au; upstairs 255 Murray St Mall; 9am-5pm Mon-Sat, from 11am Sun) Independent record shop with a massive range of CDs and lots of specials. Also good for vinyl and tickets to rock and indie gigs.
Elizabeth's Bookshop BOOKS
OFFLINE MAP GOOGLE MAP
(www.elizabethsbookshop.com.au; 820 Hay St; 9am-7pm) Fremantle institution's city-centre branch with lots of second-hand tomes.
Perth Map Centre BOOKS, MAPS
OFFLINE MAP GOOGLE MAP
(www.mapworld.com.au; 900 Hay St; 9am-5.30pm Mon-Fri, 10am-3pm Sun) Maps and travel guides.
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7 Northbridge, Highgate & Mt Lawley
William Topp DESIGN
(www.williamtopp.com; 452 William St; 11am-6pm Tue-Fri, to 5pm Sat & 4pm Sun) Lots of cool knick-knacks.
Planet BOOKS, MUSIC
OFFLINE MAP GOOGLE MAP
(www.planetvideo.com.au; 636-638 Beaufort St; 10am-late) Stacked with books, CDs and lots of obscure DVDs. Pop next door for coffee and cake at its new Daily Planet cafe.
Future Shelter HOMEWARES
(www.futureshelter.com; 56 Angove St, North Perth; 10am-6pm Mon-Sat) Quirky clothing, gifts and homewares designed and manufactured locally. Surrounding Angove St is an emerging hip North Perth neighbourhood.
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7 Leederville
Leederville's Oxford St is the place for groovy boutiques, eclectic music and bookshops.
Atlas Divine CLOTHING
OFFLINE MAP GOOGLE MAP
(www.atlasdivine.com; 121 Oxford St; 9am-9pm) Hip women's and men's clobber: jeans, quirky tees, dresses etc.
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7 Subiaco & Kings Park
Upmarket Rokeby Rd and Hay St boast fashion, art and classy gifts.
Indigenart INDIGENOUS ART
OFFLINE MAP GOOGLE MAP
(www.mossensongalleries.com.au; 115 Hay St; 10am-5pm Mon-Fri, 11am-4pm Sat) Reputable Indigenart carries art from around the country but with a particular focus on WA artists. Works include weavings, paintings on canvas, bark and paper, sculpture and limited-edition prints. See Click here for guidelines on the ethical purchase of Aboriginal art.
Aboriginal Art & Craft Gallery INDIGENOUS ART
(www.aboriginalgallery.com.au; Fraser Ave; 10.30am-4.30pm Mon-Fri, 11am-4pm Sat-Sun) Has a mixture of work from around WA; tends to be more populist than high-end or collectable.
Aspects of Kings Park ART, SOUVENIRS
(www.aspectsofkingspark.com.au; Fraser Ave; 9am-5pm) Australian art, craft and books.
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7 Other Areas
æ'lkemi CLOTHING
(www.aelkemi.com; Times Square Centre, 337 Stirling Hwy; 10am-5.30pm Mon-Sat) Top WA designer's signature store, showcasing his feminine frocks and distinctive prints.
Karrinyup MALL
(www.karrinyupcentre.com.au; 200 Karrinyup Rd) Big mall east of Trigg Beach.
Garden City MALL
(www.gardencity.com.au; 125 Riseley St) Another large shopping centre; south of the river.
8 Information
Emergency
Police Station ( 13 14 44; www.police.wa.gov.au; 60 Beaufort St)
Sexual Assault Resource Centre ( 08-9340 1828, freecall 1800 199 888; www.kemh.health.wa.gov.au/services/sarc; 24hr)
Internet Access
State Library of WA (www.slwa.wa.gov.au; Perth Cultural Centre; 9am-8pm Mon-Thu, 10am-5.30pm Fri-Sun; ) Free wi-fi and internet access. At the time of writing, Perth City was also trialling free wi-fi access in the Murray Street Mall between William St and Barrack St.
Media
Look for free listings booklets, such as _Your_ _Guide_ _to_ _Perth & Fremantle, _ available at hostels, hotels and tourist offices.
Drum Media (www.facebook.com/drumperth) Music, film and culture listings.
Go West (www.gowesternaustralia.com.au) Backpacker magazine with information on activities throughout WA and seasonal work opportunities.
Urban Walkabout (www.urbanwalkabout.com) Handy free pocket guides covering hip eating, drinking and shopping spots in key inner-Perth neighbourhoods and Fremantle.
West Australian (www.thewest.com.au) Local newspaper with entertainment and cinema listings.
X-Press Magazine (www.xpressmag.com.au) Long-running street press and a good source of live-music information.
Medical Services
Lifecare Dental ( 08-9221 2777; www.dentistsinperth.com.au; 419 Wellington St; 8am-8pm) In Forrest Chase.
Royal Perth Hospital ( 08-9224 2244; www.rph.wa.gov.au; Victoria Sq) In the CBD.
Travel Medicine Centre ( 08-9321 7888; www.travelmed.com.au; 5 Mill St; 8am-5pm Mon-Fri) Travel-specific advice and vaccinations.
Money
ATMs are plentiful, and there are currency- exchange facilities at the airport and major banks in the CBD.
Post
Main Post Office (GPO; 13 13 18; 3 Forrest Pl; 8.30am-5pm Mon-Fri, 9am-12.30pm Sat)
Tourist Information
i-City Information Kiosk OFFLINE MAP GOOGLE MAP (Murray Street Mall; 9.30am-4.30pm Mon-Thu & Sat, to 8pm Fri, 11am-3.30pm Sun) Volunteers answer your questions and run walking tours.
WA Visitor Centre OFFLINE MAP GOOGLE MAP ( 08-9483 1111, 1800 812 808; www.bestofwa.com.au; 55 William St; 9am-5.30pm Mon-Fri, 9.30am-4.30pm Sat, 11am-4.30pm Sun) A good resource for a trip anywhere in WA.
Websites
www.heatseeker.com.au Gig guide and ticketing.
www.perth.citysearch.com.au Entertainment and restaurants.
www.perthnow.com.au Perth and WA news and restaurant reviews
www.scoop.com.au Entertainment.
www.showticketing.com.au Gig guide and ticketing.
www.whatson.com.au Events and travel information.
8 Getting There & Away
Air
For details on flights to Perth from international, interstate and other WA destinations, see the Transport chapter ( Click here and Click here ).
Bus
Greyhound ( 1300 473 946; www.greyhound.com.au) has services from the East Perth terminal to Broome ($277 to $431, 34 hours, thrice weekly) via Geraldton, Carnarvon, Karratha and Port Hedland.
Integrity Coach Lines OFFLINE MAP GOOGLE MAP ( 08-9574 6707; www.integritycoachlines.com.au; Wellington Street Bus Station) runs services between Perth and Port Hedland ($232, 22 hours, weekly) via Mt Magnet, Cue, Meekatharra and Newman. Also has a service from Perth to Geraldton on Indian Ocean Dr via Lancelin, Jurien Bay and Cervantes.
South West Coach Lines ( 08-9261 7600; www.veoliatransportwa.com.au) focuses on the southwestern corner of WA, running services from the Esplanade Busport (some stopping at the airport) to most towns in the region, including:
Dunsborough (four hours, daily) via Mandurah, Bunbury and Busselton.
Augusta (five hours, daily) via Bunbury, Busselton, Cowaramup and Margaret River.
Manjimup (five hours, daily except weekends) via Mandurah, Bunbury, Balingup and Bridgetown.
Transwa ( 1300 662 205; www.transwa.wa.gov.au) operates services from the bus terminal at East Perth train station to/from many destinations around the state. These include:
SW1 to Augusta ($48, six hours, 12 per week) via Mandurah, Bunbury, Busselton and Dunsborough.
SW2 to Pemberton ($51, 5½ hours, thrice weekly) via Bunbury, Balingup and Bridgetown.
GS1 to Albany ($58, six hours, daily) via Mt Barker.
GE2 to Esperance ($87, 10 hours, thrice weekly) via Mundaring, York and Hyden.
N1 to Geraldton ($61, six hours, daily) and on to Northampton and Kalbarri ($76, 8½ hours, three weekly).
Train
Transwa runs the following services:
Australind (twice daily) Perth to Pinjarra ($16, 1¼ hours) and Bunbury ($30, 2½ hours).
AvonLink (thrice weekly) East Perth to Toodyay ($16, 1¼ hours) and Northam ($19, 1½ hours).
Prospector (daily) East Perth to Kalgoorlie–Boulder ($82, seven hours).
8 Getting Around
To/From the Airport
The domestic and international terminals of Perth's airport are 10km and 13km east of Perth respectively, near Guildford. Taxi fares to the city are around $40 from the domestic and international terminals, and about $60 to Fremantle.
Connect ( 1300 666 806; www.perthairportconnect.com.au) runs shuttles to and from hotels and hostels in the city centre (one way/return $18/30, every 50 minutes) and in Fremantle (one way/return $33/58, approximately every 1½ hours). Prices are slightly cheaper between Perth and the domestic terminal and substantially discounted for groups of two to four people (check the website for details). Bookings are essential for all services to the airport and are recommended for services to Fremantle. No bookings are taken for shuttles from the airport to Perth's city centre.
Transperth bus 37 travels to the domestic airport from St Georges Tce, near William St ($4, 55 minutes, every 10 to 30 minutes, hourly after 7pm).
Car & Motorcycle
Driving in the city takes a bit of practice, as some streets are one way and many aren't signed. There are plenty of car-parking buildings in the central city but no free parks. For unmetered street parking you'll need to look well away from the main commercial strips and check the signs carefully.
A fun way to gad about the city is on a moped. Scootamoré ( 08-9380 6580; www.scootamore.com.au; 356a Rokeby Rd, Subiaco; day/week/month $45/200/400) hires 50cc scooters with helmets (compulsory) and insurance included (for those over 21, $500 excess).
Public Transport
Transperth ( 13 62 13; www.transperth.wa.gov.au) operates Perth's public buses, trains and ferries. There are Transperth information offices at Perth station (Wellington St), Wellington St bus station, Perth underground station (off Murray St) and the Esplanade Busport (Mounts Bay Rd). There's a good online journey planner.
From the central city, the following fares apply for all public transport:
Free Transit Zone (FTZ) Covers the central commercial area, bounded (roughly) by Fraser Ave, Kings Park Rd, Thomas St, Newcastle St, Parry St, Lord St and the river (including the City West and Claisebrook train stations, to the west and east respectively).
Zone 1 Includes the city centre and the inner suburbs ($2.70).
Zone 2 Fremantle, Guildford and the beaches as far north as Sorrento ($4).
Zone 3 Hillarys Boat Harbour (AQWA), the Swan Valley and Kalamunda ($4.90).
Zone 5 Rockingham ($7.10).
Zone 7 Mandurah ($9.40).
DayRider Unlimited travel after 9am weekdays and all day on the weekend in any zone ($11).
FamilyRider Lets two adults and up to five children travel for a total of $11 on weekends, after 6pm weekdays and after 9am on weekdays during school holidays.
If you're in Perth for a while, consider buying a SmartRider card, covering bus, train and ferry travel. It's $10 to purchase, then you add value to your card. The technology deducts the fare as you go, as long as you tap in and tap out (touch your card to the electronic reader) every time you travel, including within the FTZ. The SmartRider works out 15% cheaper than buying single tickets and automatically caps itself at the DayRider rate if you're avoiding the morning rush hour.
Bus
As well as regular buses the FTZ is well covered during the day by the three free Central Area Transit (CAT) services. The Yellow and Red CATs operate east–west routes, Yellow sticking mainly to Wellington St, and Red looping roughly east on Murray St and west on Hay St. The Blue Cat does a figure eight through Northbridge and the south end of the city; this is the only one to run late – until 1am on Friday and Saturday nights only. Pick up a copy of the free timetable (widely available on buses and elsewhere) for the exact routes and stops. They run every five to eight minutes during weekdays and every 15 minutes on weekends. Digital displays at the stops advise when the next bus is due.
The metropolitan area is serviced by a wide network of Transperth buses. Pick up timetables from any of the Transperth information centres or use the online journey planner.
Ferry
The only ferry runs every 20 to 30 minutes between Barrack Street Jetty and Mends Street Jetty in South Perth – use it to get to the zoo or for a bargain from-the-river glimpse of the Perth skyline.
Train
Transperth operates five train lines from around 5.20am to midnight weekdays, and until about 2am Saturday and Sunday. Your rail ticket can also be used on Transperth buses and ferries within the ticket's zone. You're free to take your bike on the train in nonpeak times. The lines and useful stops include:
Armadale Thornlie Line Perth, Burswood.
Fremantle Line Perth, City West, West Leederville, Subiaco, Shenton Park, Swanbourne, Cottesloe, North Fremantle, Fremantle.
Joondalup Line Esplanade, Perth Underground, Leederville.
Mandurah Line Perth Underground, Esplanade, Rockingham, Mandurah.
Midland Line Perth, East Perth, Mt Lawley, Guildford, Midland.
Taxi
Perth has a decent system of metered taxis, though the distances make frequent use costly and on busy nights you may have trouble flagging one down off the street. The two main companies are Swan Taxis ( 13 13 30; www.swantaxis.com.au) and Black & White ( 13 10 08; www.bwtaxi.com.au) ; both have wheelchair-accessible cabs.
## Fremantle
pop 28,100
Creative, relaxed, open-minded: Fremantle's spirit is entirely distinct from Perth's. Perhaps it has something to do with the port and the city's working-class roots. Or the hippies, who first set up home here a few decades ago and can still be seen casually bobbling down the street on old bicycles. Or perhaps it's just that a timely 20th-century economic slump meant that the city retained an almost complete set of formerly grand Victorian and Edwardian buildings, creating a heritage precinct that's unique among Australia's cities today.
Whatever, today's clean and green Freo makes a cosy home for performers, professionals, artists and more than a few eccentrics. There's a lot to enjoy here – fantastic museums, edgy galleries, pubs thrumming with live music and a thriving coffee culture. On weekend nights the city's residents vacate the main drag, leaving it to kids from the suburbs, who move in to party hard and loud.
### FREMANTLE FOR CHILDREN
You can let the littlies off the leash at Esplanade Reserve, watch buskers at the market, make sand castles at Bathers Beach or have a proper splash about at South or Port Beaches. Older kids might appreciate the creepier aspects of the prison and the innards of the submarine at the Maritime Museum, where they can also poke about on actual boats. Adventure World ( Click here ) is nearby for funfair rides. Finish up with fish and chips at Fishing Boat Harbour.
History
This was an important area for the Wadjuk Noongar people, as it was a hub of trading paths. Some of these routes exist to this day in the form of modern roads. Before the harbour was altered, the mouth of the river was nearly covered by a sandbar and it was only a short swim from north to south. The confluence of the river and ocean, where Fremantle now stands, was known as Manjaree (sometimes translated as 'gathering place'). The Fremantle coast was called Booyeembara, while inland was Wallyalup, 'place of the eagle'.
Manjaree was mainly occupied in summer when the Wadjuk would base themselves here to fish. In winter they would head further inland, avoiding seasonal flooding.
Fremantle's European history began when the ship HMS _Challenger_ landed in 1829. The ship's captain, Charles Fremantle, took possession of the whole of the west coast 'in the name of King George IV'. Like Perth, the settlement made little progress until convict labour was used. Convicts constructed most of the town's earliest buildings; some of them, such as the Round House, Fremantle Prison and Fremantle Arts Centre, are now among the oldest in WA.
As a port, Fremantle wasn't up to much until the engineer CY O'Connor created an artificial harbour in the 1890s, destroying the Wadjuks' river crossing in the process. This caused such disruption to their traditional patterns of life that it's said that a curse was placed on O'Connor; some took his later suicide at Fremantle as evidence of its effectiveness.
The port blossomed during the gold rush and many of its distinctive buildings date from this period. Economic stagnation in the 1960s and 1970s spared the streetscape from the worst ravages of modernisation. It wasn't until 1987, when Fremantle hosted the America's Cup, that it transformed itself from a sleepy port town into today's vibrant, artsy city.
The cup was lost that year, but the legacy of a redeveloped waterfront remains. In 1995 the Fremantle Dockers played their first game, quickly developing one of the most fanatical fan bases in the AFL, boosted in 2010 and 2012 by a semifinals berth. We reckon it's only a matter of time before they go all the way.
1 Sights
Fremantle Prison HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
( 08-9336 9200; www.fremantleprison.com.au; 1 The Terrace; torchlight tours $25/21; 9am-5.30pm) With its foreboding 5m-high walls enclosing a nearly 6-hectare site, the old convict-era prison still dominates present-day Fremantle, with its tales of adventure and hardship living on in the city's imagination. In 2010 its cultural status was recognised, along with that of 10 other penal buildings, as part of the Australian Convict Sites entry on the Unesco World Heritage list.
Fremantle
Top Sights
1 Fremantle Prison F2
2 Western Australian Museum – MaritimeA2
3 Western Australian Museum – Shipwreck GalleriesB3
Sights
4 Bon Scott StatueC3
5 Chamber of Commerce BuildingC2
6 Customs House B2
7 Esplanade Hotel D3
8 Esplanade Reserve C3
9 Fremantle Grammar School F1
10 Fremantle Markets D3
11 Fremantle Train Station C1
John Curtin Statue(see 17)
12 Mark of the Century E2
13 Old German Consulate C2
Pietro Porcelli Statue(see 15)
14 Round House B3
15 St John's Anglican Church D2
16 To the Fishermen C4
17 Town Hall D2
Activities, Courses & Tours
Fremantle Tram Tours (see 17)
18 Oceanic Cruises B1
19 STS Leeuwin II B2
Sleeping
20 Bannister Suites Fremantle D2
21 Fothergills of Fremantle F1
22 Fremantle Colonial Accommodation E1
23 Norfolk Hotel E3
24 Old Firestation Backpackers C2
25 Pirates D3
26 Port Mill B&B D3
27 Terrace Central B&B Hotel E3
Eating
28 Cafe 55 C2
29 Cicerello's B3
30 Gino's D2
31 iPho D3
32 Juicy Beetroot D2
33 Kakulas Sister C2
34 Little Creatures C4
35 Maya D2
36 Moore & Moore C3
37 Wild Poppy E4
Drinking & Nightlife
Little Creatures (see 34)
Norfolk Hotel (see 23)
38 Sail & Anchor D2
39 The Monk D3
40 Whisper D3
41 Who's Your Mumma E4
Entertainment
42 Fly by Night Musicians Club E2
43 Hoyts D2
44 Kulcha D2
45 Luna on SX D3
46 Metropolis Fremantle D2
47 Newport Hotel D2
48 X-Wray Cafe D3
Shopping
49 Bill Campbell Secondhand Book SellerC2
50 Bodkin's Bootery C2
51 Chart & Map Shop D3
52 E Shed Markets B1
53 Elizabeth's Bookshop D2
Elizabeth's Bookshop (see 47)
Japingka (see 28)
54 Jarrahcorp C2
55 Love in Tokyo C2
56 Mills Records D2
57 New Edition C2
58 Record Finder C2
Remedy (see 58)
Information
59 TravelLoungeC1
60 Visitor CentreD2
Transport
61 Oceanic Cruises B1
62Rottnest ExpressB1
The first convicts were made to build their own prison, constructing it from beautiful pale limestone dug out of the hill on which it was built. From 1855 to 1991, 350,000 people were incarcerated here, although the highest numbers held at any one time were 1200 men and 58 women. Of those, 43 men and one woman were executed on-site, the last of which was serial killer Eric Edgar Cooke in 1964.
Entry to the gatehouse, including the Prison Gallery, gift shop (where you can purchase fetching arrow-printed prisoner PJs) and Convict Cafe is free. To enter the prison proper, you'll need to take a tour. During the day there are two fascinating 1¼-hour tours on offer, timed so that you can take one after the other on a combined ticket (single tour adult/child $19/10, combined adult/child $26/17), although you can return for the second tour anytime in the next fortnight.
The Doing Time Tour (departs every 30 minutes, first 10am, last 5pm) takes in the kitchens, men's cells (the original 2.1m by 1.2m convict cells are smaller than modern toilets), the black-as-hell solitary-confinement cells (the longest anyone did here was six months on bread and water), the exercise areas, the whipping post (people could be sentenced to up to 100 lashes of the cat o' nine tails, although most would die after 30), the gallows, an interesting display on the 1988 riot, and the big, light-filled chapel (daily attendance was compulsory).
The Great Escapes Tour (departs every hour, first 11.45am, last 4.45pm) introduces you to famous inmates such as bushranger and famed escape artist Moondyne Joe and bank robber Brenden Abbott, who escaped in a prison guard's uniform. It also takes in the women's prison and the rifle range.
Bookings are required for the two more intense experiences on offer. Torchlight Tours (90 minutes, adult/child $25/21, Wednesday and Friday evenings) are designed to chill, focusing on the creepy and unpleasant aspects of the prison's history. The 2½-hour Tunnels Tour (adult/child over 12yr $60/40) takes you 20m underground to tunnels built by prisoners sentenced to hard labour. You'll be kitted out in overalls and hard hats with headlamps for the descent, which includes an underground boat ride. Children must be 12 years or older for the Tunnels Tour.
Western Australian Museum – Maritime MUSEUM
OFFLINE MAP GOOGLE MAP
(www.museum.wa.gov.au; Victoria Quay; museum adult/child $10/3, submarine $10/3, museum & submarine $16/5; 9.30am-5pm) Housed in an intriguing sail-shaped building on the harbour, just west of the city centre, this is a fascinating exploration of WA's relationship with the ocean. It faces out to the sea, which has shaped so much of the state's, and Fremantle's, destiny.
Various boats are on display, including Australia II, the famous winged-keel yacht that won the America's Cup yachting race in 1983 (ending 132 years of American domination of the competition – an achievement which is the source of much Sandgroper pride). Other boats on show include an Aboriginal bark canoe; an Indonesian outrigger canoe, introduced to the Kimberley and used by the Indigenous people; and a pearl lugger used in Broome. Even a classic 1970s panel van (complete with fur lining) makes the cut – because of its status as the surfer's vehicle of choice.
Well-presented displays cover a wide range of topics, from Aboriginal fish traps to the sandalwood trade. If you're not claustrophobic, take an hour-long tour of the submarine HMAS _Ovens_ . The vessel was part of the Australian Navy's fleet from 1969 to 1997. Tours leave every half-hour from 10am to 3.30pm.
Western Australian Museum – Shipwreck Galleries MUSEUM
OFFLINE MAP GOOGLE MAP
(www.museum.wa.gov.au; Cliff St; admission by donation; 9.30am-5pm) F Housed in an 1852 commissariat store, the Shipwreck Galleries is considered the finest display of maritime archaeology in the southern hemisphere. The highlight of the display is the Batavia Gallery , where a section of the hull of Dutch merchant ship _Batavia,_ wrecked in 1629, is displayed. Nearby is a large stone gate, intended as an entrance to Batavia Castle, which was being carried when it sank.
Other items of interest include the inscribed pewter plate left on Cape Inscription by Willem de Vlamingh in 1697, positioned next to a replica of the plate left by Dirk Hartog in 1616 during the first confirmed European landing in WA.
Round House HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
( 08-9336 6897; www.fremantleroundhouse.com.au; admission by donation; 10.30am-3.30pm) F Commenced in 1830 and 1831, shortly after the founding of the colony, this odd 12-sided stone prison is the oldest surviving building in WA. It was the site of the colony's first hangings, including that of 15-year-old John Gavin (convicted of murdering his employer's son). Later, it was used for holding Aboriginal people before they were taken to Rottnest Island.
To the Noongar people, it's a sacred site because of the number of their people killed while incarcerated here. Freedom fighter Yagan was held here briefly in 1832.
On the hilltop outside is the Signal Station, where at 1pm daily a time ball and cannon blast were used to alert seamen to the correct time. The ceremony is re-enacted daily; book ahead if you want to fire the cannon.
Beneath is an impressive 1837 Whalers' Tunnel carved through sandstone and used for accessing Bathers Beach, where whales were landed and processed.
Fremantle Arts Centre GALLERY
(www.fac.org.au; 1 Finnerty St; 10am-5pm) F An impressive neo-Gothic building surrounded by lovely elm-shaded gardens, the Fremantle Arts Centre was constructed by convict labourers as a lunatic asylum in the 1860s. Saved from demolition in the 1960s, it houses interesting exhibitions and the 0excellent Canvas (Click here ) cafe. During summer there are concerts, courses and workshops.
Fremantle Markets MARKET
OFFLINE MAP GOOGLE MAP
(www.fremantlemarkets.com.au; cnr South Tce & Henderson St; 8am-8pm Fri, to 6pm Sat & Sun) F Originally opened in 1897, these colourful markets were reopened in 1975 and today draw slow-moving crowds, combing over souvenirs like plastic boomerangs and swan-shaped magnets. The fresh-produce section is a good place to stock up on snacks.
Gold Rush Buildings HISTORIC BUILDINGS
Fremantle boomed during the WA gold rush in the late 19th century, and many wonderful buildings remain that were constructed during, or shortly before, this period. High St, particularly around the bottom end, has some excellent examples including several old hotels.
Chamber of Commerce Building HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(16 Phillimore St) In its original use since 1873.
St John's Anglican Church CHURCH
OFFLINE MAP GOOGLE MAP
(Kings Sq) Built 1882.
Fremantle Grammar School HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(200 High St) Built as an Anglican public school in 1885.
Town Hall HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(Kings Sq) Opened on Queen Victoria's jubilee in 1887.
Samson House HISTORIC BUILDING
(cnr Ellen & Ord Sts) A well-preserved 1888 colonial home, owned by the National Trust but not currently open to the public.
Esplanade Hotel HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(Marine Tce) Attractive colonnaded hotel, built in 1896.
Old German Consulate HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(5 Mouat St) Built 1903; now a B&B.
Fremantle Train Station HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(Phillimore St) Built from Donnybrook sandstone in 1907; we're not sure why the swans are white rather than black.
Customs House HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(cnr Cliff & Phillimore Sts) Built in 1908 in a Georgian style.
Public Sculptures MONUMENTS
Enlivening Fremantle's streets are numerous bronze sculptures, many by local artist Greg James (www.gregjamessculpture.com). Perhaps the most popular, certainly with black-clad pilgrims, is the statue of Bon Scott OFFLINE MAP GOOGLE MAP (1946–80) strutting on a Marshall amplifier in Fishing Boat Harbour. The AC/DC singer moved to Fremantle with his family in 1956, and his ashes are interred in Fremantle Cemetery (Carrington St) ; it's reputedly the most-visited grave in Australia, with many travellers stopping in for 'a beer with Bon'. Enter the cemetery at the entrance near the corner of High and Carrington Sts. Bon's plaque is on the left around 15m along the path.
Also in Fishing Boat Harbour is To The Fishermen OFFLINE MAP GOOGLE MAP (Fishing Boat Harbour) , a cluster of bronze figures, unloading and carrying their catch up from the wharf. There's a lively statue of former member for Fremantle and wartime Labor prime minister John Curtin OFFLINE MAP GOOGLE MAP (1885–1945) in Kings Sq, outside the Town Hall. Nearby is a Greg James sculpture of fellow sculptor Pietro Porcelli OFFLINE MAP GOOGLE MAP (1872–1943), in the act of making a bust.
Another quirky bronze is Mark of the Century OFFLINE MAP GOOGLE MAP (Parry St) outside Fremantle Oval. For those not au fait with AFL, a mark is where a player cleanly catches a kicked ball, and the mark in question was by South Fremantle's John Gerovich in 1956. Gerovich is depicted leaping boldly above his opposing player Ray French.
Beaches & Parks BEACHES
There are plenty of green spaces around Fremantle, including Esplanade Reserve OFFLINE MAP GOOGLE MAP (Marine Tce) , shaded by Norfolk Island pines and dividing the city from Fishing Boat Harbour.
Although you could theoretically swim at neighbouring Bathers Beach , most people content themselves with wandering along the sand here and save the soaking for beaches further from the port. South Beach is sheltered, swimmable, only 1.5km from the city centre and on the free CAT bus route. The next major beach is Coogee Beach , 6km further south.
Army Museum of WA MUSEUM
(www.armymuseumwa.com.au; Burt St; adult/child $10/7; 11am-4pm Wed-Sun) Situated within the imposing Artillery Barracks, this little museum pulls out the big guns, literally. Howitzers and tanks line up outside, while inside you'll find cabinets full of uniforms and medals.
2 Activities
Fremantle Trails WALKING
(www.fremantlewa.com.au) Pick up trailcards from the visitor centre for the 11 self-guided walking tours on offer: Art & Culture, Convict, CY O'Connor (a pioneering civil engineer), Discovery (a Fremantle once-over), Fishing Boat Harbour, Hotels & Breweries, Maritime Heritage, Manjaree Heritage (Indigenous), Retail & Fashion, Waterfront and Writers.
Oceanic Cruises WHALE WATCHING
( 08-9325 1191; www.oceaniccruises.com.au; adult/child $67/29; mid-Sep–early Dec) Departs B Shed, Victoria Quay, at 10.15am for a two-hour tour. Days of operation vary by month, so check the website.
STS Leeuwin II SAILING
OFFLINE MAP GOOGLE MAP
( 08-9430 4105; www.sailleeuwin.com; Berth B; adult/child $95/60) Take a trip on a 55m, three-masted tall ship; see the website for details of breakfast, afternoon or twilight sails. Most sailings are from Friday to Sunday and on holidays.
T Tours
Fremantle Tram Tours CITY
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( 08-9433 6674; www.fremantletrams.com.au; departs Town Hall) Looking like a heritage tram, this bus departs from the Town Hall on an all-day hop-on, hop-off circuit around the city (adult/child $24/5). The Ghostly Tour (adult/child $70/50) runs from 6.45pm to 10.30pm Friday and visits the prison, Round House and Fremantle Arts Centre (former asylum) by torchlight. Combos include: Lunch & Tram (adult/child $79/42), which is the tram plus lunch cruise on river; Triple Tour (adult/child $85/40), the tram, river cruise and Perth sightseeing bus; Tram & Prison (adult/child $42/13), the tram and prison tour
Captain Cook Cruises CRUISES
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( 08-9325 3341; www.captaincookcruises.com.au; C Shed) Cruises between Fremantle and Perth (adult/child $25/15), departing Fremantle at 11.15am, 12.45pm and 3.45pm (the last is one-way only). A three-hour lunch cruise departs at 12.45pm (adult/child $62/41).
Fremantle Indigenous Heritage Tours WALKING TOUR
( 08-9431 7878; www.indigenouswa.com; adult/child $25/15; 10.30am daily) Highly regarded tour covering the history of Fremantle and the Noongar and Wadjuk people. Book through the Fremantle visitors centre.
Two Feet & A Heartbeat WALKING TOUR
( 1800 459 388; www.twofeet.com.au; per person $20-40; 10am daily) Operated by a younger, energetic crew, with the focus on Fremantle's often rambunctious history. 'Tight Arse Tuesdays' are good value.
z Festivals & Events
West Coast Blues 'n' Roots Festival MUSIC
(www.westcoastbluesnroots.com.au) Held late March to early April and interpreting its remit widely: recent festivals have featured Steve Earle, Grace Jones, Elvis Costello and My Morning Jacket.
Blessing of the Fleet RELIGIOUS
(Esplanade Reserve, Fishing Boat Harbour) An October tradition since 1948, brought to Fremantle by immigrants from Molfetta, Italy. It includes the procession of the Molfettese Our Lady of Martyrs statue (carried by men) and the Sicilian Madonna di Capo d'Orlando (carried by women), from St Patrick's Basilica (47 Adelaide St) to Fishing Boat Harbour, where the blessing takes place.
Fremantle Festival CULTURE
(www.fremantle.wa.gov.au) In November, the city's streets and concert venues come alive with parades and performances in Australia's longest-running festival.
4 Sleeping
Old Firestation Backpackers HOSTEL $
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( 08-9430 5454; www.old-firestation.net; 18 Phillimore St; dm $27-31, d $72; ) There's entertainment aplenty in this converted fire station: free internet, foosball, movies and a sunny courtyard. Dorms have natural light and the afternoon sea breeze fluttering in, and there's a female-only section. The hippy vibe culminates in late-night guitar-led sing-alongs around the campfire; bring earplugs if you value sleep. Yoga sessions were on offer when we last dropped by.
Pirates HOSTEL $
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( 08-9335 6635; www.piratesbackpackers.com.au; 11 Essex St; dm $29-31, d $65; ) Attracting a diverse international crew, this sun- and fun-filled hostel in the thick of the Freo action is a top spot to socialise. Rooms are small and reasonably basic, but the bathrooms are fresh and clean. The kitchen area is well equipped, there's a shady courtyard, and eye-catching marine murals remind you that an ocean swim is minutes away.
Woodman Point Holiday Park CAMPGROUND $
( 08-9434 1433; www.aspenparks.com.au; 132 Cockburn Rd; sites for 2 people $45, d $135-255; ) A particularly pleasant spot, 10km south of Fremantle. It's usually quiet, and its location makes it feel more summer beach holiday than outer-Freo staging post.
Coogee Beach Holiday Park CARAVAN PARK $
( 08-9418 1810; www.aspenparks.com.au; 3 Powell Rd; sites $50, d $120-199; ) No camp sites, only paved caravan spaces and a range of cabins, motel units and chalets. It's popular with young families, and has a tennis court and cafe. Off Cockburn Rd.
Norfolk Hotel HOTEL $$
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( 08-9335 5405; www.norfolkhotel.com.au; 47 South Tce; s/d without bathroom $100/140, d with bathroom $180; ) While eucalypts and elms stand quietly in the sun-streaked beer garden, the old limestone Norfolk harbours a secret upstairs: its rooms. Far above your standard pub digs, they've all been tastefully decorated in muted tones and crisp white linen, and there's a communal sitting room. It can be noisy on weekends, but the bar closes at midnight.
Fothergills of Fremantle B&B $$
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( 08-9335 6784; www.fothergills.net.au; 18-22 Ord St; r $175-225; ) Naked bronze women sprout from the front garden, while a life-size floral cow shelters on the verandah of these neighbouring mansions on the hill. Inside, the decor is in keeping with their venerable age (built 1892), aside from the contemporary art scattered about, which includes some wonderful Aboriginal pieces. Breakfast is served in the sunny conservatory.
Port Mill B&B B&B $$
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( 08-9433 3832; www.portmillbb.com.au; 3/17 Essex St; r $179-299; ) One of the most luxurious B&Bs in town, this is clearly the love child of Paris and Freo. Crafted from local limestone (it was built in 1862 as a mill), inside it's all modern Parisian-style, with gleaming taps, contemporary French furniture and wrought-iron balconies. French doors open out to the sun-filled decks, where you can tinkle the china on your breakfast platter.
Terrace Central B&B Hotel B&B $$
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( 08-9335 6600; www.terracecentral.com.au; 79-85 South Tce; d $190-215; ) Terrace Central may be a character-filled B&B at heart, but its larger size gives it the feel of a boutique hotel. The main section has been created from an 1888 bakery and an adjoining row of terrace houses. There are also modern one- and two-bedroom apartments out the back. You'll find ample off-street parking.
Bannister Suites Fremantle HOTEL $$
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( 08-9435 1288; www.bannistersuitesfremantle.com.au; 22 Bannister St; r from $199; ) Modern and fresh, boutiquey Bannisters is a stylish highlight of central Fremantle's accommodation scene. It's worth paying extra for one of the suites with the deep balconies, where you can enjoy views over the rooftops while lounging on the upmarket outdoor furniture.
Fremantle Colonial Accommodation APARTMENT $$
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( 08-9430 6568; www.fremantlecolonialaccommodation.com.au; 215 High St; d from $165; ) Rambling two-storey terrace or historic prison cottage? Whichever you choose, both embrace the colonial theme with gusto. White-painted wrought-iron bed frames, floral quilt covers and dusty-pink walls open out onto lacework balconies.
Number Six APARTMENT $$
( 08-9299 7107; www.numbersix.com.au; studios/1-bedroom apt from $105/150; ) Self-contained and stylish studios, apartments and houses available for overnight to long-term stays in great locations around Freo.
Quest Harbour Village APARTMENT $$$
( 08-9430 3888; www.questharbourvillage.com.au; Mews Rd, Challenger Harbour; apt from $292; ) At the end of a wharf, these attractive, two-storey, sandstone and brick one- to three-bedroom apartments make the most of their nautical setting; one-bedroom units have views over the car park to the Fishing Boat Harbour, while the others directly front the marina. Downstairs, rooms are light and simple, and kitchens are fully equipped.
Pier 21 APARTMENT $$$
( 08-9336 2555; www.pier21.com.au; 9 John St; apt from $320; ) Pier 21 is in a tucked-away spot on the riverside in North Freo. It's more like a motel than you'd expect for the price, but there's a tennis court, pool and spa.
5 Eating
Although it doesn't have Perth's variety of fine-dining places (or, thankfully, its prices), eating and drinking your way around town are two of the great pleasures of Freo. The main areas to browse before you graze are around the town centre, Fishing Boat Harbour and East Freo's George St and riverbank. People-watching from outdoor tables on South Tce is a legitimate lifestyle choice. The Fremantle Markets are a good place to stock up on fruit and other picnic items.
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5 City Centre
Moore & Moore CAFE $
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(www.mooreandmoorecafe.com; 46 Henry St; mains $8-22; 8am-4pm; ) An urban-chic cafe that spills into the adjoining art gallery and overflows into a flagstoned courtyard. With great coffee, good cooked breakfasts, pastries, wraps and free wi-fi, it's a great place to linger. Look forward to the company of a few Freo hipsters, and the international crew of students studying at Fremantle's University of Notre Dame.
iPho VIETNAMESE $
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(1/25 Collie St; mains $12.50-22; 11.30am-9.30pm Tue-Sun) This place has a damn fine name for a Vietnamese restaurant and is excellent value for Fremantle. Settle into the mod-Asian decor and multitask your way through the menu including crispy _cha gio_ (spring rolls), plump _banh xeo_ (Vietnamese crepes) and hearty noodle-filled bowls of _pho_ . A hip young crew delivers everything with a smile, making sure you leave very 'appy.
Juicy Beetroot VEGETARIAN $
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(mains $10-15; 10am-4pm Mon-Fri) S This popular meat-free zone serves tasty vego and vegan dishes of the wholefood variety (tofu burgers, curries etc), and zingy fresh juices. Look past the bad New Age art to the posters advertising Freo's more eclectic events. It's tucked up an alley off High St with outdoor seating.
Kakulas Sister DELI $
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(29-31 Market St; 9am-5pm Mon-Fri, 10am-5pm Sat & Sun) This provedore, packed with nuts, quince paste and Italian rocket seeds, is a cook's dream, and is excellent for energy-filled snacks. If you've been to Kakulas Bros in Northbridge, you'll know the deal.
Cafe 55 ASIAN $
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(55 High St; mains $8-12.50; 7.30am-3pm Mon-Fri, 9am-3pm Sat) Asian food with a Freo feel, this bright cafe's fragrant soups – _pho,_ _bun bo Hue_ (spicy beef noodle soup) and Malaysian laksa – are fantastic. Plus there are baguettes just like you'd get in the former French colony of Vietnam.
Canvas CAFE $$
(www.canvasatfremantleartscentre.com; Fremantle Arts Centre; mains $10-25; 8.30am-4pm) Freo's best cafe is stylishly concealed in the Fremantle Arts Centre with a diverse menu channelling Middle Eastern, Spanish and North African influences. Breakfast highlights are the baked-egg dishes – try the Israeli-style Red Shakshuka or the Spanish eggs Flamenco – and lunch presents every-thing from citrus-cured salmon, scallops or WA's best beef burger. Ecelctic beers and wines too.
Maya INDIAN $$
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( 08-9335 2796; www.mayarestaurant.com.au; 77 Market St; mains $18-29; 6pm-late Tue-Sun, noon-3pm Fri) Maya's white tablecloths and wooden chairs signal classic style without the pomp. Its well-executed meals have made it a popular local spot for years, earning it the reputation of WA's best Indian restaurant.
Gino's CAFE $$
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(www.ginoscafe.com.au; 1 South Tce; mains $15-30; 6am-late; ) Old-school Gino's is Freo's most famous cafe, and while it's become a tourist attraction in its own right, the locals still treat it as their second living room, only with better coffee. For the uninitiated, you'll need to order and pay and then collect your own coffee.
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5 Fishing Boat Harbour
Little Creatures PUB $$
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(www.littlecreatures.com.au; 40 Mews Rd; pizzas $18-34, shared plates $9-24; 10am-midnight) Little Creatures is classic Freo: harbour views, fantastic brews (made on the premises) and excellent food. In a cavernous converted boatshed overlooking the harbour, it can get chaotic at times, but a signature Pale Ale with a wood-fired pizza will be worth the wait. More substantial shared plates include chickpea tagine and pork belly with fennel. No bookings.
Cicerello's FISH & CHIPS $$
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(www.cicerellos.com.au; 44 Mews Rd; fish & chips $14, mains $17-28; 10am-late) Since 1903, Cicerello's has been a quintessential Freo experience. Leave the kids staring at the large aquariums (filled with living coral, bright fish, an octopus and a hemmed-in shark), choose your fish and chips, then pick a spot out on the boardwalk and soak up the sun – just watch those seagulls.
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5 East & North Fremantle
Flipside BURGERS $
(www.flipsideburgers.com.au; 239 Queen Victoria St; $10.50-13.50; 5.30-9.30pm Tue-Thu, noon-2.30pm Thu, noon-9pm Fri-Sun) Gourmet burgers with the option of dining in next door at Mrs Browns (Click here ).
Harvest MODERN AUSTRALIAN $$$
( 08-9336 1831; www.harvestrestaurant.net.au; 1 Harvest Rd; mains $38-42; 6pm-late Tue-Thu, noon-late Fri, 8am-late Sat, 8am-3pm Sun) First you'll find a green-painted cottage, complete with picket fence, next to some fields. Swing through the heavy, fuchsia-painted metal doors and into the dark-wood dining room lined with artworks and curios. Then settle down to comforting Mod Oz dishes cooked with panache. Breakfast and lunch are less expensive.
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5 South Fremantle
Wild Poppy CAFE $$
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(2 Wray Ave; breakfast $6-16, lunch $16-22; 7am-4pm; ) Lace doilies, kitschy furniture and a stupendous collection of retro portaits and landscapes make this hip cafe in up-and-coming South Freo worth seeking out. Soup and salad specials team with good coffee, beer and cider, and the chilli eggs are a great way to start the day. For lunch, ask if the Cape Malay fish curry is on the menu.
6 Drinking & Entertainment
Most of Fremantle's big pubs are lined up along South Tce and there are some character- filled old taverns on High St. Freo's pubs have long been incubators for local musos, including world-famous-in-Australia acts like Eskimo Joe and John Butler. A couple of interesting smaller bars also lurk in North and South Fremantle.
Little Creatures MICROBREWERY
(www.littlecreatures.com.au; 40 Mews Rd, Fishing Boat Harbour; 10am-midnight) Try the Pale Ale and Pilsner, and other beers and ciders under the White Rabbit and Pipsqueak labels. Pop in at 4pm on Thursday for its regular 'Firkin Experiment' where limited one-off brews are given a whirl. Creatures Loft is an adjacent lounge bar with regular live entertainment and DJs. Live jazz kicks off at 4pm on Sunday.
Who's Your Mumma BAR
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(cnr Wray Ave & South Tce; 4pm-late Mon-Thu, 8am-late Fri-Sun) Industrial-chic lightbulbs and polished-concrete floors are softened by recycled timber at the laidback Who's Your Mumma. An eclectic crew of South Freo locals crowd in for great-value combo specials (around $15) including 'Taco Tuesdays' and 'Schnitzel Mondays'. Other moreish bar snacks include fluffy pork buns, and it opens for a leisurely brekky at the weekend.
Sail & Anchor PUB
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(www.sailandanchor.com.au; 64 South Tce; 11am-midnight Mon-Sat, to 10pm Sun) Built in 1854, this Fremantle landmark has been impressively restored to recall much of its former glory. Downstairs is big and beer focused, with 43 taps delivering a stunning range of local and international beers. Welcome to the best destination for the travelling beer geek in Western Australia. Occasional live music completes the picture.
Mrs Browns BAR
(www.mrsbrownbar.com.au; 241 Queen Victoria St; 4.30pm-late Tue-Thu, 1pm-late Fri-Sun) Exposed bricks and a copper bar combine with retro and antique furniture to create North Fremantle's most atmospheric bar. The music could include all those cult bands you thought were _your_ personal secret, and an eclectic menu of beer, wine and tapas targets the more discerning, slightly older bar hound. And you can order in burgers from Flipside (Click here ) next door.
Norfolk Hotel PUB
(www.norfolkhotel.com.au; 47 South Tce; 11am-midnight Mon-Sat, to 10pm Sun) Slow down to Freo pace and take your time over one of the many beers on tap at this 1887 pub. Lots of interesting guest brews create havoc for the indecisive drinker, and the pub food and pizzas are very good. We love the heritage limestone courtyard, especially when sunlight peeks through the elms and eucalypts.
The Monk CRAFT BEER
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(www.themonk.com.au; 33 South Tce; 11.30am-late) Park yourself on the spacious front terrace or in the chic interior, partly fashioned from recycled railway sleepers, and enjoy the Monk's own brews (kolsch, mild, wheat, porter, rauch and pale ale). The bar snacks and pizzas are also good, and guest beers and regular seasonal brews always draw a know-ledgeable crowd of local craft-beer nerds.
Whisper WINE BAR
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(www.whisperwinebar.com.au; 1/15 Essex St; noon-late Wed-Sun) Yes, there is more to Freo than craft beer. In a lovely heritage building, this classy French-themed wine bar also does shared plates of charcuterie and cheese.
Fly by Night Musicians Club LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(www.flybynight.org; Parry St) Variety is the key at Fly by Night, a not-for-profit club that's been run by musos for musos for years. All kinds perform here, and many local bands made a start here. It's opposite the car park below the old Fremantle Prison.
Kulcha CLUB, LIVE MUSIC
OFFLINE MAP GOOGLE MAP
( 08-9336 4544; www.kulcha.com.au; 13 South Tce, 1st fl) World music of all sorts is the focus here. At the time we researched the line-up included Gypsy swing, Indigenous Australian reggae and rap, and melancholy Portuguese _fado_ . Book ahead.
X-Wray Cafe LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(http://xwraymusic.tumblr.com; 3-13 Essex St; 10am-11pm Mon-Wed, 9am-midnight Thu-Sat, 8am-9pm Sun) There's something on every night (live jazz, rock, open piano) at this hipster hang-out, comprising a smallish indoor area and a large canvas-covered terrace. Light meals are available.
Mojo's LIVE MUSIC
(www.mojosbar.com.au; 237 Queen Victoria St, North Fremantle; 7pm-late) Good old Mojo's is one of Freo's longest running live-music venues. Local and national bands (mainly Aussie rock and indie) and DJs play at this small place, and there's a sociable beer garden out the back. First Friday of the month is reggae night; every Monday is open-mic night.
Metropolis Fremantle LIVE MUSIC
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(www.metropolisfremantle.com.au; 58 South Tce) A great space to watch a gig, and is also a proper nightclub on the weekends. International and popular Australian bands and DJs perform here.
Newport Hotel LIVE MUSIC
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(www.thenewport.com; 2 South Tce; noon- midnight Mon-Sat, to 10pm Sun) Local bands play Saturday and Sunday, with DJs other nights. The recently opened Tiki Bar is worth a kitsch cocktail or two.
Luna on SX CINEMA
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(www.lunapalace.com.au; Essex St) Art-house films; set back in a lane between Essex and Norfolk Sts.
Hoyts CINEMA
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(www.hoyts.com.au) Blockbusters at Millennium (Collie St) and Queensgate (William St) .
7 Shopping
The bottom end of High St is the place for interesting and quirky shopping. Fashion stores run along Market St, towards the train station. Queen Victoria St in North Fremantle is the place to go for antiques. Don't forget Fremantle Markets for clothes, souvenirs and knick-knacks.
Japingka INDIGENOUS ART
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(www.japingka.com.au; 47 High St; 10am-5.30pm Mon-Fri, noon-5pm Sat & Sun) Specialising in Aboriginal fine art, from WA and beyond. Purchases come complete with extensive notes about the works and the artists that painted them.
New Edition BOOKS
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(www.newedition.com.au; 82 High St; 7.30am-6pm Mon-Sat, 9am-6pm Sun) A bookworm's dream with comfy armchairs for browsing and a funky cafe attached. See you in a leisurely three hours.
Jarrahcorp FURNITURE
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(www.jarrahcorp.com.au; cnr High & Pakenham Sts; 11am-4pm Mon-Sat, noon-4pm Sun) Traditional and contemporary furniture and gifts crafted from jarrah and marri timber salvaged from old buildings or ancient logs. At the time of writing, the owner was also planning on opening a wine bar called Epicure adjacent to the shop.
Found ARTS & CRAFTS
(www.fac.org.au; 1 Finnerty St; 10am-5pm) The Fremantle Arts Centre shop stocks an inspiring range of WA art and craft.
Love in Tokyo CLOTHING
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(www.loveintokyo.com.au; 61-63 High St; 10am-5pm Mon-Sat, 1-5pm Sun) Local designer turning out gorgeously fashioned fabrics for women.
Elizabeth's Bookshop BOOKS
(www.elizabethsbookshop.com.au) One of Australia's biggest second-hand booksellers, with a staggering range. Elizabeth's is a Fremantle institution with branches in Fremantle (High Street Mall; 9am-6pm) and South Terrace (8 South Tce; 9am-10.30pm Sun-Thu) .
Record Finder MUSIC
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(87 High St; 10am-5pm) A treasure trove of old vinyl, including rarities and collectables.
Bodkin's Bootery SHOES
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(www.bodkinsbootery.com; 72 High St; 9am-5pm Mon-Sat, noon-5pm Sun) Men's and women's boots and hats.
Chart & Map Shop MAPS
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(www.chartandmapshop.com.au; 14 Collie St; 10am-5pm) Maps and travel guides.
Bill Campbell Secondhand Book Seller BOOKS
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(48 High St; 10am-5pm Mon-Fri, noon-5pm Sat & Sun) For those out-of-print Penguin classics you always meant to read.
Remedy GIFTS
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(www.remedyonline.net.au; 95 High St; 9am-5pm) An eclectic collection of goodies, including kids' clothes, adults' tees, gifts and the Aesop range of toiletries.
Mills Records MUSIC
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(www.mills.com.au; 22 Adelaide St; 9am-5pm Mon-Sat, noon-5pm Sun) Music, including some rarities, and tickets. Check out the 'Local's Board' for recordings by Freo and WA acts.
E Shed Markets MARKET
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(www.eshedmarkets.com.au; market 9am-5pm Fri-Sun, food court to 8pm; ) An old wharf shed with market stalls, a food court, cafes and bars.
8 Information
For free wi-fi, try Moore & Moore ( Click here ), or the FREbytes hot spot in the vicinity of the Town Hall and library.
Fremantle City Library ( 08-9432 9766; www.frelibrary.wordpress.com; Kings Sq, Town Hall; 9.30am-5.30pm Mon, Fri & Sat, to 8pm Tue-Thu; ) Free wi-fi and internet terminals.
Fremantle Hospital ( 08-9431 3333; www.fhhs.health.wa.gov.au; Alma St)
Post Office ( 13 13 18; 1/13 Market St; 9am-5pm Mon-Fri)
TravelLounge OFFLINE MAP GOOGLE MAP ( 08-9335 8776; www.thetravellounge.com.au; 16 Market St; internet per hr $5; ) Private agency offering information, bookings and internet terminals.
Visitor Centre OFFLINE MAP GOOGLE MAP ( 08-9431 7878; www.fremantlewa.com.au; Kings Sq, Town Hall; 9am-5pm Mon-Fri, 10am-3pm Sat, 11.30am-2.30pm Sun) Free maps and brochures, and bookings for accommodation, tours and hire cars. Check the website for what's on.
8 Getting There & Around
Fremantle sits within Zone 2 of the Perth public-transport system (Transperth) and is only 30 minutes away by train. There are numerous buses between Perth's city centre and Fremantle, including routes 103, 106, 107, 111 and 158.
Another very pleasant way to get here from Perth is by the 1¼-hour river cruise run by Captain Cook Cruises ( Click here ).
There are numerous one-way streets and parking meters in Freo. It's easy enough to travel by foot or on the free CAT bus service, which takes in all the major sights on a continuous loop every 10 minutes from 7.30am to 6.30pm on weekdays, until 9pm on Friday and 10am to 6.30pm on the weekend.
Bicycles (Kings Sq, Fremantle Visitors Centre; 9.30am-4.30pm Mon-Fri, to 3.30pm Sat, 10.30am-3.30pm Sun) can be rented for free at the visitor centre, an ideal way to get around Freo's storied streets. A refundable bond of $200 applies.
# Around Perth
#### Around Perth Highlights
#### Rottnest Island (Wadjemup)
#### Rockingham
#### Peel Region
#### Mandurah
#### Yalgorup National Park
#### Pinjarra
#### Dwellingup
#### Jarrahdale & Serpentine National Park
#### Dryandra to Hyden
#### Hyden & Wave Rock
#### Darling Range
#### Kalamunda
#### Mundaring
#### Walyunga National Park
#### Swan Valley & Guildford
#### Avon Valley
#### York
#### Northam
#### Toodyay
#### Avon Valley National Park
#### New Norcia
#### Wildflower Way
#### Moora
#### Wongan Hills
#### Perenjori
#### Morawa, Mingenew & Mullewa
#### Sunset Coast
#### Yanchep
#### Guilderton
#### Lancelin
#### Turquoise Coast
#### Cervantes & Pinnacles Desert
#### Jurien Bay
#### Green Head & Leeman
Around Perth
### Why Go?
Although Western Australia (WA) is huge, you don't have to travel too far from the capital to treat yourself to a tantalising taste of what the state has to offer. A day trip could see you frolicking with wild dolphins, snorkelling with sea lions, scooping up brilliant-blue crabs or spotting bilbies in the bush. Active types can find themselves canoeing, rafting, surfing, windsurfing, sandboarding, diving, skydiving and ballooning. Those who prefer pursuits less likely to ruffle one's hair can linger at vineyards or craft breweries, settle down for a culinary feast, or explore historic towns classified by the National Trust.
We've designed this chapter so that the main headings can be tackled as day trips, or better still, overnighters. If you're embarking on a longer trip, whether north, south or east, you'll find your first stop within these pages.
### When to Go
Mar Good beach weather and a fine time to spot thrombolites in Lake Clifton.
Jun Food and wine excellence at the Avon Valley Gourmet Food & Wine Festival in Northam.
Aug Wildflowers bloom, and brave paddlers take on the Avon River Descent in Northam.
### Best Places to Eat
» RiverBank Estate ( Click here )
» Dear Friends ( Click here )
» M on the Point ( Click here )
» Cervantes Country Club ( Click here )
» Rustico ( Click here )
### Best Places to Stay
» Faversham House ( Click here )
» Amble Inn ( Click here )
» Mundaring Weir Hotel ( Click here )
» Rottnest Island Authority Cottages ( Click here )
» Lancelin Lodge YHA ( Click here )
## Around Perth Highlights
Cycling your way to a private slice of coastal paradise on Rottnest Island (Wadjemup; Click here ), then spending the afternoon swimming, sunning and snorkelling
Enjoying a sublime sunset over the other-worldly Pinnacles Desert (Click here )
Getting chipper with Flipper while palling about with scores of wild dolphins in Shoalwater Islands Marine Park (Click here ) off Rockingham
Splashing about with sea lions at Green Head (Click here )
Exploring the intriguing monastery town of New Norcia (Click here )
Getting your foodie fix at the vineyards, breweries and artisan producers of the Swan Valley (Click here )
Immersing yourself in the wonderful wildflowers of the Lesueur National Park (Click here )
## Rottnest Island (Wadjemup)
pop 475
'Rotto' has long been the family holiday playground of choice for Perth locals. Although it's only about 19km offshore from Fremantle, this car-free, off-the-grid slice of paradise, ringed by secluded beaches and bays, feels a million miles from the metropolis.
Cycling around the 11km-long, 4.5km-wide island is a real pleasure; just ride around and pick your own bit of beach to spend the day on. You're bound to spot quokkas on your journey. These are the island's only native land mammals, but you might also spot New Zealand fur seals splashing around off magical West End ; dolphins; and, in season, whales. King skinks are common, sunning themselves on the roads until you draw near – and then they're just as likely to scuttle into the path of your bike as they are to scuttle in the opposite direction.
Snorkelling, fishing, surfing and diving are also all excellent on the island. In fact, there's not a lot to do here that's not outdoors, so you're better off postponing your day trip if the weather is bad. It can be unpleasant when the wind really kicks up.
Rotto is also the site of annual school-leavers' and end-of-uni-exams parties, a time when the island is overrun by kids 'getting blotto on Rotto'. Depending on your age, it's either going to be the best time you've ever had or the worst – check the calendar before proceeding.
In early September, the annual Rottofest (http://rottofest.com.au) immerses the island in two days of music, film and comedy.
History
The island was originally called Wadjemup (place across the water), but Wadjuk oral history recalls that it was joined to the mainland before being cut off by rising waters. Modern scientists date that occurrence to before 6500 years ago, making these memories some of the world's oldest. Archaeological finds suggest that the island was inhabited 30,000 years ago, but not after it was separated from the mainland.
Dutch explorer Willem de Vlamingh claimed discovery of the island in 1696 and named it Rotte-nest ('rat's nest', in Dutch) because of the king-sized 'rats' (which were actually quokkas) he saw there.
From 1838 it was used as a prison for Aboriginal men and boys from all around the state. At least 3670 people were incarcerated here, in harsh conditions, with around 370 dying (at least five were hanged). Although there were no new prisoners after 1903 (by which time holiday-makers from the mainland had already discovered the island), some existing prisoners served their sentences until 1931. Even before the prison was built, Wadjemup was considered a 'place of the spirits', and it's been rendered even more sacred to indigenous people because of the hundreds of their people, including prominent resistance leaders, who died there. Many avoid it to this day.
During WWI, approximately a thousand men of German or Austrian extraction were incarcerated here, their wives and children left to fend for themselves on the mainland. Ironically most of the 'Austrians' were actually Croats who objected to Austro-Hungarian rule of their homeland. Internment resumed during WWII, although at that time it was mainly WA's Italian population who were imprisoned.
There's an ongoing push to return the island to its original name. One suggested compromise is to adopt a dual name, Wadjemup/Rottnest.
1 Sights
Most of Rottnest's historic buildings, built mainly by Aboriginal prisoners, are grouped around Thomson Bay, where the ferry lands.
Rottnest Island (Wadjemup)
Sights
1 Quod & Aboriginal Burial GroundA2
2 Rottnest Museum A2
3 Salt Store B2
4 Vlamingh's Lookout A2
Activities, Courses & Tours
5 Rottnest Air Taxi F2
6 Rottnest Island Bike Hire B2
Rottnest Voluntary Guides (see 3)
Sleeping
7 Allison Tentland F1
8 Hotel Rottnest B2
9 Kingston Barracks Youth Hostel G2
Rottnest Lodge (see 1)
Eating
10 Aristos B2
Hotel Rottnest (see 8)
Riva (see 1)
11 Rottnest Bakery A2
Quod & Aboriginal Burial Ground HISTORIC SITE
OFFLINE MAP GOOGLE MAP
(Kitson St) Built in 1864, this octagonal building with a central courtyard was once the Aboriginal prison block but is now part of the Rottnest Lodge hotel. During its time as a prison, several men would sleep in each 3m by 1.7m cell, with no sanitation (most of the deaths were due to disease). Unless you're staying here, the only part of the complex that can be visited is a small whitewashed chapel to the left of the main entrance. A weekly Sunday service is held at 9.30am. The cells have been redeveloped into hotel rooms, but an undeniable darkness and melancholia lingers around this area.
Immediately adjacent to the Quod is a wooded area where hundreds of Aboriginal prisoners are buried in unmarked graves. Until relatively recently, this area was used as a camping ground, but it's now fenced off with signs asking visitors to show respect to what is considered a sacred site. Plans are under way to convert the area into a memorial, in consultation with Aboriginal elders.
Rottnest Museum MUSEUM
OFFLINE MAP GOOGLE MAP
(Kitson St; admission by gold coin donation; 11am-3.30pm) Housed in the old hay-store building, this little museum tells the island's natural and human history, warts and all, including dark tales of shipwrecks and incarceration.
Salt Store HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
(Colebatch Ave) F A photographic exhibition in this 19th-century building looks at a different chapter of local history: when the island's salt lakes provided all of WA's salt (between 1838 and 1950). It's also the meeting point for walking tours.
Vlamingh's Lookout LOOKOUT
OFFLINE MAP GOOGLE MAP
Not far away from Thomson Bay (go up past the old European cemetery), this unsigned vantage point offers panoramic views of the island, including its salt lakes. It's on View Hill, off Digby Dr.
### QUOKKAS
These cute little docile bundles of fur have suffered a number of indignities over the years. First Willem de Vlamingh's crew mistook them for rats as big as cats. Then the British settlers misheard and mangled their name (the Noongar word was probably _quak-a_ or _gwaga_ ). But worst of all, a cruel trend of 'quokka soccer' by sadistic louts in the 1990s saw many kicked to death before a $10,000 fine was imposed; occasional cases are still reported.
These marsupials of the macropod family (relatives of kangaroos and wallabies) were once found throughout the southwest but are now confined to forest on the mainland and a population of 8000 to 10,000 on Rottnest Island. You will see plenty of them during your visit. Don't be surprised if one comes up to you looking for a titbit (don't oblige them, as human food isn't good for them) – many are almost tame, or, at least, fearless.
2 Activities
Beaches SWIMMING
Most visitors come for Rottnest's beaches and aquatic activities. The Basin is the most popular beach for family-friendly swimming as it's protected by a ring of reefs. Other popular spots are Longreach Bay and Geordie Bay , though there are many smaller secluded beaches such as Little Parakeet Bay .
Reefs & Wrecks SNORKELLING, DIVING
Excellent visibility in the temperate waters, coral reefs and shipwrecks makes Rottnest a top spot for scuba diving and snorkelling. There are snorkel trails with underwater plaques at Little Salmon Bay and Parker Point . The Basin , Little Parakeet Bay , Longreach Bay and Geordie Bay are also good. Rottnest Island Bike Hire OFFLINE MAP GOOGLE MAP ( 9292 5105; www.rottnestisland.com; cnr Bedford Ave & Welch Way; per hr $16, 1/2/3/4/5 days $28/45/56/67/79; 8.30am-4pm, to 5.30pm in summer) has masks, snorkels and fins available, as well as kayaks.
Over a dozen boats have come a cropper on Rottnest's reefs, the earliest significant one being the schooner _Transit_ in 1842. Marker plaques around the island tell the sad tales of how and when the ships sank. The only wreck that is accessible to snorkellers without a boat is at Thomson Bay . The Australasian Diving Academy ( Click here ) takes diving trips to some of the wrecks.
Surfing SURFING
The best surf breaks are at Strickland , Salmon and Stark Bays , towards the western end of the island. Boards can be hired at Rottnest Island Bike Hire.
Birds BIRDWATCHING
Rottnest is ideal for twitchers because of the varied habitats: coast, lakes, swamps, heath, woodlands and settlements. Coastal birds include pelicans, gannets, cormorants, bar-tailed godwits, whimbrels, oystercatchers, majestic ospreys and fairy, bridled and crested terns. For more, grab a copy of _A Bird's Eye View of_ _Rottnest_ _Island_ from the visitor centre.
T Tours
Check the times online or at the Salt Store, or call the visitor centre.
Rottnest Voluntary Guides WALKING
OFFLINE MAP GOOGLE MAP
( 08-9372 9757; www.rvga.asn.au) F Free, themed walks leave from the central Salt Store daily: History; Reefs, Wrecks & Daring Sailors; Vlamingh Lookout & Salt Lakes; and the Quokka Walk. They also run tours of Wadjemup Lighthouse (adult/child $7/3) and Oliver Hill Gun & Tunnels (adult/child $8/3.50); you'll need to make your own way there for the last two.
Oliver Hill Train & Tour TRAIN RIDES
(www.rottnestisland.com; adult/child $28/16) The Oliver Hill gun battery was built in the 1930s and played a major role in the defence of the WA coastline and Fremantle harbour. This trip takes you by train to Oliver Hill (departing from the train station twice daily) and includes the Gun & Tunnels tour run by Rottnest Voluntary Guides.
Discovery Coach Tour BUS TOUR
(www.rottnestisland.com; adult/child $35/17; departs 11.20am, 1.40pm & 1.50pm) Leaves from Thomson Bay three times daily (book at the visitor centre) and includes a commentary and a stop at West End.
Rottnest Adventure Tour CRUISE
(www.rottnestexpress.com.au; adult/child $50/25; late Sep-early Jun) Ninety-minute cruises around the coast with a special emphasis on spotting wildlife, including whales in season from October to November. Packages are also available from Perth (adult/child $130/67) and Fremantle ($115/57).
Charter 1 SAILING
( 0428 604 794; www.charter1.com.au; mid-Sep–Apr ) Excursions on the _Capella_ , a state-of-the-art catamaran, include whale-watching eco-cruises (adult/child $58/29), guided snorkelling trips (adult/child $68/34), and twilight sails (adult/child $48/29) for taking in a Rottnest sunset.
Rottnest Air Taxi SCENIC FLIGHTS
OFFLINE MAP GOOGLE MAP
( 1800 500 006, 0411 264 547; www.rottnest.de) Ten-minute flights over the island ($38).
4 Sleeping
Rotto is wildly popular in summer and school holidays, when accommodation is booked out months in advance. Prices can rise steeply at these times – low-season rates are given here. Check websites for off-peak deals combining transport to the island, especially incorporating a weekday visit.
Kingston Barracks Youth Hostel HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9432 9111; www.rottnestisland.com; dm/f $50/106) This hostel is located in old army barracks that still have a rather institutional feel, and few facilities. Check in at the visitor centre before you make the 1.8km walk, bike or bus trip to Kingston.
Allison Tentland CAMPGROUND $
OFFLINE MAP GOOGLE MAP
( 08-9432 9111; www.rottnestisland.com; Thomson Bay; sites per person $13) Camping on the island is restricted to this leafy camping ground with barbecues. Be vigilant about your belongings, especially your food – cheeky quokkas have been known to help themselves.
Rottnest Island Authority Cottages RENTAL HOUSE $
( 08-9432 9111; www.rottnestisland.com; cottages $100-228) There are more than 250 villas and cottages for rent around the island. Some have magnificent beachfront positions and are palatial; others are more like beach shacks. Prices rise by around $60 for Friday and Saturday nights, and they shoot up by up to $120 in peak season (late September to April). Check online for the labyrinthine pricing schedule.
Rottnest Lodge HOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9292 5161; www.rottnestlodge.com.au; Kitson St; r $190-300; mains $27-34; ) It's claimed there are ghosts in this comfortable complex, which is based around the former Quod and boys' reformatory school. If that worries you, ask for a room in the new section, looking onto a salt lake. The lodge's Riva restaurant channels Italian flavours amid the island's vaguely Mediterranean ambience, especially when the sun is shining.
Hotel Rottnest PUB $$$
OFFLINE MAP GOOGLE MAP
( 08-9292 5011; www.hotelrottnest.com.au; 1 Bedford Ave; r $270-320; ) Based around the former summer-holiday pad for the state's governors (built in 1864) the former Quokka Arms has been completely transformed by a stylish renovation. The whiter-than-white rooms are smart and modern, if a tad pricey. Some have beautiful sea views.
5 Eating & Drinking
Most visitors to Rotto self-cater. The general store is like a small supermarket (and also stocks liquor), but if you're staying a while, you're better to bring supplies with you. Another option is to pre-order food from the general store, and they'll equip your accommodation with food and drinks before your arrival. Fir details, see the general store's website: www.rottnestgeneralstore.com.au.
All of the following are in Thomson Bay, but service, quality of food, and value for money can be mediocre during weekends and holiday periods.
Rottnest Bakery BAKERY $
OFFLINE MAP GOOGLE MAP
(Malley St; mains $5-12) Traditional Aussie bakery, with pies, burgers, soup and ice cream.
Hotel Rottnest PUB $$
(www.hotelrottnest.com.au; 1 Bedford Ave; mains $19-38; 11am-late) It's hard to imagine a more inviting place for a sunset pint of Little Creatures than the AstroTurf 'lawn' of this chic waterfront hotel. A big glass pavilion creates an open and inviting space, and bistro- style food and pizza is reasonably priced given the location and ambience. Bands and DJs regularly boost the laid-back island mood during summer.
Riva SEAFOOD $$
OFFLINE MAP GOOGLE MAP
(Kitson St, Rottnest Lodge; mains $27-34; noon-late) Classy Italian restaurant with a strong focus on local seafood. Prawns, squid, mussels and oysters all receive an elegant touch of the Med, and there are also wood-fired pizzas and interesting spins on duck, chicken and lamb.
Aristos SEAFOOD $$
OFFLINE MAP GOOGLE MAP
(www.aristosrottnest.com.au; Colebatch Ave; breakfast $10-17, lunch & dinner mains $27-42; 8am-late) An upmarket, but pricey, option for seafood, steaks and salads, fish and chips, burgers, ice cream or excellent coffee, right on the waterfront near the main jetty. Grab a table on the deck for absolute sea views, and push the boat (way) out with a seafood platter for two people ($125).
8 Information
At the Thomson Bay settlement, behind the main jetty, there's a shopping area with an ATM.
Ranger ( 08-9372 9788) For fishing and boating information.
Visitor Centre (www.rottnestisland.com) Thomson Bay ( 9372 9732; www.rottnestisland.com; 7.30am-5pm Sat-Thu, 7.30am-7pm Fri, extended in summer) Fremantle ( 9432 9300; www.rottnestisland.com; E Shed, Victoria Quay) The Thomson Bay office, at the end of the main jetty, handles check-ins for all the island authority's accommodation. There's a bookings counter at the Fremantle office, near where the ferry departs.
8 Getting There & Away
Air
Rottnest Air-Taxi ( 0411 264 547; www.rottnest.de) flies from Jandakot airport in four-seater (one-way/same-day return/extended return $230/330/430) or six-seater planes (one-way/extended return $350/550). Prices include up to three passengers in the four-seater and five passengers in the six-seater.
Boat
Rottnest Express ( 1300 467 688; www.rottnestexpress.com.au) Fremantle (B Shed, Victoria Quay; adult/child $72.50/40) Northport (1 Emma Pl, Rous Head; adult/child $72.50/40) Perth (Pier 2, Barrack St Jetty; adult/child $92.50/50) The prices listed are for return day trips and include the island admission fee; add $10 for an extended return. Ferry schedules are seasonal, though those listed here are roughly the minimum: Perth (1¾ hours, twice daily), Fremantle (30 minutes, five times daily) and North Fremantle (30 minutes, three times daily). Secure parking is available at Northport; the Perth and Fremantle departure points are handy to train stations. Various packages are available, which can add bike hire, snorkelling equipment, meals and tours.
Rottnest Fast Ferries ( 08-9246 1039; www.rottnestfastferries.com.au; adult/child $83/45) Departs from Hillarys Boat Harbour (40 minutes; three times daily). Packages also available. Hillarys Boat Harbour is around 40 minutes' drive north of Perth. See www.hillarysboatharbour.com.au for public transport details.
8 Getting Around
Bike
Bicycles are the time-honoured way of getting around the island. Rottnest is just big enough (and with enough hills) to make a day's ride good exercise.
Bikes can be booked in advance online or on arrival through Rottnest Island Bike Hire ( 08-9292 5105; www.rottnestisland.com; cnr Bedford Ave & Welch Way; 8.30am-4pm, to 5.30pm summer) . A $25 bond is required if you don't have photo ID. It's the only operator to have a pick-up service if you're unable to return to the office due to injury or damage to the bike.
The ferry companies also hire out bikes. Rottnest Express has them waiting as you get off the boat ($28/41/56 per one/two/three days). They don't provide locks but neither do they check them off when you return them. Bikes aren't usually stolen (it would be too hard to smuggle them off the island without the ferry companies noticing), but it's not unheard of for an unlocked bike to be grabbed and used by someone else.
Bus
A free shuttle runs between Thomson Bay, the main accommodation areas and the airport, departing roughly every 35 minutes, with the last bus at 7pm. The Bayseeker (day pass adult/child $14/6) is a hop-on, hop-off service that does an hourly loop around the island with the first bus at 8.30am and the last at 3.30pm. Between Geordie Bay and Thomson Bay it's free.
## Rockingham
pop 100,000
Just 46km south of Perth, Rockingham's main attractions are good beaches and the Shoalwater Islands Marine Park, where you can observe dolphins, sea lions and penguins in the wild.
Rockingham was founded in 1872 as a port, although this function was taken over by Fremantle in the 1890s. There's still a substantial industrial complex to the north, at Kwinana.
Most places of interest are stretched along Rockingham Beach.
1 Sights & Activities
Shoalwater Islands
Marine Park NATURE RESERVE
(www.marineparks.wa.gov.au) S Just a few minutes' paddle, swim or boat ride from the mainland is tiny, fabulous and strictly protected Penguin Island . Home to about 600 breeding pairs of seriously cute little penguins, and several thousand pairs of ground-nesting and in-your-face silver gulls, the island also has an informal and informative feeding centre (for long-term injured or orphaned penguins), boardwalks, swimming beaches and picnic tables for day visitors. It's lovely, low-key and very ecoconscious; no food is sold on the island, toilets are composting, and the island is closed for nesting from June to mid-September.
Apart from birdwatching (pied cormorants, pelicans, crested and bridled terns, and oystercatchers), you can swim and snorkel in the crystal-clear waters. Nearby Seal Island is home to a colony of Australian sea lions and off-limits to the public. The naval base of Garden Island can be reached only by private boat.
The Penguin Island ferry (Mersey Point Jetty; ferry $12; hourly 9am-3pm mid-Sep–May) is run by Rockingham Wild Encounters (Click here ). Tickets combining the ferry with entry to the island's discovery centre penguin-feeding (adult/child $18/15) are available.
At low tide it's possible to wade the few hundred metres to the island across the sandbar. However, take heed of warning signs, as people have drowned here after being washed off the bar during strong winds and high tides.
West Coast Dive Park DIVING
(www.westcoastdivepark.com.au; diving permits per day/week $25/50) Diving within the marine park became even more interesting after the sinking of the _Saxon Ranger_ , a supposedly jinxed 400-tonne fishing vessel. Permits to dive at this site are available from the visitor centre. Contact the Australasian Diving Academy ( Click here ) about expeditions to this wreck and the wrecks of three other boats, two planes and various reefs in the vicinity.
T Tours
Capricorn Seakayaking KAYAKING
( 0427 485 123; www.capricornseakayaking.com.au; mid-Sep–early Jun) Full-day sea-kayaking tours around Penguin and Seal Islands from Perth, Fremantle or Rockingham ($159) plus wildlife-watching and snorkelling.
4 Sleeping & Eating
Beachside Apartment Hotel APARTMENT $$
( 08-9529 3777; www.beachsideapartment.com.au; 58 Kent St; apt $210-302; ) Right on the esplanade, these apartments are spacious, sunny and secure. The block's not supermodern, but there's an up-to-date feel to the decor and discounts for stays longer than a week.
Pengo's Cafe CAFE $
(153 Arcadia Dr; snacks & mains $8-18; 8am-4.30pm Sep-May, reduced hours in winter) Good coffee, gourmet burgers and fresh salads shine at this excellent cafe near the Rockingham Wild Encounters ticket office. There's a nice alfresco deck and lots of grass for the kids to run around on.
Rustico CAFE, TAPAS $$
(www.rusticotapas.com.au; 61 Rockingham Beach Rd; tapas $11-19, pizzas $14-16.50; noon-late Mon-Sat, to 10pm Sun) This stylish cafe is renowned for authentic Spanish-style tapas. Secure a seat on the expansive corner terrace with ocean views, and tuck into chicken empanadas or scallops with chorizo. Good pizzas and larger shared plates are also available, and there's live acoustic music on Sunday afternoons.
Bettyblue Bistro SEAFOOD $$
( 08-9528 4228; www.bettybluebistro.com; 3-4 The Boardwalk; mains $18-34; 8am-2pm Mon-Tue, 9am-late Wed-Sun) The vibe at this licensed bistro is casual, with tables that allow you to gaze straight out to sea. Try the pomegranate- glazed barramundi with a salad of Israeli couscous.
8 Information
Visitor Centre ( 08-9592 3464; www.rockinghamvisitorcentre.com.au; 19 Kent St; 9am-5pm; ) Accommodation listings if you want to overnight.
8 Getting There & Around
Rockingham sits within Zone 5 of the Perth public transport system, Transperth ( 13 62 13; www.transperth.wa.gov.au) . Regular trains depart, via the Mandurah line, to Perth Underground/Esplanade ($7.10, 34 minutes) and Mandurah ($4.90, 18 minutes).
Rockingham station is around 4km southeast of Rockingham Beach and around 6km east of Mersey Point, from where the Penguin Island ferries depart; catch bus 551 or 555 to the beach or stay on the 551 to Mersey Point.
## Peel Region
Taking in swaths of jarrah forest, historic towns and the increasingly glitzy coastal resort of Mandurah, the Peel region can easily be tackled as a day trip from Perth or as the first stopping point of a longer expedition down the South Western Hwy (Rte 1).
As you enter the Peel, you'll pass out of Wadjuk country and into that of their fellow Noongar neighbours, the Pinjarup (or Binjareb) people.
### HEADING SOUTH
The fastest and simplest route south from central Perth is to jump on the Kwinana Fwy. Rather than visiting Rockingham and the Peel region as separate day trips, you could turn them into a 220km loop: Perth–Rockingham– Mandurah–Pinjarra–Dwellingup– Jarrahdale–Perth. A good overnight stop is Mandurah.
Top of Chapter
Mandurah
pop 68,300
Shrugging off its fusty retirement-haven image, Mandurah has made concerted efforts to reinvent itself as an upmarket beach resort, taking advantage of its new train link to Perth's public-transport network. And, although its linked set of redeveloped 'precincts' and 'quarters' may sound a little pretentious, the overall effect is actually pretty cool. You can wander along the waterfront from the Ocean Marina (boats, cafes and the Dolphin Quay indoor market), past the Venetian Canals (glitzy apartments linked by Venetianish sandstone bridges), through the Boardwalk and Cultural Precinct (more eateries, visitor centre, cinema, arts centre) to the Bridge Quarter (still more restaurants and bars). At the time of writing the local debate was whether to continue development of Mandurah's shiny new image, or refocus on the city's more laidback and authentic past. Watch this space.
The bridge spans the Mandurah Estuary, which sits between the ocean and the large body of water known as the Peel Inlet. It's one of the best places in the region for fishing, crabbing, prawning (March and April) and dolphin spotting.
1 Sights & Activities
Beaches SWIMMING
There are plenty of beautiful beaches within walking distance of the Mandurah waterfront. Town Beach is just across from the marina, at the southern end of Silver Sands – perhaps the best of the ocean beaches. There's a designated, boat-free swimming area on the far side of the estuary, just north of Mandurah Bridge. Here dolphins have been known to swim up to unwitting kids for a frolic. Facing the ocean, west of the mouth of the estuary, is family-friendly Doddi's Beach .
Mandurah Ferry Cruises CRUISE
( 08-9535 3324; www.mandurahferrycruises.com; Boardwalk) Take a one-hour Dolphin & Mandurah Waterways Cruise (adult/child $28/14; on the hour 10am-4pm) , a half-day Murray River Lunch Cruise (adult/child $79/49; Sep-May) and, through December, a one-hour Christmas Lights Canal Cruise (adult/child $30/15; Dec–mid-Jan) , that gawps at millionaires' mansions under the pretence of admiring their festive displays. Other cruise options incorporate catching and cooking Mandurah's famous blue manna crabs, and a heritage cruise highlighting the region's history.
Mandurah Boat & Bike Hire BOATING, CYCLING
( 08-9535 5877; www.mandurahboatandbikehire.com.au; Boardwalk; bike hire per hr/day $10/33) Chase the fish on a four-seat dinghy or six-seat pontoon (per hour/day from $50/320).
Australian Sailing Museum MUSEUM
(www.australiansailingmuseum.com.au; Ormsby Tce; adult/child $10/5; 9am-5pm) A very cool building housing 200 model yachts and tall ships, as well as a replica of the America's Cup and a cafe.
Hall's Cottage HISTORIC BUILDING
(Leighton Pl, Halls Head; admission by gold coin donation; 10am-3pm Sun) An 1830s cottage and one of the first dwellings in the state.
4 Sleeping
Mandurah Ocean Marina Chalets MOTEL $$
( 08-9535 8173; www.marinachalets.com.au; 6 The Lido; studios & chalets $116-165) The ambience is a bit like a British holiday camp, but the chalets and motel units are spotless and modern with fully equipped kitchens. A shared barbecue area – complete with a crab-cooking facility – make it easy to meet other travelling families, and the canals and restaurants of Ocean Marina and Dolphin Quay are a short walk away.
Seashells Resort RESORT $$
( 08-9550 3000; www.seashells.com.au; 16 Dolphin Dr; apt from $199; ) Seashells' apartments are cool and spacious, and there's a beach on its doorstep and a lovely infinity-lipped pool just metres away. Check into one of its luxury beachfront villas and you may not want to leave.
Sebel APARTMENT $$
( 08-9512 8300; www.mirvachotels.com; 1 Marco Polo Dr; r/apt from $159/259; ) If this was actually Venice, you'd have to be staying in the Doge's Palace for a better location. This big white apartment block offers well-appointed modern apartments and studio rooms, all with views. There's plenty of free parking plus a heated pool and small gymnasium. Downstairs is the excellent M on the Point bar and restaurant.
5 Eating
Restaurants and cafes abound on the Boardwalk and Dolphin Quay. At the time of writing, planned new openings included an oyster bar, and Thai and Indian eateries.
Cafe Moka CAFE $
(www.cafemoka.com.au; Dolphin Quay; breakfast $10-17, lunch $13-26; 8am-4pm) Mandurah's best brekkie option is well positioned to soak up the morning sun on the edge of the marina.
Cicerello's FISH & CHIPS $$
(www.cicerellos.com.au; 73 Mandurah Tce; mains $18-28; 9.30am-11.30pm) A boardwalk-facing branch of the Fremantle institution.
M on the Point INTERNATIONAL $$
(www.mbarandrestaurant.com.au; 1 Marco Polo Dr; pizzas $20-25, mains $28-37; noon-late) The three classy bars beneath the Sebel are the perfect place for a Sunday sundowner, and the attached restaurant has been recognised by the _Good Food Guide_ . Either kick back with a cold one and gourmet pizza in the Long Bar, or try sophisticated food like lemongrass butter poached salmon in the restaurant.
Taste & Graze CAFE $$
(www.tasteandgraze.com.au; 16 Mandurah Tce, Shop 3/4; mains $15-30, shared-plate menus per person $45; 9am-4pm Sun-Thu, till late Fri & Sat) Back in town in 'old' Mandurah, and perfectly located to catch the afternoon sun. Outdoor seating and a versatile Modern Australian menu covering breakfast, lunch and shared smaller plates make it a cosmopolitan slice of cafe cool. It's also handily adjacent to the Brighton Hotel if you're looking to kick on.
Taku Japanese Kitchen JAPANESE $$
(52 Mandurah Tce, Shop 2, Scott's Plaza; mains $10-18; 11.30am-2.30pm & 5-9pm Tue-Sun) Away from Mandurah's tourist glitz, this friendly family-run operation across the road from the town beach turns out excellent tempura, sashimi and sushi. Grab a good-value bento box and settle in for a lazy seaside lunch.
6 Drinking & Entertainment
Brighton Hotel PUB
(www.brightonmandurah.com.au; 10-12 Mandurah Tce) Watch the sun set over the estuary with a glass of wine, and return after 9pm on the weekends to move to the DJs.
Mandurah Performing Arts Centre CONCERT VENUE
( 08-9550 3900; www.manpac.com.au; Ormsby Tce) The main regional centre for theatre, dance and concerts.
Reading Cinema CINEMA
(www.readingcinemas.com.au; 7 James Service Pl) Blockbusters and occasional arthouse surprises; located just off the boardwalk.
8 Information
Visitor Centre ( 08-9550 3999; www.visitmandurah.com; 75 Mandurah Tce; 9am-5pm; ) On the estuary boardwalk.
8 Getting There & Away
Mandurah is 72km from central Perth; take the Kwinana Fwy and follow the signs.
It sits within the outermost zone (7) of the Perth public transport system and is the terminus of Transperth's Mandurah line. There are direct trains from Mandurah to Perth Underground/Esplanade ($9.40, 50 minutes) and Rockingham ($7.10, 18 minutes).
Transwa ( 1300 662 205; www.transwa.wa.gov.au) coach routes include:
SW1 (12 per week) to East Perth ($16, 1½ hours), Bunbury ($16, two hours), Busselton ($24, 2¾ hours), Margaret River ($33, four hours) and Augusta ($35, 4¾ hours).
SW2 (thrice weekly) to Balingup ($27, three hours), Bridgetown ($30, 3½ hours) and Pemberton ($41, 4½ hours).
GS3 (weekly) to Denmark ($65, 7¼ hours) and Albany ($71, eight hours).
South West Coach Lines ( 08-9261 7600; www.veoliatransportwa.com.au) has services to/from Perth's Esplanade Busport ($18, 1¼ hours, twice daily), Bunbury ($18, 1¼ hours, twice daily), Busselton ($30, 2½ hours, daily), Dunsborough ($32, 3¼ hours, daily) and Bridgetown ($32, 3¼ hours, weekdays).
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Yalgorup National Park
Fifty kilometres south of Mandurah is this beautiful 12,000-hectare coastal park, consisting of 10 tranquil lakes and their surrounding woodlands and sand dunes. The park is recognised as a wetland of international significance for seasonally migrating waterbirds, with 130 species identified.
Amateur scientists can visit the distinctive thrombolites of Lake Clifton, which are descendants of the earliest living organisms on earth (they are the only life form known to have existed over 650 million years ago). These rocklike structures are most easily seen when the water is low, particularly during March and April. There's a viewing platform on Mt John Rd off Old Coast Rd; keep an eye out for long-neck tortoises below the boardwalk. A 5km walking track starts from here and loops around the lake.
Lake Pollard trail (6km) begins about 8km down Preston Beach North Rd (not Preston Beach Rd, as marked on some maps). The pleasant Martins Tank Lake campground is to the right of the entrance. The trail takes in tuart, jarrah and bull banksia on its way to the lake, which is known for its black swans (October to March).
The Heathlands trail (4.5km) to Lake Preston starts at the information bay on Pres- ton Beach Rd (before the turn-off to Preston Beach North Rd) and explores the tuart woodland. Further along Preston Beach Rd is Preston Beach .
### PINJARRA: BATTLE OR MASSACRE?
The popular myth of Australia's Indigenous people sitting back passively while the British took their land doesn't fly in the Peel region. From the outset, after Thomas Peel was 'granted' this land, its Pinjarup owners asserted their rights – spearing stock and destroying crops. An uneasy truce was reached, with the Pinjarup given regular rations of flour, which they probably viewed as a kind of rent.
In 1834 the cutting of flour rations led Pinjarup leader Calyute to stage a raid on a flour mill. Four of his men were arrested in Mandurah and taken to Perth, where they were publically flogged. Retribution was taken on a 19-year-old British servant (fair game under Noongar law as he was considered a member of the offending party's tribe), who was killed and then ritually mutilated.
This caused an uproar among the settlers, with Peel strongly urging Governor Stirling to take action. Stirling led a party of soldiers and settlers, including Peel, to Pinjarra, where they surprised Calyute's people and opened fire on their encampment. What happened then is contested. Stirling's official report put the death toll at 15 men, while the _Perth Gazette_ reported 25 to 30 dead. The Pinjarup claim that the camp consisted mainly of women and children and that the death toll was far higher. There was only one British casualty.
Stirling's threat to the survivors, that 'if any other person should be killed by them, not one (of their people) would be allowed to remain alive on this side of the mountain', seemed to have had the desired effect, and curtailed any future resistance.
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Pinjarra
pop 3300
Stretching along the Murray River, genteel Pinjarra now seems the epitome of peace and quiet. Yet it's best known as the site of a bloody incident in 1834 that was once remembered as the Battle of Pinjarra and is now known as the Pinjarra Massacre.
1 Sights & Activities
Town Centre HISTORIC BUILDINGS
The South Western Hwy passes through Pinjarra's small historic precinct, immediately after crossing the Murray. St John's Church , built 1861–62 from mud bricks, sits beside a heritage rose garden and the original 1860 schoolhouse (now a quilt workshop). Across Henry St is the Edenvale Complex , with tea rooms (mains $6-15; 9am-4pm) in the old homestead (1888), art and craft galleries and a machinery display in the outbuildings. On the other side of the highway, you can cross the river on foot via an old suspension bridge .
Peel Zoo ZOO
(www.peelzoo.com; Sanctuary Dr, off Pinjarra Rd; adult/child $18/9; 10am-4pm Mon-Fri, 9am-5pm Sat & Sun) Peacocks strut while parrots issue wisecracks as you wander around this cute little zoo, which focuses on Australian wildlife: kangaroos, wallabies, Tasmanian devils, koalas, wombats, possums, quolls, snakes and lots of native birds.
Old Blythewood Homestead HISTORIC BUILDING
(www.ntwa.com.au; South Western Hwy; adult/child $4/2; 11am-3pm Sat & Sun, closed Aug) An 1859 National Trust–owned farmhouse, furnished with antiques; about 4km south of Pinjarra.
WA Skydiving Academy SKYDIVING
( 1300 137 855; www.waskydiving.com.au) Tandem jumps from 6000/10,000/14,000ft for $260/340/420.
5 Eating
Raven Wines CAFE
(www.ravenwines.com.au; cnr Wilson & Pinjarra Rds; small plates $10-15, cheeseboard $24; 10am-5pm Wed-Sun) This chic cafe is part of a compact vineyard on the edge of town. Wine tasting and interesting small plates with an Asian or Med spin provide a welcome contrast to the occasionally chintzy heritage overkill of downtown Pinjarra.
8 Information
Visitor Centre ( 08-9531 1438; www.murray.wa.gov.au; Fimmel Lane; 9.30am-4pm) Housed in the heritage train-station.
8 Getting There & Away
Pinjarra is on the Transwa ( 1300 662 205; www.transwa.wa.gov.au) Australind train line, with twice-daily services to Perth ($16, 1¼ hours) and Bunbury ($16, 1¼ hours).
### ROCK & ROLL
At 350km from Perth, Wave Rock is rather a long day trip, and some people are disappointed by what's really a one-trick gig. However, you can spice up this trip by hunting out other, lesser-known granite outcrops and curiosities. All you need is a map and a sense of adventure. (Hint: most of the granite outcrops end in 'Rock'.) To get you started, try Kokerbin Rock, Jilakin Rock, Dragon Rocks and Yorkrakine Rock. Visitor centres en route can supply maps.
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Dwellingup
pop 550
Dwellingup is a small, forest-shrouded township with character, 100km south of Perth. Its reputation as an activity hub has been enhanced by the hardy long-distance walkers and cyclists passing through on the Bibbulmun Track and the Munda Biddi Trail respectively.
1 Sights & Activities
Forest Heritage Centre NATURE RESERVE
(www.forestheritagecentre.com.au; 1 Acacia St; adult/child/family $5.50/2.20/11; 10am-3pm) Set within the jarrah forest, this interesting rammed-earth building takes the shape of three interlinked gum leaves. Inside are displays about the forest's flora and fauna, and a shop that sells beautiful pieces crafted by the resident woodwork artists. Short marked trails lead into the forest, including an 11m-high canopy walk. Look for the resident flock of red-tailed black cockatoos, and keep an eye out for the laidback mob of kangaroos that surprised us on our last visit.
Hotham Valley Railway HISTORIC TRAIN
( 08-9221 4444; www.hothamvalleyrailway.com.au) On weekends (and Tuesday and Thursday during school holidays), the Dwellingup Forest Train (adult/child $24/12; departs 10.30am & 2pm) chugs along 8km of forest track on a 90-minute return trip. It's usually steam driven but in summer they revert to diesel engines due to the fire risk. There's a 30-minute stopover at the end where you can take a short bushwalk. Every Saturday night and some Fridays, the Restaurant Train (tickets $79; departs 7.45pm) follows the same route, serving up a five-course meal in a 1919 dining car. A third option is the Steam Ranger (adult/child $34/17; departs 10.30am) , travelling 14km via WA's steepest rail incline to Isandra Siding. Steam Ranger trains only run on Sunday from May to October.
Dwellingup Adventures KAYAKING, RAFTING
( 08-9538 1127; www.dwellingupadventures.com.au; 1-person kayaks & 2-person canoes per day $45; 8.30am-5pm) Don't miss the opportunity to get out on the beautiful Murray River. Hire camping gear, bikes, kayaks and canoes, or take an assisted, full day, self-guided paddling tour ($90 per one-person kayak) or full-day cycling tour ($97/124/174 per one/two/three people). White-water rafting tours are available from June to October ($130 per person).
8 Information
Visitor Centre ( 08-9538 1108; www.murraytourism.com.au; Marrinup St; 9am-3pm) Interesting displays about the 1961 bushfires that wiped out the town, destroying 75 houses but taking no lives. The centrepiece is a shiny Mack firetruck (1939).
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Jarrahdale & Serpentine National Park
pop 956
Established in 1871, Jarrahdale is another old mill village, reached by a leafy 6km drive east from the South Western Hwy. The Old Post Office (www.jarrahdale.com; walks $5; 10am-4pm Sat & Sun) , built in 1896, houses a small local museum. Guided walks run by volunteers from the heritage society depart from here.
Picturesque Millbrook Winery ( 08-9525 5796; www.millbrookwinery.com.au; Old Chestnut Lane, signed off Jarrahdale Rd; mains $36-45; 10am-5pm Wed-Sun) has a tranquil setting overlooking a small lake. Lunch bookings are recommended, especially on weekends.
The town of Jarrahdale sits on the northern fringes of Serpentine National Park (www.dec.wa.gov.au; per car $11; 8.30am-5pm) , a forested area with walking tracks, picnic areas and a leisurely 15m slide of water known as the Serpentine Falls (Falls Rd, off South Western Hwy) . If you're not in a hurry to get somewhere, it's worth taking a pleasant detour through the park from Jarrahdale, following Kingsbury Dr to the Serpentine Dam before curving back to the highway.
## Dryandra to Hyden
A beautiful forest, rare marsupials, stunning ancient granite-rock formations, salt lakes, interesting back roads and the unique Wave Rock are the scattered highlights of this widespread farming region.
WORTH A TRIP
### DRYANDRA WOODLAND
This superb, isolated remnant of eucalypt forest 164km southeast of Perth, with its thickets of white-barked wandoo, powderbark and rock she-oak, and small populations of threatened numbats, woylies and tammar wallabies, hints at what the wheat belt was like before large-scale land clearing and feral predators wreaked havoc on the local ecosystems. It also makes a great weekend getaway, and there are numerous walking trails.
The excellent Barna Mia Animal Sanctuary , home to endangered bilbies, boodies, woylies and marl, conducts 90-minute after-dark torchlight tours, providing a rare opportunity to see these cute furry creatures up close. Book through DEC ( weekdays 08-9881 9200, weekends 08-9881 2064; www.dec.wa.gov.au; Hough St, Narrogin; adult/child/family $14/7.50/37.50; 9am-4pm) for post-sunset tours on Monday, Wednesday, Friday and Saturday; book early for peak periods.
While you can hoist your tent at the pleasant Congelin Camp Ground ( 08-9881 9200; per person $10) , Dryandra is one place you should splurge a little. The Lions Dryandra Village ( 08-9884 5231; www.dryandravillage.org.au; adult/child $30/15, 2-/4-/8–12-person cabins $70/90/130) is a 1920s forestry camp in the heart of the forest, offering fully self-contained, renovated woodcutters' cabins complete with fridge, stove, fireplace, en suite and nearby grazing wallabies. Narrogin (www.dryandratourism.org.au) , serviced by Transwa buses, is 22km southeast.
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Hyden & Wave Rock
Large granite outcrops dot the area known as the Central and Southern Wheatbelts, and the most famous is the perfectly shaped, multicoloured cresting swell of Wave Rock . Formed some 60 million years ago by weathering and water erosion, Wave Rock is streaked with colours created by run-off from local mineral springs.
To get the most out of Wave Rock, 350km from Perth, grab the brochure _Walk Trails at Wave Rock and The Humps_ from the visitor centre ( 08-9880 5182; www.waverock.com.au; Wave Rock; 9am-5pm) . Park at Hippos Yawn (no fee) and follow the shady track back along the rock base to Wave Rock (1km).
Accommodation can fill quickly, so phone ahead for a spot amid the gum trees at Wave Rock Cabins & Caravan Park ( 08-9880 5022; www.waverock.com.au; unpowered/powered sites from $28/35, cabins from $140, cottages from $160; ) .
In Hyden (population 190), 4km east of the rock, the '70s brick Wave Rock Motel ( 08-9880 5052; www.waverock.com.au; 2 Lynch St; s/d from $105/150; ) has well-equipped rooms, a comfy lounge with fireplace, and an indoor bush bistro.
If heading to/from the Nullarbor, take the unsealed direct Hyden–Norseman Road to save 100km or so. Look for _The Granite and Woodlands Discovery Trail_ at Norseman or Wave Rock visitor centres.
8 Getting There & Away
This area is best seen with your own vehicle, ideally on the way to somewhere else. Transwa ( 1300 662 205; www.transwa.wa.gov.au) runs a bus from Perth to Hyden ($51, five hours) and on to Esperance ($53, five hours) every Tuesday, returning on Thursday.
Western Travel Bug ( 08-9486 4222; www.travelbug.com.au; tours $175) offers a one-day tour, or, alternatively, you could see it as part of a six-day southwest loop with Western Xposure ( 08-9414 8423; www.westernxposure.com.au; tours $750)
## Darling Range
Commonly known as the Perth Hills, this forest-covered escarpment provides the city with a green backdrop and offers great spots for picnicking, barbecues, bushwalking and rubbing shoulders with wild kangaroos. Leafy suburbs nestle at its feet, along with a few dozen wineries.
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Kalamunda
pop 54,700
Kalamunda is a well-heeled township on the crest of the Darling Range. The area began as a timber settlement, but it's since become a quieter residential haven close to the city (it's a 30-minute drive from Perth).
The main shopping area on Haynes St has good pubs and cafes. Nearby is Stirk Cottage (www.kalamundahistoricalsociety.com; Kalamunda Rd; 2-4pm Sun) F , built of mud, saplings and shingle in 1881.
For walkers, Kalamunda is the northern terminus of the Bibbulmun Track , which starts near the shops and heads into the forest of Kalamunda National Park .
From Zig-Zag Dr, just north of Kalamunda off Lascelles Pde, there are fantastic views over Perth to the coast. The drive through the forested hills to Mundaring via Mundaring Weir Rd is also wonderful, but watch out for kangaroos.
### ARALUEN BOTANIC PARK
South of Kalamunda, just off Brookton Hwy, is Araluen Botanic Park (www.araluenbotanicpark.com.au; 362 Croyden Rd, Roleystone; adult/child $4/2; 9am-6pm) . Constructed in the 1920s by the Young Australia League (YAL) as a bush retreat, the park was neglected for years and became overgrown. The state government purchased it in 1990 and has since restored its elaborate garden terraces, waterfalls and ornamental pool. The spring tulip displays are wonderful.
8 Getting There & Away
From Perth, buses 283, 295, 296, 298 and 299 all head to Kalamunda ($4.90, 47 minutes).
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Mundaring
pop 38,300
Located 35km east of Perth, Mundaring's a laid-back spot with a small artistic community. Bisected by the busy Great Eastern Hwy, the township itself isn't particularly interesting, but the Mundaring Arts Centre (www.mundaringartscentre.com; 7190 Great Eastern Hwy; 10am-5pm Mon-Fri, 11am-3pm Sat & Sun) exhibits and sells the work of local artists.
The 16-sq-km John Forrest National Park (www.dec.wa.gov.au; admission per car $11) , west of Mundaring, was the state's first national park. Protected areas of jarrah and marri trees are scattered about granite outcrops, waterfalls and a pool.
Immediately south of Mundaring is Beelu National Park (www.dec.wa.gov.au) , part of a continuous swath of forest that includes Kalamunda National Park. The Perth Hills National Parks Centre ( 08-9295 2244; www.dec.wa.gov.au/n2n; Allens Rd, off Mundaring Weir Rd) hosts a series of kids programs with a flora-and-fauna spin. There's a good camp-ground (adult/child $9/2), well positioned for the Bibbulmun Track, which passes nearby. A more secluded and primitive camp- ground is available at Paten's Brook ($5 per person).
From November to April, kick back in a deckchair at the open-air Kookaburra Cinema ( 08-9295 6190; www.kookaburracinema.com.au; Allen Rd; adult/child $13/8) , just across the road from the park centre. A little further south is Mundaring Weir , a dam built 100 years ago to supply water to the goldfields more than 500km to the east. The reservoir is a blissful spot, with walking trails and a well-positioned pub. Come dusk, the whole area swarms with kangaroos.
East from Mundaring and north of the Great Eastern Hwy, near Chidlow, is freshwater Lake Leschenaultia ( 8.30am-dusk) , a picturesque former railway dam, complete with a swimming pontoon.
4 Sleeping & Eating
Department of Education Hostel HOSTEL $
( 08-9295 0202; www.mundaringtourism.com.au; Mundaring Weir Rd; dm $25) Close to the weir, this basic hostel has a quiet bush setting, and is around 8km south of town. It's used by school groups, but there's usually room for other guests, especially if you're walking the Bibbulmun Track. Book through the Mundaring Visitors Centre, and look forward to kangaroo company at dusk.
Mundaring Weir Hotel HOTEL $
( 08-9295 1106; www.mundaringweirhotel.com.au; Weir Village Rd; r Mon-Thu $115, Fri-Sun $140; ) Overlooking the weir, this 1898 pub has bucketloads of ramshackle character. Rooms are simple but tidy, with DVD players and microwaves. The rooms also open onto an amphitheatre, which mainly functions as a beer garden but occasionally hosts concerts. Recent performers have included Aussie icons such as Kasey Chambers and Mark Seymour.
Loose Box RESTAURANT $$$
( 08-9295 1787; www.loosebox.com.au; 6825 Great Eastern Hwy; degustation $150; 7pm-late Wed-Sat, noon-3pm Sun) A French fine-dining restaurant with provincial decor, Loose Box has such a formidable reputation that it can maintain a strictly degustation-only policy and still have people clamouring to get in. Luxury cottages are available within the grounds, so you can splash out and make a night of it (B&B $450, with meal $700 to $750).
8 Information
Visitor Centre ( 08-9295 0202; www.mundaringtourism.com.au; 7225 Great Eastern Hwy; 9.30am-4pm Mon-Sat, 10.30am-2.30pm Sun)
8 Getting There & Away
You can reach Mundaring from Perth on public transport in just over an hour, by taking a train to Midland and then bus 320 ($5.80). From here it's still 6km to the weir.
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Walyunga National Park
The Avon River cuts a narrow gorge through the Darling Range at Walyunga National Park (www.dec.wa.gov.au; admission per car $11; 8am-5pm) in Upper Swan. Off the Great Northern Hwy (Rte 95), 40km northeast of Perth, this 18-sq-km park is a great place for hiking and picnics.
The bushwalks include a 5.2km-return walk to Syd's Rapids as well as a 1.2km Aboriginal Heritage Trail. The best trail is the 10.6km Echidna Loop, which has tremendous views over the Swan and Avon Valleys. The park has one of the largest known camp sites of the Noongar people, still in use in the late 1800s. The area may well have been occupied by Aboriginal people for more than 6000 years.
## Swan Valley & Guildford
Perthites love to swan around this semi-rural valley on the city's eastern fringe to partake in the finer things in life: booze, nosh and the great outdoors. Perhaps in tacit acknowledgement that its wines will never compete with the state's more prestigious regions (it doesn't really have the ideal climate), the Swan Valley compensates with plenty of galleries, breweries, provedores and restaurants.
The gateway to the valley is the National Trust–classified town of Guildford, established in 1829, around the same time as Perth and Fremantle. A clutch of interesting old buildings, one housing the visitor centre, make it the logical starting place for day trippers. Guildford is only 12km from central Perth and well served by suburban trains.
History
Guildford is built on the conjunction of three rivers and was an important meeting and ceremonial place for the Wadjuk people. When the British arrived and travelled up the Swan, access to fresh water led them to establish one of their first settlements here. In 1833, four years after the colony's founding, resistance leader Yagan was shot and decapitated in the Swan Valley.
The fertile valley land was soon turned to farming. Vines were first planted in the 1830s at Houghton's but it was after the arrival of Croatian settlers (from around 1916) that the farmland was increasingly transformed into wine production.
1 Sights & Activities
In Guildford, the centre of town is Stirling Sq, at the intersection of Swan and Meadow Sts. The cluster of buildings opposite the square includes the Old Courthouse (1866), which houses the visitor centre and has interesting historical displays. In the same grounds are the gaol (Old Courthouse; adult/child $2/free; 10am-2pm Wed, Fri & Sat) and Taylor's Cottage (1863; admission included with gaol entry). Various heritage walks start from here; get information from the visitor centre or download a trail card from its website. Two kilometres east is Woodbridge House (Ford St; adult/child $5/3; 1-4pm Thu-Sun) , an 1885 colonial mansion overlooking the river.
The following sights are in the nearby Swan Valley.
Gomboc Gallery GALLERY
(www.gomboc-gallery.com.au; 50 James Rd, Middle Swan; 10am-5pm Wed-Sun) F One of WA's best commercial galleries, surrounded by an intriguing sculpture park.
Whiteman Park PARK
(www.whitemanpark.com; 8.30am-6pm) Located in Caversham in West Swan, at 26 sq km this is Perth's biggest park, with over 30km of walkways and bike paths, and numerous picnic and barbecue spots. Enter from Lord St or Beechboro Rd, West Swan.
Caversham Wildlife Park ZOO
(www.cavershamwildlife.com.au; adult/child $23/10; 9am-5.30pm, last entry 4.30pm) Part of the Whiteman Park estate, this wildlife park features cassowaries, echidnas, kangaroos, koalas, echidnas, potoroos, quokkas and native birds. Say g'day to Neil, the very laidback southern hairy wombat, for us. There are also farm shows for the kids.
Bennet Brook Railway TRAIN RIDES
(www.whitemanpark.com; adult/child $8/4; 11am-1pm Wed, Thu, Sat & Sun) Train rides on the Whiteman Park estate.
Tram Rides TRAM RIDES
(www.pets.org.au; adult/child $5/2.50; noon-2pm Tue & Fri-Sun) Rides on heritage trams at Whiteman Park.
Revolutions MUSEUM
(www.whitemanpark.com.au; entry by gold coin donation; 10am-4pm) Museum celebrating transport in WA with horse-drawn wagons, camels, trains, boats and planes. It's located on the Whiteman Park estate.
Motor Museum of WA MUSEUM
(www.motormuseumofwa.asn.au; adult/child $10/7; 10am-4pm) Vintage cars and motorbikes. Located at Whiteman Park.
5 Eating & Drinking
In this 'Valley of Taste' eating and drinking tend to go hand in hand as many of the wineries and breweries have restaurants attached.
The Swan Valley vibe is more low-key and relaxed than that of Margaret River – don't expect grand estates. There are more than 40 vineyards, concentrated mainly along busy West Swan Rd (the road leading north from the visitor centre) and the Great Northern Hwy (running parallel to the east). There's an excellent map in the free _Food & Wine Trail Guide, _ available from the visitor centre in Guildford. Tastings are usually free.
The following are all in the Swan Valley, with the exception of the Rose & Crown and Jezebelle, both in Guildford.
Margaret River Chocolate Company CHOCOLATE, CAFE $
(www.chocolatefactory.com.au; 5123 West Swan Rd, West Swan; 9am-5pm) With free tastings, this chocolate shop is often mobbed by families and tour groups.
Jezebelle CAFE, TAPAS $$
( 08-6278 3538; www.jezebelle.com.au; 127 James St, Guildford; tapas & shared plates $10-24, breakfast $12-24; noon-late Wed-Fri, 7am-late Sat, 7am-6pm Sun) An exciting selection of WA, Spanish and Italian wines partner with interesting tapas and shared plates at Guildford's Jezebelle. Try the manchego cheese and capsicum croquettes with sweetcorn relish or chicken and rabbit paella. Leisurely weekend breakfasts are equally classy. Bookings are recommended for dinner, and it's a short walk from the Guildford train station if you're staying in Perth.
Rose & Crown PUB $$
(www.rosecrown.com.au; 105 Swan St, Guildford; mains $26-39) In Guilfdord, WA's oldest still-operating pub (1841) has a wonderful leafy beer garden and lots of different spaces to explore inside. Have a beer in the cellar bar, where there's a convict-built well, and, while you're there, check out the sealed-off tunnel that used to connect the hotel with the river.
Black Swan RESTAURANT, WINERY $$
( 08-9296 6090; www.blackswanwines.com.au; 8600 West Swan Rd, Henley Brook; mains $29-38; tastings 11am-3pm, lunch daily, dinner Wed-Sat) It's slightly ugly duckling from the outside, but inside Black Swan has an upmarket dining room with views looking over the vines to the ranges. The food is sophisticated and delicious, ranging from grilled Tasmanian salmon to top-quality eye fillet beef (the latter around $45).
Sandalford RESTAURANT $$$
(www.sandalford.com; 3210 West Swan Rd, Caversham; mains $36-45; tastings 9am-5pm, lunch noon-3pm) Sandalford has the nicest surrounds of any of the wineries, and plays host to weddings and major concerts. It's also one of the valley's big-time, long-term operators.
Lamont's TAPAS $$
(www.lamonts.com.au; 85 Bisdee Rd, Millendon; tapas $11.50-18.50; 10am-5pm Thu-Sun) Now that Lamont winery's fine-dining efforts are focused in East Perth, it's just lazy tastings and tapas up here under the open sky. The wine's very good, much of it grown in its Margaret River vineyard.
o RiverBank Estate MODERN AUSTRALIAN $$$
( 08-9377 1805; www.riverbankestate.com.au; 126 Hamersley Rd, Caversham; mains $36-40; tastings 10am-5pm, lunch) Our pick of the valley's restaurants, RiverBank winery is a wonderful place to while away a few hours over excellent Modern Australian cuisine. It's a little more dressed up than most other places and there's a charge for tastings if you're not dining in the restaurant, but we're willing to let that go when the food's this good. There's live jazz on the first Saturday of the month.
Dear Friends MODERN AUSTRALIAN $$$
( 08-9279 2815; www.dearfriends.com.au; 100 Benara Road, Caversham; degustation menu with/without wine $ 185/115, 5-course tasting menu with/without wine $ 139/89; 6pm-late Wed-Sat, noon-3pm Sat & Sun) Get ready for a culinary adventure at Dear Friends. Innovation and a host of international flavours are showcased in the restaurant's renowned degustation and tasting menus. Courses include air-dried ham with Swan Valley free-range yolks and locally foraged herbs, and dessert combining beetroot with wood sorrel and rich dark chocolate. Naturally, the wine list is one of WA's finest.
o Feral Brewing Company CRAFT BEER
(www.feralbrewing.com.au; 152 Haddrill Rd; 11am-5pm Sun-Thu, till late Fri & Sat) Here's your chance to try some of Australia's finest craft beers. Head brewer Brendan Varis is regularly lauded, with his always-interesting brews including the mighty Hop Hog American Pale Ale, or Watermelon Warhead, a wheat beer infused with watermelon (!). Beer geeks definitely should sign up for a tasting paddle of six beers, and tuck into Feral's robust pub grub menu.
Mash CRAFT BEER
(www.mashbrewing.com.au; 10250 West Swan Rd, Henley Brook; 11am-5pm Mon-Tue, till late Wed-Sun) A lively bar-like atmosphere and a selection of homemade lager, ales, wheat beer and cider. Interesting seasonal brews are always worth trying.
Houghton WINERY
(www.houghton-wines.com.au; Dale Rd, Middle Swan; 10am-5pm) The Swan's oldest and best-known winery is surrounded by pleasant grounds, which include a jacaranda grove. There's a gallery in the cellar where bushranger Moondyne Joe was caught, and a small display of old winemaking equipment.
8 Information
Visitor Centre ( 08-9379 9400; www.swanvalley.com.au; Old Courthouse, cnr Swan & Meadow Sts, Guildford; 9am-4pm) Information and maps, plus an interesting display on local history.
8 Getting There & Away
Guildford falls within Zone 2 of Perth's public transport system, and it's only $4 by bus or by train on the Midland Line from Perth, East Perth or Mt Lawley station.
To get around the Swan Valley you'll need to drive or take a tour ( Click here ). Bikes can be hired from Bike Hire at Brookleigh ( 08-9296 0012; bike.hire@brookleigh.com.au; 1235 Great Northern Hwy, Brookleigh) in the north of the valley.
For Whiteman Park, catch a train on the Midland Line from Perth to Bassendean Station. Switch to a bus to Ellenbrook and get off at Lord St (bus stop 15529).
## Avon Valley
The lush green Avon Valley – with its atmospheric homesteads featuring big verandahs, rickety wooden wagons and moss-covered rocks – was 'discovered' by European settlers in early 1830 after food shortages forced Governor Stirling to dispatch Ensign Dale to search the Darling Range for arable land. What he found was the upper reaches of the Swan River, but he presumed it was a separate river – which is why its name changes from 'the Swan' to 'the Avon' in Walyunga National Park. The valley was very soon settled, just a year after Perth was founded, and many of the historic stone buildings still stand proudly in the towns and countryside in the area.
This country traditionally belongs to the Balardung, another of the Noongar peoples.
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York
pop 2100
Unrelentingly quaint, York is the most atmospheric spot in the Avon Valley and a wonderful place to while away a couple of hours on a Sunday, when it's at its liveliest. Avon Tce is lined with restored heritage buildings, and the entire town has been classified by the National Trust.
Only 97km from Perth, York is the oldest inland town in WA, first settled in 1831, just two years after the Swan River Colony. The settlers here saw similarities in the Avon Valley and their native Yorkshire, so Governor Stirling bestowed the name York.
Convicts were brought to the region in 1851 and contributed to the development of the district; the ticket-of-leave hiring depot was not closed until 1872, four years after transportation of convicts to WA ceased. During the gold rush, York prospered as a commercial centre, servicing miners who were heading to Southern Cross, a goldfields town 273km to the east. Most of its buildings date from this time.
1 Sights & Activities
Avon Tce is lined with significant buildings , such as the town hall, Castle Hotel, police station, Old Gaol & Courthouse and Settlers House. Holy Trinity Church (Pool St) , by the Avon River, was completed in 1854 and features stained-glass windows designed by WA artist Robert Juniper, and a rare pipe organ. The suspension bridge across the Avon was built in 1906.
York Mill MARKET, GALLERY
(www.theyorkmill.com.au; 13 Broome St; 10am-4pm Wed-Sun) Built in 1892, York's four-storey flour mill now houses the Mill Cafe (www.theyorkmill.com.au; lunch $10-18; 10am-4pm Wed-Sun) and an excellent gallery selling jarrah furniture, and art and crafts by local artisans. There are free monthly exhibitions, and occasional one-off events like medieval fayres and banquets. A bistro and craft brewery are planned for late 2013.
Residency Museum MUSEUM
(www.yorksoc.org.au; Brook St; adult/child $4/1; 1-3pm Tue, Wed & Thu, 11am-3.30pm Sat & Sun) Built in 1858, this museum houses some intriguing historic exhibits and poignant old black-and-white photos of York.
Motor Museum MUSEUM
(www.yorkwa.com.au/Motor.Museum; 116 Avon Tce; adult/child $9/4; 9.30am-3pm) A must for vintage-car enthusiasts.
Skydive Express SKYDIVING
( 08-9444 4199; www.skydive.com.au; 3453 Spencers Brook Rd; tandem jumps 10,000/14,000ft $339/399) The Avon Valley is WA's skydiving centre; the drop zone is about 3km from town.
4 Sleeping & Eating
York is a popular getaway destination for charm-chasing Perthites, so prices rise on the weekends. Another good place to eat is the Mill Cafe.
York Caravan Park CARAVAN PARK $
( 08-9641 1421; york2caravan@hotmail.com; Eighth Rd; sites s/d $25/30) You can pitch your tent in a bush setting in this small park on the edge of town.
o Faversham House B&B $$
( 08-9641 1366; www.favershamhouse.com.au; 24 Grey St; r $120-275; ) If you've ever wished you were 'to the manor born', indulge your fantasies in this grand stone mansion (1840). The rooms in the main house are large, TV-free and strewn with antiques; some have four-poster beds. All have smallish private bathrooms. The cheaper rooms are in the old servants' quarters (naturally).
Imperial Inn BOUTIQUE HOTEL $$
( 08-9641 1255; www.imperialhotelyork.com.au; 83 Avon Tce; r $130-240; ) Located in a beautiful stone heritage building, the Imperial offers zooshed-up rooms across the lawn in what might well have been the old stables. There are no TVs but there are iPod docks. Check online for good midweek discounts.
Jules Cafe CAFE $
(121 Avon Tce; 8am-4pm Mon-Sat) S Putting a colourful spin on heritage York since 1990, Jules Cafe channels a Lebanese heritage for top-notch kebabs, falafel and Middle Eastern sweets. A funky new-age accent is introduced with organic, vege and gluten-free options.
8 Information
Visitor Centre ( 08-9641 1301; www.avonvalleywa.com.au; 81 Avon Tce, Town Hall; 10am-4pm)
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) coach routes include:
GE2 (three per week) to East Perth ($16, 1½ hours), Mundaring ($13, 47 minutes), Hyden ($38, 3¼ hours) and Esperance ($78, 8½ hours)
GS2 to Northam ($8, 33 minutes, six per week), Mt Barker ($53, 5¼ hours, four per week) and Albany ($58, six hours, four per week)
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Northam
pop 6000
This busy commercial centre is the major town of the Avon Valley. It's a likeable place with some fine heritage buildings and pleasant cafes, but little to justify a longer stay. The railway line from Perth once ended here and miners had to make the rest of the weary trek to the goldfields by road; it now continues all the way to Sydney.
In recent years, Northam has become the hub for various Avon Valley festivals.
z Festivals & Events
Avon Valley Vintage Festival VINTAGE, ANTIQUES
(ww.avonvalleywa.com.au; late Mar-early Apr) Three days of antiques and collectables, and vintage spins on fashion, cars and bicycles.
Avon Valley Gourmet Food & Wine Festival FOOD, WINE
(www.avonvalleywa.com.au; early Jun) A weekend of artisan food, wine and produce from the Avon Valley and around the state.
Avon River Festival SPORT
(www.avondescent.com.au; early Aug) Street parade, markets and fireworks followed by the Avon Descent, a gruelling 133km whitewater event for power dinghies, kayaks and canoes.
1 Sights & Activities
Burlong Pool NATURAL POOL
This picnic-ready natural pool on the Avon River is a very significant Noongar site. It is believed to be the summer home of the Wargal, the giant snakelike creature that created the waterways, and brought life to the land. It's customary to throw a handful of sand into the water out of respect. If the water stirs, keep out; otherwise all's well. Information boards recount this story and the site's history.
Follow the river southwest from the visitor centre for 3.5km. This is part of an 18km path along the river called Dorntj Koorliny (Walking Together). Otherwise, take Fitzgerald Rd, which becomes Burlong Rd, and follow it to the end.
Morby Cottage HISTORIC BUILDING
(Katrine Rd; adult/child $2/1; 10.30am-4pm Sun) Built in 1836 as the home of John Morrell (founder of Northam), it now houses various family heirlooms and early Northam memorabilia.
Old Railway Station Museum MUSEUM
(Fitzgerald St; adult/child $2/0.50; 10.30am-4pm Sun) This museum, housed in an 1886 National Trust–registered building, showcases railway memorabilia.
Windward Adventures BALLOONING
( 08-9621 2000; www.ballooning.net.au; weekday/weekend flights $270/320; Apr-Oct) Sunset flights followed by a champagne breakfast.
5 Eating
Cafe Yasou CAFE $
(www.cafeyasou.com.au; 175 Fitzgerald St; mains $11-18; 8am-4pm Mon-Fri, to noon Sat) This sunny cafe serves excellent coffee, grilled haloumi and Greek salads. If you're not in a Med mood, there's a selection of sandwiches and cakes. Our pick is the Yasou Breakfast, crammed with bacon, mushrooms, tomato and feta cheese on rosti potatoes.
Riversedge Cafe CAFE $
(www.riversedgecafe.com.au; 1 Grey St; breakfast $10-21, lunch $13-26; 8am-4pm) The verandahs of this big corrugated-iron building are a wonderful place to soak up the sun and river views.
8 Information
Visitor Centre ( 08-9622 2100; www.visitnorthamwa.com.au; 2 Grey St; 9am-5pm Mon-Fri, to 4pm Sat & Sun) Overlooking a picturesque portion of river with fountains and a compact island. The _Experience the Avon Valley_ brochure has good maps.
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) coach GS2 heads to East Perth ($19, 1½ hours, six per week), York ($8, 33 minutes, six per week), Mt Barker ($56, 5¾ hours, four per week) and Albany ($63, 6½ hours, four per week).
Northam is a stop on the AvonLink and Prospector lines, with trains to East Perth ($19, 1½ hours, 12 per week), Toodyay ($8, 20 minutes, 12 per week) and Kalgoorlie ($71, 5¼ hours, nine per week).
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Toodyay
pop 1100
Historic Toodyay, only 85km northeast of Perth, is a popular weekend destination for browsing the bric-a-brac shops or having a beer on the verandah of an old pub. As you'd expect of a town classified by the National Trust, it has plenty of charming heritage buildings. Originally known by the name Newcastle, Toodyay (pronounced '2J'), came from the Aboriginal word _duidgee_ (place of plenty); the name was adopted around 1910.
1 Sights & Activities
Connor's Mill MUSEUM
(Stirling Tce; admission $3; 9am-4pm) Start at the top of this aged flour mill (1870) and descend through three floors of chugging machinery and explanatory displays that cover the milling process, along with local history. Entry is through the neighbouring visitor centre. St Stephen's Church (1862), directly across the road, is also worth a look.
Newcastle Gaol MUSEUM
(17 Clinton St; admission $3; 10am-3pm) Built in the 1860s using convict labour, the gaol complex includes a courtroom, cells and stables. A gallery here tells the story of Moondyne Joe.
Coorinja WINE TASTING
(Toodyay Rd; 10am-5pm Mon-Sat) Operating continuously since the 1870s, this winery specialises in fortified wines including port, sherry, muscat and Marsala. It's 6km out of town, on the road to Perth.
z Festivals & Events
Moondyne Festival HISTORICAL
(www.moondynefestival.com.au; 1st Sun May) Costumed hijinks in honour of the outlaw..
Toodyay International Food Festival FOOD
Held on the first weekend in August on the day before the Avon Descent.
Toodyay Agricultural Show AGRICULTURE
Early October.
4 Sleeping & Eating
Avalon Homestead GUESTHOUSE $
( 08-9574 5050; www.avalonhomestead.com.au; 381 Julimar Rd; r $145) Popular with discerning oldies, Avalon has tidy, somewhat chintzy rooms in a peaceful spot 4km out of town. The gardens are lovely, and it's a popular spot for visiting arts-and-crafts groups.
Cola Café & Museum CAFE $
(www.colacafe.com.au; 128 Stirling Tce; snacks $10-21; 9am-4.30pm) Coca-Cola memorabilia runs amok here. Order a cola spider (Coke with a scoop of ice cream) and a big burger and play 'guess the 1950s tune'.
8 Information
Ye Olde Lolly Shoppe ( 08-9574 2435; www.toodyay.com; 7 Piesse St; 9am-4pm) Stock up on tourist information and fudge at the same time.
### THE MYTHOLOGY OF MOONDYNE JOE
The state of Victoria's most famous outlaw, Ned Kelly, is known for his gun battles with the law, but WA's most illustrious bushranger, Moondyne Joe, is famous for escaping. Over and over again.
Joseph Bolitho Johns (1828–1900), sent to WA for larceny, arrived in Fremantle in 1853 and was granted an immediate ticket of leave for good behaviour. This good behaviour lasted until 1861, when he was arrested on a charge of horse stealing; however, he escaped that night from Toodyay jail on the horse he rode in on, sitting snugly on the magistrate's new saddle. He was recaptured and sentenced to three years' imprisonment. Between November 1865 and March 1867 he made four attempts to escape, three of them successful. When eventually captured he was placed in a special reinforced cell with triple-barred windows in Fremantle, but in 1867 he managed to escape from the prison yard while breaking rocks. He served more time in Fremantle prison when recaptured and was conditionally pardoned in 1873. After release he worked in the Vasse district and kept his nose relatively clean, but he suffered from poor mental health later in life until his death in 1900. You can see his grave at Fremantle cemetery.
While Moondyne Joe was a criminal, these days it pays to be in the 'Moondyne Joe' business. Three books, including the latest, a prize-winning juvenile-fiction novel called _The Legend of Moondyne Joe_ (Mark Greenwood), have been written about him; a Moondyne festival is held in Toodyay on the first Sunday of May; and a cave in Margaret River is named after him, as well as a pub, a caravan park and who knows what else. Let's hope he doesn't escape his final resting place and start asking for royalties...
8 Getting There & Away
Toodyay is a stop on the Transwa ( 1300 662 205; www.transwa.wa.gov.au) AvonLink and Prospector lines, with trains to East Perth ($16, 1¼ hours, seven per week), Northam ($8, 20 minutes, 12 per week) and Kalgoorlie ($74, 5½ hours, four per week).
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Avon Valley National Park
Featuring granite outcrops, forests and wonderful fauna, this national park (www.dec.wa.gov.au; per car $11; 8am-4pm) is accessed from Toodyay and Morangup Rds. The Avon River flows through the centre of the park in winter and spring, but is usually dry at other times.
The park is the northern limit of the jarrah forests, and the jarrah and marri are mixed with wandoo woodland. Bird species include rainbow bee-eaters, honeyeaters, kingfishers and rufous treecreepers. In the understorey. honey possums and western pygmy-possums hide among the dead leaves, and skinks and geckos scuttle about.
There are campsites ( 08-9574 2540; adult/child $7/2) with basic facilities (eg pit toilets and barbecues).
## New Norcia
pop 70
The idyllic monastery settlement of New Norcia, 132km from Perth, consists of a cluster of ornate, Spanish-style buildings set incongruously in the Australian bush. Founded in 1846 by Spanish Benedictine monks as an Aboriginal mission, the working monastery today holds prayers and retreats, alongside a business producing boutique breads and gourmet goodies.
New Norcia Museum & Art Gallery ( 08-9654 8056; www.newnorcia.wa.edu.au; Great Northern Hwy; combined museum & town tours adult/family $25/60; 10am-4.30pm) traces the history of the monastery and houses impressive art, including contemporary exhibitions and one of the country's largest collections of post-Renaissance religious art. The gift shop sells souvenirs, honeys, preserves and breads baked in the monks' wood-fired oven.
Inside the abbey church , try to spot the native wildlife in the sgraffito artworks that depict the Stations of the Cross. Look hard, as there's also an astronaut.
Guided two-hour town tours (www.newnorcia.wa.edu.au; adult/child $15/10; 11am & 1.30pm) offer a look the abbey church and the frescoed college chapels; purchase tickets from the museum. At 4.30pm on Saturday afternoons, there is the opportunity to meet the monks.
New Norcia Hotel ( 08-9654 8034; www.newnorcia.wa.edu.au; Great Northern Hwy; s/d $75/95) harks back to a more genteel time, with sweeping staircases, high ceilings, understated rooms (with shared bathrooms) and wide verandahs. An international menu ($15 to $30) is available at the bar or in the elegant dining room (where you can also nab a cooked breakfast).
Sit outside on the terrace and sample the delicious but deadly New Norcia Abbey Ale, a golden, hand-crafted, Belgian-style ale brewed especially for the abbey. Sunday is a good day to visit, either for breakfast ($20), or the popular lunchtime carvery (adult/child $19.50/14.50).
The abbey also offers lodging in the Monastery Guesthouse ( 08-9654 8002; www.newnorcia.wa.edu.au; full-board suggested donation $80) within the walls of the southern cloister. Guests can also join in prayers with the monks (and males can dine with them).
## Wildflower Way
Away from the coast, there are four other common routes that head north, with three running to Geraldton and the fourth, the Great Northern Hwy, disappearing into the outback and re-emerging 1600km later at Port Hedland. The Brand Hwy (Rte 1) is the least interesting for travellers, and its wildflowers can be sampled in day trips from the Turquoise Coast. Midlands Rd (Rte 116) and the Wildflower Way (Rte 115) are home to wheat silos, wildflowers and little one-pub towns; the towns are a hive of activity between August and September as minibuses full of pensioners zoom around like frantic bees hunting blossoms. Whatever the time of year, the wheat farmers have one eye on the weather and one on their crop, no doubt wondering if it will ever rain again.
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) runs bus services along Rte 116 on Tuesday, Thursday, Saturday and Sunday, and twice weekly (to/from Geraldton on Monday, Thursday/Tuesday and Friday) on Rte 115.
Integrity ( 1800 226 339; www.integritycoachlines.com.au; to/from Perth Sat/Wed) runs buses weekly up the Great Northern Hwy (Rte 95).
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Moora
pop 2574
Tall gums, wide streets, a pub with a wide verandah, a couple of galleries, a few B&Bs and a railway line (wheat trains only) define this agricultural service centre – a good base from which to explore the surrounding area.
The excellent visitor centre ( 08-9653 1053; www.moora.wa.gov.au; Moora Railway Station; 8.30am-4pm Mon-Fri; ) can supply a map of the local wildflowers and other sites including Jingemia Cave in Watheroo National Park. An interesting town walk takes in Moora's heritage buildings and murals.
For hundreds of WA wildflowers, visit the Western Wildflower Farm (www.wildflowerswa.com.au; MIdlands Rd; 9am-5pm Mon-Sat) F , 19km north of Moora. Morning and afternoon teas are also served. The Wildflower Interpretative Education Centre at the farm is a great stop if you're heading out on a wildflower pilgrimage. See the website also for information and photographs on many variants.
Moora Caravan Park ( 0409 511 400; Dandaragan St; unpowered/powered sites $18/25, chalets $110-160) offers basic, shady sites, and some comfortable new chalets. Pay at the Gull service station. The visitor centre can arrange accommodation at well-maintained B&Bs, but you'll need a car as most are slightly out of town.
Right in town, the Drovers Inn ( 08-9651 1108; cnr Dandaragan & Padbury Sts; hotel $65-85, motel $110, mains $20-34; 11am-late) is a classic Aussie pub with standard rooms with shared bathrooms and counter meals. Out the back are more moderm motel rooms.
Moora's Pioneer Bakery & Restaurant ( 08-9651 1277; 50 Padbury St; meals $5-20; 7.30am-4pm Mon-Fri) is a great place for brekkie and pies. The best coffee (and muffins!) in town is at the Wheatbelt Gallery (Padbury St; 9am-5pm Tue-Sat) , opposite the visitor centre, while art fans can cross the tracks to Moora Art Gallery ( 0447 997 423; 95 Gardiner St; 10am-4pm Thu-Sat) .
There is a supermarket and ATMs on Dandaragan and Padbury Sts.
Transwa buses go to Perth ($30, three hours) and Geraldton ($46, four hours) via Rte 116.
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Wongan Hills
pop 1462
From New Norcia, take the back road via Yerecoin and you'll pass the intriguing Lake Ninan , a huge saltpan. Wongan Hills, with its gently undulating country and myriad verticordias, makes a pleasant change from the flat wheat-belt towns, and there are plenty of trails for bushwalkers.
The visitor centre ( 08-9671 1973; www.wongantourism.com.au; Wongan Rd, Railway Station; 9am-5pm, closed Sun Nov-Easter) has maps (and guides) for popular wildflower haunts such as Mt Matilda (8km return), 12km west of Wongan Hills, and Christmas Rock (behind the caravan park; 2km return). Reynoldson Nature Reserve (1km one way), 29km north of Wongan Hills, has spectacular verticordias, and you can drive to the top of Mt O'Brien , 11km west of Wongan Hills.
Wongan Hills Caravan Park ( 08-9671 1009; Wongan Rd; unpowered/powered site $19/24, cabins & chalets $70-110) has shady sites and a good kitchen.
Art deco Wongan Hills Hotel ( 08-9671 1022; www.wonganhillshotel.com.au; 5 Fenton Pl; hotel s/d $70/90, motel d $110, meals $18-32) offers classic hotel rooms, some opening onto the upstairs verandah, and modern motel rooms in a separate building. Meals are typical pub fare, including good pizzas.
There's a supermarket and bakery on Fenton Pl.
Transwa goes to Perth ($30, three hours), and Perenjori ($30, three hours) via Rte 115.
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Perenjori
pop 573
Perenjori, 360km from Perth, is a pretty town surrounded by abundant wildlife and, from July to November, stunning wildflowers. The visitor centre ( 08-9973 1105; www.perenjori.wa.gov.au; Fowler St; 9am-4pm Mon-Fri Jul-Oct) , also home to the pioneer museum (adult/child $2/0.50) , has self-drive brochures including _The Way of the Wildflowers_ and _Monsignor Hawes Heritage Trail._ They can provide access to the beautiful St Joseph's Church , designed by the prolific Monsignor John Hawes.
Shady Perenjori Caravan Park ( 08-9973 1193; Crossing Rd; unpowered/powered site $20/30, chalets & eco-home $20-200) offers grassy tent sites and decent facilities.
The friendly, family-owned Perenjori Hotel ( 08-9973 1020; Fowler St; d $80) has basic pub rooms and good-value bar meals.
Transwa has services to Perth ($53, six hours) and Geraldton ($35, three hours) via Rte 115.
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Morawa, Mingenew & Mullewa
The 'three Ms' form a triangle that buzzes during wildflower season but has limited appeal to travellers outside this. Most of the visitor centres close, and Port Denison-Dongara and Geraldton are only an hour away.
Each has a caravan park with tent sites, a local pub with meals and rooms, a supermarket or general store, and a Transwa bus connection several times weekly. In wildflower season, the shire may run minibuses from the visitor centres to the best sites.
Morawa and Mullewa both have distinctive churches designed by Monsignor John Hawes.
Coalseam Conservation Park (www.dec.wa.gov.au; camping per person $7) , 34km northeast of Mingenew on the Irwin River, has a variety of everlastings (paper daisies), a short loop walk with interpretive signs, and ancient fossil shells embedded in the cliffs. There are dusty, unpowered camp sites at Miners, with toilets and picnic tables.
Mullewa is famous for its wreath flower, _Lechenaultia macrantha,_ and holds an annual wildflower show at the end of August.
In season, the roads heading east to Yalgoo are normally carpeted in everlastings.
8 Information
Mingenew Visitor Centre ( 08-9928 1081; 9am-5pm Jul-Sep) At Mingenew post office.
Morawa Visitor Centre ( 08-9971 1421; www.morawa.wa.gov.au; 34 Winfield St; Jun–mid-Oct) Note restricted months of opening.
Mullewa Visitor Centre ( 08-9961 1500; www.mullewatourism.com.au; cnr Jose St & Maitland Rd; 8.30am-4.30pm, closed Sat & Sun Oct-Jun; ) Information on wildflower-viewing opportunities.
## Sunset Coast
The coast road north of Perth leads to some popular spots for travellers. Within an hour's drive, Perth's outer suburbs give way to the bushland oasis of Yanchep National Park, with wonderful wildlife and walking trails.
The coastline ranges from tranquil bays at Guilderton, good for swimming and fishing, to windswept beaches at Lancelin, with excellent conditions for windsurfing and kitesurfing.
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Yanchep
pop 2482
Yanchep and its close neighbour Two Rocks are effectively Perth's northernmost suburbs. The town was developed extensively during the 1980s by (now convicted fraudster) Alan Bond, and the legacy of this era includes a large marina and some dubious bits of sculpture (dolphins, a dragon and a giant Neptune).
Apart from nice beaches, the big drawcard is the woodlands and wetlands of Yanchep National Park (www.dec.wa.gov.au/yanchep; Wanneroo Rd; per car $11; visitor centre 9.15am-4.30pm) , home to hundreds of species of fauna and flora, including koalas, kangaroos, emus and cockatoos. The free _Wild About Walking_ brochure outlines nine walking trails, from the 20-minute Dwerta Mia walk to the four-day Coastal Plain walk. Register with the park centre for longer walks.
The park features splendid caves, which can be viewed on 45-minute tours (adult/child $10/5; five per day). On weekends at 1pm and 2pm, local Noongar guides run excellent tours on Indigenous history, lifestyle and culture (adult/child $10/5), and didgeridoo and dance performances (adult/child $10/5).
Within the national park, Yanchep Inn ( 08-9561 1001; www.yanchepinn.com.au; hotel r $80, old motel r $115, new motel r $170-210; ) is more attractive from the outside than the inside. The inn itself has basic rooms with shared facilities and a cafe downstairs. It's more comfortable in the newer of the two motel blocks, with lake views and rammed-earth walls, but perhaps a little overpriced. Prices jump up by $25 to $55 at weekends.
To get to Yanchep by public transport, catch a train on the Joondalup line from Perth's Esplanade station to Clarkson, then catch bus 490.
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Guilderton
pop 150
Some 43km north of Yanchep, Guilderton is a popular and staggeringly beautiful family-holiday spot. Children paddle safely near the mouth of the Moore River, while adults enjoy fishing and surfing on the ocean beach.
The name comes from the wreck of the _Vergulde Draeck,_ part of the Dutch East India Company fleet, which ran aground nearby in 1656, reputedly carrying a treasure in guilders. Its original name was Gabbadah, meaning 'mouth of water', although many older Perthites still refer to it as Moore River.
The Guilderton Caravan Park ( 08-9577 1021; www.guildertoncaravanpark.com.au; 2 Dewar St; sites per 2 people $29-40, chalets $165) has self-contained chalets, but you'll need your own linen. There's also a cafe and general store, and a compact volunteer-run visitor centre (with erratic hours) next door.
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Lancelin
pop 670
Afternoon offshore winds and shallows, protected by an outlying reef, make Lancelin perfect for windsurfing and kitesurfing, attracting action-seekers from around the world. In January, wind-worshippers descend for the Lancelin Ocean Classic (www.lancelinoceanclassic.com.au) windsurfer race, starting at Ledge Point to the south.
The coral and limestone reef, no-fishing zone and dazzling white sands also make Lancelin a great snorkelling spot, while the mountainous soft, white dunes on the edge of town are good for sandboarding.
2 Activities
Surfschool SURFING
( 08-9444 5399, 1800 198 121; www.surfschool.com.au; 69 Casserley Way; 3-/6-hr lessons $40/75; 8am) The main beach's gentle waves make it a good place for beginners and there are bigger breaks nearby for more experienced surfers. Three- to six-hour lessons include boards and wetsuits. There are also surf-camp packages, including lessons, transfers from Perth and accommodation.
Makanikai Kiteboarding KITEBOARDING
( 0406 807 309; www.makanikaikiteboarding.com; lessons/courses from $60/200, rental per hr/day $20/60) Lessons and tuition in the fine art of kiteboarding, and gear rental; accommodation packages are also available.
Have a Chat General Store SANDBOARDING
( 08-9655 1054; 104 Gingin Rd; 7am-7pm) Hires sandboards for $10 per two hours.
4 Sleeping & Eating
o Lancelin Lodge YHA HOSTEL $
( 08-9655 2020; www.lancelinlodge.com.au; 10 Hopkins St; dm/d/f $30/80/98; ) This laid-back hostel is well equipped and welcoming, with wide verandahs and lots of communal spaces to hang about in. The excellent facilities include big kitchen, barbecue, wood-fire pizza oven, swimming pool, ping-pong table, volleyball court and free use of bikes and boogie boards.
Ledge Point Holiday Park CARAVAN PARK $
( 1300 856 088; www.ledgepointholidaypark.com.au; 742 Old Ledge Point Rd ; sites per 2 persons $36-41, chalets & studios $120-230; ) About 10 minutes' drive south of Lancelin, with excellent facilities and spotless accommodation ranging from caravan and camping sites to chalets and studios. Lots of family-friendly attractions include pedal carts and a jumping pillow. Ledge Point's beach – good for fishing and swimming – is around 500m away.
Lancelin Caravan Park CARAVAN PARK $
( 08-9655 1056; Hopkins St; sites per person $14, on-site vans $70) Windsurfers love camping out at this neat park – not for the facilities and amenities, which are rudimentary, but for the beachfront location.
Windsurfer Beach Chalets APARTMENT $$
( 08-9655 1454; www.lancelinaccommodation.com.au; 1 Hopkins St; d $165) Self-contained two-bedroom chalets, near the windsurfing beach, are a good choice for groups of friends and families (each chalet sleeps up to six). They're functional and well equipped, and have a sun terrace backing onto a grassy area. The operators can also arrange accommodation in Lancelin and nearby Ledge Point in a variety of self-contained holiday homes.
Kombi Cafe CAFE $
(2 Robertson Rd, Ledge Point; snacks & mains $10-13.50) Cool surfing-inspired cafe a short drive south of Lancelin at Ledge Point. Good coffee, lots of local information, and fish and chips to devour on the nearby beach.
Endeavour Tavern PUB $$
(58 Gingin Rd; mains $18-34) A classic beachfront Aussie pub with a beer garden overlooking the ocean. The casual eatery serves decent seafood, pub-grub classics and a tasty Mediterranean platter.
8 Getting There & Away
Lancelin is 130km north of Perth. Greyhound ( 1300 473 946; www.greyhound.com.au) has coaches to and from East Perth ($26, 1¾ hours), Cervantes ($28, 1½ hours), Geraldton ($54, four hours) and Carnarvon ($156, 10½ hours).
A second bus company, Integrity ( 1800 226 339; www.integritycoachlines.com.au) , is now also taking advantage of the faster access possible on the recently opened Indian Ocean Dr. Buses leave from Lancelin Lodge YHA Sunday to Friday north to Cervantes ($15, one hour), Jurien Bay ($18, 1¼ hours) and Geraldton ($34, four hours). Heading south, buses travel Monday to Saturday to Perth ($18, 1¾ hours).
## Turquoise Coast
Stretching north of Lancelin to Port Denison, the relaxed Turquoise Coast is dotted with sleepy fishing villages, stunning beaches, extraordinary geological formations, rugged national parks and incredibly diverse flora. Offshore marine parks and island nature reserves provide a safe breeding habitat for Australian sea lions and other endangered species, while crayfishing brings in the dollars. Once somewhat isolated, the whole area has been brought within easy reach of Perth by the completion of the final section of Indian Ocean Dr between Lancelin and Cervantes.
### KWONGAN WILDFLOWERS
Take any road inland from the Turquoise Coast and you'll soon enter the Kwongan heathlands, where, depending on the season, the roadside verges burst with native wildflowers like banksia, grevillea, hakea, calothamnus, kangaroo paw and smokebush. While Lesueur National Park is an obvious choice for all things botanical, consider some of the following options.
» Badgingarra National Park Three-and-a-half kilometres of walking trails, kangaroo paws, banksias, grass trees, verticordia and a rare mallee. The back road linking Badgingarra to Lesueur is particularly rich in flora. Obtain details from the Badgingarra Roadhouse. There's also a picnic area on Bibby Rd.
» Alexander Morrison National Park Named after WA's first botanist. There are no trails, but you can drive through slowly on the Coorow Green Head Rd, which has loads of flora along its verge all the way from Lesueur. Expect to see dryandra, banksia, grevillea, smokebush, leschenaultia and honey myrtle.
» Tathra National Park Tathra has similar flora to Alexander Morrison National Park and the drive between the two is rich with banksia, kangaroo paw and grevillea.
» Coomallo Rest Area Orchids, feather flowers, black kangaroo paws, wandoo and river red gums can be found upstream and on the slopes of the small hill.
» Brand Highway (Rte 1) The route's not exactly conducive to slow meandering, but the highway verges are surprisingly rich in wildflowers, especially either side of Eneabba.
If you're overwhelmed and frustrated by not being able to identify all these strange new plants, consider staying at Western Flora Caravan Park ( 08-9955 2030; wfloracp@activ8.net.au; Brand Hwy, North Eneabba; unpowered/powered sites $24/26, d $65, onsite vans $75, chalets $120) where the enthusiastic owners run free two-hour wildflower walks across their 65-hectare property every day at 4.30pm.
8 Getting There & Away
Greyhound ( 1300 473 946; www.greyhound.com.au) runs services to and from Perth along Indian Ocean Dr three times per week.
Integrity ( Click here ) runs daily along the coast between Perth and Geraldton and overnight twice a week to and from Exmouth.
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Cervantes & Pinnacles Desert
pop 480
Heading north from Lancelin on Indian Ocean Dr, you will pass the tiny fishing-shack villages of Wedge Island (http://wedgewa.com.au) and Grey , where access was previously 4WD-only along the beach. Pressure from developers and government mean the future of these communities is uncertain, and although there are no facilities for tourists, you're welcome to wander.
The laid-back crayfishing town of Cervantes , 198km north of Perth, makes a pleasant overnight stop for enjoying the Pinnacles Desert and a good base for exploring the flora of the Kwongan , the inland heathland of Lesueur National Park ( Click here ) and Badgingarra National Park . There are also some lovely beaches on which to while away the time.
Grab a copy of the _Turquoise Coast Self Drive Map_ from Cervantes' combined post office and visitor centre ( 08-9652 7700, freecall 1800 610 660; www.visitpinnaclescountry.com.au; Cadiz St; 8am-5pm; ) , which also supplies accommodation and tour information. The town's general store and liquor shop are also on this strip.
Just before town, turn off for Lake Thetis, where living stromatolites – the world's oldest organisms – inhabit the shoreline. Nearby Hansen Bay Lookout has excellent views across the coast. In town, walkways wend along the coastline and provide beach access.
1 Sights & Activities
o Nambung National Park NATIONAL PARK
(per car $11) Situated 19km from Cervantes, Nambung is home to the spectacular Pinnacles Desert , a vast, alien-like plain studded with thousands of limestone pillars. Rising eerily from the desert floor, the pillars are remnants of compacted seashells that once covered the plain and, over millennia, subsequently eroded. A loop road runs through the formations, but it's more fun to wander on foot, especially at sunset, full moon or dawn, when the light is sublime and the crowds evaporate.
Nearby Kangaroo Point and Hangover Bay make nice picnic spots with BBQs and tables. The latter has the better swimming.
Lesueur National Park NATIONAL PARK
(per car $11) This botanical paradise, 50km north of Cervantes, contains a staggering 820 plant species, many of them rare and endemic, such as the pine banksia _(Banksia tricupsis)_ and Mt Lesueur grevillea _(Grevillea batrachioides)_ . Late winter sees the heath erupt into a mass of colour, and the park is also home to the endangered Carnaby's cockatoo. An 18km circuit drive is dotted with lookouts and picnic areas. Flat-topped Mt Lesueur (4km return walk) has panoramic coastal views.
T Tours
Many Perth-based companies offer day trips to the Pinnacles.
Turquoise Coast Enviro Tours GUIDED TOURS
( 08-9652 7047; www.thepinnacles.com.au; 59 Seville St; 3hr Pinnacles tours $60, full-day Kwongan tours $170) Cervantes local and ex-ranger Mike Newton runs morning (8am, three hours) and evening (2½ hours before sunset) Pinnacles trips, as well as a full-day Kwongan tour, including Lesueur National Park and the coast up to Leeman.
4 Sleeping & Eating
Watch out for school holidays, when prices surge.
o Cervantes Lodge & Pinnacles
Beach Backpackers HOSTEL $
( 1800 245 232; www.cervanteslodge.com.au; 91 Seville St; dm $30, d with/without bathroom $130/90; ) In a great location behind the dunes, this relaxing hostel has a wide verandah, small and tidy dorms, a nice communal kitchen and a cosy lounge area. Bright, spacious en-suite rooms, some with views, are next door in the lodge.
Pinnacles Caravan Park CARAVAN PARK $
( 08-9652 7060; www.pinnaclespark.com.au; 35 Aragon St; unpowered/powered sites from $27/32, on-site vans/cabins $50/75; ) Fantastic location right behind the dunes with plenty of shady, grassy sites and on-site cafe.
o Amble Inn B&B $$
( 0429 652 401; 2150 Cadda Rd, Hill River; d spa/non-spa $165/150; ) High up on the heathland, about 25km east of Cervantes, this hidden gem of a B&B has beautiful thick stone walls, cool, wide verandahs and superbly styled rooms. Watch the sunset over the coast from the nearby hill with a glass of your complimentary wine.
Cervantes Holiday Homes APARTMENT $$
( 08-9652 7115; www.cervantesholidayhomes.com.au ; cnr Malaga Ct & Valencia Rd; cottages from $130; ) These well-equipped, fully self- contained cottages are great value, especially for groups.
Pinnacles Edge Resort RESORT $$$
( 08-9652 7788; www.pinnaclesedgeresort.com.au; 7 Aragon St; studio/spa/2-bedroom $213/265/343; ) Beautifully appointed luxury rooms, the more expensive with spas and balconies, are arranged around a central pool. There's an in-house restaurant and bar, and the adjoining motel has older-style doubles from $145.
Seashells Cafe CAFE $
( 08-9652 7060; 35 Aragon St; 8am-4pm) With great coffee and the best view in town, the Seashell makes an excellent pit-stop for breakfast or that afternoon cake.
Lobster Shack SEAFOOD $$
( 08-9652 7010; www.lobstershack.com.au; 11 Madrid St; shop 9am-5pm, lunch 11.30am-2.30pm) Craving for crayfish? They don't come much fresher than at this lobster factory-turned-lunch spot, where a delicious grilled cray, chips and salad will set you back $25. Self-guided tours (adult/child $15/7.50) and take-away frozen seafood are also available.
Cervantes Country Club SEAFOOD $$$
( 08-9652 7123; Aragon St; seafood platters from $55; 6-9pm) The seafood platters at this humble sporting club (shorts and sandals OK) are legendary, and include prawns, oysters, fish, calamari, crayfish (in season, extra $10), salad and mountains of chips. Bring a friend.
8 Getting There & Away
Integrity ( Click here ) runs daily to Perth ($26, three hours), Dongara ($28, two hours) and Geraldton ($32, three hours) with a twice-weekly overnight service to Exmouth ($162, 14 hours).
Greyhound ( 1300 473 946; www.greyhound.com.au) runs three times weekly to Perth ($37, three hours) and Dongara ($40, two hours), continuing to Broome ($380, 31 hours). Locally, both buses stop at Jurien Bay (20 minutes), Green Head (40 minutes) and Leeman (55 minutes).
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Jurien Bay
pop 1500
The largest town on the Turquoise Coast is likely to become quite a lot bigger after its selection as a 'Super Town', and eligible for the 'Royalties for Regions' scheme ( Click here ). Home to a hefty fishing fleet and lots of big houses, it's already rather spread out; however, there's a nice long swimming beach and great snorkelling and diving opportunities. Anglers have a choice of jetties and the lengthy foreshore walkway links several pleasant parks.
Accommodation in town caters mostly for Perth families. Holiday houses and apartments can be booked via local real estate agents . ( 08-9652 2055; www.jurienbayholidays.com; Shop 1A, 34 Bashford Street) Plan ahead for popular Jurien Bay Tourist Park ( 08-9652 1595; www.jurienbaytouristpark.com.au; Roberts St; unpowered/powered site $28/33; on-site van from $90; 1-/2-bedroom chalet $115/145) , with its comfortable chalets right behind the beach, although the tent sites are set back against the main road. Next door, the Jetty Cafe ( 08-9652 1999; meals $5-17; 7.30am-5pm) has a great position, decent brekkies, burgers and grilled fish.
The friendly Sandpiper Tavern ( 08-9652 1229; cnr Roberts & Sandpiper Sts; mains $25-35; lunch noon-2pm, dinner 6-9pm) has a relaxed beer garden and does all the usual pub faves. There are several takeaway shops strung along Bashford St, as well as a supermarket and ATM. Sadly, there is presently no bike hire.
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Green Head & Leeman
On the way to Green Head, stop at Grigson Lookout for a panoramic view of the coast and Kwongan. Tiny Green Head (population 280) has several beautiful bays; the horseshoe-shaped Dynamite Bay is the most spectacular and sheltered for swimmers. There's good fishing, snorkelling, surfing and windsurfing here and at nearby Leeman (population 400).
o Sea Lion Charters ( 08-9953 1012; http://sealioncharters.biz; 24 Bryant St, Green Head; half-day tours adult/child $120/60) offers a magical experience interacting in shallow water with playful sea lions who mimic your every move. It helps to be a good snorkeller. Wetsuits are $10 extra.
Green Head has the best sleeping and eating options with the newly opened Centrebreak Beach Stay ( 08-9953 1896; www.centrebreakbeachstay.com.au; Lot 402 Ocean View Dr, Green Head; dm/d/f $35/150/190, meals $14-35; ) , complete with licensed cafe, close to Dynamite Bay. Cool Combination Cafe (Dynamite Bay; 9.30am-4pm Mon-Sat) is just behind the beach, the lovely Seaview B&B ( 08-9953 1487; 25 Whiteman St; per person $65) has great views, and the relaxed and shady Green Head Caravan Park ( 08-9953 1131; 9 Green Head Rd, Green Head; unpowered/powered sites $20/28, on-site vans from $70) will suit most campers.
Nearby, leafy Leeman Caravan Park ( 08-9953 1080; 43 Thomas St, Leeman; unpowered/powered sites $20/25, on-site vans $60, cabins $70-90) has lots of shade, grassy sites and a good camp kitchen all close to the dunes. Tasty meals are available all day from Fran's Kitchen ( 08-9953 1727; Indian Ocean Dr, Leeman; 6am-8pm) and there's both petrol and internet access in the village.
If you have a 4WD, Stockyard Gully Caves are 30km away, off the Coorow Green Head Rd, and you can explore the underground creek and caverns with a torch. Watch out for bees and bats.
Heading north on Indian Ocean Dr, unmarked side-roads lead to lonely beaches and rocky cliffs begging to be explored.
# Margaret River & the Southwest Coast
#### Margaret River & the Southwest Coast Highlights
#### Geographe Bay
#### Bunbury
#### Tuart Forest National Park
#### Busselton
#### Dunsborough
#### Cape Naturaliste
#### Margaret River Wine Region
#### Yallingup & Around
#### Cowaramup & Wilyabrup
#### Margaret River
#### Around Margaret River
#### Augusta & Around
#### Southern Forests
#### Nannup
#### Balingup & Greenbushes
#### Bridgetown
#### Manjimup
#### Pemberton
#### Shannon National Park
Margaret River & the Southwest Coast
### Why Go?
The farmland, forests, rivers and coast of the lush, green southwestern corner of Western Australia (WA) contrast vividly with the stark, sunburnt terrain of much of the state. On land, world-class wineries and craft breweries beckon, and tall trees provide shade for walking trails and scenic drives. Offshore, bottlenose dolphins and whales frolic, and devoted surfers search for – and often find – their perfect break.
Unusually for WA, distances between the many attractions are short, and driving time is mercifully limited, making it a fantastic area to explore for a few days – you will get much more out of your stay here if you have your own wheels. Summer brings hordes of visitors, but in the wintry months from July to September the cosy pot-bellied stove rules and visitors are scarce, and while opening hours can be somewhat erratic, prices are much more reasonable.
### When to Go
Jan Follow the party crowds from the Southbound festival to the beach.
Mar & Apr Catch surf and wine festivals in Margaret River, and the Nannup music festival.
Aug Head to empty beaches, Margaret River wineries and Busselton's film festival.
### Best Places to Eat
» Laundry Cafe ( Click here )
» Eagle Bay Brewing Co ( Click here )
» The Studio Bistro ( Click here )
» Vasse Felix ( Click here )
» Foragers Field Kitchen ( Click here )
### Best Places to Stay
» Injidup Spa Retreat ( Click here )
» Old Picture Theatre Holiday Apartments ( Click here )
» Acacia Chalets ( Click here )
» Burnside Organic Farm ( Click here )
» Foragers ( Click here )
## Margaret River & the Southwest Coast Highlights
Sampling the first-class wine, food and architecture of the vineyards of Margaret River ( Click here )
Getting active amid the dramatic seascapes and landscapes of the Margaret River (Click here ) region
Exploring the labyrinthine limestone caverns along Caves Rd, especially beautiful Lake Cave (Click here )
Fronting up to the impressive coastline at Augusta's Cape Leeuwin Lighthouse (Click here ), at the confluence of the Indian and Southern Oceans
Sinking into the dappled depths of the karri forests surrounding Pemberton ( Click here )
Revelling in the wild beauty of Cape Naturaliste (Click here ) and Bunker Bay ( Click here )
Canoeing from the forest to the sea along the Blackwood River, starting at Nannup ( Click here )
## Geographe Bay
Turquoise waters and 30km of excellent swimming beaches are the defining features of this gorgeous bay. Positioned between the Indian Ocean and a sea of wine, the beachside towns of Busselton and Dunsborough attract hordes of holidaymakers spending their vacations with sand between their toes and a glass between their lips. It may be 230km from Perth, but once you get here the attractions are close together, certainly by WA standards. Unsurprisingly, it gets _very_ busy during summer and at holiday times, when prices may rise 30% on those given here.
For 55,000 years the area from Geographe Bay to Augusta belonged to the Wardandi, one of the Noongar peoples. They lived a nomadic life linked to the seasons, heading to the coast in summer to fish, and journeying inland during the wet winter months.
The French connection to many of the current place names dates from an early-19th-century expedition by the ships _Le Géographe_ and _Naturaliste._ Thomas Vasse, a crewman who was lost at sea, is remembered in the name of a village, river, inlet, Busselton bar and Margaret River winery. The latter two are particularly fitting as it's quite possible he was drunk when he was washed away. According to local Wardandi, who found and fed him, he made it to shore but later died on the beach waiting for his ship to return.
### GEOGRAPHE WINE REGION
If it's wine that's lured you to the southwest, the Geographe wine region (www.geographewine.com.au) is the perfect primer for the glories to come. You may not have heard of it, but Geographe has 12 sq km under vines, producing 11% of the state's output in 46 wineries. The region's best-known brand is conveniently located halfway between Bunbury and Busselton. Capel Vale (www.capelvale.com.au; Mallokup Rd; 10am-4pm) offers free tastings and a restaurant overlooking the vines, serving morning and afternoon tea and lunch. It's located off the Bussell Hwy on the opposite side of the highway from Capel village.
Top of Chapter
Bunbury
pop 66,100
The southwest's only city is remaking its image from industrial port into seaside holiday destination. It's here where the main route south from Perth branches off into the Bussell Hwy (to the Margaret River wine region) and the South Western Hwy (Rte 1, to the southern forests and south coast). It's also the southernmost stop on the train network and a hub for regional buses.
Situated 170km from Perth, Bunbury has plenty of eateries and a few interesting attractions worthy of a stop. The town centre has basically one main street (Victoria), and a few blocks to the west lies the beach. Immediately to the north, the redeveloped port features waterside restaurants.
The city lies at the western end of Leschenault Inlet. The area was named Port Leschenault after the botanist on Nicolas Baudin's ship _Le Géographe_ in 1803, but in a classic case of colonial one-upmanship, Governor James Stirling renamed it Bunbury in honour of the lieutenant that he placed in charge of the original military outpost. The first British settlers arrived in 1838.
1 Sights
Bunbury Wildlife Park ZOO
(Prince Philip Dr; adult/child $8/5; 10am-5pm) Parrots, kangaroos, wallabies, possums, owls and emus all feature. Across the road, the Big Swamp has good wetlands walking tracks and stops for birdwatching. Head south on Ocean Dr, turn left at Hayward St and continue through the roundabout to Prince Philip Dr.
Bunbury
Top Sights
1 Dolphin Discovery Centre D2
Sights
2 Bunbury Regional Art Galleries B3
Activities, Courses & Tours
3 Mangrove Boardwalk D2
Sleeping
4 Dolphin Retreat YHA A3
5 Mantra B2
6 The Clifton A2
7 Wander Inn Backpackers B2
Eating
8 Benesse B3
9 Café 140 B3
10 Casella's B1
11 Mot's Cafe B3
Drinking & Nightlife
12 Mash B1
Entertainment
13 Bunbury Regional Entertainment CentreB2
14 Grand Cinemas B2
15 Prince of Wales B3
Bunbury Regional Art Galleries GALLERY
OFFLINE MAP GOOGLE MAP
(www.brag.org.au; 64 Wittenoom St; 10am-4pm) F Housed in a restored pink-painted convent (1897), this excellent gallery has a collection that includes works by Australian art luminaries Arthur Boyd and Sir Sidney Nolan.
St Mark's (Old Picton) Church CHURCH
(cnr Charterhouse Cl & Flynn St, East Bunbury) Built in 1842 using wattle and daub construction, this is WA's second-oldest church.
2 Activities
Mangrove Boardwalk WALKING
OFFLINE MAP GOOGLE MAP
Mangrove Boardwalk (enter off Koombana Dr) allows you to explore the most southerly mangroves in WA, rich with more than 70 species of bird. Interpretive signs provide information about this ancient ecosystem, thought to be about 2500 years old.
Dekked Out Adventures KAYAKING, DOLPHIN WATCHING
( 08-9796 1000; www.dekkedout.com.au; Grand Canals boat ramp, Riviera Way, Eaton; adult/student $80/60; 8.30am) Runs four-hour dolphin-spotting tours in the Collie River, Leschenault Estuary and the bay. Also hires kayaks (single per half-/full day $55/60) and sandboards ($20/30).
Tuart Forest WALKING
This stretch lined with tall trees runs along the southern end of Ocean Dr.
4 Sleeping
Wander Inn Backpackers HOSTEL $
OFFLINE MAP GOOGLE MAP
( 1800 039 032; www.bunburybackpackers.com.au; 16 Clifton St; dm $27-29, s $40-47, d $68; ) Occupying a cheerful old blue-and-yellow house down a quiet side street between the beach and the main strip, this friendly hostel offers free basic breakfasts.
Dolphin Retreat YHA HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9792 4690; www.dolphinretreatbunbury.com.au; 14 Wellington St; dm/s/d $27/47/68; ) Just around the corner from the beach, this small hostel is well located in a rabbit warren of an old house, with hammocks and a barbecue on the back verandah.
Bunbury Glade Caravan Park CARAVAN PARK $
( 08-9721 3800; www.glade.com.au; Timperley Rd; 2-person sites $25-33, cabins $70-105; ) This spotless park is a five-minute drive from the centre of town on Blair St, the main road heading south.
The Clifton MOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9721 4300; www.theclifton.com.au; 2 Molloy St; r $150-250; ) For luxurious accommodation with lots of heritage trimmings, go for the top-of-the-range rooms in the Clifton's historic Grittleton Lodge (1885). Good-value motel rooms – all recently redecorated – are also available.
### DOLPHIN DISCOVERY CENTRE
Around 60 bottlenose dolphins live in Bunbury's Koombana Bay year-round, their numbers increasing to around 260 in summer. The Dolphin Discovery Centre OFFLINE MAP GOOGLE MAP ( 08-9791 3088; www.dolphindiscovery.com.au; Koombana Beach; adult/child $10/5; 9am-2pm Jun-Sep, 8am-4pm Oct-May) has a beachside zone where dolphins regularly come to interact with people in the shallows and you can wade in alongside them, under the supervision of trained volunteers. There are no guarantees of a close encounter, but these are more likely in the early mornings between November and April. Entry tickets are valid for three separate visits, a good option if you're in town for a few days.
To maximise your chances, there are Eco Cruises (1½hr cruise adult/child $53/35; 11am Sat & Sun Jun-Sep, 11am & 3pm Oct-May) and Swim Encounter Cruises (3hr cruises $185; 7.30am mid-Oct–Jan, 11.30am mid-Dec–Apr) .
The centre also has lots of dolphin information, and tanks with lobsters and seahorses. Volunteers must commit to at least six weeks' full-time involvement.
Mantra APARTMENT $$
OFFLINE MAP GOOGLE MAP
( 08-9721 0100; www.mantra.com.au; 1 Holman St; apt from $209; ) One of the most unusual heritage conversions we've seen, the Mantra has sculpted a set of modern studios and apartments around four grain silos by the harbour. Deluxe rooms have spa baths and full kitchens.
5 Eating
Mot's Cafe MALAYSIAN $
OFFLINE MAP GOOGLE MAP
(17 Prinsep St, Shop 5, Central Arcade; snacks & mains $5-15; 10am-5pm Mon-Fri, to 3pm Sat) Tasty Cocos Malay–style food from a friendly family originally from the Cocos Islands off the northwestern coast of Australia.
Benesse CAFE $
OFFLINE MAP GOOGLE MAP
(83 Victoria St; mains $10-18; 7.30am-5.30pm) Chic and petite, Benesse serves tasty toasties, salads, pizza and all-day breakfasts.
The Happy Wife CAFE $$
(www.thehappywife.com.au; 98 Stirling St; mains $10-20; 6.30am-3.30pm Mon-Fri, 7.30am-2.30pm Sat) Grab a spot in the garden of this Cape Cod–style cottage just a short drive from the centre of town. Excellent home-style baking and regular lunch specials make it worth seeking out. Try the Asian-style sticky pork salad with nashi pear, cabbage salad and toasted peanuts.
Café 140 CAFE $$
OFFLINE MAP GOOGLE MAP
(140 Victoria St; mains $12-21; 7.30am-4.30pm Mon-Fri, 8am-2pm Sat & Sun) Hip, onto-it staff make the funky Café 140 a top spot for a leisurely Bunbury breakfast. With one of WA's best salmon omelettes, good coffee, and lots of magazines and newspapers, you can kiss goodbye to at least an hour of your travel schedule. Later in the day, gourmet burgers and grilled Turkish sandwiches are among the lunchtime stars.
Casella's SPANISH $$
OFFLINE MAP GOOGLE MAP
(www.casellas.com.au; 1 Bonnefoi Blvd, Silos Waterfront ; tapas $10-20, mains $25-40; 11.30am-late) The bland decor hardly reinforces a colourful Iberian spirit, but a waterfront location and real skill in the kitchen more than settle the ledger. Larger meals are available – try the chicken adobado with herby roast potatoes – but the recommended Casella's experience is to settle into the huge wine list and sample a few of the authentically Spanish tapas.
6 Drinking & Entertainment
Mash CRAFT BEER
OFFLINE MAP GOOGLE MAP
(www.mashbrewing.com.au; 2/11 Bonnefoi Blvd; 11am-3pm Mon & Tue, to 9pm Wed-Sun) With an absolute waterfront location, this modern microbrewery turns out seven regular beers, plus always interesting seasonal concoctions. Our pick is the award-winning 'Freo Doctor' lager. The food (mains $18 to $34) is OK pub grub, and Thursday's Pint & Parma deal ($25) is good value.
Prince of Wales LIVE MUSIC
OFFLINE MAP GOOGLE MAP
(41 Stephen St) Longstanding live-music venue.
Grand Cinemas CINEMA
OFFLINE MAP GOOGLE MAP
(www.moviemasters.com.au; cnr Victoria & Clifton Sts) Blockbuster heaven.
Bunbury Regional Entertainment Centre CONCERT HALL
OFFLINE MAP GOOGLE MAP
(www.bunburyentertainment.com; Blair St) Local and international acts.
8 Information
Visitor Centre ( 08-9792 7205; www.visitbunbury.com.au; Carmody Pl; 9am-5pm Mon-Sat, 10am-2pm Sun) In the historic 1904 train station.
8 Getting There & Around
Bus
Coaches stop at the central bus station ( 08-9722 7800; Carmody Pl) , or at the train station (Picton Rd, Woolaston) .
South West Coach Lines ( 9261 7600; www.veoliatransportwa.com.au) runs services to/from Perth's Esplanade Busport (2½ hours, three daily), Mandurah (1¼ hours, daily), Busselton (1¼ hours, five daily), Dunsborough (1¾ hours, daily) and Bridgetown (1¾ hours, daily).
TransBunbury ( 9791 1955; www.veoliatransportwa.com.au) runs buses 101 (20 minutes, seven daily) and 103 (30 minutes, five daily) between the central bus station and train station (both routes $2.60; no Sunday service).
Transwa ( 1300 662 205; www.transwa.wa.gov.au) routes include the following:
SW1 (12 weekly) to East Perth ($30, 3¼ hours), Mandurah ($16, two hours), Busselton ($9, 43 minutes), Margaret River ($16, two hours) and Augusta ($24, 2½ hours)
SW2 (three weekly) to Balingup ($13, 53 minutes), Bridgetown ($16, 1¼ hours) and Pemberton ($27, 2¼ hours)
GS3 (daily) to Walpole ($43, 4½ hours), Denmark ($48, 5½ hours) and Albany ($56, six hours)
Train
Bunbury is the terminus of the Transwa (www.transwa.wa.gov.au) Australind train line, with two daily services to Perth ($30, 2½ hours) and Pinjarra ($16, 1¼ hours).
Top of Chapter
Tuart Forest National Park
The tuart is a type of eucalypt that only grows on coastal limestone, 200km either side of Perth, and this 20-sq-km strip squeezed between the Bussell Hwy and the Indian Ocean is the last pure tuart forest left. An alternative route to Busselton from Bunbury leads through the shade cast by these giants, some more than 33m tall.
Turn off the highway at Tuart Dr, 4km southwest of Capel. After driving 11km through the forest, turn right onto Layman Rd to find Wonnerup House (www.ntwa.com.au; 935 Layman Rd; adult/child $5/3; 10am-4pm Thu-Mon) , a whitewashed National Trust homestead (1859). Continue on this road past the seaside village of Wonnerup and then follow the coast to Busselton.
Top of Chapter
Busselton
pop 15,400
Unpretentious and uncomplicated, Busselton is what passes for the big smoke in these parts. Surrounded by calm waters and white-sand beaches, its outlandishly long jetty is its most famous attraction. The family-friendly town has plenty of diversionary activities for lively kids, including sheltered beaches, water slides, animal farms and even a classic drive-in cinema. During school holidays, it really bustles – the population increases fourfold and accommodation prices soar.
1 Sights & Activities
Busselton Jetty HISTORIC SITE
( 08-9754 0900; www.busseltonjetty.com.au; adult/child $2.50/free, return train adult/child $11/6) Busselton's 1865 timber-piled jetty – the longest in the southern hemisphere (1841m) – reopened in 2011 following a $27-million refurbishment. A little train chugs along to the Underwater Observatory (adult/child incl train $29.50/14; 9am-4.25pm) , where tours take place 8m below the surface; bookings are essential. There's also an Interpretive Centre (admission free; 9am-5pm) , an attractive building in the style of 1930s bathing sheds, about 50m along the jetty.
ArtGeo Cultural Complex GALLERY
(www.artgeo.com.au; 6 Queen St) Grouped around the old courthouse (1856), this complex includes tea rooms, wood turners, an artist-in-residence and the Busselton Art Society's gallery, selling works by local artists.
Old Butter Factory Museum MUSEUM
(Peel Tce; adult/child $6/2; 10am-4pm Wed-Mon) Local history.
Dive Shed DIVING
( 08-9754 1615; www.diveshed.com.au; 21 Queen St) Runs regular dive charters along the jetty, to Four Mile Reef (a 40km limestone ledge about 6.5km off the coast) and to the scuttled navy vessel HMAS _Swan_ (off Dunsborough).
z Festivals & Events
Southbound MUSIC
(www.southboundfestival.com.au; early Jan) Start off the New Year with three days of alternative music and camping – it's WA's Glastonbury, but with less mud. Recent international acts have included Hot Chip and The Hives.
CinéfestOZ CINEMA
(www.cinefestoz.com.au; late Aug) Busselton briefly morphs into St-Tropez with this oddly glamorous festival of French and Australian cinema, including lots of Australian premieres and the odd Aussie starlet.
4 Sleeping
Accommodation sprawls along the beach for several kilometres either side of town; check the location if you don't have transport.
Beachlands Holiday Park CARAVAN PARK $
( 1800 622 107; www.beachlands.net; 10 Earnshaw Rd, West Busselton; sites per 2 people $42, chalets from $132; ) This excellent family-friendly park offers a wide range of accommodation amid shady trees, palms and flax bushes. Deluxe spa villas ($180) have corner spas, huge TVs, DVD players and full kitchens.
Blue Bay Apartments APARTMENT $
( 08-9751 1796; www.bluebayapartments.com; 66 Adelaide St; apt from $125; ) Close to the beach, these good-value self-contained apartments are bright and cheery, each with private courtyard and barbecue.
Observatory Guesthouse B&B $$
( 08-9751 3336; www.observatory-guesthouse.com; 7 Brown St; d $145-240; ) A five-minute walk from the jetty, this friendly B&B rents four bright, cheerful rooms. They're not overly big, but you can spread out on the communal sea-facing balcony and front courtyard.
Grand Mercure RESORT $$$
( 08-9754 9800; www.mercure.com; 553 Bussell Hwy, Broadwater; apt from $287; ) Located 6km from town, this sprawling complex of 87 flash apartments and villas is set among native vegetation. There's an exhausting array of tennis and squash courts, indoor and outdoor pools, and a small gym; or you can just lie around on the beach at the foot of the property. Check online for discounts from Sunday to Tuesday.
5 Eating & Drinking
o Laundry Cafe CAFE $$
(www.laundrycafe.com.au; 43 Prince St; shared plates $14-39) Brick walls and a honey-coloured jarrah bar form the backdrop for Margaret River beers and wines, great cocktails, and classy shared plates including panko-crumbed cuttlefish, kangaroo tataki, and a main-sized yellow duck curry. Definitely get ready to linger longer than you planned.
Coco's Thai THAI $$
(55 Queen St; mains $16-18; 5pm-late) A little place serving tasty Thai favourites and more adventurous dishes such as a delicious fish curry with apple. Loaded with fresh herbs, the prawn salad is also great.
Vasse CAFE $$
(www.vassebarcafe.com.au; 44 Queen St; mains $17-28; 9am-late) The menu mainstays are pizza and pasta, but Vasse also turns out more eclectic fare, including a special French menu for CinéfestOZ in August. Bearded Busselton hipsters make it surprisingly cosmopolitan, and there's a good spread of beers on tap.
The Goose CAFE $$
(www.thegoose.com.au; Geographe Bay Rd; breakfast $11-24, lunch & dinner mains $29-39; 7am-5pm Mon-Tue, till late Wed-Sun; ) Near the jetty, this stylish cafe offers an eclectic, interesting menu and views out to sea. Between meals the Goose is open for coffee, wine and tapas ($15 to $20).
Newtown House MODERN AUSTRALIAN $$$
( 08-9755 4485; www.newtownhouse.com.au; 737 Bussell Hwy, Abbey; mains $37-42; from 10am Wed-Sat) Set amid green lawns and gardens, this early-settler residence (1851), 10km west of town, has a hefty reputation for serving up the best-quality regional ingredients. The menu changes seasonally – options could include grilled scallops or Margaret River venison – and you'll need to bring your own (BYO) wine. Bookings are recommended.
3 Entertainment
Busselton Drive-In Outdoor Cinema CINEMA
( 08-9751 5638; www.busseltondrive-in.com.au; 500 Bussell Hwy, Broadwater; adult/child $15/8) Double features, under the stars. Family-friendly titles kick off at 7.30pm, followed by more grown-up flicks at around 9pm. The season starts mid-September, and note it's strictly cash only.
8 Information
Visitor Centre ( 08-9752 5800; www.geographebay.com; 38 Peel Tce; 9am-5pm Mon-Fri, to 4.30pm Sat & Sun)
8 Getting There & Around
South West Coach Lines ( 08-9261 7600; www.veoliatransportwa.com.au) Runs services to/from Perth's Esplanade Busport ($35, 3¾ hours, three daily), Bunbury ($10, one hour, five daily), Dunsborough ($10, 30 minutes, three daily), Margaret River ($10, 50 minutes, three daily) and Augusta ($17, 1¼ hours, three daily).
TransBusselton ( 08-9754 1666; 39 Albert St) The most useful bus is the 903 that follows the coast to Dunsborough (four daily, Monday to Saturday).
Transwa ( 1300 662 205; www.transwa.wa.gov.au) Coach SW1 (12 weekly) stops at the visitor centre, heading to/from East Perth ($35, 4¼ hours), Bunbury ($9, 43 minutes), Dunsborough ($7.60, 28 minutes), Margaret River ($13, 1½ hours) and Augusta ($16, 1¾ hours).
Top of Chapter
Dunsborough
pop 3400
Smaller and less sprawling than Busselton, Dunsborough is a relaxed, beach-worshipping town that goes bonkers towards the end of November when about 7000 'schoolies' descend. When it's not inundated with drunken, squealing teenagers, it's a thoroughly pleasant place to be. The beaches are better than Busselton's, but accommodation is more limited.
The name Dunsborough first appeared on maps in the 1830s, but to the Wardandi people it was always Quedjinup, meaning 'place of women'.
2 Activities
Cape Dive DIVING
( 08-9756 8778; www.capedive.com; 222 Naturaliste Tce) There is excellent diving to be done in Geographe Bay, especially since the decommissioned Navy destroyer HMAS _Swan_ was purposely scuttled in 1997 for use as a dive wreck. Marine life has colonised the ship, which lies at a depth of 30m, 2.5km offshore.
Naturaliste Charters WHALE WATCHING
( 0419 186 133; www.whales-australia.com; adult/child $80/50; 10am & 2pm Sep-Dec) Two-hour whale-watching cruises from September to December. From January to March the emphasis switches to an Eco Wilderness Tour showcasing beaches, limestone caves with Indigenous art, and wildlife including dolphins and New Zealand fur seals. Tours also run out of Augusta.
4 Sleeping
There are many options for self-contained rentals in town depending on the season; the visitor centre has current listings.
Dunsborough Beachouse YHA HOSTEL $
( 08-9755 3107; www.dunsboroughbeachouse.com.au; 205 Geographe Bay Rd; dm $32-34, s/d $55/80; ) On the Quindalup beachfront, this friendly hostel has lawns stretching languidly to the water's edge; it's an easy 2km cycle from the town centre.
Dunsborough Central Motel MOTEL $
( 08-9756 7711; www.dunsboroughmotel.com.au; 50 Dunn Bay Rd; r $120-175) Centrally located in Dunsborough town, this well-run motel is good value, especially if you can snare an online midweek discount. That means more of your travel budget to enjoy nearby wineries and breweries.
5 Eating & Drinking
Squid Lips FISH & CHIPS $
(55 Dunn Bay Rd, Shop 27A, Dunsborough Centrepoint; snacks & meals $8-15; noon-2.30pm Tue-Sat, from 5pm daily) Rated one of WA's best fish-and-chip joints.
The Pourhouse BISTRO $$
(www.pourhouse.com.au; 26 Dunn Bay Rd; mains $19-28; 4pm-late) Hip but not pretentious, with comfy couches, regular live bands, and an upstairs terrace for summer. The pizzas are excellent, and top-notch burgers come in a locally baked sourdough bun. A considered approach to beer includes rotating taps from the best of WA's craft breweries and lots of bottled surprises.
Samudra CAFE $$
(www.samudra.com.au; 226 Naturaliste Tce; mains $14-20; 7.30am-4pm daily, 5.30-8pm Fri & Sat) S Featuring a funky VW Kombi coffee van, this garden cafe is one of WA's best vegetarian restaurants. Mexican, Middle Eastern and Asian flavours underpin a super-healthy menu of salads, curries, wraps and smoothies, and there are plenty of shady places to sit and read or write. Samudra also offers relaxing and reinvigorating yoga classes, as well as surfing and spa retreats.
Cape Wine Bar MODERN AUSTRALIAN $$
(www.thecapewinebar.com; 239 Naturaliste Tce; mains $24-38; 4pm-late Tue-Sat) Buzzing most nights, this wine bar has a well-deserved reputation for fresh food. The seasonal menu includes dishes like crispy skin snapper or a prawn curry.
Artézen CAFE $$
(www.artezen.com.au; 234 Naturaliste Tce; mains $14-28; 7am-4pm; ) Funky wallpaper, good breakfasts, and packed with families and surfers at the weekend.
8 Information
Visitor Centre ( 08-9752 5800; www.geographebay.com; Seymour Blvd; 9am-5pm Mon-Fri, 9.30am-4.30pm Sat & Sun) In the same building as the post office.
8 Getting There & Around
South West Coach Lines ( 08-9261 7600; www.veoliatransportwa.com.au) Services to/from Perth's Esplanade Busport ($38, 4½ hours, daily), Mandurah ($32, 3¼ hours, daily), Bunbury ($16, 1¾ hours, daily) and Busselton ($10, 30 minutes, three daily).
TransBusselton ( 08-9754 1666; www.veoliatransportwa.com.au; 39 Albert St, Busselton) Services between Dunsborough and Busselton (four daily, Monday to Saturday).
Transwa ( 1300 662 205; www.transwa.wa.gov.au) Coach SW1 (12 weekly) stops at the visitor centre, heading to/from East Perth ($38, 4½ hours), Bunbury ($13, 1¼ hours), Busselton ($7.60, 28 minutes), Margaret River ($9, 49 minutes) and Augusta ($16, 1¼ hours).
### RED TAILS IN THE SUNSET
Between Cape Naturaliste and Cape Leeuwin is the most southerly breeding colony of the red-tailed tropicbird _(Phaethon rubricauda)_ in Australia. From September to May, look for it soaring above Sugarloaf Rock, south of Cape Naturaliste. The viewpoint can be reached by a 3.5km boardwalk from the lighthouse or by Sugarloaf Rd.
The tropicbird is distinguished by its two long, red tail streamers, which are almost twice its body length. Bring binoculars to watch this small colony soar, glide, dive and then swim with their disproportionately long tail feathers cocked up.
Top of Chapter
Cape Naturaliste
Northwest of Dunsborough, Cape Naturaliste Rd leads to the excellent beaches of Meelup , Eagle Bay and Bunker Bay , and then on to Cape Naturaliste. There are walks and lookouts along the way; pick up brochures from Dunsborough's visitor centre before heading out. Whales and hammerhead sharks like to hang out on the edge of Bunker Bay, where the continental shelf drops 75m. There's excellent snorkelling on the edge of the shelf at Shelley Cove.
Bunker Bay is also the home of Bunkers Beach Cafe OFFLINE MAP (www.bunkersbeachcafe.com.au; Farm Break Lane; breakfast $14-24, lunch $16-34; 11.30am-4pm) , which serves up an adventurous menu only metres from the sand.
The Cape Naturaliste lighthouse (adult/child $13/7; tours every 30min 9.30am-4pm) , built in 1903, can be visited on tours and there's also a free museum. Above and Below packages (adult/child $30/15), combining entry to Ngilgi Cave ( Click here ), are also available.
### CAPE TO CAPE TRACK
Stretching from Cape Naturaliste to Cape Leeuwin, the 135km Cape to Cape Track passes through the heath, forest and sand dunes of the Leeuwin-Naturaliste National Park (Caves Rd) , all the while providing Indian Ocean views. Most walkers take about seven days to complete the track, staying in a combination of national-park camp sites and commercial caravan parks along the way, but you can walk it in five days or break up the route into day walks.
## Margaret River Wine Region
z Festivals & Events
Telstra Drug Aware Pro SURFING
(www.telstradrugawarepro.com; mid–late Mar) Six-day pro-surfing competition with associated concerts and fashion shows.
Margaret River Wine Region Festival WINE, FOOD
(www.margaretriverfestival.com; mid-Apr) Five days of street carnivals, slow food and master classes.
Margaret River Gourmet Escape WINE, FOOD
(www.gourmetescape.com.au; late Nov) From David Chang and Matt Moran to Tetsuya Wakuda, the inaugural Gourmet Escape in 2012 attracted some huge names. Look forward to four days of food workshops, tastings and demonstrations.
Margaret River Wine Region
Sights
1 Boranup Gallery B5
2 Calgardup Cave A5
3 Cape Leeuwin Lighthouse B7
4 CaveWorks & Lake Cave A5
5 Ellensbrook Homestead A4
6 Giants Cave A5
7 Jewel Cave B6
8 Mammoth Cave A5
Activities, Courses & Tours
9 Eagles Heritage B4
10 Ngilgi Cave A2
11 Wardan Aboriginal Centre A2
Sleeping
12 Acacia Chalets A4
13 Boranup Campground B6
14 Burnside Organic Farm B4
15 Caves Caravan Park A2
16 Conto Campground A5
17 Empire Retreat B1
18 Hamelin Bay Holiday Park A6
19 Injidup Spa Retreat A2
Llewellin's (see 12)
Noble Grape Guesthouse (see 31)
20 Point Road Campground A5
Seashells Yallingup (see 10)
21 Surfpoint A4
22 Taunton Farm Holiday Park B3
23 Wildwood Valley Cottages & Cooking SchoolA2
24 Windmills Break A2
25 Yallingup Beach Holiday Park A2
Eating
26 Bunkers Beach Cafe A1
27 Cullen Wines A3
28 Knee Deep in Margaret RiverA2
29 Margaret River Chocolate CompanyB3
30 Margaret River Dairy Company B3
31 Margaret Riviera B3
32 Providore B3
33 The Studio Bistro A2
34 Vasse Felix A3
35 Watershed Premium Wines B4
36 Xanadu A4
Drinking & Nightlife
Ashbrook (see 32)
37 Bootleg Brewery A3
38 Bush Shack Brewery A1
39 Cheeky Monkey Brewery A4
40 Colonial Brewing Co B4
41 Cowaramup Brewing Company B3
42 Eagle Bay Brewing Co A1
43 Leeuwin Estate B5
Margaret River Regional Wine Centre(see 31)
44 Stella Bella B4
Thompson Estate (see 32)
45 Voyager Estate B4
46 Wills Domain A2
Information
National Park Information Centre(see 2)
T Tours
See visitor centres for many more options. If you're feeling active, see the tours listed on Click here .
Bushtucker Tours CANOEING, WINE
( 08-9757 9084; www.bushtuckertours.com; adult/child $90/40) Four-hour trips combine walking and canoeing up the Margaret River, and feature aspects of Aboriginal culture along with uses of flora, and a bush-tucker lunch. Winery & Brewery Tours (adult/child $90/40) run around Margaret River.
Harvest Tours WINE, FOOD
( 0429 728 687; www.harvesttours.com.au; adult/child $125/55) Food and wine tour with an emphasis on organic, sustainable and ethical producers. Lunch is included at Cullen Wines (Click here ).
Wine for Dudes WINE TASTING
( 0427 774 994; www.winefordudes.com; tours $90) Includes a brewery, a chocolate factory, three wineries, a wine-blending experience and lunch.
Margaret River Tours WINE, SIGHTSEEING
( 0419 917 166; www.margaretrivertours.com) Runs winery tours (half-/full day $80/140) and can arrange charters.
Margies Big Day Out WINE, BEER
( 0416 180 493; www.margaretriverbigdayout.com; tours $90) Three wineries, two breweries and lunch.
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) Coach SW1 (12 weekly) from Perth to Augusta stops at Yallingup and Margaret River, with three coaches weekly continuing to Pemberton.
South West Coach Lines ( 08-9261 7600; www.veoliatransportwa.com.au) Buses between Busselton and Augusta (12 weekly) stop at Cowaramup and Margaret River, linking with Perth on the weekends.
Top of Chapter
Yallingup & Around
pop 1070
Beachside Yallingup is a mecca for both surfers and wine aficionados. You're permitted to let a 'wow' escape when the surf-battered coastline first comes into view. For romantic travellers, Yallingup means 'place of love' in the Wardandi Noongar tongue.
A set of beautiful walking trails follow the coast between here and Smiths Beach . Canal Rocks , a series of rocky outcrops forming a natural canal, are just past Smiths Beach.
Sights & Activities
Wardan Aboriginal Centre INDIGENOUS CULTURE
OFFLINE MAP
( 08-9756 6566; www.wardan.com.au; Injidup Springs Rd, Yallingup; experiences adult/child $20/10; 10am-4pm daily 15 Oct-15 Mar, closed Tue & Sat 15 Mar-15 Oct, experiences Sun, Mon, Wed & Fri) S F Offers a window into the lives of the local Wardandi people. There's a gallery, an interpretive display on the six seasons that govern the Wardandi calendar (admission $5) and the opportunity to take part in various experiences , such as stone tool making, boomerang and spear throwing, or a guided bushwalk exploring Wardandi spirituality and the uses of various plants for food, medicine and shelter.
Ngilgi Cave CAVING
OFFLINE MAP
( 08-9755 2152; www.geographebay.com; Yallingup Caves Rd; adult/child $21/11; 9.30am-4.30pm) Between Dunsborough and Yallingup, this 500,000-year-old cave is associated in Wardandi spirituality with the victory of the good spirit Ngilgi over the evil spirit Wolgine. To the Wardandi people it became a kind of honeymoon location. A European man first stumbled upon it in 1899 while looking for his horse. Formations include the white Mother of Pearl Shawl and the equally beautiful Arab's Tent and Oriental Shawl . Tours depart every half-hour
More adventurous caving options include the two-hour Ancient Riverbed Tour (adult/child $49/27), 2½-hour Explorer Tour (adult/child $84/52), three-hour Crystal Crawl Tour (adults only, $104) and the four-hour Ultimate Ngilgi Adventure (adults only, $149). The Above & Below ticket (adult/child $30/15) includes entry to the Cape Naturaliste Lighthouse.
Well-marked bushwalks start from here.
Yallingup Surf School SURFING
( 08-9755 2755; www.yallingupsurfschool.com) Offers 90-minute lessons for beginners ($50/125 for one/three lessons) and private coaching ($110).
4 Sleeping
Yallingup Beach Holiday Park CARAVAN PARK $
OFFLINE MAP
( 08-9755 2164; www.yallingupbeach.com.au; Valley Rd; sites per 2 people $32, cabins $100-150; ) You'll sleep to the sound of the surf here, with the beach just across the road.
Caves Caravan Park CARAVAN PARK $
OFFLINE MAP
( 08-9755 2196; www.cavescaravanpark.com.au; cnr Caves & Yallingup Beach Rds; 2-person sites $25-35, cabins $115-180; ) This leafy caravan park features clean cabins and friendly management.
Wildwood Valley Cottages & Cooking School COTTAGES $$
OFFLINE MAP
( 08-9755 2120; www.wildwoodvalley.com.au; 1481 Wildwood Rd; cottages from $220; ) Luxury cottages trimmed by native bush are arrayed across 50 hectares, and the property's main house also hosts the Mad About Food Cooking School with Sioban and Carlo Baldini. Sioban's CV includes training with Rockpool's Neil Perry, cooking at Longrain, and living in Tuscany, so the culinary emphasis is Thai or Italian. Cooking classes start at $85 per person.
Seashells Yallingup HOTEL, APARTMENT $$
OFFLINE MAP
( 08-9750 1500; www.seashells.com.au; Yallingup Beach Rd; d from $199; ) Rooms are either in the renovated Caves House (1938) or in the adjacent modern apartments. Weekday rates are good value. It's an atmospheric spot for a drink, with live gigs on Sunday afternoon. Over summer, some of Australia's biggest touring bands sometimes drop by.
o Injidup Spa Retreat BOUTIQUE HOTEL $$$
OFFLINE MAP
( 08-9750 1300; www.injidupsparetreat.com.au; Cape Clairault Rd; ste from $650; ) S The region's most stylish and luxurious accommodation, Injidup perches atop an isolated cliff south of Yallingup. A striking carved concrete and iron facade fronts the car park, while inside there are heated polished-concrete floors, 'eco' fires and absolute sea views. Each of the 10 suites has its own plunge pool. It's off Wyadup Rd.
Empire Retreat SPA HOTEL $$$
OFFLINE MAP
( 08-9755 2065; www.empireretreat.com; Caves Rd; ste $295-575; ) Everything about the intimate Empire Retreat is stylish, from the Indonesian-inspired design to the attention to detail and service. The rooms are built around a former farmhouse, and a rustic but sophisticated ambience lingers. Check online for good packages combining accommodation and spa treatments.
Windmills Break BOUTIQUE HOTEL $$$
OFFLINE MAP
( 08-9755 2341; www.windmillsbreak.com.au; 2024 Caves Rd; r around $300-320; ) Enter through the clubby lounge, which opens onto a terrace and landscaped grounds spreading down to a lovely pool. Rooms are plush and contemporary.
5 Eating & Drinking
The Studio Bistro MODERN AUSTRALIAN $$$
OFFLINE MAP
( 08-9756 6164; www.thestudiobistro.com.au; 7 Marrinup Dr; mains $35, degustation menu with/without wine matches $125/90) S This combination art gallery and garden bistro is definitely worth seeking out. The gallery focuses on Australian artists working in all media, while the restaurant showcases subtle dishes such as pan-fried fish with cauliflower cream, radicchio, peas and crab meat. Five-course degustation menus are offered on Friday and Saturday nights. Bookings are recommended.
Wills Domain WINERY
OFFLINE MAP
(www.willsdomain.com.au; cnr Brash & Abbey Farm Rds; mains $28-43, shared platters $35-65; tastings 10am-5pm, lunch noon-3pm) Restaurant, gallery and wonderful hilltop views over vines.
### BEER IS THE NEW WINE
The Margaret River region's wine credentials are impeccable, but now the area is also becoming a destination for craft-beer fans. All the following also serve bar snacks and lunch.
Eagle Bay Brewing Co OFFLINE MAP (www.eaglebaybrewing.com.au; Eagle Bay Rd, Dunsborough; 11am-5pm) A lovely rural outlook, interesting beers and wines served in modern, spacious surroundings, and excellent food including crisp woodfired pizzas ($20 to $24). Keep an eye out for Eagle Bay's Single Batch Specials.
Colonial Brewing Co OFFLINE MAP (www.colonialbrewingco.com.au; Osmington Rd, Margaret River; 11am-5pm) This modern microbrewery has great rural views, and an excellent range of authentic beers including a witbier with coriander and mandarin, and a hop-fuelled and citrusy India Pale Ale. Our favourite is the refreshing German-style Kölsch.
Bush Shack Brewery OFFLINE MAP (www.bushshackbrewery.com.au; Hemsley Rd, Yallingup; 10am-5pm) A small-scale brewery in a great bush setting. A healthy addition of innovation results in interesting brews like chilli beer, lemon-infused lager and strawberry pale ale.
Cheeky Monkey Brewery OFFLINE MAP (www.cheekymonkeybrewery.com.au; 4259 Caves Rd, Margaret River; 10am-6pm) Craft beers and ciders stand out at Margaret River's most recently opened microbrewery. Set around a pretty lake, there's also lots of room for the kids to run around. Try the Hatseller Pilsner with bold New Zealand hops.
Bootleg Brewery OFFLINE MAP (www.bootlegbrewery.com.au; off Yelverton Rd, Wilyabrup; 11am-6pm) More rustic than some of the area's flash new breweries, but lots of fun with a pint in the sun – especially with live bands on Saturday. Try the malty and robust Raging Bull Porter.
Cowaramup Brewing Company OFFLINE MAP (www.cowaramupbrewing.com.au; North Treeton Rd, Cowaramup; 11am-5pm) Modern microbrewey with an award-winning Pilsner and a moreish English-style Special Pale Ale. Four other beers and occasional seasonal brews also feature.
Top of Chapter
Cowaramup & Wilyabrup
pop 988
Cowaramup (Cow Town to some) is little more than a couple of blocks of shops lining Bussell Hwy. The rustic area to the northwest, known as Wilyabrup, is where in the 1960s the Margaret River wine industry was born. This area has the highest concentration of wineries, and the pioneers (Cullen Wines and Vasse Felix) are still leading the way.
4 Sleeping
Taunton Farm Holiday Park CARAVAN PARK $
OFFLINE MAP
( 1800 248 777; www.tauntonfarm.com.au; Bussell Hwy, Cowaramup; sites $37-39, cottages $110-130; ) There are plenty of farm animals for the kids to meet at one of Margaret River's best family-oriented campgrounds. For caravan and tenting buffs, the amenities blocks are spotless, and also scattered about are farmstyle self-contained cottages.
Noble Grape Guesthouse B&B $$
OFFLINE MAP
( 08-9755 5538; www.noblegrape.com.au; 29 Bussell Hwy, Cowaramup; s $135-155, d $150-190; ) Noble Grape is more like an upmarket motel than a traditional B&B. Rooms offer a sense of privacy and each has a little garden courtyard as well as a microwave and DVD player. The friendly owners clearly have green fingers.
5 Eating
Providore DELI $
OFFLINE MAP
(www.providore.com.au; 448 Tom Cullity Dr, Wilyabrup; 9am-5pm) Voted one of Australia's Top 100 Gourmet Experiences by _Australian Traveller_ magazine – and, given its amazing range of artisan produce including organic olive oil, tapenades and preserved fruits, we can only agree. Look forward to loads of free samples.
Margaret Riviera DELI $
OFFLINE MAP
(www.margaretriviera.com.au; Bottrill St, Cowaramup; 10am-5pm) Gourmet food store stocking local produce including olive oils, preserves and cheeses.
Margaret River Chocolate Company CHOCOLATE $
OFFLINE MAP
(www.chocolatefactory.com.au; Harman's Mill Rd; 9am-5pm) Watch truffles being made, sample chocolate buttons, or grab a coffee.
Margaret River Dairy Company CHEESE $
OFFLINE MAP
(www.mrdc.com.au; Bussell Hwy; 9.30am-5pm) Cheese tastings at two sites on the Bussell Hwy north of Cowaramup.
Vasse Felix RESTAURANT $$$
OFFLINE MAP
( 08-9756 5050; www.vassefelix.com.au; cnr Caves Rd & Harmans Rd S, Cowaramup; mains $29-39; 10am-3pm) Vasse Felix winery is considered by many to have the finest restaurant in the region, the big wooden dining room reminiscent of an extremely flash barn. The grounds are peppered with sculptures, while the gallery displaying works from the Holmes à Court collection is worth a trip in itself.
Knee Deep in Margaret River RESTAURANT $$$
OFFLINE MAP
( 08-9755 6776; www.kneedeepwines.com.au; 61 Johnson Rd, Wilyabrup; mains $28-38, 3-/5-course degustation $70/90; cellar door 10am-5pm, lunch noon-3pm) S Small and focused could be the motto here. Only a handful of mains are offered – crafted with locally sourced, seasonal produce – and the open-sided pavilion provides a pleasantly intimate vineyard setting. Order your food then shuffle up to the tasting counter to select its liquid companion.
Cullen Wines RESTAURANT $$$
OFFLINE MAP
( 08-9755 5277; www.cullenwines.com.au; 4323 Caves Rd, Cowaramup; mains $33-39; 10am-4pm) S Grapes were first planted here in 1966 and Cullen has an ongoing commitment to organic and biodynamic principles in both food and wine. It's less formal than its fancy neighbour Vasse Felix, but the food is excellent, with many of the fruit and vegetables from Cullen's own gardens.
6 Drinking
Margaret River Regional Wine Centre WINE
OFFLINE MAP
(www.mrwines.com; 9 Bussell Hwy, Cowaramup; 10am-7pm) A one-stop shop for Margaret River wine, with daily tastings rotating between smaller wineries without cellar doors.
Ashbrook WINERY
OFFLINE MAP
(www.ashbrookwines.com.au; 448 Tom Cullity Dr, Wilyabrup; 10am-5pm) Family-owned and -operated Ashbrook grows all of its grapes on site.
Thompson Estate WINERY
OFFLINE MAP
(www.thompsonestate.com; 299 Tom Cullity Dr, Wilyabrup; 10am-5pm) A small-scale producer with an architectural-award-winning concrete tastings and barrel room.
### BEST SURF SPOTS
» Margaret River Mouth
» Southside
» Three Bears
» Yallingup
» Injidup Car Park
Top of Chapter
Margaret River
pop 4500
Although tourists usually outnumber locals, Margaret River still feels like a country town. The advantage of basing yourself here is that after 5pm, once the wineries close, it's one of the few places with any vital signs. Plus it's close to the incredible surf of Margaret River Mouth and Southside, and the swimming beaches at Prevelly and Gracetown.
Margaret River spills over with tourists every weekend and gets very busy at Easter and Christmas (book weeks, if not months, ahead). Accommodation tends to be cheaper midweek.
Margaret River
Sleeping
1 Edge of the Forest C1
2 Margaret River Backpackers C3
3 Margaret River Lodge YHA B4
4 Prideau's C3
5 Riverglen Chalets C1
6 Vintages C3
Eating
7 Blue Ginger B4
8 Margaret River Bakery C2
9 Margaret River Farmers Market B3
10 Morries Anytime C3
11 Must C2
12 Settler's Tavern C2
Shopping
13 Tunbridge Gallery C2
4 Sleeping
Margaret River Lodge YHA HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9757 9532; www.mrlodge.com.au; 220 Railway Tce; dm $31-34, r with/without bathroom $85/74; ) About 1.5km southwest of the town centre, this clean, well-run hostel has a pool, volleyball court and football field. Dorms share a big communal kitchen, and a quieter area with private rooms has its own little kitchen and lounge.
Margaret River Backpackers HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9757 9572; www.margaretriverbackpackers.com.au; 66 Town View Tce; dm $32-35; ) Margaret River Backpackers caters mainly to working holiday makers. Dorms are a little spartan (there are no private rooms), but there's a nice big deck out the back.
Edge of the Forest MOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9757 2351; www.edgeoftheforest.com.au; 25 Bussell Hwy; r $120-180; ) New owners have re-energised this motel, a pleasant stroll from Margaret River township. The six rooms have all been recently renovated – several with a chic Asian theme – and all have new bathrooms. The leafy shared garden is perfect for an end-of-day barbecue.
Riverglen Chalets CHALET $$
OFFLINE MAP GOOGLE MAP
( 08-9757 2101; www.riverglenchalets.com.au; Carters Rd; chalets from $170; ) Just north of town, these good-value and very comfortable timber chalets are spacious and fully self-contained, with verandahs looking onto bushland.
Prideau's MOTEL $$
OFFLINE MAP GOOGLE MAP
( 0438 587 180; www.prideaus.com.au; 31 Fearn Ave; r $169-229; ) Centrally located, Prideau's has recently renovated units opening onto compact private courtyards. Some units have spa baths.
Vintages MOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9758 8333; www.vintagesmargaretriver.com.au; cnr Willmott Ave & Le Souef St; r $157-220; ) This spotless motel is set in tropical gardens. It's close to the centre of town, but all windows are double-glazed, so noise isn't a problem.
Burnside Organic Farm BUNGALOW $$$
OFFLINE MAP
( 08-9757 2139; www.burnsideorganicfarm.com.au; 287 Burnside Rd; d $275; ) Rammed-earth and limestone bungalows have spacious decks and designer kitchens, and the surrounding farm hosts a menagerie of animals and organic avocado and macadamia orchards. Guests can also pick vegetables from the garden. Welcome to the perfect private retreat after a day cruising the region's wine, beer and food highlights.
5 Eating & Drinking
Margaret River Bakery CAFE $
OFFLINE MAP GOOGLE MAP
(89 Bussell Hwy; mains $10-18; 7am-4pm Mon-Sat) S Elvis on the stereo, retro furniture and kitsch needlework 'paintings' – the MRB has a rustic, playful interior. It's the perfect backdrop to the bakery's honest home-style baking, often with a vege or gluten-free spin. Soak up the previous day's wine tasting with the legendary $13 Big Breakfast.
Blue Ginger CAFE, DELI $
OFFLINE MAP GOOGLE MAP
(www.bluegingerfinefoods.com; 31 Station Rd; mains $11-17; 8am-6pm Mon-Fri, 9am-3pm Sat & Sun) Ease into the colourful, mismatched furniture on the enclosed terrace and tuck into hearty cafe fare with some adventurous twists. It's very local, crammed with regulars easing into their first coffee of the day.
Margaret River Farmers Market MARKET $
OFFLINE MAP GOOGLE MAP
(www.margaretriverfarmersmarket.com.au; cnr Tunbridge & Farrelly Sts; 8am-noon Sat) S The region's organic and sustainable artisan producers come to town twice a month. Check the website for your own foodie hit list.
Morries Anytime CAFE $$
OFFLINE MAP GOOGLE MAP
(www.morries.com.au; 2/149 Bussell Hwy; mains $15-34) Settle into the clubby, cosmopolitan atmosphere of Morrie's, either for breakfast or lunch, or later at night for cocktails and tapas or dinner. Local beers from Colonial Brewing are on tap – try the refreshing Kölsch – and the menu channels European flavours with dishes like pork belly and rabbit croquettes.
Settler's Tavern PUB $$
OFFLINE MAP GOOGLE MAP
(www.settlerstavern.com; 114 Bussell Hwy; mains $15-29; 11am-midnight Mon-Sat, to 10pm Sun) There's live entertainment Thursday to Sunday at Settler's, so pop in for good pub grub and a beer or wine from the extensive list. Dinner options are limited in Margaret River, and Settler's is often wildly popular with locals and visitors. Try the mammoth Seafood Deluxe with a pint of the pub's own Margaret River Pale Ale.
Must RESTAURANT $$$
OFFLINE MAP GOOGLE MAP
( 08-9758 8877; www.must.com.au; 107 Bussell Hwy; small plates $8-18, mains $32-38; noon-late) The sister property to one of our favourite Perth restaurants (Must Winebar), Must Margaret River doesn't disappoint. True to its location, wine bottles line the shiraz- coloured walls and dangle from the chandelier. The service here is excellent and the charcuterie plates ($28) are legendary.
7 Shopping
Tunbridge Gallery INDIGENOUS ART
OFFLINE MAP GOOGLE MAP
(www.tunbridgegallery.com.au; 101 Bussell Hwy; 10am-5pm Mon-Sat, to 3pm Sun) Excellent Aboriginal art gallery, featuring mainly WA artworks.
8 Information
Visitor Centre ( 08-9780 5911; www.margaretriver.com; 100 Bussell Hwy; 9am-5pm) Loads of information, plus displays on local wineries.
8 Getting Around
Margaret River Beach Bus ( 08-9757 9532; www.mrlodge.com.au) Minibus linking the township and the beaches around Prevelly ($10, three daily); summer only, bookings essential.
### ACTIVE MARGARET RIVER
Much of the Margaret River experience is based around sybaritic pleasures, but to balance the virtue-versus-vice ledger, get active in the region's stunning scenery.
Dirty Detours ( 08-9758 8312; www.dirtydetours.com; tours $80) Runs guided mountain-bike rides, including through the magnificent Boranup Forest, as well as a Sip 'n' Cycle cellar-door tour. Another increasingly popular option is a mountain-biking and brewery tour. Multi-day tours are also available.
Edge Tours ( 0413 892 036; www.edgetours.com.au; per person from $175) Adventurous options include rock climbing, abseiling, caving and sea-kayaking.
Margaret River Climbing ( 0415 970 522; www.margaretriverclimbing.com.au; half-/full day $130/200) Caving, rock climbing and abseiling.
Margaret River Kitesurfing & Windsurfing ( 0419 959 053; www.mrkiteandsail.com.au; 2hr from $75) Instruction and gear rental.
Top of Chapter
Around Margaret River
West of the Margaret River township, the coastline provides spectacular surfing and walks. Prevelly is the main settlement, with a few places to sleep and eat. Most of the sights are on Caves Rd or just off it.
1 Sights & Activities
CaveWorks & Lake Cave CAVE
OFFLINE MAP
(www.margaretriver.com; Conto Rd; single adult/child $22/10; 9am-5pm, Lake Cave tours hourly 9.30am-3.30pm) Acting as the main ticket office for three of the region's most impressive caves (Lake, Mammoth and Jewel), CaveWorks also has excellent displays about caves, cave conservation and local fossil discoveries. There's also an authentic model cave and a 'cave crawl' experience.
Behind the centre is Lake Cave, the prettiest of them all, where limestone formations are reflected in an underground stream. The vegetated entrance to this cave is spectacular and includes a karri tree with a girth of 7m. Lake Cave is the deepest of all the caves open to the public. There are more than 300 steps down (a 62m drop) to the entrance.
Single cave tickets include entry to CaveWorks. The Grand Pass (adult/child $50/22), covering CaveWorks and all three caves, is valid for seven days, while the Ultimate Pass (adult/child $65/27) also includes Cape Leeuwin lighthouse.
CaveWorks is 20km south of Margaret River, off Caves Rd.
Mammoth Cave CAVE
OFFLINE MAP
(www.margaretriver.com; Caves Rd; adult/child $22/10; 9am-4pm) Mammoth Cave boasts a fossilised jawbone of _Zygomaturus trilobus,_ a giant wombat-like creature, as well as other fossil remains and the impressive Mammoth Shawl formation. Visits are self-guided; an MP3 audio player is provided.
Calgardup & Giants Caves CAVES
These two self-guided caves are managed by the Department of Environment and Conservation (DEC), which provides helmets and torches. Calgardup Cave OFFLINE MAP (www.dec.wa.gov.au; Caves Rd; adult/child $15/8; 9am-4.15pm) has a seasonal underground lake and is an attractive illustration of the role of the caves in the ecosystem – a stream transports nutrients to the creatures living in the cave, while tree roots hang overhead. Giants Cave OFFLINE MAP (www.dec.wa.gov.au; Caves Rd; adult/child $15/8; 9.30am-3.30pm school & public holidays only) , further south, is deeper and longer and has some steep ladders and scrambles.
Ellensbrook Homestead HISTORIC BUILDING
OFFLINE MAP
(www.ntwa.com.au; Ellensbrook Rd; adult/child $4/2; 10am-4pm Sat & Sun) An intriguing National Trust property 8km northwest of Margaret River, Ellensbrook (1857) was the first home of pioneer settlers Alfred and Ellen Bussell. The Wardandi people welcomed them, gave them Noongar names and led them to this sheltered but isolated site, with its supply of fresh water.
The house is basic and more than a little ramshackle, constructed of paperbark, driftwood, timber, lime, dung and hair. Between 1899 and 1917, Edith Bussell, who farmed the property alone for many years, established an Aboriginal mission here. The children were taught to read and write, and two of them were beneficiaries of Edith's will.
A short walk leads to Meekadarabee ('bathing place of the moon'), a beautiful grotto set below trickling rapids and surrounded by lush bush, associated with a pair of star-crossed indigenous lovers. The grounds are open even when the house isn't.
Boranup Gallery GALLERY
OFFLINE MAP
(www.boranupgallery.com; 7981 Caves Rd; 9.30am-5pm) Local arts and crafts, 22km south of Margaret River.
Boranup Drive SCENIC DRIVE
This 14km diversion runs along an unsealed road through Leeuwin-Naturaliste National Park's beautiful karri forest. Near the southern end there's a lookout offering sea views.
Eagles Heritage WILDLIFE INTERACTION
OFFLINE MAP
( 08-9757 2960; www.eaglesheritage.com.au; adult/child $15/7.50; 10am-5pm) Housing Australia's largest collection of raptors, this centre, 5km south of Margaret River, rehabilitates many birds of prey each year. There are free-flight displays at 11am and 1.30pm.
4 Sleeping
Surfpoint HOSTEL $
OFFLINE MAP
( 08-9757 1777; www.surfpoint.com.au; Reidle Dr, Gnarabup; dm/d $32/105; ) This light and airy place offers the beach on a budget. The rooms are clean and well presented, and there's a very enticing little pool. Refurbishment aplenty was on the go when we last dropped by.
National Park Campgrounds CAMPGROUND $
(www.dec.wa.gov.au; sites per adult/child $7/2) The DEC has three basic campgrounds within Leeuwin-Naturaliste National Park. Conto Campground OFFLINE MAP (Conto Rd) has gas barbecues, toilets and running water; Boranup Campground OFFLINE MAP (off Boranup Dr) , under the tall trees off the southern end of Boranup Dr, can get damp in winter; Point Road Campground OFFLINE MAP is only accessible by foot or 4WD from the northern end of Boranup Dr.
Llewellin's B&B $$
OFFLINE MAP
( 08-9757 9516; www.llewellinsguesthouse.com.au; 64 Yates Rd; r $198-248; ) It may be a Welsh name, but the style's French provincial in the four upmarket yet homely guestrooms.
o Acacia Chalets CHALET $$$
OFFLINE MAP
( 08-9757 2718; www.acaciachalets.com.au; 113 Yates Rd; d $250-270; ) Private bushland – complete with marsupial locals – conceals three luxury chalets that are well located to explore the region's vineyards, caves and rugged nearby coastline. Limestone walls and honey-coloured jarrah floors combine for some of the area's best self-contained accommodation. Spacious decks are equipped with gas barbecues.
5 Eating & Drinking
Watershed Premium Wines RESTAURANT $$
OFFLINE MAP
(www.watershedwines.com.au; cnr Bussell Hwy & Darch Rd; cafe $17-22, restaurant $38-42; 10am-5pm) Famous for its 'Awakening' cabernet sauvignon, and regularly rated as one of WA's best vineyard restaurants. Dining options include an informal cafe and Watershed's classier restaurant with expansive views of a compact lake and trellised vines.
Xanadu RESTAURANT $$$
OFFLINE MAP
( 08-9758 9531; www.xanaduwines.com; Boodjidup Rd; mains $36; 10am-5pm, restaurant noon-3pm) Escape into your own personal pleasure dome in the hip and chic restaurant filling Xanadu's vast space. The menu changes seasonally – we had a terrific braised-goat tortilla and confit duck – and definitely leave room for dessert.
Voyager Estate WINERY
OFFLINE MAP
( 08-9757 6354; www.voyagerestate.com.au; Stevens Rd; 10am-5pm) The formal gardens and Cape Dutch–style buildings delight at Voyager Estate, the grandest of Margaret River's wineries. Tours are available ($25 including tastings).
Leeuwin Estate WINERY
OFFLINE MAP
( 08-9759 0000; www.leeuwinestate.com.au; Stevens Rd; 10am-5pm) Another impressive estate, with tall trees and lawns gently rolling down to the bush. Its Art Series Chardonnay is one of the best in the country. Behind-the-scenes wine tours and tastings take place at 11am, noon and 3pm (adult/child $12.50/4). Big open-air concerts are regularly held here.
Stella Bella WINERY
OFFLINE MAP
(www.stellabella.com.au; 205 Rosabrook Rd; 10am-5pm) No bells and whistles, just excellent wines with the prettiest labels in the region.
8 Information
National Park Information Centre OFFLINE MAP ( 08-9757 7422; www.dec.wa.gov.au; Calgardup Cave, Caves Rd; 9am-4.15pm)
Top of Chapter
Augusta & Around
pop 1700
Augusta is positioned at the mouth of the Blackwood River, 5km north of Cape Leeuwin, and quite separate from the main wine region. There are a few vineyards, but the vibe here is less epicurean, and more languid.
1 Sights & Activities
Cape Leeuwin Lighthouse LIGHTHOUSE
OFFLINE MAP
(www.margaretriver.com; adult/child $5/3; 8.45am-4.45pm) Wild and windy Cape Leeuwin, where the Indian and Southern Oceans meet, is the most southwesterly point in Australia. It takes its name from a Dutch ship that passed here in 1622. The lighthouse (1896), WA's tallest, offers magnificent views of the coastline. Tours leave every 40 minutes from 9am to 4.30pm (adult/child $17/7). Only 10 people at a time can enter, so be prepared to wait in holiday season. The Ultimate Pass (adult/child $65/27) incorporates admission to the lighthouse with Jewel, Lake and Mammoth Caves.
Jewel Cave CAVE
OFFLINE MAP
(www.margaretriver.com; Caves Rd; adult/child $22/10; tours hourly 9.30am-3.30pm) The most spectacular of the region's caves, Jewel Cave has an impressive 5.9m straw stalactite, so far the longest seen in a tourist cave. Fossil remains of a Tasmanian tiger (thylacine), believed to be 3500 years old, were discovered here. It's located near the south end of Caves Rd, 8km northwest of Augusta. The Grand Tour Pass (adult/child $50/22) incorporates admission to the Jewel, Lake and Mammoth Caves.
A new Jewel Cave Preservation Centre opened at Jewel Cave in 2011.
Reopened in late 2012, the nearby Moondyne Cave can be visited on the Moondyne Experience, a subterranean adventure combining overalls, hard hats and torches. The tour concludes wth lunch at the Jewel Cave, and prior booking is essential. Children must be at least 12 years of age.
Augusta Historical Museum MUSEUM
(Blackwood Ave; adult/child $3/1.50; 1-3pm) Interesting local exhibits.
Blackwood River Houseboats HOUSEBOAT
( 08-9758 0181; www.blackwoodriverhouseboats.com.au; Westbay) Take care of your accommodation, river cruise and fishing trip all at once with a houseboat holiday. They're easy to drive and available for two-night/three-day hire (weekend $950 to $1600, midweek $700 to $1150) or for weekly hire ($1900 to $2800).
Blackwood River CRUISES
( Oct-May) Operators running boat trips up the Blackwood River include Absolutely Eco River Cruises ( 08-9758 4003; cdragon@westnet.com.au; adult/child $30/10) and Miss Flinders ( 0409 377 809; adult/child $40/15) .
4 Sleeping & Eating
Baywatch Manor YHA HOSTEL $
( 08-9758 1290; www.baywatchmanor.com.au; 9 Heppingstone View; dm $29, d with/without bathroom $93/73; ) Clean, modern rooms with creamy brick walls and pieces of antique furniture. There is a bay view from the deck and, in winter, a roaring fire in the communal lounge. Some doubles have compact balconies.
Hamelin Bay Holiday Park CARAVAN PARK $
OFFLINE MAP
( 08-9758 5540; www.mronline.com.au/accom/hamelin; Hamelin Bay West Rd; sites per 2 people $20-25, cabins $80-180) Absolute beachfront, northwest of Augusta, this secluded place gets very busy during holiday times.
Best Western Georgiana Molloy MOTEL $$
( 08-9758 1255; www.augustaaccommodation.com.au; 84 Blackwood Ave; r $130-165) The decor is a little dated, but these spacious, self- contained units are standout value, each with a small garden area.
Deckchair Gourmet CAFE, DELI $
(Blackwood Ave; mains $7-16; 8.30am-4pm; ) Excellent coffee, delicious food and free wi-fi.
8 Information
Visitor Centre ( 08-9758 0166; www.margaretriver.com; cnr Blackwood Ave & Ellis St; 9am-5pm)
## Southern Forests
The tall forests of WA's southwest are simply magnificent, with towering gums (karri, jarrah, marri) sheltering cool undergrowth. Between the forests, small towns bear witness to the region's history of logging and mining. Many have redefined themselves as small-scale tourist centres where you can take walks, wine tours, canoe trips and trout- and marron-fishing expeditions.
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) coach routes include the following:
SW1 (three weekly) to Nannup and Pemberton from East Perth, Bunbury, Busselton, Margaret River and Augusta
SW2 (three weekly) to Balingup, Bridgetown, Manjimup and Pemberton from East Perth, Mandurah and Bunbury
GS3 (daily) to Balingup, Bridgetown, Manjimup and Pemberton from Perth, Bunbury, Walpole, Denmark and Albany
South West Coach Lines ( 08-9261 7600; www.veoliatransportwa.com.au) runs services to Nannup from Busselton (twice weekdays) and Bunbury (weekdays); and Balingup, Bridgetown and Manjimup from Bunbury, Mandurah and Perth (daily)
Top of Chapter
Nannup
pop 500
Nannup's historic weatherboard buildings and cottage gardens have an idyllic bush setting on the Blackwood River. The Noongar-derived name means 'a place to stop and rest'; it's also a good base for bushwalkers and canoeists.
Sporadic but persistent stories of sightings of a striped wolf-like animal, dubbed the Nannup tiger, have led to hopes that a Tasmanian tiger may have survived in the surrounding bush (the last known Tasmanian tiger, or thylacine, died in Hobart Zoo in 1936). Keep your camera handy and your eyes peeled!
2 Activities
Blackwood River Canoeing CANOEING
( 08-9756 1209; www.blackwoodrivercanoeing.com; hire per day from $25) Provides equipment, basic instruction and transfers for canoeing paddles and longer expeditions. The best time to paddle is in late winter and early spring, when the water levels are up.
St John Brook Conservation Park PARK
(Barrabup Rd) A pretty spot to walk, cycle, swim and camp, 8km west of Nannup along an unsealed road.
z Festivals & Events
Nannup Music Festival MUSIC
(www.nannupmusicfestival.org) Held in early March, focusing on folk and world music. Buskers are encouraged, so if you're any good, add yourself to the artists' roster.
4 Sleeping & Eating
Caravan Park CARAVAN PARK $
(1-/2-person sites from $15/25, cabins $66-80) This riverside caravan park is run by the visitor centre.
Holberry House B&B $
( 08-9756 1276; www.holberryhouse.com; 14 Grange Rd; r $120-190; ) The decor might lean towards granny-chic, but this large house on the hill has charming hosts and comfortable rooms. It's surrounded by large gardens dotted with quirky sculptures (open to nonguests for $4).
Nannup Bridge Cafe CAFE $$
(1 Warren Rd; breakfast & lunch $9-18, dinner $16-38; 9am-2pm Tue-Sun, 6-8pm Wed-Sat) Right opposite the tourist office, this cool-looking riverfront cafe morphs into a bistro at night. Standout dishes include the pork belly and the sticky-date pudding.
8 Information
Visitor Centre ( 08-9756 1211; www.nannup.wa.gov.au; 4 Brockman St; 9am-5pm Mon-Fri, 10am-3pm Sat, 10am-1pm Sun) Check out the Nannup tiger press clippings. Housed in the 1922 police station.
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Balingup & Greenbushes
It's like 1967 never ended in trippy Balingup (population 450), where coloured flags, scarecrows and murals of fairies and toadstools line the main street. Stop and rummage around eclectic stores such as the Old Cheese Factory (Nannup Rd; 9.30am-4pm) and the Tinderbox (www.cheekyherbs.com; South West Hwy; 9am-5pm) herbal remedies shop.
The visitor centre ( 08-9764 1818; www.balinguptourism.com.au; South West Hwy; 10am-4pm) is on the main street, and the village's busy social hub for dogs and their owners is the Packing Shed (Nannup Rd; 9am-4pm) . Explore the heritage exhibition and try some local fruit wine.
Greenbushes (population 342) is a historic mining and timber township, 10km south of Balingup. Some splendid decaying buildings from the boom days line the road, and heritage memorabilia is dotted through town. A series of walks loop around town and out to join the Bibbulmun track; the Balingup and Bridgetown visitor centres keep walking-trail brochures.
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Bridgetown
pop 2400
Lovely Bridgetwon is surrounded by karri forests and farmland, and spread around the Blackwood River. Weekends are busy, and the popular Blues at Bridgetown Festival (www.bluesatbridgetown.com) occurs annually on the second weekend of November.
Bridgetown's old buildings include Bridgedale House (Hampton St; admission by gold-coin donation; 10am-2pm Sat & Sun) , built of mud and clay by the area's first settler in 1862, and since restored by the National Trust.
4 Sleeping & Eating
Bridgetown Hotel PUB $$
( 08-9761 1034; www.bridgetownhotel.com.au; 157 Hampton St; r $165-265, mains $17-29; ) You don't expect quirky pizzas (lime and tequila, lamb and tzatziki) or large modern bedrooms with spa baths in an Australian country pub. A recent revamp has left this 1920s gem with both.
Bridgetown Riverside Chalets RENTAL HOUSE $
( 08-9761 1040; www.bridgetownchalets.com.au; 1338 Brockman Hwy; chalets from $125) On a rural riverside property, 5km up the road to Nannup, these four stand-alone wooden chalets (complete with pot-bellied stoves and washing machines) sleep up to six in two bedrooms.
### ELVIS SIGHTED IN BOYUP BROOK
The pretty township of Boyup Brook (population 540), 31km northeast of Bridgetown, is the centre of country music in WA. The fantastically over-the-top Harvey Dickson's Country Music Centre (www.harveydickson.com.au; adult/child $8/2; 9am-5pm) comes complete with a life-sized Elvis and Johnny Cash, an Elvis memorabilia room, and three 13.5m-tall guitar-playing men. It hosts regular rodeos (the big one's in October) and big-name country-music events, as well as the Boyup Brook Country Music Festival (www.countrymusicwa.com.au) in February. Scenic but basic bush camping (sites $8) is always available.
To combine country music with country critters, stay at Nature's Guest House (dm/cottages $20/80) . Book through the Department of Environment and Conservation (DEC; 08-9776 1207; donnelly.district@dec.wa.gov.au) in Donnelly. It's located in the 520-sq-km Perup Forest. Wildlife includes rare mammals such as the numbat, tammar wallaby and southern brown bandicoot. You'll find it south of Boyup Brook, off the Boyup Brook Cranbrook Rd.
Nelsons of Bridgetown MOTEL $$
( 08-9761 1645; www.nelsonsofbridgetown.com.au; 38 Hampton St; s $95-145, d $130-195; ) The central location is great, but go for the spacious newer rooms built adjacent to the 1898 Federation-style hotel.
The Cidery CAFE $
(www.thecidery.com.au; 43 Gifford Rd; mains $10-25; 11am-4pm Sat-Thu, to 8pm Fri) Craft beer, cider and light lunches on outdoor tables by the river. On Friday nights from 5.30pm there's live music.
8 Information
Visitor Centre ( 08-9761 1740; www.bridgetown.com.au; 154 Hampton St; 9am-5pm Mon-Fri, 10am-3pm Sat, 10am-1pm Sun; ) Includes apple-harvesting memorabilia.
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Manjimup
pop 4300
Surrounded by spectacular forest, Manjimup is at the heart of WA's timber industry. For foodies it's known for something very different: truffles. During August especially, Manjimup's black Périgord truffles make their way onto top Australian menus.
1 Sights & Activities
Wine & Truffle Co WINE, FOOD
( 08-9777 2474; www.wineandtruffle.com.au; Seven Day Rd; mains $19-35; 10am-4.30pm) To discover how the world's most expensive produce is harvested, follow your snout to the Wine & Truffle Co. Join a 2½-hour truffle hunt on Saturday or Sunday from June to August $95; book ahead), ending with breakfast of scrambled eggs with truffles. Offerings in the attached restaurant range from a truffle tasting plate to truffle fettucine.
Timber & Heritage Park PARK
(cnr Rose & Edward Sts; 9am-5pm) Located in town, with a little lake, free BBQs and logging paraphernalia, including a replica of One Tree Bridge .
One Tree Bridge & Glenoran Pool RUINED BRIDGE
(Graphite Rd) In a forest clearing 22km from town are the remains of One Tree Bridge. It was constructed from a single karri log carefully felled to span the width of the river but rendered unusable after the floods of 1966. Adjacent is gorgeous Glenoran Pool, a popular swimming hole.
Four Aces TREES
(Graphite Rd) These four 300-plus-year-old karri trees are in a straight line; stand directly in front and they disappear into one. There's a short loop walk through the surrounding karri glade, or a 1½-hour loop bushwalking trail from the Four Aces to One Tree Bridge.
Diamond Tree Lookout LOOKOUT
Nine kilometres south of Manjimup along the South Western Hwy is this lookout. Metal spikes allow you to climb this 52m karri, and there's a nature trail nearby.
4 Sleeping
Diamond Forest Cottages CHALET $$
( 08-9772 3170; www.diamondforest.com.au; 29159 South Western Hwy; chalets $180-200; ) South of Manjimup, before the turn-off to Pemberton, is this collection of well-equipped wooden chalets with decks, scattered around a farm. Turkeys and sheep wander around, and there's a petting zoo and daily animal-feeding for the kids.
8 Information
Visitor Centre ( 9771 1831; www.manjimup.wa.gov.au; Giblett St; 9am-5pm)
Top of Chapter
Pemberton
pop 760
Hidden deep in the karri forests, drowsy Pemberton has also taken an epicurean turn, producing excellent wine that rivals that of Margaret River for quality if not for scale. If Margaret River is WA's Bordeaux, Pemberton is its Burgundy – producing excellent chardonnay and pinot noir, among other varietals. Wine tourism isn't as developed here, with some of the better names only offering tastings by appointment. Grab a free map listing opening hours from the visitor centre.
The national parks circling Pemberton are impressive. Aim to spend a day or two driving the well-marked Karri Forest Explorer tracks, walking the trails and picnicking in the green depths.
1 Sights & Activities
Salitage WINE TASTING
( 08-9776 1195; www.salitage.com.au; Vasse Hwy; 10am-4pm) Sailtage's pinot noir has been rated the state's best, while its chardonnay and sauvignon blanc are also very highly regarded. Hour-long vineyard tours leave at 11am; call ahead.
Pemberton Tramway TRAM RIDES
( 08-9776 1322; www.pemtram.com.au; adult/child $18/9; 10.45am & 2pm) Built between 1929 and 1933, the route travels through lush karri and marri forests to Warren River. A commentary is provided and it's a fun – if noisy – 1¾-hour return trip.
Mountford WINE TASTING
(www.mountfordwines.com.au; Bamess Rd; 10am-4pm) S The wines and ciders produced here are all certified organic, plus there's a gallery on site. It's located north of Pemberton and easily incorporated into the Karri Forest Explorer circuit.
Pemberton Wine Centre WINE TASTING
(www.marima.com.au; 388 Old Vasse Rd; noon-4pm Mon-Fri) At the very heart of Warren National Park, this centre offers tastings of local wines and can compile a mixed case of your favourites.
Pemberton Pool SWIMMING
(Swimming Pool Rd) F Surrounded by karri trees, this natural pool is popular on a hot day – despite the warning sign (currents, venomous snakes). They breed them tough around here.
T Tours
Pemberton Hiking & Canoeing HIKING, CANOEING
( 08-9776 1559; www.hikingandcanoeing.com.au; half-/full day $50/100) S Environmentally sound tours in Warren and D'Entrecasteaux National Parks and to the Yeagarup sand dunes. Specialist tours (wildflowers, frogs, rare fauna) are also available, as are night canoeing trips ($75) to spot nocturnal wildlife.
Pemberton Discovery Tours DRIVING TOUR
( 08-9776 0484; www.pembertondiscoverytours.com.au; adult/child $95/50) S Half-day 4WD tours to the Yeagarup sand dunes and the Warren River mouth.
Donnelly River Cruises BOAT
( 08-9777 1018; www.donnellyrivercruises.com.au; adult/child $65/35) S Cruises through 12km of D'Entrecasteaux National Park to the cliffs of the Southern Ocean.
4 Sleeping
Pemberton Backpackers YHA HOSTEL $
( 08-9776 1105; www.yha.com.au; 7 Brockman St; dm/s/d $28/62/65; ) The main hostel is given over to seasonal workers, but you'll need to check in here for a room in the separate cottage (8 Dean St) that's set aside for travellers. It's cute and cosy, but book ahead as it only has three rooms, one of which is a six-person dorm.
Best Western Pemberton Hotel HOTEL $
( 08-9776 1017; www.pembertonhotel.bestwestern.com.au; 66 Brockman St; r from $115; ) Attached to an classic country pub, this comfortable accommodation occupies a striking new rammed-earth and cedar extension.
Gloucester Motel MOTEL $
( 08-9776 1266; www.gloucestermotel.com.au; Ellis St; r $80-160, apt from $140; ) The best of the town's motels, the Gloucester also has good-value budget rooms and spacious apartments. On site is the very good Sadie's restaurant.
o Foragers COTTAGE $$
( 08-9776 1580; www.foragers.com.au; cnr Roberts & Northcliffe Rds; cottages $160-270; ) S Choose between very nice, simple karri cottages, or leap to the top of the ladder with the luxury eco-chalets. The latter are light and airy, with elegant, contemporary decor, eco-conscious waste-water systems and a solar-passive design. You're also right on hand to enjoy culinary treats at the adjacent Foragers Field Kitchen (Click here ).
Old Picture Theatre Holiday Apartments APARTMENT $$
( 08-9776 1513; www.oldpicturetheatre.com.au; cnr Ellis & Guppy Sts; apt $170-300; ) The town's old cinema has been revamped into well-appointed, self-contained, spacious apartments with lots of jarrah detail and black-and-white movie photos. It offers terrific value for money and the guest laundry and spa are rare treats.
Pump Hill Farm Cottages COTTAGE $$
( 08-9776 1379; www.pumphill.com.au; Pump Hill Rd; d $135-270) Families love this farm property, where kids are taken on a daily hay ride to feed the animals. Child-free folk will enjoy the ambience of the private, well-equipped cottages too.
### KARRI FOREST EXPLORER
Punctuated by glorious walks, magnificent trees and picnic areas, the Karri Forest Explorer tourist drive wends its way along 86km of scenic (partly unsealed) roads through three national parks (vehicle entry $11).
Popular attractions include the Gloucester Tree , named after the Duke of Gloucester who visited in 1946. It's a splendid fire-lookout tree, laddered with a spiral metal stairway; if you're feeling fit and fearless, make the 58m climb to the top. The Dave Evans Bicentennial Tree , tallest of the 'climbing trees' at 68m, is in Warren National Park, 11km southwest of Pemberton. Its tree-house cage weighs 2 tonnes and can sway up to 1.5m in either direction in strong winds. The Bicentennial Tree one-way loop leads via Maiden Bush to the Heartbreak Trail . It passes through 250-year-old karri stands, and nearby Drafty's Camp and Warren Campsite are great for overnighting (sites per adult/child $7/2).
The enchanting Beedelup National Park , 15km west of town on the Vasse Hwy (Rte 104), shouldn't be missed. There's a short, scenic walk that crosses Beedelup Brook near Beedelup Falls . There are numerous bird species to be found in the tall trees; at ground level the red-winged fairy wren is commonly seen. North of town, Big Brook Arboretum features 'big' trees from all over the world.
The track loops on and off the main roads, so you can drive short sections at a time. Pick up a brochure from Pemberton's visitor centre.
Marima Cottages COTTAGE $$$
( 08-9776 1211; www.marima.com.au; 388 Old Vasse Rd; cottages $225-245) Right in the middle of Warren National Park, these four country-style rammed-earth-and-cedar cottages with pot-bellied stoves and lots of privacy are luxurious getaways.
5 Eating & Drinking
The local menu specialities are trout and marron.
Holy Smoke! SELF-CATERING $
(www.holysmoke.com.au; 3/19 Brockman St; snacks $5-15; 9am-5pm Mon-Sat) Good coffee, sourdough bread, house-smoked meat, chicken and fish. Pop in for picnic supplies.
Forest Fresh Marron SELF-CATERING $
( 0428 887 720; www.forestfreshmarron.com.au; Pump Hill Rd; 10am-5pm Mon-Fri, 4.30-5.30pm Sat & Sun) S Live sustainably farmed marron for sale. Transport packs – to keep the wee beasties alive for up to 30 hours – and cooking pots are also available. It's 300m left of the caravan park.
Millhouse Cafe CAFE $$
(Brockman St; breakfast $6-20, lunch $11-40; 7am-5pm) Breakfast – try the breakfast crostini – and coffee are good at this old cottage with wraparound verandahs, and you can feast on local marron and trout for lunch. Local art is often displayed on the walls.
Sadie's INTERNATIONAL, INDIAN $$
(Ellis St; mains $25-35; 6-9pm) Local trout and marron, and authentically good Indian curries from an authentically good Indian chef. At Gloucester Motel.
Foragers Field Kitchen INTERNATIONAL $$$
( 08-9776 1503; www.foragers.com.au; cnr Roberts & Northcliffe Rds; dinner $55-75) Join renowned chef Sophie Zalokar at one of her regular Friday or Saturday set dinners – options could include wood-fired Italian dishes or seasonal four-course menus – or sign up for one of her cooking classes (usually across a weekend or on a Wednesday night). Check the website's events calendar for dates. Booking at least 48 hours ahead is preferred.
Jarrah Jacks CRAFT BEER
(www.jarrahjacks.com.au; Kemp Rd, Lot 2; 9am-5pm) Wonderful vineyard views, six craft beers – try the refreshing wheat beer – and tasty food including shepherds pie, salt-and-pepper squid and daily sandwich specials.
8 Information
DEC ( 08-9776 1207; www.dec.wa.gov.au; Kennedy St; 8am-4.30pm) Has detailed information on the local parks and stocks the useful _Pemberton Bushwalks_ brochure.
Visitor Centre ( 08-9776 1133; www.pembertonvisitor.com.au; Brockman St; 9am-4pm; ) Includes a pioneer museum and karri-forest discovery centre. Also handles Transwa bookings.
Top of Chapter
Shannon National Park
The 535-sq-km Shannon National Park (entry per car/motorcycle $11/5) is on the South Western Hwy, 53km south of Manjimup. Until 1968 Shannon was the site of WA's biggest timber mill, and plants including deciduous trees from the northern hemisphere are reminders of the old settlement.
The 48km Great Forest Trees Drive is a one-way loop, split by the highway. Start at the park day-use area on the north of the highway. From here there's an easy 3.5km walk to the Shannon Dam and a steeper 5.5km loop to Mokare's Rock, with a boardwalk and great views. Further along, the 8km-return Great Forest Trees Walk crosses the Shannon River. Off the southern part of the drive, boardwalks look over stands of giant karri at Snake Gully and Big Tree Grove .
In the park's southwest, a 6km return walking track links Boorara Tree with a lookout point over Lane Poole Falls.
There is a sizeable campground (sites per adult/child $9/2) with showers in the spot where the original timber-milling town used to be. A self-contained bunkhouse, Shannon Lodge (per night $66, bond $150) , is available for groups of up to eight people; book this through DEC in Pemberton.
# South Coast
#### South Coast Highlights
#### Walpole & Nornalup
#### Denmark
#### Albany
#### Around Albany
#### Mt Barker
#### Porongurup National Park
#### Stirling Range National Park
#### Bremer Bay
#### Fitzgerald River National Park
#### Hopetoun
#### Esperance
#### Around Esperance
South Coast
### Why Go?
Standing on the cliffs of the wild South Coast as the waves pound below is a truly exhilarating experience. And on calm days, when the sea is various shades of aquamarine and the glorious white-sand beaches lie pristine and welcoming, it's an altogether different type of magnificent. If you're seeking to get away from it all, even busy holiday periods here in the 'Great Southern' are relaxed; it's just that bit too far from Perth for the holiday hordes. Marine visitors come this way, though – the winter months bring a steady stream of migrating whales.
When you need a change from the great outdoors, Albany – the earliest European settlement in the state – has a wealth of colonial history, and towns such as Denmark and Esperance invite you to sit back with a glass of fine local wine and watch the world go by.
### When to Go
Jan The best beach weather – and it's not as hot or crowded as the west coast.
Sep Go wild for wildflowers and whales.
Dec Perfect weather for the Stirling Range and Porongurup National Parks.
### Best Places to Eat
» York Street Cafe ( Click here )
» Mrs Jones ( Click here )
» Maleeya's Thai Cafe ( Click here )
» Pepper & Salt ( Click here )
» Boston Brewery ( Click here )
### Best Places to Stay
» Cape Howe Cottages ( Click here )
» Beach House at Bayside ( Click here )
» Esperance B&B by the Sea ( Click here )
» Riverside Retreat ( Click here )
» 1849 Backpackers ( Click here )
## South Coast Highlights
Walking among and above the giant tingle trees in the Valley of the Giants Tree Top Walk (Click here )
Competing to see who can spot the most whales in Albany's King George Sound (Click here )
Pondering our fractious human-cetacean relations at the Whale World Museum (Click here ) near Albany
Hiking among the tall trees and granite outcrops of Porongurup National Park (Click here )
Wandering through wildflowers along the walking tracks of Fitzgerald River National Park (Click here )
Marvelling at the surf-battered coast from the Great Ocean Drive (Click here ) near Esperance
Swimming, surfing and soaking up the sun at the squeaky-clean beaches of Cape Le Grand National Park (Click here )
Top of Chapter
Walpole & Nornalup
The peaceful twin inlets of Walpole (population 320) and Nornalup (population 50) make good bases from which to explore the heavily forested Walpole Wilderness Area – an immense wilderness incorporating a rugged coastline, several national parks, marine parks, nature reserves and forest conservation areas – covering a whopping 3630-sq-km (an area considerably bigger than Samoa and 57 other countries). Look for _Exploring the Walpole Wilderness and Surrounding Area_ pamphlet produced by the Department of Environment & Conservation (DEC).
Walpole is the bigger settlement, and the only spot in the area with mobile-phone coverage. It's here that the South Western Hwy (Rte 1) becomes the South Coast Hwy.
1 Sights & Activities
Walpole-Nornalup National Park NATIONAL PARK
(www.valleyofthegiants.com.au; Valley of the Giants Tree Top Walk adult/child $12.50/5; Valley of the Giants Tree Top Walk 9am-4.15pm) The giant trees of this park include red, yellow and Rates tingle trees (all types of eucalypt or gum trees) and, closer to the coast, the red flowering gum.
In the Valley of the Giants the Tree Top Walk is Walpole's main drawcard. A 600m-long ramp rises from the floor of the valley, allowing visitors access high into the canopy of the giant tingle trees. At its highest point, the ramp is 40m above the ground. It's on a gentle incline so it's easy to walk and is even accessible by assisted wheelchair. The ramp is an engineering feat in itself, though vertigo sufferers might have a few problems; it's designed to sway gently in the breeze to mimic life in the treetops. At ground level, the Ancient Empire boardwalk meanders around and through the base of veteran red tingles, some of which are 16m in circumference, including one that soars to 46m.
There are numerous good walking tracks around, including a section of the Bibbulmun Track , which passes through Walpole to Coalmine Beach. Scenic drives include the Knoll Drive , 3km east of Walpole; the Valley of the Giants Road ; and through pastoral country to Mt Frankland , 29km north of Walpole. Here you can climb to the summit for panoramic views or walk around the trail at its base. Opposite Knoll Drive, Hilltop Rd leads to a giant tingle tree ; this road continues to the Circular Pool on the Frankland River, a popular canoeing spot. You can hire canoes from Nornalup Riverside Chalets (Click here ).
Midway between Nornalup and Peaceful Bay, check out Conspicuous Cliffs . It's a great spot for whale watching from July to November, with a boardwalk, a hilltop lookout and a steepish 800m walk to the beach.
Dinosaur World WILDLIFE RESERVE
(www.dinosaurworld.com.au; Bow Bridge; adult/child $12/6; 9.30am-4.30pm) Replica dinosaur skeletons and information boards have been added to spice up this bird and reptile park, off the South Coast Hwy at Bow Bridge. Kangaroos, lizards and snakes feature, but the parrots (most with clipped wings) are the real stars.
T Tours
WOW Wilderness Ecocruises CRUISE
( 08-9840 1036; www.wowwilderness.com.au; adult/child $40/15) S The magnificent landscape and its ecology are brought to life with anecdotes about Aboriginal settlement, salmon fishers and shipwrecked pirates. The 2½-hour cruise through the inlets and river systems leaves at 10am daily; book at the visitor centre.
Naturally Walpole Eco Tours DRIVING TOUR
( 08-9840 1019; www.naturallywalpole.com.au) Half-day tours through the Walpole Wilderness (adult/child $75/40), and customised winery and wildflower tours.
4 Sleeping
Walpole Wilderness Area bush camping sites (adult/child $7/2) are located at Crystal Springs and Fernhook Falls.
Coalmine Beach CARAVAN PARK $
( 08-9840 1026; www.coalminebeach.com.au; Coalmine Beach Rd, Walpole; sites per 2 people $31-35, cabins $115-180; ) You couldn't get a better location than this, under shady trees above the sheltered waters of the inlet. A new recreation room and redecorated chalets are recent improvements.
Walpole Lodge HOSTEL $
( 08-9840 1244; www.walpolelodge.com.au; Pier St, Walpole; dm/s/d $26/45/65; ) This popular place is basic, open plan and informal, with great info boards around the walls and casual, cheery owners. Ensuite rooms are excellent value.
Tingle All Over YHA HOSTEL $
( 08-9840 1041; www.yha.com.au; 60 Nockolds St, Walpole; dm/s/d $31/54/74; ) Help yourself to lemons and chillies from the garden of this clean, basic option near the highway. Lots of advice on local walks is on offer.
Rest Point Holiday Village CARAVAN PARK $
( 08-9840 1032; www.restpoint.com.au; Rest Point; sites per 2 people $22, cabins $75-115) Set on wide lawns with direct water frontage, this spacious holiday park has shade for campers and self-contained accommodation.
Nornalup Riverside Chalets CHALET $$
( 08-9840 1107; www.walpole.org.au/nornalupriv ersidechalets; Riverside Dr, Nornalup; chalets $110-180) Stay a night in sleepy Nornalup in these comfortable, colourful self-contained chalets, just a rod's throw from the fish in the Frankland River. The chalets are well spaced out, giving a feeling of privacy.
Riverside Retreat CHALET $$
( 08-9840 1255; www.riversideretreat.com.au; South Coast Hwy, Nornalup; chalets $140-200) Off the road and on the banks of the beautiful Frankland River, these spotless and well-equipped chalets are great value, with pot-bellied stoves for cosy winter warmth, and tennis and canoeing as outdoor pursuits. Frequent visits from local wildlife make Riverside Retreat a good option for families.
5 Eating
Flaming Hot Takeaways FAST FOOD $
(Vista St, Walpole; mains $10-15; 11.30am-8pm) The local chippie is a solid choice for burgers, pizza, and excellent fish and chips.
Thurlby Herb Farm CAFE $$
(www.thurlbyherb.com.au; 3 Gardiner Rd; mains $15-20; 9am-4.30pm Mon-Fri) Apart from distilling its own essential oils and making herb-based products including soap and aromatherapy treatments, Thurlby serves up tasty light lunches and cakes accompanied by fresh-picked herbal teas. Try the delicious rosemary-infused scones.
Top Deck Cafe CAFE $$
(25 Nockolds St; mains $15-27; 9am-8pm) Tucked away in Walpole's compact main-road shopping centre, Top Deck kicks off with breakfast, and graduates to dinner options including spinach-and-feta pie and a daily curry special. Order a glass of local wine and kick back in the sunny deck at the front.
8 Information
DEC ( 08-9840 0400; www.dec.wa.gov.au; South Coast Hwy, Walpole; 8am-4.30pm Mon-Fri) For national-park and bushwalking information.
Visitor Centre ( 08-9840 1111; www.walpole.com.au; South Coast Hwy, Walpole; 9am-5pm; )
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) Bus GS3 heads daily to/from Bunbury ($43, 4½ hours), Bridgetown ($24, 3¼ hours), Pemberton ($19, 1¾ hours), Denmark ($13, 42 minutes) and Albany ($21, 1½ hours).
### THE ROAD TO MANDALAY
About 13km west of Walpole, at Crystal Springs, is an 8km gravel road to Mandalay Beach , where the _Mandalay,_ a Norwegian barque, was wrecked in 1911. As the sand gradually erodes with storms, the wreck eerily appears every 10 years or so, in shallow water that is walkable at low tide (check out the photos at Walpole visitor centre). The beach is glorious, often deserted, and accessed by an impressive boardwalk across sand dunes and cliffs. It's now part of D'Entrecasteaux National Park.
Top of Chapter
Denmark
pop 2800
Denmark's beaches and coastline, river and sheltered inlet, forested backdrop and hinterland have attracted a varied, creative and environmentally aware community. Farmers, ferals, fishers and families all mingle during the town's four market days each year.
Denmark was established to supply timber to the early goldfields. Known by the Minang Noongar people as Koorabup (place of the black swan), there's evidence of early Aboriginal settlement in the 3000-year-old fish traps found in Wilson Inlet.
1 Sights & Activities
The town is located in the cool-climate Great Southern wine region and notable wineries include Howard Park (www.howardparkwines.com.au; Scotsdale Rd; 10am-4pm) and Forest Hill (www.foresthillwines.com.au; cnr South Coast Hwy & Myers Rd; 10am-5pm) . The latter has an architecturally impressive tasting room and restaurant.
Surfers and anglers should head to ruggedly beautiful Ocean Beach . Accredited local instructor Mike Neunuebel gives surfing lessons ( 0401 349 854; www.southcoastsurfinglessons.com.au; 2hr lessons incl equipment from $50) and hires out boards and wetsuits (per hour $20).
To get your bearings, walk the Mokare Heritage Trail (a 3km circuit along the Denmark River) or the Wilson Inlet Trail (12km return, starting at the river mouth), which forms part of the longer Nornalup Trail . The Mt Shadforth Lookout has fine coastal views, and lush Mt Shadforth Rd , running from town to the South Coast Hwy west of town, makes a great scenic drive. A longer pastoral loop is via Scotsdale Rd . Attractions include alpaca farms, wineries, cheese farms, and art-and-craft galleries.
William Bay National Park , about 20km west of town, offers sheltered swimming in gorgeous Greens Pool and Elephant Rocks , and has good walking tracks. Swing by Bartholomews Meadery (www.honeywine.com.au; 2620 South Coast Hwy; 9.30am-4.30pm) for a post-beach treat of mead (honey wine) or delicious homemade honey-rose-almond ice cream ($4).
T Tours
Out of Sight! DRIVING TOUR
( 08-9848 2814; www.outofsighttours.com) Nature trips into the Walpole Wilderness (three hours, adult/child $90/45), West Cape Howe (six hours, adult/child $150/75) or Stirling Range (eight hours, adult/child $200/100); sightseeing around Denmark (two hours, adult/child $50/25); or sampling tours of the local wineries (full day $100). Visit its Eco-Discovery shop at the newly expanded Denmark Visitor Centre to hire canoes and bikes. In 2013 the Munda Biddi Trail was extended to Denmark, completing the trail's total of 1000km.
Denmark Wine Lovers Tour BUS TOUR, WINERY
( 0410 423 262; www.denmarkwinelovers.com.au) Full-day tours taking in Denmark wineries ($95), or further afield to Porongurup or Mt Barker (price on application).
z Festivals & Events
Market Days MARKET
Four times a year (early December, early and late January and Easter) Denmark hosts a colourful market day on the parkland by the river, with an unusual range of high-quality craft stalls, music and food. Accommodation rates rise on these weekends. See www.denmarkarts.com.au for relevant dates.
Festival of Voice MUSIC FESTIVAL
(www.dfov.org.au) Performances and workshops, on the early-June long weekend.
4 Sleeping
Blue Wren Travellers' Rest YHA HOSTEL $
( 08-9848 3300; www.denmarkbluewren.com.au; 17 Price St; dm/d $27/73) Chooks live under this little timber house and everyone spoils the goofy house dog. Great info panels cover the walls, and it's small enough (just 20 beds) to have a homey feel. Bikes can also be rented – $25 per day or just $15 if you're a guest – and friendly owner Graham is a whiz at bike repairs.
Denmark Ocean Beach Holiday Park CARAVAN PARK $
( 08-9848 1106; www.denmarkobhp.com.au; Ocean Beach Rd; sites per 2 people $28-30, cabins $110-180; ) S This large, long-standing complex has lots of family-friendly facilities, new kitchen and ablution blocks, and a brand-new array of stylish motel units. The surf, sun and sand of Ocean Beach are just a short stroll away, and the kids will love the giant bouncy pillow.
Denmark Rivermouth Caravan Park CARAVAN PARK $
( 08-9848 1262; www.denmarkrivermouthcaravanpark.com.au; Inlet Dr; sites per 2 people $30, cabins & chalets $130-200) Ideally located for nautical pursuits, this caravan park sits along Wilson Inlet beside the boat ramp. Some of the units are properly flash, although they are quite tightly arranged. There's also a kids playground and kayaks for hire.
Riverbend Caravan Park CARAVAN PARK $
( 08-9848 1107; www.riverbend-caravanpark.com.au; River Bend Lane; sites per 1/2 people from $22/26, chalets from $110) About 2km from town on a quiet stretch of river, this lovely shaded site has well-equipped cabins with private verandahs.
31 on the Terrace BOUTIQUE HOTEL $
( 08-9848 1700; www.denmarkaccommodation.com.au; 31 Strickland St; r $99-115; ) Good-value ensuite rooms – some with compact balconies – fill this renovated corner pub in the centre of town. Themed decor of the different rooms travels from New York to Paris via Egypt, but the ambience is classic and restrained rather than brash and showy. Compact apartments are good for families and groups up to five people.
o Cape Howe Cottages COTTAGE $$
( 08-9845 1295; www.capehowe.com.au; 322 Tennessee Rd S; cottages $170-280; ) For a remote getaway, these five cottages in bushland southeast of Denmark really make the grade. They're all different, but the best is only 1½km from dolphin-favoured Lowlands Beach and is properly plush – with a BBQ on the deck, a dishwasher in the kitchen and laundry facilities.
Sensational Heights B&B $$
( 08-9840 9000; www.sensationalheightsbandb.com.au; 159 Suttons Rd; r $190-260; ) Yep, it's on top of a hill (off Scotsdale Rd) and, yes, the views are sensational. It's a new house, so expect contemporary decor, shiny new fixtures, luxurious linen and very comfy beds. The pricier rooms have spa baths.
Willowleigh B&B B&B $$
( 08-9848 1089; www.denmarkbedandbreakfast.com.au; Kearsley Rd; r $160; ) Enjoy the 0.8 hectares of gorgeous gardens from your conservatory or verandah at this B&B on the edge of town.
Celestine Retreat CHALET $$$
( 08-9848 3000; www.celestineretreat.com; 413 Mt Shadforth Rd; d $239-289; ) With just four spa chalets scattered on 13 hectares, there are definitely plenty of stunning views to go around at this luxury retreat. Romance is also on the agenda, with private spas, fluffy bathrobes and high-end bathroom goodies. The bright lights of Denmark are just 3km back down Mt Shadforth when you want to rejoin the real world.
Aiyana Retreat APARTMENT $$$
( 08-9848 3258; www.aiyanaretreat.com.au; 28 Anning Rd; apt $195-250) Three luxurious apartments, tucked down a quiet cul-de-sac; spa treatments are also available.
5 Eating
Denmark Bakery BAKERY $
(Strickland St; pies $5-6; 7am-5pm) Prize-winning and proud of it, this bakery is an institution because of its pies, and the bread is also good.
Mrs Jones CAFE $$
( 0467 481 878; www.mrsjonescafe.com; 12 Mt Shadforth Rd; breakfast $9-18, lunch $14-21; 7am-4pm) Denmark's best coffee is at this spacious spot with high ceilings and exposed beams – you can even pre-order your personal java fix by SMS. If you're not in a hurry, settle in with locals and tourists for interesting cafe fare such as Turkish eggs with roasted pumpkin, chorizo and lentils, or Asian-style duck pancakes with plum sauce.
Denmark Tavern PUB $$
(623 South Coast Hwy; mains $25-34; 11am-late) Easily the best pub meals for many a mile, and a good selection of draught beers and local wines.
o Pepper & Salt MODERN AUSTRALIAN $$$
( 08-9848 3053; www.matildasestate.com; 18 Hamilton St, Matilda's Estate; mains $35-40; noon-10pm) With his Fijian-Indian heritage, chef Silas Masih's knowledge of spices and herbs is wonderfully showcased in his fresh and vibrant food. Highlights include chilli-and-coconut prawns, or the great- value tasting platter ($48), which effortlessly detours from Asia to the Middle East. Buy some wine from the adjacent Matilda's Estate before settling in for a foodies adventure. Bookings recommended.
6 Drinking
o Boston Brewery CRAFT BEER
(www.willoughbypark.com.au; Willoughby Park Winery, South Coast Hwy; pizzas $18-23, mains $24-32; 10am-7pm Mon-Thu, to 10pm Fri & Sat, to 9pm Sun) The industrial chic of the brewery gives way to an absolute edge-of-vineyard location, and wood-fired pizzas, meals and bar snacks go well with Boston's hoppy portfolio of four beers. The Willoughby Park Winery is also right on site, and there's live music from 4pm to 8pm every second Saturday.
Southern End CRAFT BEER
(www.denmarkbrewery.com.au; 427 Mt Shadforth Rd; 11.30am-4.30pm Thu-Mon) Home to Denmark Brews & Ales, the Southern End Restaurant has the best views in town from a hilltop terrace. Dinner is a slightly more formal affair than lunch.
Denmark Hotel PUB
(www.denmarkhotel.com.au; Hollings Rd) Overlooking the river, the local boozer is the hub of nocturnal activity, with live music every Friday night.
8 Information
Visitor Centre ( 08-9848 2055; www.denmark.com.au; 73 South Coast Hwy; 9am-5pm) Information, accommodation bookings, and an excellent display on the local wine scene. Ask for _The Wine Lovers' Guide to Denmark_ brochure and get exploring.
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) Bus service GS3 heads daily to/from Bunbury ($48, 5½ hours), Bridgetown ($33, 4¾ hours), Pemberton ($27, 2¾ hours), Walpole ($13, 42 minutes) and Albany ($9, 42 minutes).
### WEST CAPE HOWE NATIONAL PARK
Midway between Denmark and Albany, this 35-sq-km coastal park is a playground for naturalists, bushwalkers, rock climbers and anglers. Inland are areas of coastal heath, lakes, swamp and karri forest. With the exception of the road to Shelley Beach, access is restricted to 4WDs, mostly travelling through sand dunes, to explore the wild coast.
Camping is permitted at Shelley Beach, although campfires are banned.
Top of Chapter
Albany
pop 25,200
Established shortly before Perth in 1826, the oldest European settlement in the state is now the bustling commercial centre of the southern region. Albany is a mixed bag comprising a stately and genteel decaying colonial quarter, a waterfront in the midst of sophisticated redevelopment and a hectic sprawl of malls and fast-food joints. Less ambivalent is its spectacular coastline, from Torndirrup National Park's surf-pummelled cliffs to Middleton Beach's white sands, and the calm waters of King George Sound.
The town is in an area that's seen the violence of weather and whaling. Whales are still a part of the Albany experience, but these days are hunted through a camera lens.
The Bibbulmun Track ( Click here ) ends (or starts) here, just outside the visitor centre; the exhausted and/or exuberant comments in the walkers' log books make great reading.
History
The Minang Noongar people called this place Kinjarling (the place of rain) and believed that fighting Wargals (mystical giant serpents) created the fractured landscape. The Minang set up sophisticated fish traps on Oyster Harbour, the remains of which can still be seen.
Initial contacts with Europeans were friendly, with over 60 ships visiting between 1622 and 1826. The Minang traded crops with the early arrivals, in exchange for ship biscuits. The establishment of a British settlement here was welcomed as it regulated the behaviour of sealers and whalers, who had been responsible for kidnaps, rapes and murder of Minang people. Yet by the end of the 19th century, every shop in Albany refused entry to Aboriginal people, and control over every aspect of their lives (including the right to bring up their own children) had been lost.
For the British, Albany's raison d'être was its sheltered harbour, which made it a thriving whaling port. Later the city became a coaling station for British ships bound for the east coast, and during WWI it was the mustering point for transport ships for Australian and New Zealand troops heading for Egypt and the Gallipoli campaign.
1 Sights
Middleton & Emu Beaches BEACHES
Just around the headland, east of the town centre, these beautiful beaches facing King George Sound share one long stretch of family-friendly sand. In winter, you'll often see pods of mother whales and their calves here. Head around Emu Point to Oyster Harbour for swimming pontoons and even calmer waters.
A clifftop walking track hugs much of the waterfront between the town centre and Middleton Beach. Boardwalks continue along Emu Beach.
Albany
Top Sights
1Western Australian Museum – AlbanyB3
Sights
2 Albany Convict Gaol B3
3 Brig Amity B3
4 Dog Rock C1
5 Old Post Office C3
6 Patrick Taylor Cottage B2
7 Vancouver Arts Centre A2
Activities, Courses & Tours
8 Albany Whale Tours C3
9 Alkoomi Wines B3
10 Southcoast Diving Supplies B1
Sleeping
11 1849 Backpackers B2
12 Albany Harbourside B2
13 Bayview Backpackers YHA B2
Dog Rock Motel (see 16)
14 My Place C2
Eating
15 14 Peels Place C2
16 Lime 303 C1
17 Vancouver Cafe & Store A2
18 White Star Hotel C2
19 York Street Cafe C2
Drinking & Nightlife
20 Earl of Spencer C2
21 Liberté B2
Entertainment
22 Albany Entertainment Centre C3
23 Town Hall B2
Western Australian Museum – Albany MUSEUM
OFFLINE MAP GOOGLE MAP
(www.museum.wa.gov.au; Residency Rd; admission by donation; 10am-4.30pm) This branch of the state museum is split between two neighbouring buildings. The newer Eclipse building has a kids' discovery section, a lighthouse exhibition, a gallery for temporary exhibitions and a gift shop. The restored 1850s home of the resident magistrate illuminates Minang Noongar history, local natural history and seafaring stories.
Brig Amity SHIP
OFFLINE MAP GOOGLE MAP
(www.historicalbany.com.au; adult/child $5/2; 9am-4pm) This full-scale replica of the brig that carried Albany's first British settlers from Sydney in 1826 was completed for the city's 150th anniversary. Self-guided audio tours bring to life the ship's history.
Town Centre HISTORIC BUILDINGS
Near the foreshore is Albany's historic precinct. Take a stroll down Stirling Tce – noted for its Victorian shopfronts, Courthouse and Old Post Office OFFLINE MAP GOOGLE MAP – and up York St to St John's Anglican Church and Albany's Town Hall OFFLINE MAP GOOGLE MAP . A guided walking-tour brochure is available from the visitor centre.
Patrick Taylor Cottage MUSEUM
OFFLINE MAP GOOGLE MAP
(www.historicalbany.com.au; 39 Duke St; admission $2; 11am-3pm) Believed to be the oldest colonial dwelling in Western Australia (WA), this 1832 wattle-and-daub cottage is packed with antiques, freaky mannequins and displays on its former residents.
Albany Convict Gaol MUSEUM
OFFLINE MAP GOOGLE MAP
(www.historicalbany.com.au; Stirling Tce; adult/child $5/2.50; 10am-4pm) The old gaol was built in 1851 as a hiring depot for ticket-of-leave convicts, but by 1855 most were in private employment. In 1872 the building was extended and reopened as a civil gaol, and is now a folk museum.
Old Farm at Strawberry Hill HISTORIC BUILDING
(www.ntwa.com.au; 174 Middleton Rd; adult/child $5/3; 10am-4pm) National Trust–owned Strawberry Hill is one of the oldest farms in WA, established in 1827 as the town's government farm. The homestead (1836) features antiques and artefacts that belonged to the original owner.
Vancouver Arts Centre GALLERY
OFFLINE MAP GOOGLE MAP
(Vancouver St; 9am-4pm Mon-Fri, 10am-3pm Sat) Housed in a former hospital (1887), this is the centre of the city's arts community, hosting regular touring exhibitions and cultural events.
Mt Melville & Mt Clarence LANDMARK
There are more fine views over the coast and inland from the twin peaks, Mt Clarence and Mt Melville, which overlook the town. On top of Mt Clarence is the Desert Mounted Corps Memorial , originally erected in Port Said as a WWI memorial. It was irreparably damaged during the Suez crisis in 1956, when colonial reminders were less than popular in Egypt. This copy was made from masonry salvaged from the original.
To climb Mt Clarence follow the track accessible from the end of Grey St E, turn left, take the first turn on the right and follow the path by the water tanks. The walk is tough, but the views make it worthwhile; take a picnic and enjoy a well-earned rest at the top. By car, take Apex Dr.
Princess Royal Fortress HISTORIC SITE
(www.forts.albany.wa.gov.au; Forts Rd; adult/child $12/4.50; 9am-5pm) As a strategic port, Albany was historically regarded as being vulnerable to attack. Built in 1893 on Mt Adelaide, this fort was initially constructed as a defence against potential attacks from the Russians and French. The restored buildings, gun emplacements and views are interesting, and there are also poignant photos of Anzac troops leaving for Gallipoli. Forts Rd is off Marine Dr.
Dog Rock LANDMARK
OFFLINE MAP GOOGLE MAP
On Middleton Rd, this large rock resembles a dog's head (the locals have even painted on a dog collar to reinforce the point). The Minang believed the dog had been decapitated by an angry Wargal.
2 Activities
Whale Watching WHALE WATCHING
After whaling ended in 1978, whales slowly began returning to the waters of Albany. They're now here to the extent that it can sometimes be hard _not_ to see southern right and humpback whales near the bays and coves of King George Sound from July to mid-October. You can usually spot them from the beach, but if you fancy a closer look, both Albany Dolphin & Whale Cruises ( 0428 429 876; www.whales.com.au; adult/child $80/45; Jul–mid-Oct) and Albany Whale Tours OFFLINE MAP GOOGLE MAP ( 08-9845 1068; www.albanywhaletours.com.au; Albany Waterfront Marina, cnr Princess Royal Dr & Toll Pl; adult/child $80/45; late May-early Oct) run regular whale-watching trips in season.
Diving DIVING
Albany's appeal as a top-class diving destination grew after the 2001 scuttling of the warship HMAS _Perth_ to create an artificial reef for divers; visit www.hmasperth.com.au. Its natural reefs feature temperate and tropical corals, and are home to the bizarre and wonderful leafy and weedy sea dragons. Southcoast Diving Supplies OFFLINE MAP GOOGLE MAP ( 08-9841 7176; www.divealbany.com.au; 84b Serpentine Rd) can show you the underwater world.
Fishing FISHING
Beach fishing at Middleton and Emu Beaches is popular, and Spinners Charters ( 08-9844 1906; www.spinnerscharters.com.au; Emu Point) run deep-sea fishing trips. Emu Point Boat Hire ( 08-9844 1562; Emu Point; Sep-May) provides paddle boats, kayaks and motorised dinghies.
Alkoomi Wines WINE TASTING
OFFLINE MAP GOOGLE MAP
(www.alkoomiwines.com.au; 225 Stirling Tce; 11am-5pm Mon-Sat) Just in case you were having withdrawals from wine tasting, Frankland River's Alkoomi has set up a handy tasting room right in the middle of town.
### ALBANY'S WHALING BATTLEGROUND
Talk to some Western Australians about their childhood holidays in Albany and, as well as carefree days of fishing and swimming, they're also likely to recall an almighty stench in the air and sharks circling in bloody corners of Frenchman Bay. The local whales, whose blubber created the vile smell while being melted down in pressure cookers, and whose blood spilled into water around the then Cheynes Beach Whaling Station, also appear to remember this scene far too well. It took them well over a decade to return in full strength to the waters around Albany after the last whale was hunted on 20 November 1978.
The whaling industry was gruesome in a most public way – whales were hunted, harpooned and dragged back to shore to be cut up and boiled – which is perhaps why the environmental movement managed to make its closure one of their earlier successes. It became harder for the industry to make the smell, the blood and the sight of harpooned carcasses being towed into the harbour anything but unattractive.
One of Tim Winton's earlier novels ( _Shallows,_ 1984), set in Albany, where Winton lived for some time as an adolescent, describes how whaling became an emotional battleground for environmentalists and the many local employees of the industry, similar to the situation in timber towns throughout the southwest in recent years. This pressure from protesters, as well as dwindling whale numbers and a drop in world whale-oil prices, sounded the death knell for the industry.
But Albany has cleverly managed to turn this now-unacceptable industry into a quaint tourist attraction, with the fascinating Whale World Museum and maritime festivals, which celebrate its rough-and-ready history on the seas. The whales who play in the surrounding waters are all the happier for it – as are the town's tourism-boosted coffers.
T Tours
Kalgan Queen BOAT
( 08-9844 3166; www.albanyaustralia.com; Emu Point; adult/child $75/40; 9am Sep-Jun) Take a four-hour cruise up the Kalgan River in a glass-bottomed boat and learn about the history and wildlife of the area.
Down Under ADVENTURE TOUR
( 08-9842 2468; www.harleytours.com.au; per 30min/hr/half-day $60/110/300) Hop on a hog and see Albany from a Harley Davidson. In addition, 'Quick Thrills' are available from Middleton Beach during the Christmas and Easter school holidays ($10).
4 Sleeping
o 1849 Backpackers HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9842 1554; www.albanybackpackersaccommodation.com.au; 45 Peels Pl; dm from $25, r from $70; ) Big flags from many nations provide a colourful international welcome at this well-run hostel. A huge, modern kitchen, sunny rooms and a laidback social ambience make this one of WA's best places to stay for budget travellers. Make sure you book in for 1849's free BBQ on Sunday night.
Albany Discovery Inn GUESTHOUSE $
( 08-9842 5535; www.discoveryinn.com.au; 9 Middleton Rd, Middleton Beach; s $55, d $80-90; ) Close to the beach, this guesthouse has a homey atmosphere. Guests congregate amid tropical plants in the central conservatory, and the recently refurbished rooms are colourful and individually decorated. A recent addition is an on-site cafe offering good-value evening meals ($20). Non-guests are welcome, but book ahead. Rates include a cooked breakfast.
Middleton Beach Holiday Park CARAVAN PARK $
( 08-9841 3593; www.holidayalbany.com.au; 28 Flinders Pde, Middleton Beach; sites per 2 people from $40, chalets $125-270; ) This excellent beachfront caravan park is sheltered by high sand dunes. Book early – it's popular. Newly built spa villas are particularly flash.
Emu Beach Holiday Park CARAVAN PARK $
( 08-9844 1147; www.emubeach.com; 8 Medcalf Pde, Emu Point; sites for 2 people from $35, chalets $130-190; ) Families love the Emu Beach area, and this holiday park, close to the beach, has good facilities, including a BBQ area and kids playground. Newly constructed motel units are spacious and modern.
Bayview Backpackers YHA HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9842 3388; www.bayviewbackpackers.com.au; 49 Duke St; dm/r $28/76; ) In a quiet street 400m from Albany's historic centre, this rambling backpackers has an easygoing vibe.
Albany Harbourside APARTMENT $$
OFFLINE MAP GOOGLE MAP
( 08-9842 1769; www.albanyharbourside.com.au; 8 Festing St; d $159-219; ) Albany Harbourside's portfolio includes a brace of spacious and spotless apartments on Festing St, and three other self-contained options arrayed around central Albany. Decor is modern and colourful, and some apartments have ocean views. For a touch of 19th-century charm, book the pretty Harbourside Cottage.
My Place APARTMENT $$
OFFLINE MAP GOOGLE MAP
( 08-9842 3242; www.myplace.com.au; 47-61 Grey St E; r $135-175; ) We love the tongue-in-cheek nana-ish vibe to the studios, with floral duvets and a trio of flying ducks on the wall. The considerably larger one-bedroom options aren't as kooky, but they're all clean, central and excellent value.
Dog Rock Motel MOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9841 4422; www.dogrockmotel.com.au; 303 Middleton Rd; s $115-188, d $135-208; ) The renovated 'deluxe' rooms in this large brick motel complex have a tasteful, contemporary feel, although we quite like the unintentional 1970s retro chic of the older, cheaper rooms. On site is the excellent Lime 303 restaurant, discreetly channelling the 21st century.
Beach House at Bayside BOUTIQUE HOTEL $$$
( 08-9844 8844; www.thebeachhouseatbayside.com.au; 33 Barry Ct, Collingwood Park; r $249-335; ) Positioned right by the beach and the golf course in a quiet cul-de-sac, midway between Middleton Beach and Emu Point, this modern block distinguishes itself with absolutely wonderful service. Rates include breakfast, afternoon tea, and evening port and chocolates.
5 Eating & Drinking
Bay Merchants CAFE $
(18 Adelaide Cres, Middleton Beach; mains $10-18; 6am-6pm) Just a sandy-footed stroll from the beach, this cafe-provedore makes good coffee, enticing cakes and to-die-for gourmet sandwiches. The deli section has a good selection of local wines.
York Street Cafe CAFE $$
OFFLINE MAP GOOGLE MAP
(www.184york.com; 184 York St; lunch $10-22, dinner $22-36; 7.30am-3pm Mon-Tue, 7.30am-late Wed-Fri. 8.30am-2.30pm Sat & Sun) The food is wonderful at this cosmopolitan place on the main strip. Lunch includes roasted tomato and prosciutto salad or chicken pot pie, while at dinner the attention turns to bistro items like prawns with pasta and a hearty goat tagine. It's BYO wine.
14 Peels Place CAFE $$
OFFLINE MAP GOOGLE MAP
(14 Peels Pl; breakfast $7-21, lunch $14-22; 8.30am-4pm Mon-Fri, to 1pm Sat & Sun) S A colourful haven for in-the-know local foodies, 14 Peels Place's combo of good coffee and cool jazz is a great way to start the day. Browse the huge library of cookbooks while tucking into dishes like the chilli-infused Eggs on Fire or fluffy pancakes with berries. Freshly baked cakes include lots of gluten-free options.
Vancouver Cafe & Store CAFE $$
OFFLINE MAP GOOGLE MAP
( 08-9841 2475; 65 Vancouver St; mains $12-25; 7.30am-3.30pm) Perched above the coast, this great little heritage cafe features balcony views and delicious home baking. More substantial lunchtime goodies include garlic-prawn risotto or bangers and mash. Book ahead for its music and pizza events on Thursday nights.
White Star Hotel PUB $$
OFFLINE MAP GOOGLE MAP
(72 Stirling Tce; mains $16-34; 11am-late) With 20 beers on tap (including its own Tanglehead brews), excellent pub grub, a beer garden and lots of live music, this old pub gets a gold star. Sunday-night folk and blues gigs are a good opportunity to share a pint with Albany's laidback locals.
Lime 303 MODERN AUSTRALIAN $$$
OFFLINE MAP GOOGLE MAP
( 08-9845 7298; www.dogrockmotel.com.au; 303 Middleton Rd; mains $28-40; dinner 6pm-late, tapas 5-7pm Thu & Fri) Ignore the incongruous setting in the Dog Rock Motel, and book for dinner at this chic Albany surprise. Highly sophisticated for regional WA, Lime 303 showcases local produce in dishes like the Game Plate – with barramundi, buffalo and crocodile – and the lamb shanks with spiced pomegranate and rosehip.
Liberté CAFE, BAR
OFFLINE MAP GOOGLE MAP
(162 Stirling Tce, London Hotel; 8.30am-5pm Mon & Tue, till late Wed-Sat) Classy proof that not all heritage Aussie pubs need to die a slow death. Channelling a louche Parisian cafe and a velvet-trimmed speakeasy, Liberté's Gallic-inspired versatility includes good coffee and cake during the day, and craft beer, potent cocktails and Med- inspired tapas later at night. It's a big hit with hip Albanians.
Earl of Spencer PUB
OFFLINE MAP GOOGLE MAP
(cnr Earl & Spencer Sts; mains $20-30; 11am-late) New owners have reinvigorated Albany's oldest pub, and locals crowd in for the Earl's famous pie and a pint or hearty lamb shanks. Live bands are regular visitors on weekends, often with a jaunty Irish brogue.
3 Entertainment
Albany Entertainment Centre CONCERT HALL
OFFLINE MAP GOOGLE MAP
(www.albanyentertainment.com.au; Princess Royal Dr) Vaguely reminiscent of a scaled-down Sydney Opera House in terms of its location and architectural audacity, this $58-million, 600-seat venue features Oz touring acts like Xavier Rudd and Kasey Chambers.
Town Hall THEATRE
(www.albanytownhall.com.au; 217 York St) Has regular shows.
Orana Cinemas CINEMA
( 08-9842 2210; www.oranacinemas.com.au; 451 Albany Hwy) For the latest snog-and-shoot blockbusters.
8 Information
DEC ( 08-9842 4500; 120 Albany Hwy; 8am-4.30pm Mon-Fri) For national-park information.
Visitor Centre ( 08-9841 9290; www.amazingalbany.com; Proudlove Pde; 9am-5pm) In the old train station.
8 Getting There & Away
Albany Airport (ALH; Albany Hwy) is 11km northwest of the city centre. Skywest ( 1300 660 088; www.skywest.com.au) has 18 flights a week to and from Perth (70 minutes).
Transwa ( 1300 662 205; www.transwa.wa.gov.au) services stop at the visitor centre. These include:
GS1 to/from Perth ($58, six hours) and Mt Barker ($9, 39 minutes) daily
GS2 to/from Perth ($58, eight hours), Northam ($63, 6½ hours), York ($58, six hours) and Mt Barker ($9, 41 minutes) four times a week
GS3 to/from Bunbury ($56, six hours), Bridgetown ($43, 4¾ hours), Pemberton ($35, 3½ hours), Walpole ($22, 1½ hours) and Denmark ($9, 42 minutes) daily
GE4 to/from Esperance ($64, 6½ hours, twice weekly)
8 Getting Around
Loves ( 08-9841 1211) runs local bus services weekdays and Saturday morning. The visitor centre has information on getting to Emu Point and Middleton Beach.
Rent a car from King Sound Vehicle Hire ( 08-9841 8150; www.kingsoundcars.com; 6 Sanford Rd) . Avis ( 08-9842 2833; www.avis.com.au) and Budget ( 08-9841 7799; www.budget.com.au) have agencies at the airport.
Top of Chapter
Around Albany
1 Sights
Whale World Museum MUSEUM
( 08-9844 4019; www.whaleworld.org; Frenchman Bay Rd; adult/child $29/10; 9am-5pm) When the Cheynes Beach Whaling Station ceased operations in November 1978, few could have guessed that its gore-covered decks would eventually be covered in tourists, craning to see whales passing within harpoon-shot of the slaughterhouse itself. The museum screens several films about marine life and whaling operations, and displays giant skeletons, harpoons, whaleboat models and scrimshaw (etchings on whalebone). Outside there's the rusting _Cheynes IV_ whale chaser and station equipment to inspect. Free guided tours depart on the hour from 10am to 3pm.
Attached to the complex is the Walk on the Wild Side wildlife park. Entrance is included with admission to Whale World. Planned to open in 2013, an adjacent Biodiversity Park will include Faunatopia and Floracopia, two areas showcasing the diverse animal and plant species of the surrounding region.
Torndirrup National Park NATIONAL PARK
(Frenchman Bay Rd) F Covering much of the peninsula that encloses the southern reaches of Albany's Princess Royal Harbour and King George Sound, this national park is known for its windswept, ocean-bashed cliffs. Rocks in this area have been proved to be direct matches to those in Antarctica, to which they were once joined. This is a dangerous coastline, so beware of freakish, large waves – many people have lost their lives after being swept off the rocks. The Gap is a natural cleft in the rock, channelling blistering surf through giant walls of granite. Close by is the Natural Bridge , a self-explanatory landmark. Further east, the Blowholes can put on a show when the surf is up; it's worth the 78 steps down and back up.
Where the cliffs give way to beach, the results are just as spectacular. Steep, rocky, green-water coves such as Jimmy Newells Harbour and Salmon Holes are popular with surfers but quite scary for swimmers. You're better to head to the peninsula's sheltered side, where beautiful Misery Beach (a contradiction in terms) is often deserted and is an easy drive in/walk down. It's next to Frenchman Bay , a fine swimming beach with a shady barbecue area.
At Stony Hill , a short heritage trail leads around the site of an observatory station from both world wars. Keen walkers can tackle the hard 10km-return bushwalk (over five hours) over Isthmus Hill to Bald Head , at the eastern edge of the park. The views are spectacular. Whales are frequently seen from the cliffs, and the park's varied vegetation provides habitats for many native animals and reptiles.
Albany's Wind Farm , immediately west of the park, has a walking track winding surreally among the 12 turbines.
Two Peoples Bay NATURE RESERVE
(Two Peoples Bay Rd) Some 20km east of Albany, Two Peoples Bay is a scenic 46-sq-km nature reserve with a good swimming beach. From the main beach, walk east around the headland (or drive) to lovely Little Beach . Not much of the rest of the reserve is easily accessible and permits are required from the DEC in Albany to visit some special conservation zones. It's a significant area, home to two once-thought-to-be-extinct animals: the noisy scrub bird and Australia's rarest marsupial mammal, the Gilbert's potoroo.
The bay was named after a meeting of French and US ships here in 1803.
Waychinicup National Park NATIONAL PARK
(Cheyne Beach Rd; campsite adult/child $7/3) F Gilbert's potoroos and noisy scrub birds are also protected at this little national park, east of Two Peoples Bay. Unlike at the bay, the DEC operates a camp site here. It's a beautiful spot, by the inlet of the Waychinicup River; vault toilets are provided, but no fresh water is available.
### ALBANY TO ESPERANCE ALTERNATIVES
The rural 480km of South Coast Hwy (Rte 1) between Albany and Esperance is a relatively unpopulated stretch. Break up the first leg by taking the Albany Hwy (Rte 30) to Mt Barker, and then head east to Porongurup. Then travel north through the Stirling Ranges, and turn east again through Ongerup, and rejoin the highway at Jerramungup. This route adds 57km to the trip.
At Ongerup, the Yongergnow Malleefowl Centre ( 08-9828 2325; www.yongergnow.com.au; adult/child $6/3; 10am-4pm Sat-Mon, Wed & Thu) is devoted to the conservation of a curious endangered bird that creates huge mounds to incubate its chicks.
Near Jerramungup is Fitzgerald River National Park – base yourself at Hopetoun or Bremer Bay. Note that Bremer Bay is best reached by taking the South Coast Hwy from Albany.
Top of Chapter
Mt Barker
pop 1770
Mt Barker (50km north of Albany) is the gateway to the Porongurup and Stirling Range National Parks. It's also the hub for the local wine industry, and Plantagenet Wines (www.plantagenetwines.com; Albany Hwy; 10am-4.30pm) is conveniently situated in town. Pick up the _Mt Barker Wineries_ map from the town's visitor centre ( 08-9851 1163; www.mountbarkertourismwa.com.au; Albany Hwy, Railway Station) , located in the railway station. See www.mountbarkerwine.com.au.
The town has been settled since the 1830s; the 1868 convict-built police station and gaol are preserved as a museum (Albany Hwy; adult/child $5/free; 10am-3pm Sat & Sun) .
See all 78 types and 24 subtypes of Australia's Banksia plant at the Banksia Farm ( 08-9851 1770; www.banksiafarm.com.au; Pearce Rd; admission $11; 9.30am-4.30pm Mon-Fri Mar-Jun, daily Aug-Nov) ; admission includes an introductory talk. Also on offer are a fully guided tour ($25), morning and afternoon tea, and comfortable B&B accommodation (singles/doubles from $95/150).
It's well worth heading up Mt Barker itself, 5km south of town, for excellent views of the neighbouring ranges. Southwest of Mt Barker, on the rolling grounds of the Egerton-Warburton estate, is the exquisitely photogenic St Werburgh's Chapel , built between 1872 and 1873. The wrought-iron chancel screen and altar rail were shaped on the property.
A surprising sight is the authentic Mongolian yurt (felt tent) and gallery of eclectic Mongolian and Chinese art in the grounds of Nomads Guest House ( 08-9851 2131; www.nomadsguesthousewa.com.au; 12 Morpeth St; s/d/yurts/chalets $70/90/100/110) . The owners frequently play host to orphaned joeys (baby kangaroos), so don't be surprised to see a few temporary marsupial visitors in the main house.
If you're stopping for lunch, try the Old Station Cafe (11 Albany Hwy; mains $11-20; 9am-4pm Mon-Fri,10am-3pm Sun) , which offers a big selection of cakes in a little cottage.
8 Getting There & Away
Transwa ( 1300 662 205; www.transwa.wa.gov.au) operates the following bus services:
GS1 to/from Perth ($51, 5½ hours) and Albany ($9; 39 minutes) daily.
GS2 to/from Perth ($51, 7¼ hours), Northam ($56, 5¾ hours), York ($53, 5¼ hours) and Albany ($9, 41 minutes) four times a week.
Top of Chapter
Porongurup National Park
The 24-sq-km, 12km-long Porongurup National Park (entry per car/motorcycle $11/5) has 1100-million-year-old granite outcrops, panoramic views, beautiful scenery, large karri trees and some excellent bushwalks.
Karris grow in the deep-red soil (known as karri loam) of the range's upper slopes; nurtured by run-off from the granite, this area's karris are 100km east of their usual range. The rich forest also supports 65 species of orchid in spring and, in September and October, there are wildflowers among the trees.
Bushwalks range from the 100m Tree-in-the-Rock stroll (just what it sounds like) to the harder Hayward and Nancy Peaks (5.5km loop). The Devil's Slide (5km return) is a walk of contrasts that takes you through a pass of karri forest and on to the stumpy vegetation of the granite. These walks start from the main day-use area (Bolganup Rd). The Castle Rock Trail to Balancing Rock (3km return) starts further east, signposted off the Mt Barker–Porongurup Rd. In 2012, the newly opened Castle Rock Granite Skywalk provided spectacular and more convenient access to the summit of the rock.
A very lovely 6km scenic drive along the northern edge of the park has great views towards the Stirling Range, which from this angle looks like a woman lying on her back. If you're driving here near dusk, take it slow and watch out for kangaroos.
Porongurup is also part of the Great Southern wine region and there are 11 wineries in the immediate vicinity.
4 Sleeping & Eating
There is no accommodation within the national park, but these options are close by. Eating options are very limited.
Porongurup Village Inn, Shop & Tearooms B&B $
( 08-9853 1110; www.porongurupinn.com.au; s/d/cottages $30/60/100) This welcoming hostel-like place also serves home-cooked food (breakfast $5 to $14, lunch $16 to $18) with veggies from the organic garden. Standouts are the salmon patties and the ploughman's lunch, and there are plenty of grassy expanses and a trampoline for younger visitors.
Porongurup Range Tourist Park CARAVAN PARK $
( 08-9853 1057; www.poronguruprangetouristpark.com.au; 1304 Porongurup Rd; sites per 2 people $30, cabins $90-110; ) Tidy, with good facilities; credit cards not accepted.
Ty-Jarrah CHALET $
( 08-9853 1255; www.tyjarrah.com; 3 Bolganup Rd; 1-/2-bedroom chalets from $125/145) Located in a shady forest setting, these self-contained A-frame chalets are very cosy and comfortable. Twilight visitors include a menagerie of local marsupials.
Maleeya's Thai Cafe THAI $$
( 08-9853 1123; www.maleeya.com.au; 1376 Porongurup Rd; mains $25-30; 11.30am-3pm & 6-9pm Fri-Sun) S Foodies and chefs venture all the way to Porongorup for some of WA's most authentic Thai food. Curries, soups and stir-fries all come studded with fresh herbs straight from Maleeya's garden, and other ingredients are organic and free range. Bookings recommended.
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Stirling Range National Park
Ever seen a Queen of Sheba orchid or a Stirling bell? Here's your chance. Rising abruptly from the surrounding flat and sandy plains, the Stirling Range's propensity to change colour through blues, reds and purples will captivate photographers during the spectacular wildflower season from late August to early December.
This 1156-sq-km national park consists of a single chain of peaks pushed up by plate tectonics to form a range 10km wide and 65km long. Running most of its length are isolated summits, some knobbly and some perfect pyramids, towering above broad valleys covered in shrubs and heath. Bluff Knoll (Bular Mai), at 1095m, is the highest point in the southwest.
Due to the altitude and climate there are many localised plants in the Stirlings. It is estimated that there are more than 1500 species of native plants, 80 of which are endemic. The most beautiful are the Darwinias or mountain bells, which occur only above 300m; one species may be seen in season on the Mt Talyuberlup walk.
The range was named after James Stirling, first governor of the Swan River Colony. For tens of thousands of years before that it was known as Koi Kyenunu-ruff, meaning 'mist moving around the mountains'. It's recognised by Noongar people as a place of special significance – a place where the spirits of the dead return. Every summit has an ancestral being associated with it, so it's appropriate to show proper respect when visiting here.
Park fees are charged at the start of Bluff Knoll Rd (entry per car/motorcycle $11/5).
2 Activities
The Stirlings are renowned for serious bushwalking . Keen walkers can choose from a number of high points: Toolbrunup (for views and a good climb; 1052m, 4km return), Bluff Knoll (a well-graded tourist track; 1095m, 6km return), and Mt Hassell (848m, 3km return) and Talyuberlup (783m, 2.6km return) are popular half-day walks.
Challenging walks cross the eastern sector of the range from Bluff Knoll to Ellen Peak , which should take three days, or the shorter traverse from The Arrows to Ellen Peak (two days). The latter option is a loop, but the former, from Bluff Knoll, will require a car shuttle. Walkers must be suitably experienced and equipped as the range is subject to sudden drops in temperature, driving rain and sometimes snow; register in and out of your walk with the rangers ( 08-9827 9230) .
4 Sleeping & Eating
Options are very limited, so stock up on food in Mt Barker.
Stirling Range Retreat CARAVAN PARK $
( 08-9827 9229; www.stirlingrange.com.au; 8639 Chester Pass Rd; unpowered/powered sites per 2 people $30/32, cabins $55-79, units $145-175; ) S Also on the park's northern boundary, this shaded site has accommodation including campsites, simple cabins and vans, and self-contained, rammed-earth units. Wildflower and orchid bus tours and walkabouts (three hours, per person $49) are conducted from mid-August to the end of October. The swimming pool only opens from November to April.
Mount Trio Bush Camping & Caravan Park CARAVAN PARK $
( 08-9827 9270; www.mounttrio.com.au; Salt River Rd; unpowered/powered sites per person $12/14) Rustic bush campground on a farm property close to the walking tracks, north of the centre of the park, has hot showers, a kitchen, free gas BBQs and a campfire pit. Guided walks are on offer.
Moingup Springs CAMPGROUND $
(Chester Pass Rd; sites per adult/child $7/2) The DEC's only campground within the park; no showers or electricity.
The Lily COTTAGES $$
( 08-9827 9205; www.thelily.com.au; Chester Pass Rd; cottages $139-169) Looking like a 16th-century Dutch farm, these cottages 12km north of the park are grouped around a working windmill. Accommodation is self-contained, and meals ($36) are also available for guests at the neighbouring restaurant (a 1924 railway-station building). Call to enquire which nights the restaurant is open to the public (hours vary), and to arrange mill tours ($50, minimum of four people).
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Bremer Bay
pop 250
Edged with brilliant white sand and translucent green waters, this sleepy fishing and holiday hamlet is 61km from the South Coast Hwy. From July to November, the bay is a cetacean maternity ward for southern right whales.
The visitor centre ( 08-9837 4171; www.bremerbay.com; Mary St; 9am-5pm Mon-Fri; ) in the shire library also has internet access. Holiday homes can be booked through the visitor centre.
Bremer Bay Beaches Resort & Tourist Park ( 08-9837 4290; www.bremerbaybeaches.com.au; Wellstead Rd; sites per 2 people from $32, cabins & chalets $115-185; ) has shady campsites, a well-equipped campers' kitchen and a seasonal pizzeria. It's a 1.5km walk through the dunes to the beach.
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Fitzgerald River National Park
Midway between Albany and Esperance, this gem of a national park (entry per car/motorcycle $11/5) has been declared a Unesco Biosphere Reserve. Its 3300 sq km contains half of the orchid species in WA (more than 80, 70 of which occur nowhere else), 22 mammal species, 200 species of bird and 1700 species of plant (20% of WA's described species). It's also the blossoming ground of the royal hakea _(Hakea victoria)_ and Qualup bell _(Pimelia physodes)_ flowers. Wildflowers are most abundant in spring, but flowers – especially the hardy proteas – bloom throughout the year.
Walkers will discover beautiful coastline, sand plains, rugged coastal hills (known as 'the Barrens') and deep, wide river valleys. In season, you'll almost certainly see whales and their calves from the shore at Point Ann , where there's a lookout and a heritage walk that follows a short stretch of the 1164km No 2 rabbit-proof fence (built between 1904 and 1960). Short walks are also accessible at East Mt Barren (three hours) and West Mt Barren (two hours). For information on wilderness walks, check with the DEC rangers at Jerramungup ( 08-9835 5043; Quiss Rd) , Bremer Bay ( 08-9837 1022; Murray Rd) and East Mt Barren ( 08-9838 3060; Hamersley Dr) .
Although the park is one of the areas in southern WA least affected by the dieback fungus (a killer of native trees), precautions are in place to ensure it remains so; respect the 'no entry – dieback' signs, and clean your shoes before each walk.
The three main 2WD entry points to the park are from the South Coast Hwy (Quiss Rd and Pabelup Dr), Hopetoun (Hamersley Dr) and Bremer Bay (along Swamp and Murray Rds). This last is the prettiest route, winding through acres of flowering shrubs. All roads are gravel, and likely to be impassable after rain, so check locally before you set out.
4 Sleeping
Quaalup Homestead CAMPGROUND $
( 08-9837 4124; www.whalesandwildflowers.com.au; Quaalup Rd; sites per person from $12, on-site vans $60, r $90-120) S Completely isolated, this 1858 homestead is secluded deep within the southern reaches of the park. Electricity is solar, so leave the gadgets behind and forget about mobile-phone coverage. Sleeping options range from a bush camp site with gas BBQs to a set of cosy units and chalets scattered around the grounds. Quaalup Rd is reached from Pabelup Dr.
DEC Campsites CAMPGROUND $
(sites per adult/child $7/2) Of the five national- park camp sites run by the DEC, only St Mary Inlet (near Point Ann) can be reached by 2WD. The two at Hamersley Inlet and the others at Whale Bone Beach, Quoin Head and Fitzgerald Inlet can only be reached by 4WD or on foot.
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Hopetoun
pop 590
Once as sleepy as Bremer Bay, Hopetoun has nearly doubled in size in recent years due to the opening of a nickel mine. The beauty of the beaches hasn't changed, but there are now more eating options and the local pub fills up with young workers in dusty overalls. From the jetty at the end of the main drag (Veal St) there are wonderful views. Beside it is a child-friendly beach with a swimming pontoon.
The old train route between Ravensthorpe and Hopetoun is now a heritage walking track . To the west of town, separating it from Fitzgerald River National Park, is the almost landlocked Culham Inlet (great for fishing – especially for black bream). To the east is the scenic but in parts extremely rough Southern Ocean East Drive , heading to beaches with camp sites at Mason Bay and Starvation Bay . If you're in a 2WD, don't be tempted to head to Esperance this way; if you'd prefer not to double back to the highway at Ravensthorpe, take Jerdacuttup Rd (past the airport) instead.
The world's longest fence – the 1833km-long No 1 rabbit-proof fence – enters the sea at Starvation Bay; it starts at Eighty Mile Beach on the Indian Ocean, north of Port Hedland. The fence was built during the height of the rabbit plague between 1901 and 1907. However, the bunnies beat the fence-builders to the west side, so it wasn't as effective a barrier as hoped.
4 Sleeping & Eating
Hopetoun Motel & Chalet Village MOTEL $$
( 08-9838 3219; www.hopetounmotel.com.au; 458 Veal St; r $140-200; ) A very nice rammed-earth complex with comfy beds and quality linen. A larger townhouse ($310) is also available for families.
Toun Beach Cafe CAFE $
(19 Veal St; pizzas $18-25, burgers $12-14; 8.30am-2.30pm & 5.30-8pm Tue-Sat, 8.30am-2.30pm Sun) Sit upstairs for excellent breakfasts and water views at this cool-looking cafe. Wood-fired pizzas and good burgers seal the deal.
Deck Treasures CAFE $
(www.gotothedeck.com.au; Veal St; 9am-4.30pm Mon-Fri & 9am-12.30pm Sat Sep-May; ) Part gift shop, part cafe, and part visitor centre with its own Southern Ocean Discovery Centre with lots of information on local wildlife. Free wi-fi and internet access too. Ask for its free self-guide driving map to the surrounding area.
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Esperance
pop 9600
Esperance sits in solitary splendour on the Bay of Isles, a seascape of aquamarine waters fringed with squeaky white beaches. There's no need to fight for space here, as the town's isolation all but guarantees it. Yet Esperance has its share of devotees who will bundle up the kids for the mammoth pilgrimage from Perth, just to plug into the low-key, community-oriented vibe. In Kalgoorlie, nobody would question the wisdom of driving 390km to this, their nearest beach. For travellers taking the coastal route across the continent, it's the last sizeable town before hitting the Nullarbor wilderness.
Some of Australia's most picture-perfect beaches can be found in the even more remote national parks to the town's southeast. Out in the bay, the pristine environment of the Recherche Archipelago can be wild and windy, or turn on a calmly charming show. The archipelago's 105 islands are home to fur seals, penguins and sea birds.
History
Esperance's Indigenous name, Kepa Kurl (water boomerang), refers to the shape of the bay. Archaeological finds on Middle Island suggest that it was occupied before the last Ice Age, when it was still part of the mainland.
Esperance received its current name in 1792 when the _Recherche_ and _l'Espérance_ sailed through the archipelago and into the bay to shelter from a storm. In the 1820s and 1830s the Recharge Archipelago was home to Black Jack Anderson – Australia's only pirate. From his base on Middle Island he raided ships and kept a harem of Aboriginal women, whose husbands he had killed. He was eventually murdered in his sleep by one of his own men.
Although the first settlers came in 1863, it wasn't until the gold rush of the 1890s that the town really became established as a port. When the gold fever subsided, Esperance went into a state of suspended animation until after WWII.
In the 1950s it was discovered that adding missing trace elements to the soil around Esperance restored its fertility. The town has since rapidly become an agricultural centre and it continues to export grain and minerals from the region's farms and mines.
1 Sights & Activities
Esperance Museum MUSEUM
(cnr James & Dempster Sts; adult/child $6/2; 1.30-4.30pm) Glass cabinets are crammed with collections of sea shells, frog ornaments, tennis rackets and bed pans. It's absolutely charming, though, even if most of the displays wouldn't look amiss in a junk shop. Bigger items include boats, a train carriage and the remains of the USA's spacecraft _Skylab,_ which made its fiery re-entry at Balladonia, east of Esperance, in 1979.
Museum Village HISTORIC BUILDING
The museum includes galleries and cafes occupying restored heritage buildings; markets are held here every second Sunday morning. Aboriginal-run Kepa Kurl Art Gallery (see boxed text, Click here ) has reasonably priced works by local and Central Desert artists.
Lake Warden Wetland System LAKE
Esperance is surrounded by extensive wetlands, which include seven large lakes and over 90 smaller ones. The 7.2km-return Kepwari Wetland Trail (off Fisheries Rd) takes in Lake Wheatfield and Woody Lake , with boardwalks, interpretive displays and good birdwatching. Lake Monjimup , 14km to the northwest along the South Coast Hwy, is divided by Telegraph Rd into a conservation area (to the west) and a recreation area (to the east). The conservation side has boardwalks over inky black water where it's hard to see where the paperbark trees end and their mirror image begins. The much more orderly recreation side has themed banksia, hakea and grevillea gardens, a hedge maze and great grassy areas for throwing a ball around.
Cannery Arts Centre GALLERY
(1018 Norseman Rd; admission by gold-coin donation; 1-4pm Mon-Fri) Has artists studios, interesting exhibitions and a shop selling local artwork. For more local art, pick up the _Esperance Art Trail_ brochure at the visitor centre, listing 14 stops.
Great Ocean Drive SCENIC DRIVE
Many of Esperance's most dramatic sights can be seen on this well-signposted 40km loop. Starting from the waterfront, it heads southwest along the breathtaking stretch of coast that includes a series of popular surfing and swimming spots, including Blue Haven Beach and Twilight Cove . Stop to enjoy the rollers breaking against the cliffs from Observatory Point and the lookout on Wireless Hill . A turn-off leads to the wind farm , which supplies about 23% of Esperance's electricity. Among the turbines there's a walking track, which can be quite surreal when it's windy – and it often is.
The route then turns back and passes by the Pink Lake – or should that be the-lake-formerly-known-as-pink? Salt-tolerant algae once provided an unmistakeable rosy tint, but a storm a few years back flushed it out.
Ralph Bower Adventureland Park PARK
(Taylor Street Jetty; train rides $3; train rides 9am-4pm Sat & Sun May-Sep, daily Oct-Apr) F Popular children's playground with a miniature train.
T Tours
Esperance Island Cruises BOAT
( 08-9071 5757; www.woodyisland.com.au; 72 The Esplanade; daily late Sep-May) Tours include Esperance Bay and Woody Island in a power catamaran (half-/full day $95/150), getting close to fur seals, sea lions, Cape Barren geese and (with luck) dolphins. In January, there's a ferry to Woody Island (adult/child return $60/30).
Kepa Kurl Eco Cultural Discovery Tours INDIGENOUS CULTURE
( 08-9072 1688; www.kepakurl.com.au; Museum Village) S Explore the country from an Aboriginal perspective: visit rock-art and waterholes, sample bush food and hear ancient stories (adult/child $105/90, minimum of two people).
Eco-Discovery Tours DRIVING TOUR
( 0407 737 261; www.esperancetours.com.au) Runs 4WD tours along the sand to Cape Le Grand National Park (half-/full day $95/165, minimum of two/four people) and two-hour circuits of Great Ocean Dr (adult/child $55/40).
Aussie Bight Expeditions DRIVING TOUR
( 0427 536 674; www.aussiebight.com; half/full day $90/160; Aug-Apr) Exciting and entertaining 4WD expeditions covering wildflowers and Cape Le Grand National Park. Sandboarding is available from mid-December to April. Book at the Esperance visitor centre.
Esperance Diving & Fishing DIVING, FISHING
( 08-9071 5111; www.esperancedivingandfishing.com.au; 72 The Esplanade) Takes you wreck diving on the _Sanko Harvest_ (two-tank dive including all gear $260) or charter fishing throughout the archipelago.
4 Sleeping
Woody Island Eco-Stays CAMPGROUND $
( 08-9071 5757; www.woodyisland.com.au; sites per person $25, on-site tents $41-61, huts $140-165; late Sep-Apr; ) S It's not every day you get to stay in an A-class nature reserve. Choose between leafy camp sites (very close together) or canvas-sided bush huts, a few of which have a private deck and their own lighting. Power is mostly solar, and rainwater supplies the island – both are highly valued. Count on adding on a $60 return-ferry transfer as well.
Blue Waters Lodge YHA HOSTEL $
( 08-9071 1040; www.yha.com.au; 299 Goldfields Rd; dm/s/d $28/50/70) On the beachfront about 1.5km from the town centre, this rambling place feels a little institutional, but the new management are friendly and it looks out over a tidy lawn to the water. Hire bikes to cycle the waterfront.
Esperance B&B by the Sea B&B $$
( 08-9071 5640; www.esperancebb.com; 34 Stewart St; s/d $120/170; ) This great-value beachhouse features a private guest wing, and the views from the deck overlooking Blue Haven Beach are breathtaking, especially at sunset. It's just a stroll from the ocean and a five-minute drive from central Esperance.
Clearwater Motel Apartments MOTEL $$
( 08-9071 3587; www.clearwatermotel.com.au; 1a William St; s $110, d $140-195; ) The bright and spacious rooms and apartments here have balconies and are fully self-contained, and there's a well-equipped shared barbecue area. It's just a short walk from both waterfront and town.
Driftwood Apartments APARTMENT $$
( 0428 716 677; www.driftwoodapartments.com.au; 69 The Esplanade; apt $165-220; ) Each of these seven smart blue-and-yellow apartments, right across from the waterfront, has its own BBQ and outdoor table setting. The two-storey, two-bedroom units have decks and a bit more privacy.
Island View Esperance APARTMENT $$
( 08-9072 0044; www.esperanceapartments.com.au; 14-15 The Esplanade; apt from $200; ) It's easy living in these architect-designed and tastefully furnished one- to three-bedroom apartments, some with floor-to-ceiling windows overlooking the waterfront. The kitchens have all the mod cons, and there's a spacious living area.
5 Eating & Drinking
Onshore Cafe CAFE $
(105 Dempster St; mains $7-14; 8am-6pm Mon-Fri & 9am-3pm Sat) A homewares store–cafe in a breezy modern space next to the cinema, this place serves light lunches, as well as excellent coffee, croissants and cake. The wraps and Turkish sandwiches are good value.
Taylor's Beach Bar & Cafe CAFE $$
(Taylor Street Jetty; lunch $7-24, dinner $24-32; 7am-2pm Wed, to 9pm Thu-Mon; ) This attractive, sprawling cafe by the jetty serves cafe fare, tapas, seafood and salads. Locals hang out at the tables on the grass or read on the covered terrace. Sandwiches ($6.50 to $9.50) are good value if you're heading for the beach, and it's good for a glass of wine or chilled pint of Little Creatures.
Ocean Blues CAFE $$
(19 The Esplanade; mains $22-34; 9.30am-8.30pm Tue-Sat & 8am-4pm Sun) Wander in sandy-footed and order a simple lunch (burgers, salads, sandwiches, wraps) from this unpretentious eatery. Dinners are more adventurous, representing good value for the price.
Alimento CAFE $$
(94 Dempster St; mains $13-18; 7am-3pm Mon-Fri, 8am-1pm Sat, 7.30am-11.30am Sun) Excellent coffee and colourful local art feature at this centrally located cafe. Try the tasting platter with homemade hummus and warm Turkish bread, or see what's inspiring the chef for the popular 'Curry of the Day'.
Pier Hotel PUB $$
(www.pierhotelesperance.net.au; 47 The Esplanade; mains $20-35; 11.30am-late) Lots of beers on tap, wood-fired pizzas and good-value bistro meals conspire to make the local pub a firm favourite with both locals and visitors.
Coffee Cat CAFE
(Tanker Jetty; 7am-2pm Mon-Fri) WA's hippest coffee caravan also serves up yummy home-baked cakes and muffins. Grab an early-morning java to fuel you for a stroll to the end of nearby Tanker Jetty. Keep an eye out for yawning seals and sea lions also greeting the new day.
3 Entertainment
Fenwick 3 Cinemas CINEMA
( 08-9072 1355; www.ausaf.com.au; 105 Dempster St) Blockbusters and arty movies.
8 Information
DEC ( 08-9083 2100; 92 Dempster St) Has information on the national parks in the Esperance region.
Visitor Centre ( 08-9083 1555; www.visitesperance.com; cnr Kemp & Dempster Sts; 9am-5pm Mon-Fri, to 2pm Sat, to noon Sun)
8 Getting There & Away
Esperance Airport (EPR; Coolgardie-Esperance Hwy) is 18km north of the town centre. Skywest ( 1300 660 088; www.skywest.com.au) has one to three flights per day to and from Perth (1¾ hours).
Transwa ( 1300 662 205; www.transwa.wa.gov.au) services stop at the visitor centre:
GE1 to/from Perth ($87, 10¼ hours, thrice weekly)
GE2 to/from Perth ($87, 10 hours), Mundaring ($86, 9¼ hours), York ($78, 8½ hours) and Hyden ($53, five hours) thrice weekly
GE3 to/from Kalgoorlie ($56, five hours, thrice weekly), Coolgardie ($53, 4¾ hours, weekly) and Norseman ($30, 2¼ hours, thrice weekly)
GE4 to/from Albany ($62, 6½ hours, twice weekly)
8 Getting Around
Try Avis ( 08-9071 3998; www.avis.com.au; 63 The Esplanade) or Budget ( 08-9071 2775; www.budget.com.au) at the airport. Hollywood Car Hire ( 08-9071 3144; Wood St) is the local car-rental mob.
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Around Esperance
1 Sights
Cape Le Grand National Park NATIONAL PARK
(entry per car/motorcycle $11/5, sites adult/child $9/2) An easy day tour from Esperance, Cape Le Grand National Park starts 60km to the east of town and boasts spectacular coastal scenery, turquoise water, dazzling talcum-powder-soft beaches and excellent walking tracks. It offers good fishing, swimming and camping at Lucky Bay and Le Grand Beach , and day-use facilities at gorgeous Hellfire Bay . Make the effort to climb Frenchman Peak (a steep 3km return, allow two hours), as the views from the top and through the 'eye', especially during the late afternoon, are superb.
Rossiter Bay is where the British and Aboriginal duo Edward John Eyre and Wylie fortuitously met the French whaling ship _Mississippi_ , in the course of their epic 1841 overland crossing, and spent two weeks resting on board. The 15km Le Grand Coastal Trail links the bays; you can do shorter stretches between beaches.
### STOKES NATIONAL PARK
Pretty Stokes National Park (entry per car/motorcycle $11/5) , 90km west of Esperance, is set around Stokes Inlet, known for its long beaches and rocky headlands. Most of its 107 sq km is covered in scrub and coastal heath, sheltering kangaroos and birds. You might also spot seals. It's a popular spot for anglers and there's a bush campground (sites adult/child $7/2) , which is 2WD accessible.
Cape Arid National Park NATIONAL PARK
(entry per car/motorcycle $11/5, sites adult/child $7/2) At the start of the Great Australian Bight and on the fringes of the Nullarbor Plain, is Cape Arid National Park. Rugged and isolated, the park has good bushwalking, great beaches, camp sites and crazy squeaky sand.
Whales (in season), seals and Cape Barren geese are seen regularly here. Most of the park is 4WD-accessible only, although the Thomas River Rd leading to the shire camp site is accessible to all vehicles. For the hardy, there's a tough walk to the top of Tower Peak on Mt Ragged (3km return, three hours). The world's most primitive species of ant was found thriving here in 1930.
Peak Charles National Park NATIONAL PARK
F There are no charges to visit or camp at this granite wilderness area, 130km north of Esperance. There are only basic facilities provided (long-drop toilets); you'll need to be completely self-sufficient here.
# Monkey Mia & the Central West
#### Monkey Mia & the Central West Highlights
#### Batavia Coast
#### Dongara-Port Denison
#### Geraldton
#### Kalbarri
#### Shark Bay
#### Overlander Roadhouse to Denham
#### Denham
#### François Peron National Park
#### Monkey Mia
#### Gascoyne Coast
#### Carnarvon
#### Point Quobba to Gnaraloo Bay
Monkey Mia & the Central West
### Why Go?
The pristine coastline and sheltered turquoise waters of Malgana country draw tourists and marine life from around the world. Aside from Monkey Mia's famous dolphins, the submerged sea-grass meadows of World Heritage–listed Shark Bay host dugongs, rays, sharks and turtles, while rare marsupials take refuge in remote national parks. Limestone cliffs, red sand and salt lakes litter the stark interior.
Further south in the land of the Nhanda people, the gorges of Kalbarri invite adventurers to explore their depths, while above, wildflowers carpet the plains and ospreys wheel away from battered Indian Ocean cliffs as humpback whales migrate slowly southwards.
Vegies are ripening in Carnarvon as anglers and board riders check the tides, and windsurfers are waiting for the 'Doctor' (strong afternoon sea breeze) to blow. In Geraldton, the only decision to make is whether to have that second macchiato before a brisk walk along the foreshore.
### When to Go
Jun & Aug The winter swells pump the breaks off Gnaraloo and Quobba.
Aug & Sep Kalbarri erupts in wildflowers.
Nov–Feb Windsurfers clutch their sails from Geraldton to Carnarvon.
### Best Places for Sunset
» Steep Point ( Click here )
» Fishermens Lookout ( Click here )
» Red Bluff ( Click here )
» Shark Bay Hotel ( Click here )
» Horrocks ( Click here )
### Best Places to Stay
» Gnaraloo Station ( Click here )
» Ospreys Beach Chalet ( Click here )
» Fish & Whistle ( Click here )
» Bentwood Olive Grove ( Click here )
» Bay Lodge ( Click here )
## Monkey Mia & the Central West Highlights
Watching the wild dolphins feed at Monkey Mia (Click here )
Canoeing through the deep gorges of Kalbarri National Park (Click here )
Surfing the wild Tomb-stones break at Gnaraloo (Click here )
Driving out to Steep Point (Click here ), the mainland's most westerly tip
Sailing out to look for dugongs in Shark Bay (Click here )
Immersing yourself in Malgana culture on a Monkey Mia Wula Guda Nyinda (Click here )
Diving on ancient shipwrecks at the Houtman Abrolhos Islands (Click here )
Horse riding along the mighty Murchison River (p )
Spotting marine life from a coastal walk in the François Peron National Park (Click here )
a Soaking up the coffee and culture at the museums, galleries and cafes of Geraldton (Click here )
8 Getting There & Around
Air
Skywest ( 1300 660 088; www.skywest.com.au) Flies regularly to Geraldton.
Skippers ( 1300 729 924; www.skippers.com.au) Services Kalbarri, Geraldton, Shark Bay and Carnarvon.
Qantas ( 13 13 13; www.qantas.com.au) Perth to Geraldton daily.
Bus
Integrity ( 1800 226 339; www.integritycoachlines.com.au) Runs a handy daily coastal connection between Perth and Geraldton, and a twice-weekly overnighter to Exmouth.
Greyhound ( 1300 473 946; www.greyhound.com.au) Runs services three times weekly between Broome and Perth along the coast.
Transwa ( 1300 662 205; www.transwa.wa.gov.au) Runs regular buses between Perth and Kalbarri, Geraldton and Dongara along the Brand Hwy (Rte 1).
## Batavia Coast
From tranquil Dongara-Port Denison to the remote, wind-scoured Zuytdorp Cliffs stretches a dramatic coastline steeped in history, littered with shipwrecks and abounding in marine life. While the region proved the undoing of many early European sailors, today modern fleets make the most of a lucrative crayfish industry.
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Dongara-Port Denison
pop 3100
Pretty little Dongara and Port Denison, twin seaside towns 359km from Perth, make an idyllic spot to break up a long drive. Surrounded by beautiful beaches, walking trails and historic buildings, the towns have a laid-back atmosphere that's hard to beat. Port Denison has most of the beaches and accommodation, while Dongara's main street, shaded by century-old figs, offers banks, internet and food options.
1 Sights & Activities
Pick up the free _Walk Dongara Denison_ brochure from the visitor centre and choose from 12 historic or nature-based rambles, including the Irwin River Nature Trail , where you might spot black swans, pelicans or cormorants. For $2 you can purchase the Heritage Trail booklet detailing a 1.6km route linking buildings such as the 1860s Russ Cottage (Point Leander Dr) , with a kitchen floor made from compacted anthills, and the landmark Royal Steam Flour Mill (Brand Hwy) . In the old police station, the cells of the Irwin District Museum ( 08-9927 1404; admission $2.50; 10am-noon Mon-Sat) hold crusty historical displays.
Denison Beach Marina brims with boats that haul crayfish, the towns' livelihood, while sunsets are dazzling from nearby Fishermens Lookout .
4 Sleeping & Eating
Note that public and school holidays attract a surcharge.
There is a supermarket, cafes and takeaways on Moreton Tce and a good bakery on Waldeck St in Dongara; the Port Store ( 08-9927 1030; 52 Point Leander Dr; 7.30am-6pm) in Port Denison has most necessities.
Dongara Backpackers HOSTEL $
(Breeze Inn; 08-9927 1332; www.dongarabackpackers.com.au; 32 Waldeck St, Dongara; dm/d/f $30/85/130) The cheapest beds in town look onto a leafy garden at this popular backpackers, which has stylish doubles, rustic dorms (in a vintage railway carriage) and free bike hire for guests.
Dongara Tourist Park CARAVAN PARK $
( 08-9927 1210; www.dongaratouristpark.com.au ; 8 George St, Port Denison; unpowered/powered sites $25/33, 1-/2-bedroom cabins $105/145; ) The best camping option has shaded, spacious sites behind South Beach. The two-bed cabins on the hill have great views, and there's a lush pergola for dining outdoors.
Port Denison Holiday Units APARTMENTS $$
( 08-9927 1104; www.portdenisonholidayunits.com.au; 14 Carnarvon St, Port Denison; d $110-120; ) These spotless, spacious, self-catering units, some with views, are just a block from the beach.
Priory Hotel GUESTHOUSE $
( 08-9927 1090; www.prioryhotel.com.au; 11 St Dominics Rd, Dongara; r $70-130; ) There's a touch of _Picnic at Hanging Rock_ about this leafy former nunnery and ladies college with its period furniture, polished floorboards, black-and-white photos and wide verandahs. Sundays bring roasts and wood-fired pizza (mains $20 to $32), several nights offer live music, and steaks are available every evening.
Little Starfish CAFE $
( 0448 344 215; White Tops Rd, Port Denison; mains $6-18; 8am-4pm Wed-Mon) Hidden away in the South Beach car park, this casual snack shack offers coffee, jaffles, winter soups and summer salads.
Dongara Hotel Motel AUSTRALIAN, ASIAN $$
( 08-9927 1023; www.dongaramotel.com.au; 12 Moreton Tce, Dongara; mains $20-40; breakfast, lunch & dinner; ) Locals love the Dongara's legendary servings of fresh seafood, steaks and 'Asian Corner' curries, _mie goreng_ and _phàt thai_ . The motel rooms (doubles $130), popular with corporates, are adequate if not flash.
8 Information
Moreton Tce has several banks with ATMs.
Telecentre (CRC; 08-9927 2111; 11 Moreton Tce; 8.30am-4.30pm Mon-Fri; )
Visitor Centre ( 08-9927 1404; www.irwin.wa.gov.au; 9 Waldeck St, Dongara; 9am-5pm Mon-Fri, to noon Sat)
8 Getting There & Around
Dongara-Port Denison is accessible via the Brand Hwy, Indian Ocean Dr or Midlands Rd (Rte 116).
Greyhound has services to Broome ($356, 29 hours, Monday, Wednesday and Friday) and Perth ($60, five hours, Wednesday, Friday and Sunday). Transwa runs daily to Perth ($53, five hours) and Geraldton ($13, one hour). runs daily to Perth ($49, five hours) and Geraldton ($16, one hour) and twice weekly overnight to Exmouth ($149, 12 hours). Buses arrive/depart from the visitor centre.
For a taxi, call 9927 1555.
Top of Chapter
Geraldton
pop 39,000
Capital of the midwest, sun-drenched 'Gero' is surrounded by excellent beaches offering myriad aquatic opportunities – swimming, snorkelling, surfing and, in particular, wind and kite surfing. The largest town between Perth and Darwin has huge wheat-handling and fishing industries that make it independent of the fickle tourist dollar, and seasonal workers flood the town during crayfish season. Still a work in progress, Gero blends big-city sophistication with small-town friendliness, offering a strong arts culture, a blossoming foodie scene and some great local music.
1 Sights
o Western Australian Museum MUSEUM
OFFLINE MAP GOOGLE MAP
( 08-9921 5080; www.museum.wa.gov.au; 1 Museum Pl; admission by donation; 9.30am-4pm) At one of the state's best museums, intelligent multimedia displays relate the area's natural, cultural and indigenous history. The Shipwreck Gallery documents the tragic story of the _Batavia,_ while video footage reveals the sunken HMAS _Sydney II_ . Enquire about sailing open days held on the longboat moored behind the museum.
Geraldton
Sights
1 Cathedral of St Francis Xavier Church C4
2 Geraldton Regional Art Gallery C3
3 HMAS Sydney II Memorial D2
4Old Geraldton Gaol Craft CentreD1
5 Western Australian Museum C1
Activities, Courses & Tours
6 Batavia Coast Dive Academy B3
7 G-Spot Xtreme B4
8 Revolutions C2
Sleeping
9 Foreshore Backpackers B3
Eating
10 Culinary HQ B3
11 Go Health Lunch Bar B2
12 Provincial B3
13 Saltdish C2
14 Topolinis Caffe B3
Drinking & Nightlife
15 Freemasons Hotel C2
16 Vibe B4
Entertainment
17Breakers BarC2
18 Camel Bar C3
19Orana CinemasB3
20Queens Park TheatreC4
Cathedral of St Francis Xavier Church CHURCH
OFFLINE MAP GOOGLE MAP
( 08-9921 3221; www.geraldtondiocese.org.au; Cathedral Ave; tours 10am Mon & Fri, 4pm Wed) Arguably the finest example of the architectural achievements of the multi-skilled Monsignor John Hawes. The cathedral's striking features include imposing twin towers with arched openings, a central dome, Romanesque columns and boldly striped walls.
Geraldton Regional Art Gallery GALLERY
OFFLINE MAP GOOGLE MAP
( 08-9964 7170; 24 Chapman Rd; 10am-4pm Tue-Sat, from 1pm Sun) F Featuring an excellent permanent collection, including paintings by Norman Lindsay and Elizabeth Durack, this gallery also presents provocative contemporary work and regular touring exhibitions.
Old Geraldton Gaol Craft Centre HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
( 08-9921 1614; Bill Sewell Complex, Chapman Rd; 10am-4pm Mon-Sat) The crafts are secondary to the gloomy cells that housed prisoners from 1858 to 1986, and the historic documents that detail their grim circumstances.
HMAS Sydney II Memorial MONUMENT
OFFLINE MAP GOOGLE MAP
(Mt Scott; tours free; tours 10am) Commanding the hill overlooking Geraldton is this memorial commemorating the 1941 loss of the _Sydney_ and its 645 men after a skirmish with the German raider _Kormoran_ .
2 Activities
With all that beachfront it's no surprise most activities are water based, but land-lubbers can take heart from Geraldton's excellent network of bike paths, including the 10km-long coastal route from Tarcoola Beach to Chapman River . Grab the _Local Travelsmart Guide_ from the visitor centre. Bikes can be hired from Revolutions OFFLINE MAP GOOGLE MAP ( 08-9964 1399; 1/27 Chapman Rd; bike hire per day $20; 9am-5.30pm Mon-Fri, to noon Sat) .
### GREENOUGH
Located 24km south of Geraldton, the rural area of historic Greenough makes for a pleasant overnight alternative. Historic sights such as the Central Greenough Historical Settlement ( 08-9926 1084; www.centralgreenough.com; Brand Hwy; adult/child $6/3, cafe meals $7-28; 9am-5pm, shorter hours Feb-Mar) , with its handful of 19th-century buildings, and the Pioneer Museum (www.greenough-pioneer-museum.com; Phillips Rd; adult/child $4.50/free; 9.30am-3.30pm) detail early settler life and offer a chance to stretch the legs, although the area's main attractions are its excellent food and lodgings.
Bentwood Olive Grove ( 08-9926 1196; www.bentwood.com.au; Brand Hwy; d from $120; ) has a long connection to gourmet food, though its focus is now on accommodation, with a beautiful stone cabin sleeping six, and more rooms slated. WWOOFers (Willing Workers on Organic Farms) are welcome and there are lovely gardens to wander through and enjoy.
You can almost picture horse-drawn coaches pulling up to the Hampton Arms Inn ( 08-9926 1057; www.hamptonarms.com.au; Company Rd; s/d $75/95; Tue-Sun, meals Wed-Sun) , built in 1863. It features period bedrooms (some with fireplaces), a cluttered bookshop crammed with rare titles, a formal dining room (mains $12 to $34)and a cosy, well-stocked bar.
While away the days swimming and fishing at Double Beach Holiday Park ( 08-9921 5845; www.doublebeach.com.au; 4 Hull St, Cape Burnery; unpowered/powered sites $25/30, cabins $100-140) , with its quiet, shady sites and great BBQ pergola. It's located behind the dunes at the mouth of the Greenough River.
The Transwa daily service to Geraldton will drop you on the Brand Hwy.
G-Spot Xtreme WINDSURFING
OFFLINE MAP GOOGLE MAP
( 08-9965 5577; www.gspotxtreme.com.au; 241a Lester Ave; hire per day windsurfers $100, paddleboards $100, electric bikes $25) You can hire or buy windsurfing and paddleboard equipment here.
Batavia Coast Dive Academy DIVING
OFFLINE MAP GOOGLE MAP
( 08-9921 4229; www.bcda.com.au; 153 Marine Tce; local dives with/without equipment $140/100) Offers open-water courses (full PADI $630) and a range of diving trips, including chartered trips to the Abrolhos (from $300 per person per day).
Midwest Surf School SURFING
( 0419 988 756; http://surf2skool.com; lessons from $60, board hire $30) Ever wanted to surf but don't know how? Courses run from absolute beginners to advanced at Geraldton's back beach.
KiteWest KITEBOARDING
( 0449 021 784; www.kitewest.com.au; coaching per hr from $80) Kitesurfing courses and 4WD camping tours.
4 Sleeping
Expect price hikes during school and public holidays.
Foreshore Backpackers HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9921 3275; 172 Marine Tce; dm/s/d $30/45/65; ) Shambolic, rambling and oozing character, this central hostel is full of hidden nooks, sunny balconies and world-weary travellers. Recently renovated and under new management, it's still the best place to find a job, lift or travel buddy. Discounts apply for longer stays.
Sunset Beach Holiday Park CARAVAN PARK $
( 1800 353 389; www.sunsetbeachpark.com.au; Bosley St; powered sites $35, cabins $100-152) About 6km north of the CBD, Sunset Beach has roomy, shaded sites just a few steps from a lovely beach, and an ultramodern camp kitchen with the biggest plasma TV on the entire coast.
o Ospreys Beach Chalet COTTAGE $$
( 0447 647 994; enerhkalm@gmail.com; 40 Bosuns Cr, Point Moore; for 2 persons from $145) S Both ospreys and beach are near this sustainably restored cottage, which began life as a proof-of-concept project. Rainwater tanks and solar panels complement recycled materials in a restoration that doesn't skimp on comfort. There are plenty of outdoor areas and the rear native garden is a gem.
o Weelaway B&B $$
( 08-9965 5232; www.weelaway.com.au; 104 Gregory St; r $100-145, 2-bedroom cottages $175; ) Weelaway offers exquisitely decorated rooms in a heritage-listed house dating from 1862. There are formal lounge rooms, shady wide verandahs and a well-stocked library, and it's all within walking distance of the centre of town.
Ocean West APARTMENTS $$
( 08-9921 1047; www.oceanwest.com.au; 1 Hadda Way; 1-/3-bedroom apt from $135/215; ) Don't let the '60s brick put you off; these fully self-contained units have all been tastefully renovated, making them one of the better deals in town. The wildly beautiful back beach is just across the road.
5 Eating
Geraldton has great food options including Asian, takeaways, coffee lounges, bakeries and supermarkets. Free BBQs and picnic tables dot the foreshore.
Go Health Lunch Bar CAFE $
OFFLINE MAP GOOGLE MAP
( 08-9965 5200; 122 Marine Tce; light meals around $10; 8.30am-3pm Mon-Fri, to 1pm Sat; ) Vegetarians can rejoice at the choice of fresh juices and smoothies, excellent espresso, healthy burritos, lentil burgers, focaccias and other light meals from this popular lunch bar in the middle of the mall.
Culinary HQ CAFE $
OFFLINE MAP GOOGLE MAP
( 08-9964 8308; culinaryhq@westnet.com.au; 202 Marine Tce; lunch $8-13, cooking class $95; 9am-5pm Mon-Fri) An eclectic gourmet menu changes weekly at this fledgling providore and includes soups, baguettes and cooked meals that are also available for takeaway – perfect for that hostel or camper-van reheat. Phone ahead for the Thursday-evening cooking class.
o Saltdish CAFE $$
OFFLINE MAP GOOGLE MAP
( 08-9964 6030; 35 Marine Tce; breakfasts $6-20, lunches $18-30; 7.30am-2.30pm Mon-Sat; ) The hippest cafe in town offers innovative, contemporary brekkies, light lunches and industrial-strength coffee, and screens films in its courtyard on summer evenings. Try the Spanish omelette or coconut lime chicken. BYO.
Provincial MODERN AUSTRALIAN $$
OFFLINE MAP GOOGLE MAP
( 08-9964 1887; www.theprovincial.com.au; 167 Marine Tce; tapas $8-12, pizza $24-30, mains $28-42; 5.30pm-late, lunch Fri-Sun, breakfast Sat & Sun) Stencil art adorns this atmospheric wine bar serving up tapas, wood-fired pizzas and Mod Oz/Mediterranean–inspired dishes like pork belly with pine nuts, goats cheese tortellini or angel-hair pasta with crab meat. Live music Friday nights.
Topolinis Caffe ITALIAN $$
OFFLINE MAP GOOGLE MAP
( 08-9964 5866; 158 Marine Tce; mains $22-36; 8.30am-late; ) This home-style licensed bistro is perfect for an afternoon coffee, cake and wi-fi, a preshow bite, or just a relaxed family feed. The $34 dinner-and-movie deal (Sunday to Thursday) and Monday half-price pasta are popular.
6 Drinking & Nightlife
Freemasons Hotel PUB
OFFLINE MAP GOOGLE MAP
( 08-9964 3457; www.freemasonshotel.com.au; cnr Marine Tce & Durlacher St; 11am-late) The heritage-listed Freo has been serving beer to thirsty travellers since the 1800s. Nowadays it's a popular hangout, with live music, DJs and open-mic and trivia nights complemented by a good range of bar meals ($16 to $33; try the sizzling stones!). There's also a small number of budget rooms (with/without ensuite $100/50).
Vibe CLUB
OFFLINE MAP GOOGLE MAP
( 08-9921 3700; 38-42 Fitzgerald St; from 11pm Thu-Sun) Expect all the usual nightclub action of DJs, chill rooms and dance floors.
3 Entertainment
Live-music options include Breakers OFFLINE MAP GOOGLE MAP ( 08-9921 8924; 41 Chapman Rd; from 9pm) , Camel Bar OFFLINE MAP GOOGLE MAP ( 08-9965 5500; 20 Chapman Rd, Geraldton) , Provincial and Freemasons. There's also a cinema ( 08-9965 0568; www.oranacinemas.com.au; cnr Marine Tce & Fitzgerald St; tickets $16) and theatre ( 08-9956 6662; cnr Cathedral Ave & Maitland St) .
8 Information
The best free wi-fi in town is at the library ( 08-9956 6659; library.cgg.wa.gov.au; 37 Marine Tce; wi-fi 1st hr free; from 9am Tue-Sat, from 1pm Sun & Mon; ) . There are several banks with ATMs along Marine Tce.
Sun City Books & Internet Corner ( 08-9964 7258; 49 Marine Tce; 9am-5pm Mon-Fri, to 1pm Sat; ) Lots of terminals and a decent selection of books.
Visitor Centre ( 08-9921 3999; www.geraldtontourist.com.au; Bill Sewell Complex, Chapman Rd; 9am-5pm Mon-Fri, 10am-4pm Sat & Sun) One of the best around, with lots of great info sheets and helpful staff who'll book accommodation, tours and transport.
8 Getting There & Around
Air
SkyWest and Qantas both fly daily to/from Perth. Skippers flies direct to/from Carnarvon several times weekly. The airport is 12km from Marine Tce.
Bus
Integrity coaches service Perth ($54, six hours) daily via the coast and run twice weekly to Carnarvon ($99, six hours) and Exmouth ($135, 11 hours). Transwa has daily inland services to Perth ($61, six hours) and thrice weekly to Kalbarri ($27, two hours). There's also a twice-weekly service to Meekatharra ($73, seven hours). Greyhound runs three times weekly to Perth ($65, six hours) and north to Carnarvon ($105, six hours) and Broome ($350, 27 hours). All long-distance buses leave from the old railway station (Greyhound from the rear). Transgeraldton ( 08-9923 2225; www.buswest.com.au) operates eight routes to local suburbs.
Batavia Tickets ( 08-9964 8881; www.bataviatickets.com.au; old railway station; 8am-4.30pm Mon-Fri, to 9.30am Sat) Sells tickets for the long-distance buses departing outside.
Taxi
Call 1300 008.
OFF THE BEATEN TRACK
### Houtman Abrolhos Islands
Better known as 'the Abrolhos', this archipelago of 122 coral islands, 60km off the coast of Geraldton, is home to some amazing wildlife, including sea lions, green turtles, carpet pythons, over 90 seabird species and the Tammar wallaby. Much of the flora is rare, endemic and protected, and the surrounding reefs offer great diving thanks to the warm Leeuwin Current, which allows tropical species such as _Acropora_ (staghorn) coral to flourish further south than normal.
These gnarly reefs have claimed many ships over the years, including the ill-fated _Batavia_ (1629) and _Hadda_ (1877), and you can dive on the wreck sites, as well as follow a number of self-guided dive trails (see the WA Fisheries _Abrolhos Islands Information Guide_ for details). Because the general public can't stay overnight, divers (and surfers) normally need a multi-day boat charter. If you're content with a day trip, where you can bushwalk, picnic, snorkel or fish, then flying is your best bet.
Batavia Coast Dive Academy ( Click here ) can help you get a boat together. Those wanting to fly could try the following operators.
Shine Aviation Services ( 9923 3600; www.shineaviation.com.au; 90min/full-day tours $175/240)
Geraldton Air Charter ( 08-9923 3434; www.geraldtonaircharter.com.au; Brierly Terminal, Geraldton Airport; half-/full-day tours $230/250)
Top of Chapter
Kalbarri
pop 2000
Magnificent red-sandstone cliffs border the Indian Ocean. The beautiful Murchison River snakes through tall, steep gorges before ending treacherously at Gantheaume Bay. Wildflowers line paths frequented by kangaroos, emus and thorny devils, while whales breach just offshore, and rare orchids struggle in the rocky ground. To the north, the towering line of the limestone Zuytdorp Cliffs remains aloof, pristine and remote.
Kalbarri is surrounded by stunning nature, and there's great surfing, swimming, fishing, bushwalking, horse riding and canoeing near town and in Kalbarri National Park. While the vibe is mostly low key, school holidays see Kalbarri stretched to the limit.
1 Sights & Activities
Kalbarri National Park
With its magnificent river red gums and Tumblagooda sandstone, rugged Kalbarri National Park (admission per car $11) contains almost 2000 sq km of wild bushland, stunning river gorges and savagely eroded coastal cliffs. There's abundant wildlife, including 200 species of birds, and spectacular wildflowers between July and November.
A string of lookouts dot the impressive coast south of town and the easy Bigurda Trail (8km one way) follows the clifftops between Natural Bridge and Eagle Gorge; from July to November you may spot migrating whales. Closer to town are Pot Alley , Rainbow Valley , Mushroom Rock and Red Bluff – the last being accessible via a walking trail from Kalbarri (5.5km one way).
The river gorges are east of Kalbarri, 11km down Ajana Kalbarri Rd to the turn-off, and then 20km unsealed to a T-intersection. Turn left for lookouts over The Loop and the superb Nature's Window (1km return). Bring lots of water for the unshaded Loop Trail (8km return). Turning right at the T leads to Z-Bend with a breathtaking lookout (1.2km return) or you can continue steeply down to the gorge bottom (2.6km return). Head back to Ajana Kalbarri Rd and travel a further 24km before turning off to Hawk's Head , where there are great views and picnic tables, and Ross Graham lookout , where you can access the river. It's possible to hike 38km from Ross Graham to The Loop in a demanding four-day epic, but be warned: there are no marked trails and several river crossings.
Kalbarri
Sights
1Chinamans BeachA3
2Swimming BeachB3
Activities, Courses & Tours
3 Kalbarri Air Charter C3
4 Kalbarri Boat Hire C3
5 Kalbarri Wilderness Cruises C3
6 Pelican Feeding C3
Sleeping
7 Anchorage Caravan Park C1
8 Kalbarri Backpackers D2
9 Kalbarri Reef Villas C2
10 Pelican Shore Villas B4
Pelican's Nest (see 8)
11 Ray White Kalbarri Accommodation Service B4
Eating
Angies Cafe (see 11)
12 Finlay's Fresh Fish BBQ C4
13 Gorges Café C1
14 Kalbarri Motor Hotel C3
Shopping
15 Marudi Designs C4
The Art Place (see 15)
Other Attractions
Kalbarri has a network of cycle paths along the foreshore, and you can ride out to Blue Holes for snorkelling, Jakes Point for surfing and fishing, and Red Bluff Beach , 5.5km away. Any of the lookouts along the coast are perfect for watching the sunset. Look for wildflowers along Siles Rd, River Rd and out near the airport; the visitor centre publishes regular wildflower updates in season.
Kalbarri Wildflower Centre GARDENS
( 08-9937 1229; adult/child $5/2, tours $10; 9am-1pm Wed-Mon Jun-Oct, tours 10am) Stroll 1.8km along a labelled wildflower trail, or take a guided tour. There's a small cafe on site. The gardens are located off Ajana Kal-barri Rd.
Pelican Feeding WILDLIFE WATCHING
OFFLINE MAP GOOGLE MAP
( 08-9937 1104; 8.45am) F Kalbarri's most popular attraction.
Kalbarri Boat Hire CANOEING
OFFLINE MAP GOOGLE MAP
( 08-9937 1245; www.kalbarriboathire.com; Grey St; kayak/canoe/surf cat/powerboat per hr $15/15/45/50) If it goes in the water, then these guys hire it out. They also run four-hour breakfast and lunch canoe trips down the Murchison (adult/child $65/45). You'll find them on the waterfront.
Kalbarri Abseil CANYONING
( 08-9937 1618; www.abseilaustralia.com.au; half-day abseil year round/full-day canyoning tours Apr-Nov only $80/135) Abseil into the sheer gorges of Kalbarri National Park, then float along the bottom on inner tubes.
Kalbarri Sandboarding SANDBOARDING
( 08-9937 2377; www.sandboardingaustralia.com.au; adult/child $80/70) Muck around on sand dunes, then go for a snorkel on these fun half-day tours.
Kalbarri Adventure Tours CANOEING
( 08-9937 1677; www.kalbarritours.com.au; adult/child $90/70) Combine canoeing, bushwalking and swimming around the park's Z-Bend/Loop area.
Big River Ranch HORSE RIDING
( 08-9937 1214; www.bigriverranch.net; 90min trail rides $85) Track through the beautiful Murchsion River floodplain on horseback. All experience levels catered for, and the overnight rides are the highlight. Camping (sites per person $10, powered sites $25) and rustic bunkhouse rooms (from $25 per person) are available. Off Ajana Kalbarri Rd.
T Tours
Here's a selection; the visitor centre has a full list and arranges bookings.
Kalbarri Air Charter SCENIC FLIGHTS
OFFLINE MAP GOOGLE MAP
( 08-9937 1130; www.kalbarriaircharter.com.au; 62 Grey St; flights $65-300) Offers 20-minute scenic flights over the coastal cliffs, and longer flights over gorges, the Zuytdorp Cliffs, Monkey Mia and the Abrolhos Islands.
Kalbarri Wilderness Cruises CRUISES
OFFLINE MAP GOOGLE MAP
( 08-9937 1601; kalbarricruises@westnet.com.au; adult/child $44/22) Runs popular two-hour licensed nature cruises along the Murchison.
Reefwalker Adventure Tours WHALE WATCHING
( 0417 931 091; www.reefwalker.com.au; adult/child $85/55) A chance to get up close to those migrating humpbacks (from July to November). Also runs ocean fishing and sightseeing tours.
OFF THE BEATEN TRACK
### Wooleen Station
Well and truly off the beaten track at roughly 200km from the closest asphalt, Wooleen Station ( 08-9963 7973; www.wooleen.com.au; Murchison; camp sites $25, d $170, homestead full board per person $190; Apr-Oct) S is a historic pastoral lease reinventing itself as an ecotourism destination. The emphasis is on conservation and land regeneration, trying to undo decades of erosion and degradation due to outdated farming practices. There's a variety of accommodation from dusty camp sites to an all-meals-included room in the heritage-listed homestead, but space is strictly limited, so book first before making that long drive. Wooleen is always looking for workers, and backpackers are welcome.
Head north from Mullewa on the Carnarvon Mullewa Rd or east on the Butchers Track just north of Billabong Roadhouse.
4 Sleeping
There's a lot of choice, but avoid school holidays, when prices skyrocket. The visitor centre is your friend.
Kalbarri Backpackers HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9937 1430; www.yha.com.au; cnr Woods & Mortimer Sts; dm/d $29/77, bike hire $20; ) This nice, shady hostel with a decent pool and BBQ is one block back from the beach. Bikes are available and staff also handle the shuttle out to the Greyhound stop on the highway at Binnu ($41).
Anchorage Caravan Park CARAVAN PARK $
OFFLINE MAP GOOGLE MAP
( 08-9937 1181; www.kalbarrianchorage.com.au; cnr Anchorage Lane & Grey St; powered sites $34, cabins with/without bathroom $100/70; ) The best option for campers, Anchorage has roomy, shaded sites overlooking the river mouth.
o Pelican's Nest MOTEL $$
OFFLINE MAP GOOGLE MAP
( 08-9937 1430; www.pelicansnestkalbarri.com.au; 45-47 Mortimer St; d $100-140; ) Adjoining Kalbarri Backpackers, the Nest has a selection of neat motel-style rooms (some with kitchenettes), and excellent facilities.
Pelican Shore Villas APARTMENTS $$
OFFLINE MAP GOOGLE MAP
( 08-9937 1708; www.pelicanshorevillas.com.au; cnr Grey & Kaiber Sts; villas $136-188; ) These beautiful manicured town houses have all the mod cons, and the best view in town.
Kalbarri Reef Villas APARTMENTS $$
OFFLINE MAP GOOGLE MAP
( 08-9937 1165; www.reefvillas.com.au; cnr Coles & Mortimer Sts; units $130-180; ) One block behind the foreshore, these fully self-contained two-storey, two-bedroom apartments face onto a palm-filled garden.
Ray White Kalbarri Accommodation Service ACCOMMODATION SERVICES $$$
OFFLINE MAP GOOGLE MAP
( 08-9937 1700; www.kalbarriaccommodation.com.au; Kalbarri Arcade, 44 Grey St; houses per week from $460) Has a wide range of self- contained apartments and houses.
5 Eating
Supermarkets and takeaways are at the shopping centres; bistros are at the taverns.
Angies Cafe CAFE $
OFFLINE MAP GOOGLE MAP
( 08-9937 1738; Shop 6, 46 Grey St; meals $8-20; 8am-4pm) Great little cafe offering fresh, tasty meals with a good selection of salads.
o Gorges Café CAFE $$
OFFLINE MAP GOOGLE MAP
( 08-9937 1200; Marina Complex, Grey St; meals $8-25; 7am-5pm Mon & Wed-Fri, to 2pm Sat & Sun) Ask at this airy cafe for its Morning Cure and you won't be disappointed; it serves up wonderful breakfasts and lunches, just opposite the jetty.
Kalbarri Motor Hotel PUB $$
OFFLINE MAP GOOGLE MAP
( 08-9937 1400; 50 Grey St; pizzas $22, mains $22-45) A cut above normal pub fare, with gourmet wood-fired pizzas, 'wok-of-the-day' and stand-out local seafood. Also has clean, basic rooms (doubles $105).
Finlay's Fresh Fish BBQ SEAFOOD $$
OFFLINE MAP GOOGLE MAP
( 08-9937 1260; 24 Magee Cres; mains $15-30; 5.30-8.30pm Tue-Sun) You'll either love it or hate it, but you'll certainly always remember your no-frills BBQ fish dinner at this Kalbarri institution, where the huge portions of fish come with lashings of (usually, but not always) tongue-in-cheek abuse.
7 Shopping
Marudi Designs ARTS & CRAFTS
OFFLINE MAP GOOGLE MAP
( 0487 419 820; Shop 2, 51 Hackney St; 9am-4pm) Fully indigenous owned and run gallery showcasing local Nhanda arts and crafts. Behind the tavern.
The Art Place ARTS & CRAFTS
OFFLINE MAP GOOGLE MAP
(Shop 3, 51 Hackney St; 10am-4pm Wed-Sun) Quirky gallery featuring local artists, glassblowers, jewellers and photographers. Behind the tavern.
8 Information
There are ATMs at the shopping centres on Grey and Porter Sts.
Kalbarri Community Resource Centre ( 08-9937 1933; Hackney St; 9am-3pm Mon-Fri; ) Fax and internet.
Book Nook ( 08-9937 2676; 10am-5pm Mon-Fri, to 4pm Sat & Sun; ) Internet and secondhand books.
Visitor Centre ( 1800 639 468; www.kalbarri.org.au; Grey St; 9am-5pm Mon-Sat) Great wildflower and activities info; also can book accommodation and tours. Internet is available at the library next door.
8 Getting There & Around
Skippers flies to Perth, Shark Bay and Carnarvon several times weekly.
Getting to/from Perth ($76, nine hours) and Geraldton ($27, two hours) by bus is easiest with Transwa at the visitor centre. Heading to/from points further north, Greyhound stops at Binnu on the highway, 77km away – arrange a shuttle from the YHA ( Click here ). From Binnu you can reach Overlander Roadhouse (for Monkey Mia, $52, two hours), Coral Bay ($106, eight hours) and Broome ($325, 26 hours). Integrity passes through Ajana on the way to Exmouth ($126, 10 hours).
Kalbarri Auto Centre ( 08-9937 1290) rents out 4WDs and sedans from $60 per day. Both bikes and scooters can be hired from Kalbarri Air Charter ( 08-9937 1130; 62 Grey St; bikes half-/full day $10/20, scooters half-/full day $45/85) , and bikes are also available from the YHA and the entertainment centre ( 08-9937 1105; 15 Magee Cres) . For a taxi, call 0419 371 888.
WORTH A TRIP
### HORROCKS & PORT GREGORY
The tiny seaside villages of Horrocks and Port Gregory, 92km and 68km south of Kalbarri, respectively, are as quiet as they come. Horrocks, the smaller and prettier of the two, has several accommodation options including the laid-back Horrocks Beach Caravan Park ( 08-9934 3039; www.horrocksbeachcaravanpark.com.au; sites $24-32, cabins $75-90; ) , right behind the dunes, and the nearby bargain, Beachside Cottages ( 08-9934 3031; www.northamptonaccommodation.com.au/horrocks_beachside_cottages.htm; 5 Glance St; d $75-85) . Port Gregory, on the far side of the mysterious Pink Lakes, and with a fringing reef, is great for fishing and snorkelling. Port Gregory Caravan Park ( 08-9935 1052; www.portgregorycaravanpark.com.au; powered sites $32, cabins $85-115) is your best choice.
## Shark Bay
The World Heritage–listed area of Shark Bay, stretching from Kalbarri to Carnarvon, consists of more than 1500km of spectacular coastline, containing turquoise lagoons, barren finger-like peninsulas, hidden bays, white-sand beaches, towering limestone cliffs and numerous islands. It's the westernmost part of the Australian mainland, and one of WA's most biologically rich habitats, with an array of plant and animal life found nowhere else on earth. Lush beds of sea-grass and sheltered bays nourish dugongs, sea turtles, humpback whales, dolphins, stingrays, sharks and other aquatic life. On land, Shark Bay's biodiversity has benefited from Project Eden, an ambitious ecosystem-regeneration program that has sought to eradicate feral animals and reintroduce endemic species. Shark Bay is also home to the amazing stromatolites of Hamelin Pool.
The Malgana, Nhanda and Inggarda peoples originally inhabited the area, and visitors can take indigenous cultural tours to learn about country. Shark Bay played host to early European explorers and many geographical names display this legacy. In 1616, Dutch explorer Dirk Hartog nailed a pewter dinner plate (now in Amsterdam's Rijksmuseum) to a post on the island that now bears his name. Dirk Hartog Island is WA's largest.
### 8 SEASIDE BUSH CAMPING
Shark Bay shire offers a choice of four coastal bush camp sites, Goulet Bluff , Whalebone , Fowlers Camp and Eagle Bluff , all 20km to 40km south of Denham in the area known as South Peron. To camp here, you must first obtain a permit ($10 per vehicle) from the Shark Bay visitor centre ( Click here ). While this is easily arranged via phone (if yours has any reception), in practice it's better to scope the sites first, then get the permit. There are no facilities and a one-night limit applies to the whole area.
8 Getting There & Away
Shark Bay airport is located between Denham and Monkey Mia. Skippers flies to Perth six times weekly, with some return flights via Kalbarri.
The closest Greyhound and Integrity approach is the Overlander Roadhouse, 128km away on the North West Coastal Hwy. Shark Bay Car Hire ( 0427 483 032; www.carhire.net.au; 65 Knight Tce, Denham; shuttle $67, car/4WD hire per day $95/185) runs a connecting shuttle (book ahead!).
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Overlander Roadhouse to Denham
Twenty-nine kilometres along Shark Bay Rd from the Overlander Roadhouse is the turn-off for Hamelin Pool (not nearby Hamelin Station!), a marine reserve that contains the world's best-known colony of stromatolites. These coral-like formations consist of cyanobacteria almost identical to organisms that existed 3.5 billion years ago, and, through their use of photosynthesis, are considered largely responsible for creating our current atmosphere, paving the way for more complex life. There's an excellent boardwalk with information panels, best seen at low tide.
The nearby 1884 Telegraph Office (admission $5.50; check at shop) houses a fascinating museum containing possibly the only living stromatolites in captivity. The Postmasters Residence is also the office for the tiny Hamelin Pool Caravan Park ( 08-9942 5905; Hamelin Pool; unpowered/powered sites $22/27) and serves Devonshire teas, pies and ice creams.
Along the road you pass the turn-off for Hamelin Station ( 08-9948 5145; www.hamelinstationstay.com.au; sites per person $12, s/d/f $60/90/120) , which has lovely rooms in converted shearers' quarters, top-class amenities and somewhat arid camp sites. There's great bird life at the nearby waterhole.
As Shark Bay Rd swings north, you'll pass the turn-off for Useless Loop (a closed salt-mining town), Edel Land and Steep Point , the Australian mainland's most westerly tip.
The dusty former sheep station Nanga Bay Resort ( 08-9948 3992; www.nangabayresort.com.au; Nanga Bay; unpowered/powered sites $25/30, dongas/motel r/huts/villas $50/165/180/250; ) has a range of accommodation. The Fishermens Huts, which sleep four to six people, have good views, but some of the other options are a little depressing.
Inside the vermin-proof fence, and 55km from the Hamelin turn-off, is the road to deserted Shell Beach , where tiny cockle shells, densely compacted over time, were once quarried as building material for places like the Old Pearler Restaurant in Denham.
You'll pass turn-offs to bush camp sites before reaching Eagle Bluff , which has cliff-top views overlooking an azure lagoon. You may spot turtles, sharks or manta rays.
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Denham
pop 1500
Beautiful, laid-back Denham, with its aquamarine sea and palm-fringed beachfront, makes a great base for trips to the surrounding Shark Bay Marine Park, nearby François Peron and Dirk Hartog Island National Parks, and Monkey Mia, 26km away.
Australia's westernmost town originated as a pearling base, and the streets were once paved with pearl shell. Knight Tce, the now-tarmac main drag, has everything you will need.
1 Sights & Activities
o Shark Bay World Heritage Discovery Centre MUSEUM
( 08-9948 1590; www.sharkbayvisit.com; 53 Knight Tce; adult/child $11/6; 9am-5pm Mon-Fri, 10am-4pm Sat & Sun) Informative and evocative displays of Shark Bay's ecosystems, marine and animal life, indigenous culture, early explorers, settlers and shipwrecks.
Ocean Park AQUARIUM
( 08-9948 1765; www.oceanpark.com.au; Shark Bay Rd; adult/child $20/12; 9am-5pm) Superbly located on a headland just before town, this family-run aquaculture farm features an artificial lagoon where you can take a 60-minute guided tour to observe feeding sharks, turtles, stingrays and fish. The licensed cafe has sensational views, and it also conducts full-day 4WD tours with bushwalks and snorkelling to François Peron National Park ($180) and Steep Point ($350).
Little Lagoon LANDMARK
Little Lagoon, 4km from town, is a pleasant picnic spot with tables and barbecues; you can walk, drive or cycle there. Don't be surprised if an emu wanders by.
OFF THE BEATEN TRACK
### Way Out West in Edel Land
The Australian mainland's westernmost tip is Steep Point , just below Dirk Hartog Island. It's a wild, wind-scarred, barren clifftop with a beauty born of desolation and remoteness. The Zuytdorp Cliffs stretch away to the south, the limestone peppered with blowholes, while leeward, bays with white sandy beaches provide sheltered camp sites. The entire area is known as Edel Land , soon to become a national park. Anglers have been coming here for years to go game fishing off the towering cliffs, but few tourists make the 140km rough drive down a dead-end road.
Access to the area is via Useless Loop Rd, and is controlled by the Department of Environment and Conservation (DEC; 08-9948 3993; entry permit per vehicle $11, sites per person $7) . There is a ranger station at Shelter Bay , with camping nearby; at Steep Point (rocky and exposed); and at False Entrance to the south. Sites are strictly limited and must be booked in advance. You'll need a high-clearance 4WD as the road deteriorates past the Useless Loop turn-off (approximately 100km from Shark Bay Rd). Tyres should be deflated to 20psi. Ensure you bring ample water and enough fuel to return to the Overlander Roadhouse (185km) or Denham (230km). During winter, a barge runs from Shelter Bay to Dirk Hartog Island (bookings essential). The website www.sharkbay.org.au has all the details and downloadable permits. Hire-car companies will not insure for this road, though (expensive) tours can be arranged from Denham. The drive is pure adventure; Steep Point is probably more easily reached by boat, but then that's not the Point, is it?
T Tours
Aussie Off Road Tours DRIVING TOUR
( 0429 929 175; www.aussieoffroadtours.com.au) Culture, history, wildlife and bush tucker feature in these excellent indigenous-owned and -operated 4WD tours, including twilight wildlife ($90), full-day François Peron National Park ($189) or Shell Beach/Hamelin ($200), overnight camping in François Peron ($300) and overnight to Steep Point ($390).
Shark Bay Scenic Flights SCENIC FLIGHTS
( 0417 919 059; www.sharkbayair.com.au) Offers various scenic flights, including 15-minute Monkey Mia flyovers ($59) and a sensational 40-minute trip over Steep Point and the Zuytdorp Cliffs ($175). Ask if the planned Dirk Hartog Island fly/drive tour to Cape Inscription is running, as this would be spectacular. Planes are also available for one-way charters to/from the Overlander Roadhouse ($140).
Shark Bay Coaches & Tours TOUR
( 08-9948 1081; www.sbcoaches.com; bus/quad bike $80/$90) Half-day bus tours to all key sights and two-hour quad-bike tours to Little Lagoon.
4 Sleeping & Eating
Denham has accommodation for all budgets, and some places offer long-stay discounts and/or school-holiday surcharges. There's a pub, a supermarket, a bakery, cafes and takeaways on Knight Tce.
o Bay Lodge HOSTEL $
( 08-9948 1278; www.baylodge.info; 113 Knight Tce; dm/d from $26/68; ) Every room at this YHA hostel has its own en suite, kitchenette and TV/DVD player. Ideally located across from the beach, it also has a great pool, a large common kitchen, and a shuttle bus to Monkey Mia.
Denham Seaside Tourist Village CARAVAN PARK $
( 1300 133 733; www.sharkbayfun.com; Knight Tce; sites unpowered/powered/with bathroom $30/37/45, d cabins $80, 1-/2-bedroom chalets $125/135; ) This lovely, shady park on the water's edge is the best in town, though you will need to borrow the drill for your tent pegs. Cover up at night against the insects and ring first if arriving after 6pm.
Oceanside Village CABINS $$
( 1800 680 600; www.oceanside.com.au; 117 Knight Tce; cabins $160-200; ) These neat self-catering cottages with sunny balconies are perfectly located directly opposite the beach.
Tradewinds APARTMENTS $$
( 1800 816 160; www.tradewindsdenham.com.au; Knight Tce; units $140-160; ) Spacious, fully self-contained, modern units right across from the beach.
Ray White ACCOMMODATION SERVICES $$
( 08-99481323; www.raywhitesb.com; Knight Tce; flats per night $100-240; 8am-5pm Mon-Fri, 9am-noon Sat) Looking for a self-contained flat? These guys usually have a list of everything available in town.
o Old Pearler Restaurant SEAFOOD $$$
( 08-9948 1373; 71 Knight Tce; meals $30-49; dinner Mon-Sat) Built from shell bricks, this atmospheric nautical haven serves fantastic seafood. The exceptional platter features local snapper, whiting, cray, oysters, prawns and squid – all grilled, not fried. BYO.
Ocean Restaurant CAFE $$
(www.oceanpark.com.au; Shark Bay Rd; mains $19-32; 9am-5pm; ) The most refined lunch in Shark Bay also comes with the best view. Inside Ocean Park, overlooking turquoise waters, you can choose from mouth-watering tapas, all-day brekkies or tantalising local seafood dishes. Fully licensed.
6 Drinking
Shark Bay Hotel PUB
( 08-9948 1203; www.sharkbayhotelwa.com.au; 43 Knight Tce; 10am-late) Sunsets are dynamite from the beer garden of the mainland's most westerly pub (dinner $22 to $38).
8 Information
There are ATMs at Heritage Resort and Shark Bay Hotel, and internet access at the CRC ( 08-9948 1787; 67 Knight Tce; ) and post office.
Department of Environment & Conservation ( 08-9948 1208; www.dec.gov.au; 61-63 Knight Tce; 8am-5pm Mon-Fri) Park passes and information.
Shark Bay Home Page (www.sharkbay.org.au) Great information, interactive maps and downloadable permits.
Shark Bay Visitor Centre ( 08-9948 1590; www.sharkbayvisit.com; 53 Knight Tce; 9am-5pm Mon-Fri, 10am-4pm Sat & Sun) The very informative staff handle accommodation and tour bookings and issue bush-camping permits for South Peron. Located in the foyer of the Shark Bay World Heritage Discovery Centre.
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François Peron National Park
Covering the whole peninsula north of Denham is an area of low scrub, salt lakes and red sandy dunes, home to the rare bilby, mallee fowl and woma python. There's a scattering of rough camp sites (per person $7) alongside brilliant white beaches, all accessible via 4WD (deflate tyres to 20psi). Don't miss the fantastic Wanamalu Trail (3km return), which follows the cliff top between Cape Peron and Skipjack Point, from where you can spot marine life in the crystal waters below. Those with 2WD can enter only as far as the old Peron Homestead , where there's a short 'lifestyle' walk around the shearing sheds, and an artesian-bore hot tub to soak in. Park entry is $11 per vehicle. Tours start at around $180 from Denham or Monkey Mia, but if there's a group of you, consider hiring your own 4WD from Denham for the same price.
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Monkey Mia
Watching the wild dolphins turning up for a feed each morning in the shallow waters of Monkey Mia (adult/child/family $8/3/16) , 26km northeast of Denham, is a highlight of every traveller's trip to the region. Don't be put off by the resort vibe – once you see these beautiful, intelligent mammals up close you'll forget about everything else. Watch the way they herd fish upside down, trying to trap them against the surface. The pier makes a good vantage point. The first feed is around 7.45am, but you'll see them arrive earlier, and hang around after the session, as the dolphins commonly come a second, and sometimes even a third time.
Monkey Mia Visitors Centre ( 08-9948 1366; 8am-4pm) has a good range of publications, information and tours.
You can volunteer to work full time with the dolphins for between four and 14 days; it's popular, so apply several months in advance and specify availability dates, though sometimes there are last-minute openings. Contact the volunteer coordinator ( 08-9948 1366; monkeymiavolunteers@westnet.com.au) .
T Tours
Wula Guda Nyinda Aboriginal Cultural Tours INDIGENOUS CULTURE
( 0429 708 847; www.wulaguda.com.au; 90min tours adult/child from $50/25) Learn 'how to let country talk to you' on these amazing bushwalks led by local Aboriginal guide Darren 'Capes' Capewell. You'll pick up some local Malgana language and identify bush tucker and indigenous medicine. The evening 'Didgeridoo Dreaming' tours (adult/child $60/30) are magical. There are also 'Saltwater Dreaming' kayak tours (adult half-/full day $120/165).
Aristocat II CRUISE
( 1800 030 427; www.monkey-mia.net; 1/2½hr tours $45/80) Cruise in comfort on this large catamaran, and you might see dugongs, dolphins and loggerhead turtles. You'll also stop off at the Blue Lagoon Pearl Farm .
Wildsights ADVENTURE TOUR
( 1800 241 481; www.monkeymiawildsights.com.au) On the small _Shotover_ catamaran you're close to the action; 2½-hour wildlife cruises start from $79. There are also 1½-hour sunset cruises ($39) and full-day 4WD trips to François Peron National Park ($195); discounts are available for multiple trips.
4 Sleeping & Eating
Monkey Mia is a resort and not a town, so eating and sleeping options are limited to the Monkey Mia Dolphin Resort. Self-catering is a good option.
Monkey Mia Dolphin Resort RESORT $$$
( 1800 653 611; www.monkeymia.com.au; tent sites per person $15, van sites from $39, dm/d $30/89, garden units $223, beachfront villas $315; ) Although the location is stunning, trying to cater for all markets, including campers, backpackers, package and top-end tourists, is never a great idea. The staff are friendly, and the backpacker 'shared en suites' are good value, but the same can't be said of the top-end rooms. This place gets seriously crowded and at times sounds like a continuous party. The restaurant has sensational water views but bland, overpriced meals, while the backpacker bar has cheaper food and liquored-up backpackers.
8 Getting There & Away
There is no public transport to Monkey Mia from Denham. If you stay at Bay Lodge in Denham, you can use its shuttle but it only runs alternate days. Your other options are hiring a car or bicycle.
## Gascoyne Coast
This wild, rugged, largely unpopulated coastline stretches from Shark Bay to Ningaloo, with excellent fishing, and waves that attract surfers from around the world. Subtropical Carnarvon, the region's hub, is an important fruit- and vegetable-growing district, and farms are always looking for seasonal workers. The 760km Gascoyne River, WA's longest, is responsible for all that lushness, though it flows underground for most of the year. Inland, the distances are huge and the temperatures high; here you'll find the ancient eroded rocks of the Kennedy Range, as well as massive Mt Augustus (Burringurrah).
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Carnarvon
pop 9000
On Yinggarda country at the mouth of the Gascoyne River, fertile Carnarvon, with its fruit and vegetable plantations and thriving fishing industry, makes a pleasant stop-over between Denham and Exmouth. This friendly, vibrant town has quirky attractions, a range of decent accommodation, well-stocked supermarkets and great local produce. The tree-lined CBD exudes a tropical feel, and the palm-fringed waterfront is a relaxing place to amble. The long picking season from March to January ensures plenty of seasonal work. Floods devastated the area in December 2010 and many businesses are still recovering.
1 Sights & Activities
Established jointly with NASA in 1966, the OTC Dish (Mahony Ave) at the edge of town tracked Gemini and Apollo space missions, as well as Halley's Comet, before closing in 1987. Stage One of the small but fascinating Carnarvon Space and Technology Museum (Mahony Ave; admission $5; 10am-3pm) is nearby.
Carnarvon's luxuriant plantations along North and South River Rds provide a large proportion of WA's fruit and veg; grab the Gascoyne Food Trail (www.gascoynefood.com.au) brochure from the visitor centre. Bumbak's ( 08-9941 8006; 449 North River Rd; 1hr tours $8.80; shop 9am-4pm Mon-Fri, tours 10am Mon, Wed & Fri Apr-Oct) offers tours and sells a variety of fresh and dried fruit, preserves and yummy home-made ice cream. Check out the delicious produce at the Gascoyne Arts, Crafts & Growers Market (Civic Centre car park; 8-11.30am Sat May-Oct) .
You can walk or ride 2.5km along the old tramway to the Heritage Precinct on Babbage Island, once the city's port. One Mile Jetty (admission tram/walking $7/4; 9am-4.30pm) provides great fishing and views; walk or take the vintage tram to the end. The nearby Lighthouse Keepers Cottage (Heritage Precinct; 10am-1pm) has been painstakingly restored; don't miss the view from the top of the creaky water tower in the Railway Station Museum ( 9am-5pm) .
Gwoonwardu Mia ( 08-9941 1989; gahcc@gahcc.com.au; 146 Robinson St; 10am-3pm Mon-Fri) , built to depict a cyclone, represents the five local Aboriginal language groups and houses a cultural centre, art gallery, interpretive garden and the hospitality-training Yallibiddi Café.
September to March windsurfers head to Pelican Point, while novice (or advanced) kiteboarders can learn some new skills from Kitemix ( 0400 648 706; www.kitemix.com; lessons per hr from $80; Sep-Mar) .
The last weekend of October sees the town taken over by desert riders competing in the gruelling 511km Gascoyne Dash (Gassy Dash; www.gasdash.com) .
The palm-lined walking path along the side of the Fascine (the body of water at the end of Robinson St) is a pleasant place for a wander, especially at sunset.
4 Sleeping
Most accommodation, including numerous caravan parks, is spread out along the 5km feeder road from the highway. Try to arrive before 6pm.
o Fish & Whistle HOSTEL $
( 08-9941 1704; 35 Robinson St; dm/s $30/45, motel r $99; ) Travellers love this big, breezy backpackers with its wide verandahs, bunk-free rooms, enormous communal spaces, excellent kitchen and happy vibe. There are air-con motel rooms out the back, discounts for longer stays and the revamped Port Hotel serving decent beer downstairs. The owners can help guests find seasonal jobs, and provide transport to work every day ($25 per week).
Capricorn Holiday Park CARAVAN PARK $
( 08-9941 8153; www.capricornholidaypark.com.au; 1042 North West Coastal Hwy; sites d $36, cabins $120; ) Out on the highway, this peaceful, friendly park has lots of shade, a covered pool, grassy sites and lovely bougainvillea.
Coral Coast Tourist Park CARAVAN PARK $
( 08-9941 1438; www.coralcoasttouristpark.com.au; 108 Robinson St; powered sites $35, cabins $75-155, bicycles half-/full day $10/15; ) This pleasant, shady park, with tropical pool and grassy sites, is the closest to the town centre. There's a variety of well-appointed cabins, a decent camp kitchen, and bicycles for hire.
Carnarvon Central Apartments APARTMENTS $$
( 08-9941 1317; www.carnarvonholidays.com; 120 Robinson St; 2-bedroom apt $135; ) These neat, fully self-contained apartments are popular with business travellers.
Hospitality Inn MOTEL $$
(Best Western; 08-9941 1600; www.carnarvon.wa.hospitalityinns.com.au; 6 West St; d/f $169/199) The best of the motels in town. Rooms are clean and quiet and there's a nice on-site restaurant (meals $19 to $42).
5 Eating
The 2010 floods nobbled the fine-dining scene, and most eateries reverted to standards like burgers and steaks. Hopefully all that great produce will lure the chefs back. Otherwise, hit the markets and cook your own on the free BBQs along the Fascine and at Baxter Park. Knight Tce has takeaways and some early-opening cafes.
Morel's Orchard MARKET $
( 08-9941 8368; 486 Robinson St; 8.30am-5.30pm) A great selection of local fresh fruit and vegetables, as well as natural fruit ice creams.
Yallibiddi Café CAFE $$
( 08-9941 3127; 146 Robinson St; mains $10-20; 9am-3pm Mon-Fri) This training cafe was previously doing great things with bush tucker but now seems content to churn out roo burgers and chicken satays.
Hacienda Crab Shack SEAFOOD $$
( 08-9941 4078; Small Boat Harbour; 9am-4pm, shorter hr Sun) Got an esky? Then fill it with freshly steamed crabs, prawns, mussels, shucked oysters and fish fillets from this fishmonger.
Waters Edge MODERN AUSTRALIAN $$
( 08-9941 1181; www.thecarnarvon.com.au; 121 Olivia Tce; mains $25-46; 6-9pm Tue-Sat) Perfectly situated to capture the sunset over the Fascine, the restaurant out the back of the Carnarvon Hotel has a good selection of seafood and steaks. It also has clean, basic rooms (singles/doubles $65/80).
7 Shopping
Books & Stuff BOOKS
( 08-9941 2265; 2 Robinson St; 10am-1pm Mon-Fri) An eclectic collection of new, old and local books, with a nice 'reading' courtyard. BYO coffee.
8 Information
There's a post office on Camel Lane and ATMs on Robinson St.
Visitor Centre ( 08-9941 1146; www.carnarvon.org.au; Civic Centre, 21 Robinson St; 9am-5pm Mon-Fri, to noon Sat; ) Very helpful, with information, maps, local books and produce.
8 Getting There & Around
Skippers flies daily to Perth, and less often to Geraldton, Shark Bay and Kalbarri.
Greyhound buses head to Perth ($175, 13 hours), Broome ($293, 21 hours) and Coral Bay ($37, three hours) three times per week. Integrity runs twice weekly to Exmouth ($79, four hours), Geraldton ($99, six hours) and Perth ($144, 12 hours). All buses depart from the visitor centre.
Bikes can be hired from Coral Coast Tourist Park ( Click here ).
For a taxi, call 131 008.
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Point Quobba to Gnaraloo Bay
While the North West Coastal Hwy heads inland, the coast north of Carnarvon is wild, windswept and desolate, a favourite haunt of surfers and fisherfolk. Not many make it this far, but those who do are rewarded by huge winter swells, high summer temperatures, relentless winds, amazing marine life, breathtaking scenery and some truly magical experiences.
Turn down Blowholes Rd, 12km after the Gascoyne bridge, then proceed 49km along the sealed road to the coast. The blowholes (waves spraying out of limestone chimneys during a big swell) are just left of the T-intersection. Point Quobba , 1km further south, has beach shacks, excellent fishing, some gritty camp sites (sites $5.50) , and not much else.
Heading right from the T onto dirt, after 8km you'll come across a lonely little cairn staring out to sea, commemorating HMAS _Sydney II._ Two kilometres further is Quobba Station ( 9948 5098; www.quobba.com.au; unpowered/powered sites $11/13.50, cabins per person $25-60) , with plenty of rustic accommodation, a small store and legendary fishing.
Still on Quobba, 60km north of the homestead, Red Bluff ( 08-9948 5001; www.quobba.com.au; unpowered sites per person $12, shacks per person from $20, bungalows/safari retreats $170/$345) is a spectacular headland with a wicked surf break, excellent fishing and the southern boundary of Ningaloo Marine Park. Accommodation comes in all forms, from exposed camp sites and palm shelters, to exclusive upmarket safari tents with decking and superb views. Red Bluff's first shark attack happened in 2012.
The jewel, however, is at the end of the road around 150km from Carnarvon: Gnaraloo Station ( 08-9942 5927; www.gnaraloo.com; unpowered sites per person $20, cabins d $130-210; ) S . Surfers from around the world come every winter to ride the notorious Tombstones , while summer brings turtle monitoring and windsurfers trying to catch the strong afternoon sea breeze, the 'Carnarvon Doctor'. There's excellent snorkelling close to shore and the coastline north from Gnaraloo Bay is eye-burningly pristine. You can stay in rough camp sites next to the beach at 3-Mile , or there's a range of options up at the homestead, the nicest being stone cabins with uninterrupted ocean views – great for spotting migrating whales (June to November) and sea eagles. Gnaraloo is dedicated to sustainability and has implemented a number of visionary environmental programs. The station is always looking for willing workers, and there's such a nice vibe happening that many folk come for a night and end up staying months. Who could blame them?
# Coral Coast & the Pilbara
#### Coral Coast & the Pilbara Highlights
#### Coral Coast
#### Coral Bay
#### Exmouth
#### Around Exmouth
#### Ningaloo Marine Park
#### Cape Range National Park
#### The Pilbara
#### Dampier to Roebourne
#### Millstream-Chichester National Park
#### Karijini National Park
#### Port Hedland
Coral Coast & the Pilbara
### Why Go?
Lapping on the edge of the Indian Ocean, the shallow, turquoise waters of the Coral Coast nurture a unique marine paradise. World Heritage–listed Ningaloo Reef is one of the very few places you can swim with the world's largest fish, the gentle whale shark. Lonely bays, deserted beaches and crystal-clear lagoons offer superb snorkelling and diving among myriad sea life including humpback whales, manta rays and loggerhead turtles. Development is low-key, towns few and far between, and seafood and sunsets legendary.
Inland, miners swarm like ants over the high, eroded ranges of the Pilbara, while ore trains snake down to a string of busy ports stretching from Dampier to Port Hedland. But hidden in the hills are two beautiful gems – Karijini and Millstream-Chichester National Parks, home to spectacular gorges, remote peaks, deep tranquil pools and abundant wildlife.
### When to Go
Apr–Jul Whale shark season – don't miss the swim of a lifetime.
Sep & Oct Karijini's gorges warm up and wildflowers blanket the ranges.
Nov–Mar Ningaloo is full of turtle love, eggs and hatchlings.
### Best Places to Eat
» Whalers ( Click here )
» Karijini Eco Retreat ( Click here )
» Ningaloo Health ( Click here )
» Silver Star ( Click here )
» Samson Beach Bistro ( Click here )
### Best Places to Swim
» Turquoise Bay ( Click here )
» Coral Bay ( Click here )
» Fern Pool ( Click here )
» Deep Reach Pool ( Click here )
» Hamersley Gorge ( Click here )
## Coral Coast & the Pilbara Highlights
Swimming with whale sharks in Ningaloo Marine Park (Click here )
Snorkelling over marine life at Turquoise Bay (Click here )
Descending to the 'centre of the earth' on a gorge tour of Karijini National Park (Click here )
Scuba diving off the Navy Pier at Point Murat ( Click here ), one of the world's finest shore dives
Watching the annual humpback-whale migration at the North West Cape (Click here )
Cooling off in an idyllic waterhole at Millstream-Chichester National Park (Click here )
Tracking turtles on remote beaches and becoming a certified 'turtle guide' at the Jurabi Turtle Centre (Click here )
Spotting rare black-flanked rock wallabies on a cruise into stunning Yardie Creek Gorge (Click here )
Peak bagging on the state's highest peaks in Karijini National Park (Click here )
Enjoying a real coffee in the 1930s American Silver Star Railcar in Port Hedland ( Click here )
8 Getting There & Around
Air
The following airlines service the Coral Coast and the Pilbara.
Airnorth ( 1800 627 474; www.airnorth.com.au)
Alliance Airlines ( 1300 780 970; www.allianceairlines.com.au) Perth to Karratha.
Qantas ( 13 13 13; www.qantas.com.au)
Skywest ( 1300 660 088; www.skywest.com.au)
Virgin Australia ( 13 67 89; www.virginaustralia.com)
Bus
Greyhound ( 1300 473 946; www.greyhound.com.au) runs three times weekly between Broome and Perth along the coast.
Integrity ( 1800 226 339; www.integritycoachlines.com.au) runs weekly between Perth and Port Hedland via Newman on the inland Great Northern Hwy and twice weekly to Exmouth on the coastal route.
## Coral Coast
Top of Chapter
Coral Bay
pop 255
Beautifully situated just north of the Tropic of Capricorn, the tiny seaside village of Coral Bay is one of the easiest locations to access the exquisite Ningaloo Marine Park. Consisting of only one street and a sweeping white-sand beach, the town is small enough to enjoy on foot, making it popular with families. It's also a great base for outer-reef activities like scuba diving, fishing and whale watching (June to November), and tourists flock here in the winter months to swim with whale sharks (April to July) and manta rays.
Development is strictly limited, so expect higher prices for food and accommodation. Exmouth, 118km away, has more options. There are ATMs at the shopping centre and the Peoples Park grocer, and internet access at some of the tour outlets and Fins Cafe. The town is chockers from April to October.
1 Sights & Activities
Keep to the southern end of Bills Bay when swimming; the northern end (Skeleton Bay) is a breeding ground for reef sharks. There's good snorkelling in the bay, and it's even better at Purdy Point ; walk 500m south along the coast until you see the 8km/h marker, then drift with the current back to the bay. You can hire snorkel gear anywhere in town.
Fish feeding occurs on the beach at 3.30pm every day and sunsets are sublime from the lookout above the beach car park.
Ningaloo Kayak Adventures KAYAKING
( 08-9948 5034; www.ningalookayakadventures.com; 2/3hr tours $50/70) Various length kayak tours with snorkelling are available from the main beach. You can also hire a glass-bottom canoe ($25 per hour), wetsuit and snorkelling gear ($15 per day).
Ningaloo Reef Dive DIVING
( 08-9942 5824; www.ningalooreefdive.com) This PADI and eco-certified dive crew offers snorkelling with whale sharks ($390, late March to July) and manta rays ($150, all year), half-day reef dives ($170) and a full range of dive courses (from $380).
Ningaloo Marine Interactions SNORKELLING
( 08-9948 5190; www.mantaraycoralbay.com.au; 2hr/half-/full day $75/170/210; Jun-Oct, manta rays all year) S Informative and sustainably run tours to the outer reef include whale watching, manta-ray interaction and wildlife spotting with snorkelling.
T Tours
Popular tours from Coral Bay include swimming with whale sharks, spotting marine life (whales, dolphins, dugongs, turtles and manta rays), coral viewing from glass-bottom boats, and quad-bike trips. Tour operators have offices in the shopping centre and caravan parks; the following is only a small selection.
Coral Bay Ecotours BOAT TOUR
( 08-9942 5885; www.coralbayecotours.com.au; 1/2/3hr $39/54/75, all day $140) S Eco-certified and carbon-neutral tours include glass-bottom boat cruises with snorkelling, and all-day wildlife-spotting trips with manta-ray interaction. Scenic flights are also available.
Coral Coast Tours DRIVING TOUR
( 0427 180 568; www.coralcoasttours.com.au; half-day 4WD adult/child $135/78, snorkelling 2/3hr $55/75) Explore the wildlife along the rugged 4WD coastal tracks of Warroora Station, or try your hand at Blo Karting (sand yachting) on nearby salt lakes ($50 per hour). It also runs reef tours and offers airport transfers ($80), continuing on to Exmouth ($100).
Sail Ningaloo SAILING
( 1800 197 194; www.sailningaloo.com.au; 3-day tours from $1700; Mar-Dec) The fully cashed-up can select from a number of multi-day reef-sailing cruises aboard the catamaran _Shore Thing_ .
### STATION STAYS
If you're sick of cramped caravan parks and want to escape the hordes, or just stay somewhere a little more relaxed and off the beaten track, consider a station stay. Scattered around the Coral Coast are a number of sheep and cattle stations (some former, some still working) that offer varying styles of accommodation – it may be an exquisite slice of empty coast or a dusty spot in the home paddock, a basic room in the shearers' quarters or a fully self-contained, air-conditioned cottage.
Don't expect top-notch facilities; in fact, a lot of sites don't have any at all. Power and water are at a premium, so the more self-sufficient you are, the more you will enjoy your stay – remember, you're getting away from it all. What you will find is loads of wildlife, stars you've never seen before, oodles of space, some fair-dinkum outback and an insight into station life.
Some stations offer wilderness camping away from the main homestead (usually by the coast) and you'll need a 4WD for access and a chemical toilet. These places tend to cater for fisher-types with boats and grey nomads who stay by the week.
Some stations only offer accommodation during the peak season (April to October).
» Warroora ( 08-9942 5920; www.warroora.com; Minilya Exmouth Rd; camping per day/week $7.50/37.50, r per person $30, cottages $130) Offers wilderness camp sites along the coast and cheap rooms in the shearers' quarters as well as a self-contained cottage and homestead. It's 47km north of Minilya.
» Bullara ( 08-9942 5938; www.bullara-station.com.au; Burkett Rd; camping $12, tw/d/ cottages $100/130/220; Apr-Oct) Has four queen and two twin-share rooms in renovated shearers' quarters, unpowered camping and a communal kitchen (BYO food). Also runs half-day station tours ($110). It's 70km north of Coral Bay.
» Giralia ( 08-9942 5937; www.giraliastation.com.au; Burkett Rd; camping per person $10, budget s/d $60/70, 4-person cottages $160, homestead r $260; ) Well set up for travellers, with a bush-camping area (some powered sites) and kitchen, budget rooms with shared bathroom, a family cottage and air-conditioned homestead rooms with breakfast and dinner included. The coast is 40 minutes away by 4WD. Meals and liquor are available. It's 110km north of Coral Bay.
4 Sleeping & Eating
Avoid school holidays and book well ahead for peak season (April to October). Holiday houses can be rented online from www.coralbay.org, starting from $950 per week.
The shopping-centre bakery (Robinson St ; 6.30am-5.30pm) is the best option for early risers and vegetarians with its muesli and salad rolls. Seriously consider self-catering, as eating out is expensive.
Peoples Park Caravan Village CARAVAN PARK $
( 08-9942 5933; www.peoplesparkcoralbay.com; sites unpowered $36, powered $42-52, 1-/2-bedroom cabins $240/260, hilltop villas $285; ) This excellent park offers grassy, shaded sites and a variety of fully self-contained cabins. Friendly staff keep the modern amenities and spacious camp kitchen spotless, and it's the only place with freshwater showers. The hilltop villas have superb views, there are plenty of BBQs scattered around, and internet access is available at nearby Fins Cafe.
Ningaloo Club HOSTEL $
( 08-9948 5100; www.ningalooclub.com; Robinson St; dm $27-30, d with/without bathroom $120/95; ) Popular with the party crowd, this friendly, vibey hostel is a great place to meet people, and boasts a central pool, a well-equipped kitchen and a bar featuring live music. The rooms could be cleaner, and forget about sleeping before the bar closes. It also sells bus tickets (coach stop outside) and discounted tours.
Ningaloo Reef Resort RESORT $$$
( 1800 795 522; www.ningalooreefresort.com.au; d/apt from $216/276, penthouses $385; ) Among palms just above the beach, this resort has a combination of well-appointed motel-style rooms and larger apartments, with garden or ocean views. It's also the local pub, with happy hours (Tuesday and Friday) and live-music Thursday attracting a crowd. Shades restaurant (mains $13 to $45) delivers predictable fare.
Fins Cafe INTERNATIONAL $$
( 08-9942 5900; Peoples Park; dinner mains $28-36; breakfast, lunch & dinner; ) Book ahead for dinner at this intimate, outdoor BYO cafe with its ever-changing blackboard menu showcasing local seafood, Asian-style curries and Mediterranean–Oz fusion dishes.
Reef Cafe ITALIAN $$
( 08-9942 5882; mains $21-36; 6pm-late) While this licensed family-friendly bistro features seafood and steaks, most people come for its pizzas and gelato.
8 Getting There & Away
Coral Bay is 1144km north of Perth and 152km south of Exmouth, off the Minilya–Exmouth Rd.
Both Qantas and Skywest fly into Exmouth's Learmonth Airport, 118km to the north; most Coral Bay resorts can arrange a private shuttle on request.
Integrity coaches run twice weekly to Perth ($176, 15 hours) and Exmouth ($45, 90 minutes). Greyhound buses run between Perth ($198, 16 hours) and Broome ($265, 19 hours) three times weekly.
### NINGA TURTLE GUIDES
Between November and March each year, volunteer turtle-monitoring programs run up and down the coast, providing an amazing experience for those with time to spare. You'll be working at strange hours during the hottest season in remote areas with little comfort, but seeing these magnificent creatures up close, knowing that you're actively taking part in their conservation, is incredibly satisfying. Applications usually open around August, but check individual program timelines.
Exmouth volunteers need to commit to a five-week period and be prepared to spend most of that time at a remote base. Days start at sunrise with five hours' work collecting data on turtle nesting, habitat and predation, then the rest of the day is free to enjoy the surroundings. Volunteers pay around $1300 (depending on funding), which covers all equipment, meals, transport from Exmouth and insurance. Accommodation is usually in tents or swags at a Department of Environment and Conservation (DEC) research station or remote beach. See the Ningaloo Turtle Program (NTP; www.ningalooturtles.org.au) website for more information.
If you enjoy interaction of the human kind, consider the NTP's Turtle Guide Program. You will need to complete at least the first module of the Exmouth TAFE formal training course, Turtle Tour Guiding, before commencing at the Jurabi Turtle Centre ( Click here ) and this course gains credits towards a Certificate III in Tourism. The JCT plays an important role in minimising the disturbance to nesting turtles and hatchlings by educating tourists and supervising interaction during the breeding period.
Port Hedland volunteers can apply for Pendoley Environmental's (www.penv.com.au) tagging program, which works alongside the oil and gas industry at sites like Barrow Island. Typical placements are for 17 days with all expenses covered, there's a strict selection process and you'll be working mostly at night with minimal free time. The environmental group Care for Hedland ( 0439 941 431; www.careforhedland.org.au) also runs volunteer monitoring programs, and training sessions kick off in November.
Science graduates (any discipline) prepared to commit for six months can apply to Gnaraloo Station's Turtle Conservation Program (GTCP; www.gnaraloo.com) , where all food, accommodation, transport and training are supplied, and volunteers work at the world's third-largest loggerhead rookery.
Top of Chapter
Exmouth
pop 2500
Exmouth began life during WWII as a US submarine base, though the town didn't flourish until the 1960s with the establishment of the Very Low Frequency (VLF) communications facility at the North West Cape. Fishing (especially prawns) and oil and gas exploration commenced, and both industries are still thriving – the flares of gas platforms are visible from Vlamingh Head at night.
With the protection of pristine Ningaloo Reef, tourism now accounts for the bulk of all visitors, many coming to see the magnificent and enigmatic whale sharks (April to July). Peak season (April to October) sees this laid-back town stretched to epic proportions, but don't be put off, as it's still the perfect base to explore nearby Ningaloo Marine and Cape Range National Parks. Alternatively, just relax, wash away the dust after a long road trip and enjoy the local wildlife; emus walking down the street, 'roos lounging in the shade, lizards ambling across the highway and corellas, galahs and ringnecks screeching and swooping through the trees.
Exmouth is at the western end of the Pilbara's 'cyclone alley', and in 1999 Cyclone Vance caused widespread devastation, reaching wind speeds of 267km/h. Once hailed as 'New Broome' (the marina development that stalled during the 2009 global financial crisis is showing signs of life again), with Rio Tinto's successful application to billet its FIFO workers in local accommodation, hopefully the town won't become 'New Karratha'.
1 Sights & Activities
Exmouth is flat, hot and sprawling, with most of the attractions outside town and no public transport. Town Beach OFFLINE MAP GOOGLE MAP is an easy 1km walk east, though swimmers and anglers usually head to Bundegi Beach , 14km north in the shadow of the VLF antenna array. A set of cycle paths ring the town and continue out to the Harold E Holt Naval Base (HEH), where you can follow the road on to Bundegi; watch out for dingos! Bikes can be hired from Exmouth Minigolf OFFLINE MAP GOOGLE MAP ( 08-9949 4644; www.exmouthminigolf.com.au; Murat Rd; bike/kayak/snorkel gear per day $20/50/10; 9am-5pm) .
The sewerage works (Willersdorf Rd) and golf course (Willersdorf Rd) are good places for birdwatching, while turtle volunteering (see boxed text, Click here ) is popular from November to January. From April to October a Sunday crafts market runs in the mall area.
Snorkellers and divers head to Ningaloo Marine Park or the Muiron Islands. Try to find the informative Department for Environment and Conservation (DEC) book _Dive and Snorkel Sites in Western Australia_ . Several dive shops in town offer PADI courses.
Surfers flock to Dunes ( Click here ) on the western cape during winter, while in the summer months windsurfing and kiteboarding are popular.
Exmouth
Sights
1 Town Beach C3
Activities, Courses & Tours
2 Exmouth Minigolf B2
3 Ningaloo Kite & Board B2
Sleeping
4 Exmouth Cape Holiday Park B2
Exmouth Holiday Accommodation/Ray White(see 11)
5Exmouth Ningaloo Caravan & Holiday ResortB2
6 Ningaloo Lodge B2
7 Potshot Hotel Resort B1
Eating
8 Ningaloo Health A1
Pinocchio (see 5)
Whalers Restaurant (see 8)
Drinking & Nightlife
9 Grace's Tavern B2
10 Potshot Hotel B1
Shopping
11 Exmouth Shopping Centre A1
Information
12Department of Environment & ConservationB2
13 Visitor Centre B2
Transport
14Integrity Coach StopB2
Ningaloo Kite & Board KITEBOARDING
OFFLINE MAP GOOGLE MAP
( 08-9949 2770; www.ningalooexcape.com.au; 16 Nimitz St; 2hr lessons $200; 10am-1pm Mon-Sat) Talk to the experts about the best windsurfing and kiteboarding locations, book a lesson or even buy a secondhand kite.
Capricorn Kayak Tours KAYAKING
( 0427 485 123; www.capricornseakayaking.com.au; half-/1-/2-/5-day $89/169/665/1650) Capricorn offers single- and multi-day kayaking and snorkelling tours along the lagoons of Ningaloo Reef.
Ningaloo Whaleshark-N-Dive DIVING
( 1800 224 060; www.ningaloowhalesharkndive.com.au) Offers daily dives to Lighthouse Bay ($165) and the Muiron Islands ($200) as well as longer liveaboard tours to the Muiron and Montebello Islands. Currently holds the exclusive licence to Navy Pier ($145). Dive courses also available from introductory ($215) to full PADI ($600).
T Tours
Adventure tours from Exmouth include swimming with whale sharks, wildlife spotting, diving, sea kayaking, fishing and surf charters, and coral viewing from glass-bottom boats. Some companies only operate during peak season. Check conditions carefully regarding 'no sighting' policies and cancellations.
Outside the whale-shark season, tours focus on manta rays. You need to be a capable snorkeller to get the most out of these experiences. It's normally 30% cheaper if you don't swim. Also be wary of snorkelling on what may essentially be a dive tour – the action may be too deep. Most ocean tours usually depart from Tantabiddi on the western Cape and include free transfers from Exmouth. Here is just a selection of operators – see the visitor centre for a full list.
Kings Ningaloo Reef Tours WILDLIFE
( 08-9949 1764; www.kingsningalooreeftours.com.au; snorkeller/observer $385/285) Longtime player Kings still gets rave reviews for its whale-shark tours. It's renowned for staying out longer than everyone else, and has a 'next available tour' no-sighting policy.
Ningaloo Ecology Cruises CRUISE
( 1800 554 062; www.ningalootreasures.com.au; 1/2½hr $40/60) Has one-hour glass-bottom boat trips (April to October), and longer 2½-hour trips (all year) including snorkelling.
WestTreks DRIVING TOUR
( 08-9949 2659; www.westtreksafaritours.com.au; night/half-/full-day 4WD tours $90/$110/$199) Caves, canyons, a boat cruise and snorkelling are only part of these full-day 4WD tours that traverse the Cape Range to the west coast. Perfect for those without their own transport; shorter tours also available.
Montebello Island Safaris CRUISE
( 0419 091 670; www.montebello.com.au; Apr-Oct) Has a permanent houseboat moored at the Montebello Islands where you can dive, snorkel, surf and fish to your heart's content on a six-night tour.
4 Sleeping
Accommodation is limited; book ahead, especially in peak season (April to October).
Exmouth Ningaloo Caravan & Holiday Resort CARAVAN PARK $
OFFLINE MAP GOOGLE MAP
( 08-9949 2377; www.exmouthresort.com; Murat Rd; unpowered/powered sites $38/48, dm/d $39/80, chalets $200; ) Across from the visitor centre, this friendly, spacious park has grassy sites, self-contained chalets, four-bed dorms, an on-site restaurant and even a pet section. If you're tenting, this is your best bet.
Exmouth Cape Holiday Park CARAVAN PARK $
OFFLINE MAP GOOGLE MAP
(Blue Reef Backpackers; 1800 621 101; www.aspenparks.com.au; cnr Truscott Cres & Murat Rd; sites unpowered/powered/with bathroom $35/49/76, dm/d $32/100, cabin d $130-297; ) The Cape offers van sites with their own en suites, as well as four-bed dorms, budget twins and a host of different cabin options. There's a good camp kitchen and an excellent pool. The few unpowered tent sites are rather cramped.
Ningaloo Lodge GUESTHOUSE $$
OFFLINE MAP GOOGLE MAP
( 1800 880 949; www.ningaloolodge.com.au; Lefroy St; d $140; ) These clean, tastefully appointed motel rooms are one of the better deals, with a modern communal kitchen, barbecue, shady pool and free wi-fi.
Potshot Hotel Resort RESORT $$
OFFLINE MAP GOOGLE MAP
( 08-9949 1200; www.potshotresort.com; Murat Rd; dm/d $30/70, motel d $120, studios $225, apt from $245; ) A town-within-a-town, this bustling resort has seven-bed dorms, standard motel rooms, luxury Osprey apartments and several bars, catering for all comers. The backpacker rooms can be noisy.
Exmouth Holiday Accommodation/Ray White RENTAL HOUSES $$
OFFLINE MAP GOOGLE MAP
( 08-9949 1144; www.exmouthholidays.com.au; 3 Kennedy St; per week from $600; ) Ray White has a wide range of weekly rentals, from fibro shacks to double-storey mansions.
Novotel Ningaloo Resort RESORT $$$
( 08-9949 0000; www.novotelningaloo.com.au; Madaffari Dr; d/apt from $275/355; ) In the marina, the Novotel Ningaloo is at the pointy end of sophistication (and expense) in Exmouth. The tastefully designed rooms are spacious and well equipped and all include balconies.
5 Eating & Drinking
Ther's a supermarket, a bakery and several takeaways at Exmouth Shopping Centre OFFLINE MAP GOOGLE MAP (Maidstone Cres) .
Grace's Tavern OFFLINE MAP GOOGLE MAP ( 08-9949 1000; Murat Rd; dinner) and Potshot Hotel OFFLINE MAP GOOGLE MAP ( 08-9949 1200; Murat Rd; dinner) are your drinking options and both serve decent pub meals.
Ningaloo Health CAFE $
OFFLINE MAP GOOGLE MAP
( 08-9949 1400; www.ningaloohealth.com.au; 3A Kennedy St; mains $7-19; 7.30am-4pm) Breakfasts start with a bang at this tiny cafe – try the chilli eggs on blue vein toast with jalapenos, or a bowl of Vietnamese _pho_ (beef-and-rice-noodle soup). The less brave can dive into a berry-pancake stack, bircher muesli or a detox juice. NH also offers light lunches, salads, smoothies, takeaway picnic hampers (great for a day trip to Cape Range National Park) and the best coffee around.
o Whalers Restaurant SEAFOOD $$
OFFLINE MAP GOOGLE MAP
( 08-9949 2416; www.whalersrestaurant.com.au; 5 Kennedy St; mains lunch $8-24, dinner $29-40; 9am-2pm & 6pm-late) Delicious Creole- influenced seafood is the star attraction at this Exmouth institution. Sit back on the leafy verandah and share a seafood tasting plate with soft-shell crab and local prawns, or try the signature New Orleans gumbo. Non-fishheads can hook into char-grilled kangaroo or Mexican fajitas. The lunch menu is more bistro-like.
Pinocchio ITALIAN $$
OFFLINE MAP GOOGLE MAP
( 08-9949 2577; Murat Rd; mains $16-35; 6-9pm) Located inside the Exmouth Ningaloo Caravan Park, this licensed alfresco _ristorante_ is popular with locals and travellers alike. Families are well catered for, there's a pleasant deck by the pool, and the tasty pasta and pizza servings are huge.
Mantaray's Bar & Brasserie INTERNATIONAL $$$
( 08-9949 0000; www.novotelningaloo.com.au; Madaffari Dr; mains lunch $16-28, dinner $36-44; lunch & dinner; ) Novotel Ningaloo's in-house restaurant is the perfect place for a long, lazy waterside lunch with local, quality ingredients, affordable dishes and the best view in town.
7 Shopping
Exmouth Shopping Centre SHOPPING CENTRE
(Maidstone Cres) The centre includes several dive shops, a gift shop and a surf and camping store.
8 Information
Internet access is available at the library ( 08-9949 1462; 22 Maidstone Cres; 8.30am-4pm Mon-Thu, to noon Sat; ) , Exmouth Diner (Maidstone Cr; free with $5 minimum purchase; 4.30-8.30pm; ) , Potshot ( Click here ) and the dive shops.
Department of Environment & Conservation OFFLINE MAP GOOGLE MAP (DEC; 08-9947 8000; www.dec.wa.gov.au; 20 Nimitz St; 8am-5pm Mon-Fri) Supplies maps, brochures and permits for Ningaloo, Cape Range and Muiron Islands, including excellent wildlife guides. Can advise on turtle volunteering.
Cape Conservation Group (www.ccg.org.au) Website listing environmental projects around the cape.
Visitor Centre ( 08-9949 1176; www.exmouthwa.com.au; Murat Rd; 9am-5pm Mon-Sat, to 1pm Sun) Tour bookings, bus tickets, accommodation service and parks information.
8 Getting There & Away
Exmouth's Learmonth Airport is 37km south of town. Both Qantas and Skywest fly to Perth daily. Skywest also flies direct to Broome on Sunday (April to October). The airport shuttle ( 08-9949 4623; $25) meets all flights.
Integrity coaches run to Perth twice weekly ($200, 17 hours) via Coral Bay ($45, 90 minutes). Greyhound no longer visits Exmouth, so if you're heading north it's easiest to depart from Coral Bay via the charter shuttle ( Click here ; $100, two hours). Buses leave from the visitors centre.
Red Earth Safaris ( 1800 501 968; www.redearthsafaris.com.au) offers a weekly Perth express departing from Exmouth 7am Sunday (one way $200, 30 hours) with an overnight stop.
8 Getting Around
Allens ( 08-9949 2403; rear 24 Nimitz St) Cars start from $60 per day with 150 free kilometres; Budget, Avis and Europcar also have agents.
Exmouth Boat & Kayak Hire ( 0438 230 269; www.exmouthboathire.com; kayaks per day $50) Tinnies (small dinghies) or something larger (including a skipper!) can be hired from $150 per day.
Exmouth Camper Hire ( 08-9949 4050; www.exmouthcamperhire.com.au; 16 Nimitz St; 4 days from $600) Camper vans with everything you need to spend time in Cape Range National Park, including solar panels.
Scooters2go ( 08-9949 4488; www.scooters2go.com.au; cnr Murat Rd & Pellew St; per day/week $80/$175) You only need a car licence for these 50cc scooters, which are much cheaper by the week.
Top of Chapter
Around Exmouth
Heading north past HEH, the VLF antenna array dominates the cape's northern tip, and was once the tallest structure in the southern hemisphere.
Keep straight at the Yardie Creek turn-off for Bundegi Beach , 14km north of Exmouth, where clear, sheltered waters mean pleasant swimming, snorkelling and fishing.
There's great diving at nearby Bundegi Reef , but even better slightly north under the Navy Pier at Point Murat (named for Napoleon's brother-in-law by French explorers). Rated one of the world's best shore dives, there's a bewildering array of marine life including nudibranchs, scorpion fish, moray eels and reef sharks. As it's on defence territory, you'll need to join a tour; the exclusive licence rotates regularly among Exmouth dive shops.
Turn back onto Yardie Creek Rd and head west for the best beaches. Take the first right, signposted 'Mildura Wreck' , to the end to see the 1907 cattle ship that ran aground on the reef. Along the way are turn-offs leading to ruggedly beautiful Surfers Beach (Dunes) .
Ideally located just south of Dunes, Ningaloo Lighthouse Caravan Park ( 08-9949 1478; www.ningaloolighthouse.com; Yardie Creek Rd; unpowered/powered sites $29/35, cabins $95, bungalows $125, lighthouse/lookout chalets $150/245; ) has cliff-top chalets with fantastic views and shady sites for mere mortals.
It's hard to miss the hilltop Vlamingh Head Lighthouse (1912), where spectacular views of the entire cape make it a great place for whale spotting and watching sunsets.
Nearby is the excellent Jurabi Turtle Centre (JTC; Yardie Creek Rd) . Visit by day to read about the turtle life cycle, and obtain the DEC pamphlet _Marine Turtles in Ningaloo Marine Park_ . Return at night to observe nesting turtles and hatchlings (November to March), remembering to keep the correct distance and never to shine a light or camera flash directly at any animal. Those people who have more time can volunteer to become a 'turtle tracker'. See the Ningaloo Turtle Program (NTP; www.ningalooturtles.org.au) website to obtain more information.
Fantastic beaches continue down the western side of the cape, such as clothing-optional Mauritius Beach , 21km from Exmouth, and the snorkelling favourites of Lakeside (54km), Turquoise Bay (65km) and Oyster Stacks (69km).
The entrance to Cape Range National Park ( Click here ) is at 40km and camp sites are allocated here (when open). At 53km you'll find the Milyering visitor centre ( 08-9949 2808; Yardie Creek Rd; 9am-3.45pm) , which serves Ningaloo Marine Park and Cape Range National Park. You can buy tickets here for the Yardie Creek cruise and hire snorkelling gear ($10). Experienced 4WD-ers can check road conditions for the rough coastal track continuing south to Coral Bay.
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Ningaloo Marine Park
Recently extended and World Heritage listed, the Ningaloo Marine Park now protects the full 300km length of the exquisite Ningaloo Reef, from Bundegi Reef on the eastern tip of the peninsula to Red Bluff on Quobba Station far to the south.
Ningaloo is Australia's largest fringing reef, and in places only 100m offshore. It's this accessibility, and the fact that it's home to a staggering array of marine life , that makes it so popular. Sharks, manta rays, humpback whales, turtles, dugongs and dolphins complement more than 500 species of fish.
### 8 CAPE RANGE & NINGALOO CAMP SITES
Try to check out the different camping areas a day before if possible, or use the DEC website (www.dec.wa.gov.au/campgrounds) . Shade, size and shelter are more important than closeness to the beach. Neds Camp (18 sites) and Osprey Bay (20 sites) are the largest campgrounds, while North T-Bone (three sites) and North Mandu (five sites) are the smallest. Milyering visitor centre ( Click here ) also has a poster showing the different beaches. During peak season there's normally a camp host residing at each site.
There are excellent marine activities to enjoy year-round:
» November to March Turtles – three endangered species nestle and hatch in the dunes.
» March Coral spawning – an amazing event seven days after the full moon.
» Mid-March to July Whale sharks – the biggest fish on the planet arrive for the coral spawning.
» May to November Manta rays – present all year round; their numbers increase dramatically over winter and spring.
» June to November Humpback whales – breed in the warm tropics then head back south to feed in the Antarctic.
Over 220 species of hard coral have been recorded in Ningaloo, ranging from bulbous brain corals found on bommies, to delicate branching staghorns and the slow-growing massive coral. While less colourful than soft corals (normally found in deeper water on the outer reef), the hard corals have incredible formations. Spawning, where branches of hermaphroditic coral simultaneously eject eggs and sperm into the water, occurs after full and new moons between February and May, but the peak action is usually six to 10 days after the March full moon.
It's this spawning that attracts the park's biggest drawcard, the solitary speckled whale shark _(Rhiniodon typus)_ . Ningaloo is one of the few places in the world where these gentle giants arrive like clockwork each year to feed on plankton and small fish, making it a mecca for marine biologists and visitors alike. The largest fish in the world, the whale shark can weigh up to 21 tonnes, although most weigh between 13 and 15 tonnes, and reach up to 18m long. They can live for 70 years.
Upload your amazing whale-shark pics to Ecocean (www.whaleshark.org) , which will identify and track your whale shark. To learn more about Ningaloo's denizens, grab a copy of the DEC's _The Marine Life of Ningaloo Marine Park & Coral Bay. _
2 Activities
Most travellers visit Ningaloo Marine Park to snorkel . Stop at Milyering visitor centre ( Click here ) for maps and information on the best spots and conditions. Check its tide chart and know your limits, as the currents can be dangerous. The shop next to the park office sells and rents snorkelling equipment ($10 per day, $15 overnight). The following are the most popular snorkelling spots.
Lakeside SNORKELLING
Walk 500m south along the beach from the car park, then snorkel out with the current before returning close to your original point.
Oyster Stacks SNORKELLING
These spectacular bommies are just metres offshore, but you need a tide of at least 1.2m and sharp rocks make entry/exit difficult. If you tire, don't stand on the bommies; look for some sand.
Turquoise Bay SNORKELLING
The Bay Snorkel Area is suitable for all skill levels and provides myriad fish and corals just off the beach to the right of the bay car park. Stronger swimmers will want to head to the Drift Snorkel Area: 300m south along the beach from the Drift car park, swim out for about 40m then float face down. The current will carry you over coral bommies and abundant sea life. Get out before the sandy point, then run back along the beach and start all over! Beware of strong currents and don't miss the exit point or you'll be carried out through the gap in the reef.
Lighthouse Bay SCUBA DIVING
There's great scuba diving at Lighthouse Bay at sites like the Labyrinth, Blizzard Ridge and Mandu Wall. Check out the DEC book _Dive and Snorkel Sites in Western Australia_ for other ideas.
Top of Chapter
Cape Range National Park
The jagged limestone peaks and gorges of rugged 510-sq-km Cape Range National Park (per car $11) offer relief from the other-wise flat, arid expanse of the North West Cape, and are rich in wildlife, including the rare black-flanked rock wallaby, five types of bat and over 200 species of bird. Spectacular deep canyons cut dramatically into the range, before emptying out onto the wind-blown coastal dunes and turquoise waters of Ningaloo Reef.
The main park access is via Yardie Creek Rd. Several areas in the east are accessible from unsealed roads off Minilya–Exmouth Rd, south of Exmouth. Milyering visitor centre ( Click here ) has comprehensive natural and cultural displays, maps and publications.
1 Sights & Activities
On the east coast, 23km south of Exmouth, the scenic and at times incredible Charles Knife Rd climbs dramatically above the canyon of the same name. The road follows the knife-edge ridge up through rickety corners and you'll need frequent stops to take make the most of the breathtaking views. A rough track continues to Thomas Carter lookout , where (in the cooler months) you can walk the 8km Badjirrajirra loop trail through spinifex and rocky gullies; be aware that there's no shade or water. Under no circumstances attempt this during summer.
Don't miss beautiful Shothole Canyon (turn-off 16km south of Exmouth), with its colourful walls, pretty picnic area and plenty of exploration options.
On the west coast, spot migratory birds at the Mangrove Bay Bird Hide , 8km from the entrance station. Mandu Mandu Gorge is a pleasant but dry walk (3km return) from a car park 20km south of the Milyering visitor centre.
Much nicer is the 2km return walk to Yardie Creek Gorge with its permanent water, sheer cliffs and excellent views. You can take the relaxing one-hour Yardie Creek Cruise ( 08-9949 2808; adult/child $25/12; 11am daily) up the short, sheer gorge to spot rare black-flanked rock wallabies.
Only experienced 4WD-ers should contemplate the hazardous Yardie Creek crossing (low tide only!), and the sandy coastal track that continues south to Coral Bay.
### SURFING THE CAPE
The big swells arrive on the North West Cape between July and October. Dunes ( Click here ) has a popular reef break accessible from the first car park. Lighthouse Bombie , a couple of kilometres south, is further out and a bit more challenging. Beginners should continue south down the cape to Wobiri Access , where the waves are gentler and surf classes are sometimes held.
Serious surfers should consider getting a few mates together for a boat charter to the outer reef and the Muiron Islands , where there are countless breaks and no one to ride them. You can camp on South Muiron with a permit from Exmouth DEC (Click here ). Your charter fee should include all meals, accommodation (onboard or camping) and fishing and snorkelling gear. Charters may be arranged from both Exmouth and Coral Bay, but check with the Exmouth visitor centre first, as the owner may have just sailed off for the Mentawais. You could try Ningaloo Fusion Charters ( 0438 993 284; www.ningaloofusioncharters.com) .
4 Sleeping
A string of sandy, compact camp sites (per person $7) line the coast within the park. Facilities and shade are minimal, though most have toilets and some shelter from prevailing winds. To avoid long peak-season queues (from 7am!) at the park entrance station, consider pre-booking a site (at least 48 hours ahead) through the DEC. Only certain sites can be booked online; the rest are allocated upon arrival at the entrance station (not the visitor centre!) – ask for a generator-free site if you're after peace and quiet.
Yardie Homestead Caravan Park CARAVAN PARK $
( 08-9949 1389; www.yardie.com.au; Yardie Creek Rd; unpowered/powered sites $26/30, d $75, cabins $110, chalets $180; ) Located just outside the park boundary, this former sheep station caters mainly for anglers, though travellers are also welcome and there are some nice grassy tent sites. There's a range of cabins (most require a security bond) plus a pool, shop and camp kitchen.
Sal Salis LUXURY WILDERNESS $$$
( 1300 790 561; www.salsalis.com; wilderness tent s/d $1088/1450; Mar-Dec) Want to watch that flaming crimson Indian Ocean sunset from between 500-threadcount pure cotton sheets? Pass the Chablis! For those who want their camp without the cramp, there's a minimum two-night stay, three gourmet meals a day, a free bar (!) and the same things to do as the couple over the dune in the pop-up camper.
## The Pilbara
Top of Chapter
Dampier to Roebourne
Most travellers skip this mining-services section of the coast as there's not much to see, unless you like huge industrial facilities. Accommodation is ludicrously overpriced and almost impossible to find thanks to the resources boom and the flood of FIFO (fly-in, fly-out) workers. House prices and rents are among the highest in the country, and huge suburbs of donga (small, transportable buildings) are springing up on town outskirts to handle the overflow. However, the area has good transport, well-stocked supermarkets and useful repair shops.
z Festivals
Red Earth Arts Festival ARTS
(www.reaf.com.au; Sep) An annual celebration of music, theatre and visual arts spread across the towns of the Pilbara coast.
#### Dampier
Dampier is the region's main port. Spread around King Bay, it overlooks the 42 pristine islands of the Dampier Archipelago , and supports a wealth of marine life in its coral waters, but heavy industry has blighted Dampier's shores. The nearby Burrup Peninsula contains possibly the greatest number of rock-art petroglyphs on the planet but is under threat from continued industrial expansion (see www.burrup.org.au). The most accessible are at Deep Gorge near Hearson Cove, where you can also view the Staircase to the Moon (see boxed text, Click here ); you'll need a 4WD for the rest of the peninsula.
4 Sleeping
Dampier Transit Caravan Park CARAVAN PARK $
( 08-9183 1109; The Esplanade; unpowered/ powered sites $18/22) Has a handful of grassy sites overlooking the water.
#### Karratha
Most travellers bank, restock, repair stuff and get out of town before their wallet ignites.
From behind the visitor centre, the Jaburara Heritage Trail (3.5km one way) takes visitors through significant traditional sites and details the displacement and eventual extinction of the Jaburara people. Bring plenty of water and start early.
4 Sleeping & Eating
Accommodation prospects are dire in Karratha; try to stay at beautiful Point Samson instead. Otherwise, search online for last-minute deals. Due to FIFO, weekends are usually cheaper than midweek.
The shopping centre has most things you'll need, including ATMs, takeaway food and supermarkets. The JavaVan coffee, in the visitor centre car park, is the best in town.
Pilbara Holiday Park CARAVAN PARK $
( 08-9185 1855; www.aspenparks.com.au; Rosemary Rd; powered sites $40, motel/studio d $229/220; ) Neat and well run with good facilities.
All Seasons Karratha HOTEL $$$
( 08-9185 1155; www.accorhotels.com.au; Searipple Rd; d from $309; ) This hotel has pleasant rooms with data ports (15 minutes free), several bars, a pool and an outdoor bistro.
Karratha Sushi Bar JAPANESE $
( 08-9183 8789; Balmoral Rd; 10am-9pm) Sick of pub grub? Try the excellent sushi.
8 Information
Karratha Visitor Centre ( 08-9144 4600; www.pilbaracoast.com; Karratha Rd; 9am-5pm Mon-Fri, 10am-1pm Sat & Sun, shorter hr Nov-Apr; ) Has good local info, supplies Hamersley Iron (HI) road permits, books tours (including to mining infrastructure) and may be able to find you a room.
OFF THE BEATEN TRACK
### Mt Augustus (Burringurrah) National Park
In Wajarri country, the huge monocline of Mt Augustus (Burringurrah; 1105m), twice as large as Uluru and a good deal more remote, rises 717m above the surrounding plains. There are several walking trails and Aboriginal rock-art sites to explore, including the superb summit trail (12km return, six hours). In a 2WD it's a rough, unsealed 450km from Carnarvon via Gascoyne Junction or 350km from Meekatharra. With a 4WD there are at least three other routes including a handy back door to Karijini via Dooley Downs and Tom Price. All of these routes see little traffic, so be prepared for the worst. There's no camping in the park, though you can stay at nearby dusty Mt Augustus Tourist Park ( 08-9943 0527; www.mtaugustustouristpark.com; unpowered/powered sites $22/33, donga d $88, units $176; ) . Worth a look 60km to the west is the historic Cobra Bangemail Inn ( 08-9943 9565; sites per person $15, d $160) . If you get to Gascoyne Junction and decide to give up, nearby Bidgemia Station ( 08-9943 0501; caunt@harboursat.com.au; Gascoyne Junction; sites per person $15, shearers quarters $65) offers shearers quarters and shady camping.
8 Getting There & Away
Karratha is exceptionally well connected. Virgin, Qantas and Alliance all fly daily to Perth, while Qantas also offers weekly direct flights to most other capitals. Airnorth flies to Broome (with a Darwin connection) and Port Hedland weekly.
Greyhound coaches run to Perth ($286, 22 hours), Port Hedland ($61, three hours) and Broome ($168, 11 hours) three times weekly.
#### Roebourne
Roebourne, 40km east of Karratha, is the oldest (1866) Pilbara town still functioning, and sits on Ngaluma country. It's home to a large Aboriginal community; Yindjibarndi is the dominant language group. There are some beautiful old buildings, including the old gaol, which houses the visitor centre OFFLINE MAP GOOGLE MAP ( 08-9182 1060; www.pilbaracoast.com/towns/roebourne-visitor-centre; Queen St; 9am-4pm Mon-Fri, to 3pm Sat & Sun, shorter hr Nov-Apr) and museum. Don't miss the mineral display in the courtyard.
Roebourne has a thriving indigenous art scene, and you'll pass the odd gallery on the highway. See www.roebourneart.com.au for more details.
#### Cossack
The scenic ghost town of Cossack, at the mouth of the Harding River, was previously the district's main port but was usurped by Point Samson and then eventually abandoned. Many of the historic bluestone buildings date from the late 1800s; there's a 6km Heritage Trail around the town that links all the major sites (pick up the brochure from Roebourne visitor centre). Attractions include the self-guided Social History Museum (adult/child $2/1; 9am-4pm) , and the pioneer cemetery with a tiny Japanese section dating from Cossack's pearling days. Past the cemetery, Reader Head Lookout has great views of the river mouth and the Staircase to the Moon (see boxed text, Click here ).
4 Sleeping
Cossack Budget Accommodation GUESTHOUSE $$
( 08-9182 1190; www.roebourne.wa.gov.au/cossack.aspx ; d with/without air-con $110/90; ) There are five basic rooms in this atmospheric old police barracks. BYO food.
#### Point Samson
Point Samson is a small, industrial-free seaside village, home to great seafood and clean beaches, making it the nicest place to stay in the area. There's good snorkelling off Point Samson, and the picturesque curved beach of Honeymoon Cove.
4 Sleeping & Eating
Samson Beach Caravan Park CARAVAN PARK $
( 08-9187 1414; Samson Rd; powered sites $39) A tiny park in lovely, leafy surrounds, close to the water and tavern. Bookings are essential in school holidays.
The Cove CARAVAN PARK $
( 08-9187 0199; www.thecovecaravanpark.com.au; Macleod St; sites $49.50, 1-/2-bedroom units $240/310) It's a bit 'van city', but the modern, clean facilities complement a great location an easy walk to all attractions.
Samson Beach Chalets COTTAGES $$$
( 08-9187 0202; www.samsonbeach.com.au; Samson Rd; chalets $250-600; ) Offers beautifully appointed self-contained chalets (various sizes) just a short walk from the beach. There's a shady pool, free wi-fi and in-house movies.
Samson Beach Bistro SEAFOOD $$
( 08-9187 1435; mains $11-44; 11am-8.30pm daily, closed 2-5pm Mon-Fri) Serves up great seafood on a shady deck overlooking the ocean. Underneath the pub.
### 8 TOM PRICE & NEWMAN
Bookending Karijini National Park are the neat, company-built mining towns of Tom Price and Newman. Newman, to the east on the Great Northern Hwy, is the larger of the two, with better transport and accommodation options, although it's a lot further from Karijini. Both have good (ie air-con) supermarkets, fuel and excellent visitor centres, which can book you on mine tours if huge holes are your thing. The local libraries have internet access, and Newman's caravan parks are OK for a tent.
Newman Visitor Centre ( 08-9175 2888; www.newman-wa.org; Fortescue Ave; 8am-5pm, closed Sun Jan) Ask for its mud-map of local sights.
Tom Price Visitor Centre ( 08-9188 1112; www.tompricewa.com.au; Central Rd; 8.30am-5pm Mon-Fri, to 12.30pm Sat & Sun, shorter hr Nov-Apr) Can supply HI road permits and also books tours.
Top of Chapter
Millstream-Chichester National Park
Among the arid, spinifex-covered plateaus and basalt ranges between Karijini and the coast, the tranquil Millstream waterholes of the Fortescue River form cool, lush oases. Lovely Crossing Pool (sites per person $7; ) , with palms, pelicans and gas barbecues, makes an idyllic camp site, though some may prefer the larger Milliyanha Campground (sites per person $7) , with its camp kitchen and nearby visitor centre. Murlamunyjunha Trail (7km, two hours return) links both areas and features interpretive plaques by the traditional Yindjibarndi owners.
Once the station homestead, the unmanned visitor centre OFFLINE MAP GOOGLE MAP ( 08-9184 5144; 8am-4pm) houses historical, ecological and cultural displays; as a lifeline for flora and fauna during dry spells, the park is one of the most important indigenous sites in WA. The nearby lily- and palm-fringed Jirndarwurrunha Pool is especially significant and swimming is not permitted.
You can swim at Deep Reach Pool (Nhangganggunha) , believed to be the resting place of the Warlu (the creation serpent) and the shady tables and barbecues are perfect for a lazy picnic.
In the park's north are the stunning breakaways and eroded mesas of the Chichester Range . Don't miss the amazing panorama from the top of Mt Herbert (the viewpoint is a 10-minute walk from the car park) and on the road to Roebourne. You can continue walking to McKenzie Spring (4.5km, one hour return). Lower down the range, Python Pool is worth a look, though check for algal bloom before diving in; the pool is linked to Mt Herbert by the Chichester Range Camel Trail (16km, six hours return).
Top of Chapter
Karijini National Park
Arguably one of WA's most magnificent destinations, Karijini National Park (per car $11) reveals itself slowly. Ragged ranges, upthrust and twisted by nature, glow in the setting sun. Wedge-tailed eagles soar above grey-green spinifex and goannas shelter under stunted mulga. Kangaroos and wildflowers dot the plains, criss-crossed by deep, dark chasms emitting the enticing sound of distant water.
While the narrow, breathtaking gorges, with their hidden, sculptured pools are Karijini's biggest drawcard, the park is also home to a wide variety of fauna and flora, with an estimated 800 plant species, including some 50 varieties of wattle (acacia). Dragon lizards scurry over stones, rock wallabies cling to sheer cliffs, and endangered olive pythons lurk on the far side of pools. The park also contains the state's three highest peaks: Mt Meharry, Mt Bruce and Mt Frederick.
Banyjima Dr, the park's main thoroughfare, connects with Karijini Dr at two entrance stations. The eastern access is sealed to the visitor centre and Dales Gorge, while the rest of the park is unsealed. Take extra care driving as tourist rollovers are common. Avoid driving at night.
Choose walks wisely, dress appropriately and never enter a restricted area without a certified guide. Avoid the gorges during and after rain, as flash flooding does occur.
1 Sights & Activities
Scenic Dales Gorge and its campground are 19km from the eastern entrance. A short, sharp descent leads to Fortescue Falls , behind which a leafy stroll upstream reveals the beautiful Fern Pool ; head downstream from Fortescue Falls to picturesque Circular Pool ; ascend to Three Ways Lookout and return along the cliff top.
Wide Kalamina Gorge , 24km from the visitor centre, has a small tranquil pool and falls with easy access suitable for families. Joffre Falls Rd leads to stunning Knox Gorge , passing the lookout over the spectacular Joffre Falls . Knox Gorge has several nice swimming holes, fringed by native figs, while in Joffre Gorge the frigid pools are perennially shaded.
Weano Rd junction is 32km from the visitor centre, and the Eco Retreat is nearby. The final 13km to the breathtaking Oxers Lookout can be rough, but it's worth it for the magnificent views of the junction of Red, Weano, Joffre and Hancock Gorges some 130m below.
A steep descent into Hancock Gorge (partly on ladders) will bring you first to the sunny Amphitheatre , then along the slippery Spider Walk to the sublime Kermits Pool . On the other side of the car park, a rough track winds down to the surreal Handrail Pool in the bowels of Weano Gorge . Swimming in these pools is a magical experience, but obey all signs and don't even think about entering a restricted area
Hamersley Gorge SWIMMING
In Karijini's northwest corner, off Nanutarra- Wittenoom Rd, this makes a pleasant stopover if you're heading north towards the coast. Idyllic swimming holes and a waterfall lie only minutes from the car park.
Punurrunha WALKING
(Mt Bruce) Gorged out? Go and grab some altitude on WA's second-highest mountain (1235m), a superb ridge walk with fantastic views all the way to the summit. Start early, carry lots of water and allow five hours (the route's 9km return). The access road is off Karijini Dr opposite the western end of Banyjima Dr.
T Tours
To fully appreciate the magical quality of Karijini's gorges, consider an accredited adventure tour through the restricted areas.
o West Oz Active Adventure Tours ADVENTURE TOUR
( 0438 913 713; www.westozactive.com.au; Karijini Eco Retreat; 1-/3-/5-day tours $245/$745/1450; Apr-Nov) Offers action-packed day trips through the restricted gorges and combines hiking, swimming, floating on inner tubes, climbing, sliding off waterfalls and abseiling. All equipment and lunch provided. Also offers longer all-inclusive multi-day tours with airport pickups and a Ningaloo option.
Lestok Tours BUS TOUR
( 08-9188 1112; www.lestoktours.com.au; tours $155) Offers full-day outings to Karijini from Tom Price.
4 Sleeping & Eating
Dales Gorge CAMPGROUND
(sites adult/child $7/2) Though somewhat dusty, this large DEC campground offers shady, spacious sites with nearby toilets and picnic tables. Forget tent pegs – you'll be using rocks as anchors.
Karijini Eco Retreat RESORT
( 08-9425 5591; www.karijiniecoretreat.com.au; sites $35, tent d low/high season $177/315) This 100% indigenous-owned retreat is a model for sustainable tourism, and the attached bar and restaurant has fantastic food (mains $32 to $38), including the best barra within light years. Campers get hot showers and the same rocks as elsewhere in the park. Peak-season astronomy tours are popular ($30, two hours). Things are cheaper in summer when the retreat winds down and temperatures soar.
8 Information
Visitor Centre ( 08-9189 8121; Banyjima Dr; 9am-4pm Apr-Oct, from 10am Nov-Mar) Indigenous managed with excellent interpretive displays highlighting Banyjima culture and park wildlife, good maps and walks information, a public phone and great air-con.
8 Getting There & Away
There's no public transport. The closest airports are at the mining towns of Paraburdoo (101km southwest) and Newman (201km southeast). Integrity coaches stop at Munjina (Auski) Roadhouse on Thursday (northbound) and Friday (southbound). Munjina is the best place to wait for a lift.
### JOURNEY TO THE CENTRE OF THE EARTH
The instructor sits down in the Water Slide, pushes off, then disappears. I hear a splash echo from below. He's done this a thousand times. I haven't done it once, and I'm next.
We're in the depths of Karijini's Knox Gorge. It's 35˚C 'upstairs', but the water in the gorge is freezing, and while we're all in summer wetsuits, everybody's shivering. The day started early when our guides, Dan and Pete, kitted us out with wetsuits, gorge slippers, harnesses, helmets and inner tubes. A short, sunny stroll down from Knox Lookout brought our small group to a pool ringed by native figs, where we practised paddling. A quick 'jump test' off a 2m rock to check we won't 'choke' at the first obstacle (the one I'm staring at), and we were off into the restricted zone, with the gorge shrinking rapidly to a single body width.
I sit down, give the thumbs up, and push off and over a 4m drop into an enclosed plunge pool. An involuntary scream and I'm underwater. It's scary and exhilarating; I'd love to do it again, but once over the edge, there's no way back. Soon we're all down, and floating in the Styx-like water, and Dan sets up the 8m abseil into the next pool. Light falls in narrow shafts as sheer walls tower overhead.
Eventually we escape shady Knox into the sun at the bottom of Red Gorge and warm our bodies on a nearby 'beach'. Soon we're back on our inner tubes, this time for a sunny, relaxed paddle across long, tranquil pools. We pass the entrance to Weano Gorge, a 40m-high waterfall, on the way to our lunch spot at Junction Pool, 130m below Oxers Lookout. As we munch sandwiches, we watch a rock wallaby bounding around halfway up the vertical face, seemingly oblivious to the sheer drop only centimetres away.
Joffre Gorge leads off darkly to the south, but we head into Hancock Gorge, and a tight, steep, slippery climb beside a cascade leading through The Centre of the Earth to Garden Pool. Sublime and sobering, Regans Pool (named after a local SES volunteer who died during a rescue) is next and as Pete lays in the rope for the climb above the pool, the rest of us float silently, lost in our thoughts.
The climb is the last hurdle as we ascend steeply, doubly clipped into the anchor rope. A short traverse and we're out of the restricted area into Kermits Pool, and our final swim. The Spider Walk holds no challenge and soon we're through the sunny Amphitheatre and up the exit ladders to the car park. We've been out all day, and it's been one action-packed, adrenalin-charged adventure.
_Steve Waters_
Top of Chapter
Port Hedland
pop 16,000
Port Hedland ain't the prettiest place. Confronted by its railway yards, iron-ore stockpiles, salt mountains, furnaces and massive deepwater port, the average tourist might instinctively floor the accelerator. Yet Hedland is not just another bland prefab Pilbara town. With a heritage spanning over 115 years, it's been battered by cyclones, plundered by pearlers and bombed by the Japanese – it's even hosted royalty.
Iron ore plays a huge part in the town's fortunes, and Port Hedland is riding the current resources boom. While this pushes up prices and squeezes accommodation, it's also sparked a renaissance. Old pubs are being renovated, the art and cafe (real coffee!) scenes are expanding, fine dining is flourishing, cocktail and tapas bars are sprouting and cycle paths are spreading along the foreshore. Just don't mind the red dust.
1 Sights & Activities
Collect the excellent _Port Hedland Cultural & Heritage Sites _ brochure from the visitor centre and take a self-guided tour around the CBD, or hire a bicycle and meander along the Richardson Street Bike Path to a cold beer at the Yacht Club (Click here ).
Between November and February flatback turtles nest on nearby beaches. Check at the visitor centre for volunteer options.
Goode St, near Pretty Pool, is handy to observe Port Hedland's Staircase to the Moon (see boxed text, Click here ).
o Courthouse Gallery GALLERY
( 08-9173 1064; www.courthousegallery.com.au; 16 Edgar St; 9am-4pm Mon-Fri, to 2pm Sat & Sun) More than a gallery, this leafy arts HQ is the centre of all goodness in Hedland. Inside are stunning local contemporary and indigenous exhibitions, while the shady surrounds host sporadic craft markets. If something is happening, these folks will know about it.
Marapikurrinya Park PARK
(end of Wedge St) The visitor centre publishes shipping times for the ridiculously large tankers passing by. After dark, the park's Finucane Lookout provides a view into BHP Billiton's smouldering Hot Briquetted Iron plant on Finucane Island.
Pretty Pool FISHING, PICNIC SPOT
A popular fishing and picnicking spot (beware of stonefish), 7km east of the town centre.
T Tours
BHP Billiton IRON-ORE PLANT
(adult/child $26/20; 9.30am Mon, Wed & Fri) This popular iron-ore plant tour departs from the visitor centre.
4 Sleeping
As in most mining towns, finding a room in Hedland isn't easy or cheap, and weekends are cheaper than midweek. If you haven't booked well ahead, the visitor centre may be able to help.
There are supermarkets, cafes and take-aways at both the Boulevard (cnr Wilson & McGregor Sts) and South Hedland (Throssell Rd) shopping centres.
OFF THE BEATEN TRACK
### Christmas & Cocos (Keeling) Islands
#### Christmas Island
A mountainous lump of bird poo in the Indian Ocean, not far from Java, Christmas Island (population 1600) was originally settled in 1888 by guano (phosphate) miners, which is still the main economic activity. Its people are a mix of Chinese, Malays and European-Australians, a blend reflected in the island's food, languages and customs. In recent years, CI has gained notoriety as the number-one destination for illegal asylum-seeker boats, causing an influx of government workers.
Don't be put off, as nature here is stunning and more than half the island remains protected as CI National Park . Tall rainforest covers the plateau, and a series of limestone cliffs and terraces attract rare and endemic sea birds. A network of trails runs through the park, and it's possible to camp at Dolly Beach . CI is famous for the spectacular annual migration in November-December of millions of red land crabs marching from the forest down to the coast to breed, covering everything in sight. On the edge of the Java Trench , diving is superb all year, and snorkelling on the fringing reefs is popular during the Dry. The Wet (December to March) brings a swell and decent surf.
While the island is keen to shake off the detention-centre vibe and encourage tourists, the reality is that most facilities are overtaken by government contractors. Hopefully the situation will change. CI is one hour behind Perth (WST; Western Standard Time).
Christmas Island Tourism ( 08-9164 8382; www.christmas.net.au) Your best bet to sniff out a room, car, boat, airport transfer and whatever else is happening on CI.
#### Cocos (Keeling) Islands
Situated 2750km west of Perth are the Cocos (Keeling) Islands (population 650), a necklace of 27 idyllic, low-lying islands around a blue lagoon that inspired Charles Darwin's theory of coral-atoll formation. CKI was settled by John Clunies-Ross in 1826 and his family remained in control of the islands and their Malay workers until 1978, when CKI became part of Australia's Indian Ocean territories. Today about 550 Malays and 100 European-Australians live on Home and West Islands . It's a very low-key place in which to walk, snorkel, dive, fish, windsurf, birdwatch and relax. While most people come on a package, you can visit independently, and camping is allowed at Scout Park on West Island, and on Direction and South Islands . You will need to bring all your own gear. Bring lots of cash as there are no ATMs, though some places accept credit cards. CKI is 90 minutes behind WST.
Cocos-Keeling Islands ( 08-9162 6790; www.cocos-tourism.cc) Great CKI website includes accommodation, tours and activities.
Cocos Dive ( 08-9162 6515; www.cocosdive.com; per day from $210) Able to arrange single dives, week-long packages or SSI courses.
#### Getting There & Away
Virgin flies from Perth to both islands several times weekly. Prices start at around $500 for either island, and at $220 between the two. There's also a return charter flight on Saturday from Kuala Lumpur to CI, bookable through Island Explorer Holidays ( 1300 884 855; www.islandexplorer.com.au) . Twitchers could consider an all-inclusive tour of both islands from Birding Tours Australia ( 02-4927 1808; www.birdingtours.com.au; 14-day tours $3800; Feb-Mar & Nov-Dec) . Australian visa requirements apply, and Australians should bring their passports.
Cooke Point Caravan Park CARAVAN PARK $$
( 08-9173 1271; www.aspenparks.com.au; cnr Athol & Taylor Sts; powered sites $52, d without bathroom $150, unit d from $320; ) You might be able to snag a dusty van or tent site here, but the other options are usually full. There's a nice view over the mangroves and the amenities are well maintained.
OFF THE BEATEN TRACK
### Marble Bar
Marble Bar, population 196, and a long way off everybody's beaten track, has burnt itself into the Australian psyche as the country's hottest town, when back in 1921 the mercury didn't dip below 37.8°C (100°F) for 161 consecutive days. The town is (mistakenly) named after a bar of jasper beside a pool on the Coongan River, 5km southwest.
Most days there's not much to do. You can pore over the minerals at the Comet Gold Mine ( 08-9176 1015; Hillside Rd; admission $3; 9am-4pm) , 8km out of town on the Hillside Rd, or you can prop at the bar and have a yarn with Foxie at the Iron Clad Hotel ( 08-9176 1066; 15 Francis St; d $120) . This classic outback pub offers comfy motel rooms, decent meals and a welcome to budget travellers.
But come the first weekend in July, the town swells to 10 times its normal size for a weekend of drinking, gambling, fashion crime, country music, nudie runs and horse racing known as the Marble Bar Cup. The caravan park ( 08-9176 1569; 64 Contest St) overflows and the Iron Clad is besieged as punters from far and wide come for a bit of an outback knees-up.
The shire office ( 08-9176 1008) runs a weekly bus service to Port Hedland and Newman (via Nullagine) and provides tourist information. If you're heading south, the easiest route back to bitumen is the lonely but beautiful Hillside Rd.
Esplanade Hotel RESORT $$$
( 08-9173 9700; www.theesplanadeporthedland.com.au; 2-4 Anderson St; d Fri-Sun from $295, Mon-Thu from 495; ) Previously one of the roughest pubs in Port Hedland, the 'Nard' is now an exclusive 4.5-star resort with fully clothed staff, sumptuous though hideously expensive doubles, à la carte dining ($24 to $48; from 6pm) and popular all-you-can-eat buffets ($42).
5 Eating & Drinking
o Silver Star CAFE $$
( 0411 143 663; Edgar St; breakfast $12-18, lunch $18-24; 8am-2pm daily, tapas from 6pm Fri & Sat) Possibly the coolest cafe in the Pilbara, this 1930s American Silver Star railcar serves up decent coffee, brekkies and burgers in the original observation lounge. A tapas selection ($40 per head) is available Friday and Saturday evenings.
Port Hedland Yacht Club BAR
( 08-9173 1198; Sutherland St; Thu-Sun) Grab a cold one, find a table in the shade and enjoy the view at the yachties' brand-new premises. Sadly, the food doesn't match the surroundings.
8 Information
There are ATMs along Wedge St and in the Boulevard shopping centre. Internet access is available at the visitor centre, the library ( 08-9158 9378; Dempster St; 9am-5pm Mon-Fri, 10am-1pm Sat; ) and the Seafarers Centre ( 08-9173 1315; www.phseafarers.org; cnr Wedge & Wilson Sts; 9am-9pm) .
Visitor Centre ( 08-9173 1711; www.phvc.com.au; 13 Wedge St; 9am-4pm Mon-Fri, 10am-2pm Sat; ) Newly refurbished, the centre sells bus tickets, publishes shipping times, arranges iron-ore plant tours, and helps with accommodation and turtle monitoring (November to February). Check here for bicycle hire.
8 Getting There & Away
Virgin and Qantas both fly to Perth daily, and on Tuesday Qantas also flies direct to Brisbane and Melbourne. Skywest offers handy weekend Bali flights as well as flights to Broome and Perth weekly. Airnorth heads to Broome (Tuesday and Friday) with a Darwin connection, and Karratha (Friday).
Greyhound coaches run to Perth ($258, 26 hours) and Broome ($87, eight hours) three times weekly. Integrity departs from Perth Wednesday using the quicker ($232, 22 hours) inland route via Newman, returning Friday. Both depart from the visitor centre and South Hedland shopping centre.
8 Getting Around
The airport is 13km from town; Airport Shuttle Service ( 08-9173 4554; per person $22) meets every flight, while Hedland Taxis ( 08-9172 1010) charge around $35. Hedland Bus Lines ( 08-9172 1394) runs limited weekday services between Port Hedland and Cooke Point (via the visitor centre) and on to South Hedland ($3.50). McLaren Hire ( 08-9140 2200; www.rawhire.com.au) offers a large range of rental 4WDs. Rent scooters from Port Hedland Scooter Hire ( 0450 481 765; www.phsh.com.au; from $45 per day) .
# Broome & the Kimberley
#### Broome & the Kimberley Highlights
#### Broome Region
#### Port Hedland to Broome
#### Broome
#### Around Broome
#### Dampier Peninsula
#### The Kimberley
#### Derby
#### Gibb River Road
#### Derby to Wyndham & Kununurra
#### Devonian Reef National Parks
#### Fitzroy Crossing to Halls Creek
#### Wyndham
#### Kununurra
Broome & the Kimberley
### Why Go?
Australia's last frontier is a wild land of remote, spectacular scenery spread over huge distances, with a severe climate, a sparse population and minimal infrastructure. Larger than 75% of the world's countries, the Kimberley is hemmed by impenetrable coastline and unforgiving deserts. In between lie vast boab-studded spinifex plains, palm-fringed gorges, desolate mountains and magnificent waterfalls. It is a true adventure: each dry season a steady flow of explorers search for the real outback along the Gibb River Road.
Aboriginal culture runs deep, from the Dampier Peninsula, where neat communities welcome visitors to country, to distant Mitchell Plateau, where ancient Wandjina and Gwion Gwion stand vigil over sacred waterholes.
Swashbuckling Broome (home to iconic Cable Beach, camel-tinged sunsets and amber-hued watering holes) and practical Kununurra (with its irrigation miracle) bookend the region.
### When to Go
Apr Fly over thundering Mitchell and King George Falls.
May Broome's at its greenest right before the tourist tide.
Sep & Oct Hit Purnululu and the Gibb River Road as the season winds down.
### Best Cafes
» Whale Song ( Click here )
» 12 Mile ( Click here )
» Wild Mango ( Click here )
» Five Rivers ( Click here )
» Jila Gallery ( Click here )
### Best off the Beaten Track Locations
» Middle Lagoon ( Click here )
» Mornington Wilderness Camp ( Click here )
» Mitchell Falls ( Click here )
» Duncan Road ( Click here )
» Kalumburu ( Click here )
## Broome & the Kimberley Highlights
Taking a camel ride at sunset along Broome's Cable Beach (Click here )
Learning about traditional culture with Aboriginal communities on the pristine Dampier Peninsula ( Click here )
Tackling the notorious Gibb River Road (Click here ) in a 4WD adventure
Flying over the stunning Mitchell and King George Falls (Click here ) after the Wet
Riding the wild Horizontal Waterfalls (Click here )
Losing yourself among the ancient beehive domes of Purnululu National Park (Click here )
Canoeing the mighty Ord River (Click here ) in a three-day self-guided epic
Immersing yourself in indigenous art at Aboriginal art cooperatives (Click here )
Trekking through the bowels of the earth at Tunnel Creek National Park (Click here )
Following the Lurujarri Song Cycle on the Lurujarri Dreaming Trail (Click here ) to James Price Point and beyond
8 Getting There & Around
Air
The following airlines service Broome and the Kimberley.
Airnorth ( 1800 627 474; www.airnorth.com.au )
Qantas ( 13 13 13; www.qantas.com.au)
Skippers ( 1300 729 924; www.skippers.com.au) Flies between Broome, Derby, Halls Creek and Fitzroy Crossing.
Skywest ( 1300 660 088; www.skywest.com.au)
Slingair (Heliwork; 1800 095 500; www.slingair.com.au) Runs helicopters and fixed-wing sightseeing tours across the Kimberley.
Virgin Australia ( 13 67 89; www.virginaustralia.com.au)
Bus
Greyhound ( 1300 473 946; www.greyhound.com.au) Runs three times weekly Broome to Perth and daily Broome to Darwin.
## Broome Region
Top of Chapter
Port Hedland to Broome
The Big Empty stretches from Port Hedland to Broome, as the highway skirts the Great Sandy Desert. It's 609km of willy-willies and dust and not much else. There are only two roadhouses, Pardoo (148km) and Sandfire (288km), so keep the tank full. The coast, wild and unspoilt, is never far away.
4 Sleeping
The following places are all packed from May to September.
Eighty Mile Beach Caravan Park CARAVAN PARK $
( 08-9176 5941; www.eightymilebeach.com.au; unpowered/powered sites $32/37, cabins $180; ) Popular with fishermen and 250km from Port Hedland, this shady, laid-back park backs onto a beautiful white-sand beach. Turtles nest November to March.
Port Smith Caravan Park CARAVAN PARK $
( 9192 4983; www.portsmithcaravanpark.com.au; unpowered/powered sites $30/35, dongas d $75, cabins $175) There's loads of wildlife at this caravan park situated on a tidal lagoon, 487km from Port Hedland.
Barn Hill Station ACCOMMODATION $
( 08-9192 4975; www.barnhill.com.au; unpowered sites $20, powered sites $25-30, cabins from $100) A working cattle station, 490km from Port Hedland, with its own 'mini-Pinnacles'.
Top of Chapter
Broome
pop 16,000
Like a paste jewel set in a tiara of natural splendours, Broome clings to a narrow strip of red pindan on the Kimberley's far-western edge, at the base of the pristine Dampier Peninsula. Surrounded by the aquamarine waters of the Indian Ocean and the creeks, mangroves and mudflats of Roebuck Bay, this Yawuru country is a good 2000km from the nearest capital city.
Broome's cemeteries are a stark reminder of its pearling heritage, which claimed the lives of many Japanese, Chinese, Malay and Aboriginal divers. Today, Broome's pearls are still exported around the world, produced on modern sea farms.
Cable Beach, with its luxury resorts, hauls in the tourists during the Dry (April to October), with romantic notions of camels, surf and sunsets. Magnificent, sure, but there's a lot more to Broome than postcards, and tourists are sometimes surprised when they scratch the surface and find pindan just below.
Broome's centre is Chinatown, on the shores of Roebuck Bay, while Cable Beach and its resorts are 6km west on the Indian Ocean. The airport stretches between the two; the port and Gantheaume Point are 7km south.
The Dry's a great time to find casual work, in hospitality or out on the pearl farms. In the Wet, it feels like you're swimming in a warm, moist glove, and while many places close or restrict their hours, others offer amazingly good deals as prices plummet.
Each evening, the whole town pauses, collective drinks in mid-air, while the sun slips slowly seawards.
1 Sights & Activities
#### 1 Cable Beach Area
o Cable Beach BEACH
OFFLINE MAP GOOGLE MAP
The state's most famous landmark offers turquoise waters and beautiful, white sand curving away to the sunset. Clothing is optional north of the rocks, while south, walking trails lead through the red dunes of Minyirr Park , a spiritual place for the Rubibi people. Cable Beach is synonymous with camels, and an evening ride along the sand is a highlight for many visitors.
Cable Beach
Sights
1 Cable Beach A2
Activities, Courses & Tours
2 Broome Camel Safaris B1
3 Red Sun Camels B1
4 Ships of the Desert A1
Sleeping
5 Bali Hai Resort & Spa C3
6 Beaches of Broome C2
7 Broome Beach Resort C3
8 Cable Beach Backpackers D2
9 Tarangau Caravan Park D1
Eating
10 Cable Beach General Store B3
Drinking & Nightlife
11Broome SLSCA2
12 Sunset Bar & Grill B1
Entertainment
13 Diver's Tavern C3
14 ZeeBar C2
Gantheaume Point & Dinosaur Prints LANDMARK
OFFLINE MAP GOOGLE MAP
Beautiful at dawn or sunset when the pindan cliffs turn scarlet, this peaceful lookout holds a 135-million-year-old secret. Nearby lies one of the world's most varied collections of dinosaur footprints , impossible to find except at very low tides.
Reddell Beach BEACH
OFFLINE MAP GOOGLE MAP
For a blistering sunset without the tourists, camels or 4WDs, pull into any of the turn-offs along Kavite Rd between Gantheaume Point and the port and watch the pindan cliffs turn into molten lava above wild and lonely Reddell Beach.
Lurujarri Dreaming Trail WALKING
OFFLINE MAP GOOGLE MAP
( Frans 0423 817 925; www.goolarabooloo.org.au ; May-Jul) This 82km song cycle follows the coast north from Gantheaume Point (Minyirr) to Coulomb Point (Minarriny). The Goolarabooloo organise a yearly guided nine-day trip ($1600), staying at traditional camp sites. Independent walkers should first check with the Goolarabooloo for route conditions as water is scarce.
#### 1 Chinatown Area
A number of cemeteries testify to Broome's multicultural past; the most striking is the Japanese Cemetery OFFLINE MAP GOOGLE MAP (Frederick St) , with 919 graves (mostly those of pearl divers), while Chinese (Frederick St) and Muslim (Frederick St) cemeteries are nearby. There's a small pioneer cemetery OFFLINE MAP GOOGLE MAP by Town Beach overlooking the bay.
Town Beach is fine for a dip if it's not stinger season, and the port jetty is good for fishing and whale watching.
Sun Pictures HISTORIC BUILDING
OFFLINE MAP GOOGLE MAP
( 08-9192 1077; www.sunpictures.com.au ; 27 Carnarvon St; adult/child/family $16.50/ 11.50/55, History Tours per person $5; tours 10.30am & 1pm Mon-Fri) Sink back in a canvas deckchair in the world's oldest operating picture gardens and enjoy the latest movies. The history of the Sun building is the history of Broome itself – don't miss the informative History Tours .
Broome Museum MUSEUM
OFFLINE MAP GOOGLE MAP
( 08-9192 2075; www.broomemuseum.org.au; 67 Robinson St; adult/child $5/1; 10am-4pm Mon-Fri, to 1pm Sat & Sun Jun-Sep, to 1pm daily Oct-May) Discover Cable Beach and Chinatown's origins as you examine pearling history and WWII bombing in this quirky museum.
o Short Street Gallery GALLERY
OFFLINE MAP GOOGLE MAP
( 08-9192 2658; www.shortstgallery.com.au ; 7 Short St; 10am-5pm Mon-Fri, to 2pm Sat) Broome's oldest gallery is now an artist-run space, though several curated exhibitions still run each year. Its studio at 3 Hopton St, Old Broome, holds a stunning collection of canvases.
OFF THE BEATEN TRACK
### WWII Flying Boat Wrecks
On a very low tide it's possible to walk out across the mudflats from Town Beach to the wrecks of _Catalina_ and _Dornier_ flying boats attacked by Japanese 'Zeroes' during WWII. The planes had been evacuating refugees from Java and many still had passengers aboard. Over 60 people and 15 flying boats (mostly Dutch and British) were lost. Only six wrecks are visible, with the rest in deep water.
Start walking an hour before low tide, and head roughly southeast for 1.5km (about 30 minutes). Wear appropriate footwear – the mud's sticky and can hide sharp objects, not all of them inanimate. Watch out for other marine hazards like jellyfish and check with the visitor centre for tide times. The museum also has a handy brochure. Or just take the hovercraft ( 08-9193 5025; www.broomehovercraft.com.au; 1hr adult/child $111/80, sunset/flying boat $159/101) .
T Tours
Camels
It's a feisty business, but at last count there were three camel-tour operators running at Cable Beach offering similar trips.
Broome Camel Safaris CAMEL TOUR
OFFLINE MAP GOOGLE MAP
( 0419 916 101; www.broomecamelsafaris.com.au; 30min afternoon rides $25, 1hr sunset rides adult/child $70/55) Alison, the only female camel-tour operator in Broome, offers afternoon and evening trips.
Red Sun Camels CAMEL TOUR
OFFLINE MAP GOOGLE MAP
( 1800 184 488; www.redsuncamels.com.au ; 40min morning rides adult/child $55/35, 1hr sunset rides $75/55) Red Sun runs both morning and sunset tours, with a shorter trip at 4pm (30 minutes, $30).
Ships of the Desert CAMEL TOUR
OFFLINE MAP GOOGLE MAP
( 08-9192 2958; www.shipsofthedesert.com.au; 40min morning rides adult/child $50/30, 1hr sunset rides $70/50) The original camel-tour company offers morning and sunset trips, and a shorter afternoon option (30 minutes, $30).
Not Camels
There's a million of them; head to the visitor centre for the full selection.
Kujurta Buru INDIGENOUS CULTURE
( 08-9192 1662; www.kujurtaburu.com.au; adult/child from $77/39; Tue, Thu & Sun) Nagula half-day tours explore Yawuru culture and country, including spear throwing and bush tucker tasting.
Broome Adventure Company KAYAKING
( 1300 665 888; www.broomeadventure.com.au; 3/4hr trips $70/90) Glide past turtles on these eco-certified coastal kayaking trips.
Astro Tours ASTRONOMY TOUR
( 0417 949 958; www.astrotours.net; adult/child $75/45) Fascinating after-dark two-hour stargazing tours, held just outside Broome. Self-drive and save $10.
Kimberley Dreamtime Adventure Tours INDIGENOUS CULTURE
( 0447 214 681; www.kimberleydreamtimeadventures.com.au; 1-/2-day cultural tours $299/492; year round) Immerse yourself in Nyikina culture and learn bush skills on these amazing tours to Mt Andersen on the Fitzroy River. Longer tours and camel treks also available.
Kimberley Birdwatching BIRDWATCHING
( 08-9192 1246; www.kimberleybirdwatching.com.au ; 3/5/10hr tours $100/150/290) Join ornithologist George Swann on his informative Broome nature tours. Overnight trips are also available.
z Festivals & Events
Dates (and festivals!) vary from year to year. Check with the visitor centre and consult the community website ( Click here ).
Staircase to the Moon MOON FESTIVAL
( Mar-Oct) A festival of three magical nights each month at the full moon.
Gimme Fest MUSIC FESTIVAL
(www.goolarri.com; May) Showcasing the best of indigenous music.
Kullari NAIDOC Week INDIGENOUS CULTURE
(www.goolarri.com; late Jun–mid-Jul) Celebration of Aboriginal and Torres Strait Islander culture.
Environs Annual Art Auction ART FESTIVAL
(www.environskimberley.org.au; Jul) Annual environment fundraiser auctioning work by local and indigenous Kimberley artists.
Broome Race Round HORSE RACING
(www.broometurfclub.com.au; Jul/Aug) Kimberley Cup, Ladies Day and Broome Cup are when locals and tourists frock up and party hard.
Corrugated Lines WRITING FESTIVAL
(http://broome.wa.au/events/corrugated-lines; Aug) A three-day festival of the written word.
Opera Under the Stars OPERA FESTIVAL
(www.operaunderthestars.com.au; Aug) Opera al fresco; one night only at the Cable Beach Amphitheatre.
Shinju Matsuri Festival of the Pearl PEARLS
(www.shinjumatsuri.com.au; Aug or Sep) This homage to the pearl includes a week of parades, food, art, concerts, fireworks and dragon-boat races.
Mango Festival MANGOES
( last weekend Nov) A celebration of the fruit in all its forms.
### STAIRCASE TO THE MOON
The reflections of a rising full moon, rippling over low-tide-exposed mudflats, create the optical illusion of a golden stairway leading to the moon. Between March and October, full moons see Broome buzzing with everyone eager to see the spectacle. At Town Beachthere's a lively evening market with food stalls, and people bring their fold-up chairs, although the small headland at the end of Hamersley St has a better view. While Roebuck Bay parties like nowhere else, this phenomenon happens across the Kimberley and Pilbara coasts – anywhere with some east-facing mudflats. Other good viewing spots are One Arm Point at Cape Leveque, Cooke Point in Port Hedland, Sunrise Beach at Onslow, Hearson Cove near Dampier and the lookout at Cossack. Most visitor centres publish the dates on their websites.
4 Sleeping
Accommodation is plentiful, but either book ahead or be flexible. If you're travelling in a group, consider an apartment. Prices plummet in the Wet.
Kimberley Klub HOSTEL $
OFFLINE MAP GOOGLE MAP
( 08-9192 3233; www.kimberleyklub.com; 62 Frederick St; dm $26-33, d $95-135; ) Handy to the airport, this big, laid-back tropical backpackers is a great place to meet other travellers. Features include poolside bar, games room, massive kitchen, an excellent noticeboard and organised activities most nights.
Tarangau Caravan Park CARAVAN PARK $
OFFLINE MAP GOOGLE MAP
( 08-9193 5084; www.tarangaucaravanpark.com; 16 Millington Rd; unpowered/powered sites $34/42) A quieter alternative to often noisy Cable Beach caravan parks, Tarangau has pleasant grassy sites 1km from the beach, though at times it can be overly officious.
Cable Beach Backpackers HOSTEL $
OFFLINE MAP GOOGLE MAP
( 1800 655 011; www.cablebeachbackpackers.com; 12 Sanctuary Rd; dm $30, d $85; ) Within splashing distance of Cable Beach, this relaxed place has a lush tropical courtyard, swimming pool, big communal kitchen and bar.
Roebuck Bay Caravan Park CARAVAN PARK $
OFFLINE MAP GOOGLE MAP
( 08-9192 1366; www.roebuckbaycp.com.au; 91 Walcott St; unpowered sites d $28-40, powered sites d $37-50, on-site van d $90) Right next to Town Beach, this shady, popular park has several camp-site options, though the sandflies can be menacing.
o Beaches of Broome HOSTEL $$
OFFLINE MAP GOOGLE MAP
( 1300 881 031; www.beachesofbroome.com.au; 4 Sanctuary Rd, Cable Beach; dm $32-45, motel d $140-180; ) More resort than hostel; spotless, air-conditioned rooms are complemented by shady common areas, poolside bar and a modern self-catering kitchen. Dorms come in a variety of sizes, and the motel rooms are beautifully appointed. Scooter hire available.
o Old Broome Guesthouse GUESTHOUSE $$$
OFFLINE MAP GOOGLE MAP
( 08-9192 6106; www.oldbroomeguesthouse.com.au; 64 Walcott St; s/d $265/285; ) Exotically appointed rooms with a Southeast Asian aesthetic surround a shady common area and leafy pool. High ceilings, sunken baths, an immaculate common kitchen and drooping palms create a tropical Eden.
Bali Hai Resort & Spa RESORT $$$
OFFLINE MAP GOOGLE MAP
( 08-9191 3100; www.balihairesort.com; 6 Murray Rd, Cable Beach; d $298-525; ) Lush and tranquil, this beautiful small resort has gorgeously decorated studios and villas, each with individual outside dining areas and open-roofed bathrooms. The emphasis is on relaxation, and the on-site spa offers a range of exotic therapies. The off-season prices are a bargain.
Broome Beach Resort APARTMENTS $$$
OFFLINE MAP GOOGLE MAP
( 08-9158 3300; www.broomebeachresort.com.au; 4 Murray Rd, Cable Beach; 1-/2-/3-bed apt $300/340/375; ) Great for families and groups. Large, modest apartments surround a central pool within easy walking distance of Cable Beach.
5 Eating
Be prepared for 'Broome prices' (exorbitant), 'Broome time' (when it should be open but it's closed) and surcharges: credit cards, public holidays, bad karma. Service can fluctuate wildly, as most staff are just passing through. Most places close in the Wet.
The back lanes of Chinatown, especially around Johnny Chi Lane , have cheap weekday lunch options. All pubs and resorts have in-house restaurants; some are good value, at others you're just paying for the view.
Self-caterers can enjoy well-stocked supermarkets and bakeries at Paspaley and Boulevard Shopping Centres and Yuen Wing OFFLINE MAP GOOGLE MAP ( 08-9192 1267; 19 Carnarvon St; 8.30am-5.30pm Mon-Fri, to 2pm Sat & Sun) , an Asian grocery.
Cable Beach General Store CAFE $
OFFLINE MAP GOOGLE MAP
( 08-9192 5572; www.cablebeachstore.com.au; cnr Cable Beach & Murray Rds; 6am-8.30pm daily; ) Cable Beach unplugged – a typical Aussie corner shop with coffee, pancakes, barra burgers, pies, internet and no hidden charges. You can even play a round of mini-golf (adult/child/family $7/5/20) and there's internet access ($4 per hour).
Central Broome
Sights
1 Broome Museum B6
2 Pioneer Cemetery B7
3 Short Street Gallery C1
4 Sun Pictures D2
5Town BeachB7
6WWII Flying Boat WrecksC7
Sleeping
7 Kimberley Klub B2
8 Old Broome Guesthouse A6
9 Roebuck Bay Caravan Park A7
Eating
10 Aarli C2
11 Azuki C2
12 Noodlefish C2
13 Town Beach Cafe A7
14 Yuen Wing D1
Drinking & Nightlife
15 Tides Garden Bar C4
Entertainment
16 Matso's Broome Brewery C4
17 Roebuck Bay Hotel D2
Shopping
18 Courthouse Markets C2
19 Gecko Gallery C1
20 Kimberley Bookshop D2
21 Magabala Books C1
22Paspaley Shopping CentreD1
23Town Beach MarketsA7
Information
24Broome Visitor CentreC1
Transport
25Broome AirportA1
Coach Stop(see 24)
o 12 Mile Cafe CAFE $$
( 08-9192 8552; 12milecafe@westnet.com.au; 53 Yamashita Rd, 12 Mile; mains $16-30; 8am-4pm Thu-Mon dry season, Sat & Sun wet season) S Out among the shady mango plantations of 12 Mile, lovely Asian flavours are fused with local organic produce, sending vegoes to instant heaven, kids to smoothie and pikelet bliss and crusty old hippies to cake nirvana. Reduce, reuse, recycle...
o Aarli TAPAS $$
OFFLINE MAP GOOGLE MAP
( 08-9192 5529; 2/6 Hamersley St, cnr Frederick St; tapas $13-19, pizzas $20, fish by weight; 8am-late Dry) Meaning 'fish' in Bardi, Aarli cooks up some of the most inventive and tasty titbits in Broome. The Med-Asian fusion tapas are excellent with a cold beer or chilled wine, and the pizzas are simple and scrumptious, but you really want to share the signature baked whole fish because it is superb – just check the price first!
Noodlefish ASIAN $$
OFFLINE MAP GOOGLE MAP
( 08-9192 1697; 6 Hamersley St, cnr Fred-erick St; mains $21-36; 6-9pm Tue-Sat) This quirky al-fresco BYO is doing fantastic contemporary Asian dishes using classic Kimberley ingredients. Get there early, because you can't book, and it's cash-only.
Azuki JAPANESE $$
OFFLINE MAP GOOGLE MAP
( 08-9193 7211; 1/15 Napier Tce; sushi $8-10, mains $19-36; 11am-2pm, 6-9pm Mon-Fri, dinner Sat) Enjoy the exquisite subtlety of authentic Japanese cuisine at this tiny BYO, from the takeaway fresh sushi rolls to the wonderfully tasty bento boxes.
Town Beach Cafe CAFE $$
OFFLINE MAP GOOGLE MAP
( 08-9193 5585; Robinson St; breakfast $11-20, lunch $18-24; 7.30am-2pm Tue-Sun, from 6pm Fri & Sat) With a great view over Roebuck Bay, the al-fresco tables of the Town are an ideal spot for an early brekkie.
Wharf Restaurant SEAFOOD $$$
OFFLINE MAP GOOGLE MAP
( 08-9192 5800; Port of Pearls House, Port Dr; mains $20-42; 11am-11pm) Settle back for a long, lazy seafood lunch with waterside ambience and the chance of a whale sighting. OK, it's pricey, but the wine's cold, the sea stunning and the chilli blue swimmer crab sensational. Just wait until after 2pm before ordering oysters.
### 8 CHEAP SUNDAY BRUNCH
The cheapest Sunday brunch at Cable Beach also has the best view. In a time-honoured Australian tradition you can support the local Broome Surf Life Saving Club OFFLINE MAP (SLSC; 08-9193 7327; www.broomeslsc.com; Cable Beach foreshore; sausage sangers $2; bar 5-7pm Wed, Fri & Sun, sausages morning Sun) by buying a 'snag sanger'. Your $2 secures one barbecued sausage on a piece of white bread, possibly with onions, definitely with a choice of sauce (tomato or HP). Sit on the grass, munch away and stare at that Indian Ocean. The club also runs a 'members-only' bar some evenings, and they're pretty relaxed as to who's a member.
6 Drinking & Entertainment
Check the gig guide on www.broome.wa.au. Avoid wandering around late at night, alone and off your dial; it's not as safe as it may seem.
Tides Garden Bar BAR
OFFLINE MAP GOOGLE MAP
( 08-9192 1303; www.mangrovehotel.com.au; 47 Carnarvon St) The Mangrove Resort's casual outdoor bar is perfect for a few early bevvies while contemplating Roebuck Bay. Decent bistro meals, half-price oysters (5.30pm to 6.30pm) and live music (Thursday to Sunday) complement excellent Staircase to the Moon viewing.
Broome
Sights
1Gantheaume Point & Dinosaur PrintsA3
2Japanese, Chinese & Muslim CemeteriesC2
3LighthouseA3
4PortB4
5 Reddell Beach A3
Activities, Courses & Tours
6Hovercraft ToursB4
7 Lurujarri Dreaming Trail A3
Eating
8 Wharf Restaurant B4
Shopping
9Boulevard Shopping CentreC2
10 Kimberley Camping & Outback SuppliesC2
Sunset Bar & Grill BAR
OFFLINE MAP GOOGLE MAP
( 08-9192 0470; Cable Beach Club Resort, Cable Beach Rd) Arrive around 4.45pm, grab a front-row seat, order a drink and watch the show – backpackers, package tourists, locals, camels and a searing Indian Ocean sunset shaded by imported coconut palms.
Roebuck Bay Hotel PUB
OFFLINE MAP GOOGLE MAP
( 08-9192 1221; www.roebuckbayhotel.com.au; 45 Dampier Tce; noon-late) Party central, the Roey's labyrinthine bars offer sports on TV, live music, DJs, cocktails and wet T-shirts until the wee hours.
Matso's Broome Brewery PUB
OFFLINE MAP GOOGLE MAP
( 08-9193 5811; www.matsos.com.au; 60 Hamersley St; music 3-6pm Sun) Get a Smokey Bishop into you at this casual backpackers pub and kick back to live music on the verandah. Bring something for the sandflies.
Diver's Tavern LIVE MUSIC
OFFLINE MAP GOOGLE MAP
( 08-9193 6066; www.diverstavern.com.au ; Cable Beach Rd; noon-midnight) Diver's pumps most nights. Don't miss Wednesday jams and the Sunday Session.
ZeeBar COCKTAIL BAR
OFFLINE MAP GOOGLE MAP
( 08-9193 6511; www.zeebar.com.au; 4 Sanctuary Rd; 6pm-late) This stylish bar and bistro near Cable Beach mixes up tasty cocktails, great tapas and DJs. Tuesday is trivia night.
7 Shopping
The old tin shanties of Short St and Dampier Tce are chock-full of extraordinary indigenous art, beautiful, expensive jewellery and cheap, tacky souvenirs.
Gecko Gallery INDIGENOUS ART
OFFLINE MAP GOOGLE MAP
( 08-9192 8909; www.geckogallery.com.au; 9 Short St; 10am-6pm Mon-Fri, to 2pm Sat & Sun Dry, shorter hr Wet) Gecko specialises in East Kimberley and Western Desert art, including canvases, prints and etchings.
Kimberley Bookshop BOOKS
OFFLINE MAP GOOGLE MAP
( 08-9192 1944; www.kimberleybookshop.com.au; 4 Napier Tce; 9am-5pm Mon-Fri, 10am-2pm Sat) Extensive range of books on Broome and the Kimberley.
Kimberley Camping & Outback Supplies OUTDOOR EQUIPMENT
OFFLINE MAP GOOGLE MAP
( 08-9193 5909; www.kimberleycamping.com.au; cnr Frederick St & Cable Beach Rd) Camp ovens, jaffle irons and everything else you need for a successful expedition.
Magabala Books BOOKS
OFFLINE MAP GOOGLE MAP
( 08-9192 1991; www.magabala.com; 1 Bagot St; 9am-4.30pm Mon-Fri) Indigenous publishers with selection of novels, social history, biographies and children's literature.
Courthouse Markets MARKET
OFFLINE MAP GOOGLE MAP
( Hamersley St; mornings Sat, additional Sun Apr-Oct) Local arts, crafts, music and general hippie gear.
8 Information
The hostels, Fongs (29 Saville St) and Yuen Wing (Click here ); all have great noticeboards.
Internet Access
Broome Community Resource Centre (CRC; 08-9193 7153; 40 Dampier Tce; per hr $5; 9am-5pm Mon-Fri, to noon Sat; ) Cheap printing and wi-fi.
Galactica DMZ Internet Café ( 08-9192 5897; 4/2 Hamersley St; per hr $5; 10am-8pm; ) The usual geek stuff; behind Macca's.
Internet Resources
Broome Community Website (www.broome.wa.au) Gig guide and what's on.
Environs Kimberley (www.environskimberley.org.au) Latest environmental issues and projects across the Kimberley.
Chunes of Broome (www.chunesofbroome.com.au) Online Kimberley music and DVDs.
Permits
Department of Indigenous Affairs (DIA; 1300 651 077; www.dia.wa.gov.au) Apply online for free permits to visit Aboriginal communities. Processing usually takes three days.
Tourist Information
Broome Visitor Centre ( 08-9195 2200; www.broomevisitorcentre.com.au; Male Oval, Hamersley St; 8.30am-5pm Mon-Fri, to 4.30pm Sat & Sun Dry, shorter hr Wet) On the roundabout entering town. Good info on road conditions, Staircase to the Moon, dinosaur footprints, WWII wrecks and tide times; can book most things.
8 Getting There & Away
Virgin and Qantas fly daily to Perth, and Qantas also has seasonal direct flights to eastern capitals. Airnorth flies daily to Darwin (except Saturday) and Kununurra, and to Karratha and Port Hedland twice weekly (Tuesday and Friday). Skywest flies daily to Perth, and to Darwin and Exmouth during the Dry. It also has a handy weekly connection to Bali (via Port Hedland). Skippers flies to Fitzroy Crossing, Halls Creek and Port Hedland four times weekly.
Greyhound buses leave the visitor centre daily for Darwin, and Tuesday, Thursday and Saturday for Perth. The local Derby bus ( Click here ) leaves on Monday, Wednesday and Friday. Broome is a popular destination for car pooling (www.findalift.com.au) .
8 Getting Around
Town Bus Service ( 08-9193 6585; www.broomebus.com.au; adult/child $3.50/1.50, day pass $10) links Chinatown with Cable Beach every hour (7.10am to 6.23pm year-round), plus half-hourly (8.40am to 6.40pm) from May to mid-October. Under 16s ride free with an adult.
No rental-car company offers unlimited kilometres. Local operator Broome Broome ( 08-9192 2210; www.broomebroome.com.au ; cars/4WDs/scooters from $63/153/40) has cars, 4WDs and scooters. Britz ( 08-9192 2647; www.britz.com; 10 Livingston St) hires out campervans and 4WD Toyota Land Cruisers (from $176 per day) – essential for the Gibb River Road.
Broome Cycles ( 08-9192 1871; www.broomecycles.com.au; 2 Hamersley St, China-town; per day/week $24/84, deposit $50; 8.30am-5pm Mon-Fri, to 2pm Sat) has locations in Chinatown and Cable Beach ( 0409 192 289; Old Crocodile Park car park, Cable Beach; 9am-noon May-Oct) . For a taxi, try Broome Taxis ( 13 10 08) or Chinatown Taxis ( 1800 811 772) .
Top of Chapter
Around Broome
1 Sights
Malcolm Douglas Wilderness Park WILDLIFE RESERVE
( 08-9193 6580; www.malcolmdouglas.com.au ; Broome Hwy; adult/child/family $35/25/95; 2-5pm daily, from 10am Dry) Visitors enter through the jaws of a giant crocodile at this 30-hectare animal refuge 16km northeast of Broome. The park is home to dozens of crocs (feedings 3pm), as well as kangaroos, cassowaries, emus, dingos, jabirus and numerous birds.
Broome Bird Observatory WILDLIFE RESERVE
( 08-9193 5600; www.broomebirdobservatory.com; Crab Creek Rd; admission by donation, camping per person $15, donga s/d $50/85, chalets $165; 8am-5pm) On Roebuck Bay, 25km from Broome, this amazing bird observatory is a vital staging post for hundreds of migratory species, some travelling over 12,000km. Tours range from an excellent two-hour walk ($70) to a five-day all-inclusive course ($1290). Self-guided trails, accommodation and binoculars are available. The unsealed access road can close during the Wet.
Top of Chapter
Dampier Peninsula
Stretching north from Broome, the red pindan of the Dampier Peninsula ends abruptly above deserted beaches, secluded mangrove bays and cliffs burnished crimson by the setting sun. This country is home to the thriving indigenous settlements of the Ngumbarl, Jabirr Jabirr, Nyul Nyul, Nimanburu, Bardi, Jawi and Goolarabooloo peoples.
Access is by 4WD, along the largely unsealed 215km-long Cape Leveque Rd. Visiting Aboriginal communities requires both a DIA ( Click here ) permit and one from the community (there are exceptions), payable at the office on arrival. Communities can close suddenly, so always book ahead from the Broome Visitor Centre ( Click here ). Look for the booklet _Ardi – Dampier Peninsula Travellers Guide_ . You should be self-sufficient, though limited supplies are available.
On Cape Leveque Rd, turn left after 14km onto Manari Rd, and head north along the spectacular coast. There are bush camping sites (no facilities) at Barred Creek, Quandong Point, James Price Point and Coulomb Point, where there is a nature reserve . Conventional vehicles should make it to James Price Point , the Kimberley's foremost environmental battleground, where there are plans to construct a large LNG facility. See it in its pristine state while you still can.
Back on Cape Leveque Rd, it's 110km to Beagle Bay ( 08-9192 4913) , notable for the extraordinarily beautiful mother-of-pearl altar at Beagle Bay church, built by Pallottine monks in 1918. There's no accommodation, but fuel is available (weekdays only). Contact the office on arrival.
o Middle Lagoon ( 08-9192 4002; www.middlelagoon.com.au; unpowered/powered sites $30/40, beach shelter d $50, cabins d $140-240) , 180km from Broome and surrounded by empty beaches, is superb for swimming, snorkelling, fishing and doing nothing. There's plenty of shade and bird life, and the cabins are great value, though the access road is terrible. Other options include quiet Gnylmarung Retreat ( 0429 411 241; http://gnylmarung.org.au; sites per person $20, bungalows from $90) and upmarket Mercedes Cove ( 08-9192 4687; www.mercedescove.com.au; eco tents/air-con cabins $150/300) . Don't miss Whale Song Cafe at nearby Munget, overlooking exquisite Pender Bay. This eco-cafe serves fabulous mango smoothies, lovingly made pizzas and the best coffee on the peninsula. There's a tiny bush campground with stunning views, a funky outdoor bathroom and not a caravan in sight.
Between Middle Lagoon and Cape Leveque, Lombadina ( 08-9192 4936; www.lombadina.com; entry per car $10, s/d $80/150, cabin 4-person $200-260; office 8am-noon, 1-4pm Mon-Fri) , 200km from Broome, is a beautiful tree-fringed village offering various tours (minimum of three people) including fishing, whale watching, 4WDing, mudcrabbing, kayaking and walking. There are lodge-style rooms and self-contained cabins, but no camping. Fuel is available weekdays; lovely artifacts are for sale at the Arts Centre.
Tiny Chile Creek ( 08-9192 4141; www.chilecreek.com; sites per person $16.50, bush bungalows $100, 4-person safari tents $185) , 7km from Lombadina down a disintegrating track, offers basic bush camp sites, modern en-suite safari tents and renovated bungalows, all just a short stroll to a lovely beach. Ask Roma if she's running her legendary cultural tours.
Cape Leveque is spectacular, with gorgeous white beaches and stunning red cliffs. Ecotourism award-winner Kooljaman ( 08-9192 4970; www.kooljaman.com.au; per car $10, unpowered/powered sites d $38/43, dome tents $65, cabins with/without bathroom d $170/145, safari tents d $275; ) offers grassy camp sites, driftwood beach shelters, hilltop safari tents with superb views, and stuffy budget tents. There's a minimum two-night stay, and the place is packed from June to October. The BYO restaurant ( 08-9192 4970; mains $29-38, BBQ packs $22-26; 11.30am-1.30pm & 6pm-late Apr-Oct) opens for lunch and dinner, or you can order a BBQ pack.
If you prefer less bling, a couple of outstations offer camp sites between Cape Leveque and One Arm Point. Goombading ( 0457 138 027; unpowered/powered sites per person $15/20) , with fantastic water views, is very relaxed. Hosts Unja and Jenny are keen to share Bardi culture, and offer spear-making, fishing and crabbing tours.
You can't camp at Ardiyooloon (One Arm Point; per person $10) , but you can visit this neat community with a well-stocked store, fuel, a barramundi hatchery and great fishing and swimming with views of the Buccaneer Archipelago.
A handful of other outstations offer camping, fishing and crabbing opportunities.
Chomley's Tours ( 08-9192 6195; www.chomleystours.com.au; 1-/2-day tours $260/490) has several day and overnight tours (including mudcrabbing) on the peninsula, plus one-way transfers (from $110). Kujurta Buru ( 08-9192 1662; www.kujurtaburu.com.au) has transport Sunday, Tuesday and Thursday from Broome to Beagle Bay ($95) and Lombadina, Kooljaman and Ardiyooloon (all $155), returning the same day.
## The Kimberley
Top of Chapter
Derby
pop 5000
Late at night while Derby sleeps, the boabs cut loose and wander around town, marauding mobs flailing their many limbs in battle against an army of giant, killer croc-people emerging from the encircling mudflats... If only.
There are crocs hiding in the mangroves, but you're more likely to see birds, over 200 different varieties, while the boabs are firmly rooted along the two main parallel drags, Loch and Clarendon Sts. Derby, sitting on King Sound, is the departure point for tours to the Horizontal Waterfalls and Buccaneer Archipelago, and the western terminus of the Gibb River Rd (GRR). It is also West Kimberley's administrative centre, and the asylum seeker detention facility at nearby RAAF Curtin brings in hordes of contractors.
### KIMBERLEY ART COOPERATIVES
Indigenous art of the Kimberley is unique. Encompassing powerful and strongly guarded Wandjina, prolific and puzzling Gwion Gwion (Bradshaws), bright tropical coastal x-rays, subtle and sombre bush ochres and topographical dots of the western desert, every work sings a story about country.
To experience it firsthand, visit some of these Aboriginal-owned cooperatives; most are accessible by 2WD:
» Mowanjum Art & Culture Centre ( 08-9191 1008; www.mowanjumarts.com; Gibb River Rd, Derby; 9am-5pm daily Dry, closed Sat & Sun Wet) Just 4km along the Gibb River Rd, Mowanjum artists recreate Wandjina and Gwion Gwion images in this incredible gallery shaped like their artwork.
» Waringarri Aboriginal Arts Centre ( 08-9168 2212; www.waringarriarts.com.au; 16 Speargrass Rd; 8.30am-4.30pm Mon-Fri, 10am-2pm Sat Dry, weekdays only Wet) This excellent Kununurra gallery-studio hosts local artists working with ochres in a unique abstract style. It also represents artists from Kalumburu.
» Warmun Arts ( 08-9168 7496; www.warmunart.com; Great Northern Hwy, Warmun; 9am-4pm Mon-Fri) Between Kununurra and Halls Creek, Warmun artists create beautiful works, using ochres to explore Gija identity. Phone first from Warmun Roadhouse for a verbal permit.
» Laarri Gallery ( 08-9191 7195; yiyilischool@activ8.net.au; Yiyilli; 8am-4pm school days) This tiny not-for-profit gallery in the back of the community school has interesting contemporary-style art detailing local history. It's 120km west of Halls Creek and 5km from the Great Northern Hwy. Phone ahead.
» Mangkaja Arts ( 08-9191 5833; www.mangkaja.com; 8 Bell Rd , Fitzroy Crossing; 11am-4pm Mon-Fri) A Fitzroy Crossing gallery where desert and river tribes interact, producing unique acrylics, prints and baskets.
» Yaruman Artists Centre ( 08-9168 8208; Kundat Djaru) Sitting on the edge of the Tanami, 162km from Halls Creek, Yaruman has acrylic works featuring the many local soaks (waterholes). The weekly mail run from Kununurra stops here (Ringer Soak).
» Yarliyil Gallery ( 08-9168 6723; www.yarliyil.com.au; Great Northern Hwy, Halls Creek; 9am-4.30pm Mon-Fri) Great new Halls Creek gallery showcasing talented local artists as well as some of the Ringer Soak mob.
» Warlayirti Artists Centre ( 08-9168 8960; www.balgoart.org.au; Balgo; 9am-5pm) This centre, 255km down the Tanami Track, is a conduit for artists around the area and features bright acrylic dot-style as well as lithographs and glass. Phone first to arrange an entry permit.
1 Sights & Activities
The visitor centre's excellent town map lists every conceivable attraction.
o Norval Gallery GALLERY
(Loch St; varies) Kimberley art legends Mark and Mary Norval have set up an exciting gallery-cafe in an old tin shed on the edge of town. Featuring striking artworks, exquisite jewellery, decent coffee and 5000 vinyl records (brought out on themed nights), any visit here is a delight to the senses.
Wharefinger Museum MUSEUM
(admission by donation) Grab the key from the visitor centre and have a peek inside the nearby museum, with its atmospheric shipping and aviation displays.
Jetty LANDMARK
Check out King Sound's colossal 11.5m tides from the circular jetty, 1km north of town, a popular fishing, crabbing, bird-spotting and staring-into-the-distance haunt. Yep, there are crocs in the mangroves.
Kimberley School of the Air SCHOOL
(Marmion St; admission $5) Fascinating look at how school is conducted over the radio for children on remote stations. Tour times vary, so check with the visitor centre first.
Old Derby Gaol HISTORICAL BUILDING
(Loch St) Along with the Boab Prison Tree (7km south), this old gaol is a sad reminder of man's inhumanity to man.
Bird Hide BIRDWATCHING
There's a bird hide in the wetlands (aka sewerage ponds) at the end of Conway St.
Joonjoo Botanical Trail WALKING
This 2.3km trail, opposite the GRR turn-off, has neat interpretive displays from the local Nyikina people.
T Tours
The Horizontal Waterfalls are Derby's top draw and most cruises also include the natural splendours of remote King Sound and the Buccaneer Archipelago. There are many operators to choose from (see the visitor centre for a full list). Most tours only operate during peak season.
Horizontal Falls Seaplane Adventures SCENIC FLIGHTS
( 08-9192 1172; www.horizontalfallsadventures.com.au; 6hr tours from Derby/Broome $695/745) Flights to Horizontal Falls include a speedboat ride through the falls. There's also an overnight-stay option (ex-Derby) for $845.
Bush Flight SCENIC FLIGHTS
( 08-9193 2680; www.bushflight.com.au; flights from $352) Scenic tours of the Horizontal Waterfalls and the Buccaneer Archipelago – you can look but not touch.
One Tide Charters CRUISES
( 08-9193 1358; www.onetide.com; 5-12 days $3200-7680) Offers eco-certified all-inclusive multiday 'sea safaris' with overnight camping on remote beaches, a ride through the Horizontal Waterfalls, mudcrabbing, fishing and freshwater swimming on exotic islands.
Derby Bus Service BUS TOUR, CAMPING
(West Kimberley Tours/Windjana Tours; 08-9193 1550; www.derbybus.com.au; day tours $150, camping tours per day from $200) The local bus company runs a full-day tour to Windjana Gorge and Tunnel Creek National Parks, and tailored two- to seven-day Kimberley camping trips.
z Festivals & Events
Boab Festival MUSIC, CULTURE
(www.derbyboabfestival.org.au; Jul) Derby goes off with concerts, mud footy, horse and mudcrab races, poetry readings, art exhibitions and street parades. Try to catch the Long Table dinner out on the mudflats.
4 Sleeping & Eating
Any decent accommodation is normally full of contract workers. Try the visitor centre, but if you're heading to/from the Gibb, consider stopping at Birdwood Downs Station (20km) instead.
There are several takeaways and cafes along Loch and Clarendon Sts.
Kimberley Entrance Caravan Park CARAVAN PARK $
( 08-9193 1055; www.kimberleyentrancecaravanpark.com; 2 Rowan St; unpowered/powered sites $32/38) You'll always find room here, though not all sites are shaded. There's a nice outdoor area with tables, although expect lots of insects this close to the mudflats.
Spinifex Hotel RESORT $$
( 08-9191 1233; www.spinifexhotel.com.au; Clarendon St; dongas/motel r $160/250; ) Rising phoenix-like from the ashes of the old Spini, this sleek new resort has corporate-class rooms (some with kitchenettes) and an on-site restaurant.
o Desert Rose B&B $$$
( 08-9193 2813; 4 Marmion St; d $250; ) It's worth booking ahead for the best sleep in town: spacious, individually styled rooms with a nice shady pool, leadlight windows and a sumptuous breakfast. Host Anne is a font of local information.
Boab Inn PUB $$
( 08-9191 1044; www.derbyboabinn.com; Loch St; lunches $16-18, dinners $22-39; ) Excellent counter meals and free wi-fi make this the lunch stop of choice. The motel-style rooms (doubles $225) are clean, comfortable and normally booked out.
Jila Gallery ITALIAN $$
( 08-9193 2560; 18 Clarendon St; pizzas $19-25, mains $19-35; 10am-2pm & 6pm-late Tue-Fri, 6pm-late Sat) Great wood-fired pizzas, shady al-fresco dining and wonderful cakes are the highlights of this friendly trattoria.
Catch SEAFOOD $$
( 08-9191 2664; Jetty; meals $18-25; 10am-9pm) Gloriously overlooking the jetty, Catch offers (mainly) seafood meals that are quite reasonable, though quality can fluctuate. Takeaway is also available.
Sampey Meats BUTCHER $
( 08-9193 2455; 59 Rowan St; 7am-5pm Mon-Fri, to noon Sat) Homemade jerkies, biltong and cryovaced roasts, all ready for the Gibb.
8 Information
The supermarkets and ATMs are on Loch and Clarendon Sts.
DARC (http://darcinc.wordpress.com) Online resource listing everything arty going down in Derbs.
Derby Visitor Centre ( 1800 621 426; www.derbytourism.com.au; 30 Loch St; 8.30am-5pm Mon-Fri, 9am-4pm Sat & Sun) Recently relocated, this super-helpful centre has the low-down on road conditions, accommodation, transport and tour bookings.
Library (Clarendon St; closed Sun; ) Internet; first five minutes free.
8 Getting There & Away
Skywest heads to Perth Monday to Friday. Skippers flies to Broome, Fitzroy Crossing and Halls Creek several times weekly. There's an airport shuttle ( 08-9193 2568; per person $30) to/from Curtin.
Greyhound buses to Darwin ($350, 25 hours) and Broome ($68, two hours) stop at the visitor centre.
Derby Bus Service ( 08-9193 1550; www.derbybus.com.au; one way/return $50/80; Mon, Wed & Fri) runs to Broome three times weekly, leaving early and returning the same day.
For a taxi, call 13 10 08.
### HORIZONTAL WATERFALLS
One of the most intriguing features of the Kimberley coastline is the phenomenon known as 'horizontal waterfalls'. Despite the name, the falls are simply tides gushing through narrow coastal gorges in the Buccaneer Archipelago, north of Derby. What creates such a spectacle are the huge tides, often varying up to 11m. The water flow reaches an astonishing 30 knots as it's forced through two narrow gaps 20m and 10m wide – resulting in a 'waterfall' reaching 4m in height.
Many tours leave Derby (and some from Broome) each Dry, by air, sea or a combination of both. It's become de rigueur to 'ride' the tide change through the gorge on a high-powered speedboat, but this is risky at best, and accidents have occurred. Scenic flights are the quickest and cheapest option, and some seaplanes will land and transfer passengers to a waiting speedboat for the adrenalin hit. If you prefer to be stirred, not shaken, then consider seeing the falls as part of a longer cruise through the archipelago. Book tours at Derby and Broome visitor centres.
Top of Chapter
Gibb River Road
Cutting a brown swathe through the scorched heart of the Kimberley, the legendary Gibb River Road ('the Gibb' or GRR) provides one of Australia's wildest outback experiences. Stretching some 660km between Derby and Kununurra, the largely unpaved GRR is an endless sea of red dirt, big open skies and dramatic terrain. Rough, sometimes deeply corrugated side roads lead to remote gorges, shady pools, distant waterfalls and million-acre cattle stations. Rain can close the road any time and permanently during the Wet. This is true wilderness with minimal services, so good planning and self-sufficiency are vital.
Several pastoral stations offer overnight accommodation from mid-April to late October; advance bookings are essential during the peak period of June to August. Hema Maps' _Kimberley Atlas & Guide _ provides the best coverage, while visitor centres sell copies of _The_ _Gibb River & Kalumburu Road Guide _ ($5).
A high-clearance 4WD (such as a Toyota Land Cruiser) is mandatory, with two spare tyres, tools, emergency water (20L minimum) and several days' food in case of breakdown. Britz ( Click here ) in Broome is a reputable hire outfit. Fuel supplies are limited and expensive, most mobile phones won't work, and temperatures can be life-threatening. Broome and Kununurra are best for supplies.
For just a sniff of outback adventure, try the 'tourist loop' along the GRR from Derby onto Fairfield Leopold Downs Rd to Windjana Gorge and Tunnel Creek National Parks, then exit onto the Great Northern Hwy near Fitzroy Crossing.
T Tours
Western Xposure DRIVING TOUR
( 08-9414 8423; www.westernxposure.com.au; 7 days $1795) Runs seven-day and longer camping trips through the GRR.
Kimberley Wild Expeditions DRIVING TOUR
( 1300 738 870; www.kimberleywild.com.au) A consistent award winner. Tours from Broome range from one- ($250) to nine-day GRR ($2050).
Kimberley Adventure Tours DRIVING TOUR
( 1800 083 368; www.kimberleyadventures.com.au ) Runs between Broome and Darwin including the GRR and Purnululu National Park ($1825, nine days).
8 Information
Try the online resources listed below and the Derby and Kununurra visitor centre sites.
For maps, take Hema's _Kimberley Atlas & Guide _ ($35) or _Regional Map – The Kimberley_ ($10).
Department of Environment & Conservation (DEC; www.dec.wa.gov.au) Park permits, camping fees, info. A Holiday Pass ($40) works out cheaper if visiting more than three parks in one month.
Mainroads Western Australia (MRWA; 138 138; www.mainroads.wa.gov.au; 24hr) Highway and GRR conditions.
Online Resources (www.gibbriverroad.net)
Shire of Derby/West Kimberley ( 08-9191 0999; www.sdwk.wa.gov.au) Provides side road conditions.
Shire of Wyndham/East Kimberley ( 08-9168 4100; www.swek.wa.gov.au) Kalumburu/Mitchell Falls road conditions.
OFF THE BEATEN TRACK
### Kalumburu
The road to Kalumburu deteriorates quickly after the Mitchell Plateau turn-off and eventually becomes very rocky. You'll need a permit from the DIA ( Click here ) to visit Kalumburu and a visitors pass (valid for seven days) on entry from the Kalumburu Aboriginal Community (KAC; 08-9161 4300; www.kalumburu.org; per car $50) . Kalumburu is a picturesque mission nestled beneath giant mango trees and coconut palms with two shops and fuel ( 7.30-11.30am & 1.30-4.30pm Mon-Fri) . Ask around if you need any repairs. There's some interesting rock art nearby, and the odd WWII bomber wreck. You can stay at the Kalumburu Mission ( 08-9161 4333; kalumburumission@bigpond.com; sites per person $20, donga s/d $120/175) , which has a small museum (admission $10; 8.30-10.30am) , or obtain a permit from the KAC office to camp at Honeymoon Bay ( 08-9161 4378) or McGowan Island ( 08-9161 4748; www.mcgowanisland.com.au) , 20km further out on the coast – the end of the road. Alcohol is banned at Kalumburu.
Top of Chapter
Derby to Wyndham & Kununurra
The first 100-odd kilometres of the GRR from Derby are sealed.
After only 4km, Mowanjum Art & Culture Centre (see boxed text, Click here ), with its striking Wandjina and Gwion Gwion images, is well worth a stop. Nine kilometres further, 2000-hectare Birdwood Downs Station ( 08-9191 1275; www.birdwooddowns.com; camping $13, savannah huts per person incl breakfast & dinner $135) offers rustic savannah huts and dusty camping. WWOOFers are welcome and it's also the Kimberley School of Horsemanship , with lessons, riding camps and trail rides (two-hour sunset rides $99).
At the 40km mark, a rough track heads left 12km to several bush camp sites on the May River . Windjana Gorge turn-off arrives at the 119km mark – your last chance to head back to the highway. The scenery improves after crossing the Lennard River into Napier Downs Station as the ancient King Leopold ranges loom straight ahead. Just after Inglis Gap is the turn-off (a rough 50km) to the remote Mt Hart Wilderness Lodge ( 08-9191 4645; sites per person $18, r per person incl dinner & breakfast $200; dry season) with grassy camp sites, pleasant gorges, swimming and fishing holes. Seven kilometres past the Mt Hart turn-off brings the narrow Lennard River Gorge (3km return walk).
March Fly Glen , at the 204km mark, despite its name, is a pleasant, shady picnic area ringed by pandanus. Don't miss stunning Bell Gorge , 29km down a rough track, with a picturesque waterfall and popular plunge pool; you can camp at Silent Grove (adult/child $11/2) . Refuel (diesel only) and grab an ice cream at Imintji Store ( 08-9191 7471; 7am-4.30pm dry season, shorter hours wet season) , your last chance for supplies. Next door is Over the Range Repairs ( 08-9191 7887; 8am-5pm dry season) , where Neville is your best, if not only, hope of mechanical salvation on the whole Gibb.
Part of the Australian Wildlife Conser-vancy, the superb Mornington Wilderness Camp ( 08-9191 7406; www.awc.org.au; entry fee per vehicle $25, sites adult/child $17.50/8, safari tents incl full board s/d $315/540; dry season) is as remote as it gets, lying on the Fitzroy River, a very rough, incredibly scenic 95km drive south of the Gibb's 247km mark. Nearly 400,000 hectares are devoted to conserving the Kimberley's endangered fauna and there's excellent canoeing, birdwatching and bushwalking. Choose from shady camp sites or spacious, raised tents with verandahs. The bar and restaurant offer picnic hampers and the best cheese platter this side of Margaret River.
Just 4km past Mornington's turn-off is the entrance to historic Charnley River Station ( 08-9191 4646; www.charnleyriverstation.com; camp sites d $35, rondavels & guesthouse incl full board s/d $230/310, day visit $20) and its alluring gorges. Grassy camp sites come with hot showers, or you can opt for full board up at the homestead. Meals and home-grown vegies are available.
Beautiful Galvans Gorge , with waterfall, swimming hole, rock wallabies and Wandjina art, is the most accessible of all gorges, less than 1km from the road. Fuel up at Mt Barnett Roadhouse ( 08-9191 7007; 8am-5pm) , at the 300km point, and get your camping permit if choosing to stay at Manning River Gorge (per person $20) , 7km behind the roadhouse. The campground is often full of travellers waiting for fuel but at least there's a good swimming hole and even hot showers. Better still are the free bush camp sites at Barnett River Gorge ; turn off 29km from the roadhouse – they're several kilometres down a sandy track.
Further up the Gibb (at the 338km mark) is the turn-off to Mt Elizabeth Station ( 08-9191 4644; www.mountelizabethstation.com; sites per person $15, s/d incl breakfast & dinner $170/340; dry season) , one of the few remaining private leaseholders in the Kimberley. Peter Lacy's 200,000-hectare property is a good base for exploring the nearby gorges, waterfalls and indigenous rock art; don't miss the 4WD tag-along tour ($50). Wallabies frequent the camp site, and the home-style three-course dinners ($45) hit the spot.
At 406km you reach the Kalumburu turn-off. Head right on the GRR, and pull into atmospheric Ellenbrae Station ( 08-9161 4325; sites per person $15, bungalow d $155) for fresh scones and quirky bungalows. The GRR continues through spectacular country, crossing the mighty Durack River and, at 579km, providing panoramic views of the Cockburn Ranges, Cambridge Gulf and Pentecost River.
The privations of the Gibb are left behind after pulling into amazing Home Valley Station ( 08-9161 4322; www.homevalley.com.au ; sites adult/child $17/5, eco tents for 4 people $190, homestead d from $250; ) , an indigenous hospitality training resort with a superb range of luxurious accommodation. There are excellent grassy camp sites and motel-style rooms, a fantastic open bistro, tyre repairs and activities including trail rides, fishing and cattle mustering.
At 589km cross the infamous Pentecost River . Take care: water levels are unpredictable and saltwater crocs lurk nearby. Slightly further is 400,000-hectare El Questro Wilderness Park ( 08-9169 1777; www.elquestro.com.au; 7-day park permit $20; dry season) , a vast former cattle station with scenic gorges (Amelia, El Questro) and Zebedee thermal springs (mornings only). Boat tours explore Chamberlain Gorge (adult/child $64/34; tours 3pm) or hire your own boat ($70). There are shady camp sites and air-con bungalows at El Questro Station Township (sites per person $20-25, bungalow d from $329; ) and also an outdoor bar and upmarket steak-house (mains $28-42) . There are a million activities, but you'll pay for most of them.
The rest of the GRR is sealed. Ten kilometres along is El Questro's Emma Gorge Resort (safari cabin d from $289; dry season; ) , where a 40-minute walk reaches a sublime plunge pool and waterfall, one of the prettiest in the whole Kimberley. The resort has an open-air bar and restaurant, though the non-air-con cabins are stuffy and overpriced.
At 630km you cross King River and at 647km you finally hit the highway – turn left for Wyndham (48km) and right for Kununurra (53km).
WORTH A TRIP
### MITCHELL FALLS & DRYSDALE RIVER
In the Dry, Kalumburu Rd is normally navigable as far as Drysdale River Station ( 08-9161 4326; www.drysdaleriver.com.au; sites $10-15, d $150; 8am-5pm Apr-Dec) , 59km from the GRR, where fuel, meals and accommodation are available, and you can check ongoing conditions. Scenic flights to Mitchell Falls operate April to September (from $400 per person).
The Ngauwudu (Mitchell Plateau) turn-off is 160km from the GRR, and within 6km a deep, rocky ford crosses the King Edward River, formidable early in the season. Another 2km brings pleasant, shady Munurru Campground (adult/child $7/2) , with excellent nearby rock art. Many people prefer to camp here and visit Mitchell Falls as a day trip. From the Kalumburu Rd it's a rough 87km, past lookouts and forests of _livistona_ palms to the dusty camping ground at Mitchell River National Park (entry per vehicle $11, camping adult/child $7/2) .
Leave early if walking to Mitchell Falls (Punamii-unpuu). The easy trail (8.6km return) meanders through spinifex, woodlands and gorge country, dotted with Wandjina and Gwion Gwion rock-art sites, secluded waterholes, lizards, wallabies and brolga. The falls are stunning, whether trickling in the Dry, or raging in the Wet (when only visible from the air). You can swim in the long pool above the falls, but swimming in the lower pools is strictly forbidden because of their cultural importance to the Wunambal people. Most people will complete the walk in three hours.
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Devonian Reef National Parks
Three national parks with three stunning gorges were once part of a western 'great barrier reef' in the Devonian era, 350 million years ago. Windjana Gorge and Tunnel Creek National Parks are accessed via Fairfield Leopold Downs Rd (linking the Great Northern Hwy with the Gibb River Rd), while Geikie Gorge National Park is just northeast of Fitzroy Crossing.
The walls of beautiful Windjana Gorge (per car $11) soar 100m above the Lennard River, which surges in the Wet but is a series of pools in the Dry. Scores of freshwater crocodiles lurk along the banks. Bring plenty of water for the 7km return walk from the campground (per person $10) .
Sick of the sun? Then cool down underground at Tunnel Creek (per car $11, no camping) , which cuts through a spur of the Napier Range for almost 1km. It was famously the hideout of rebel Jandamarra. In the Dry, the full length is walkable by wading partly through knee-deep water; watch out for bats and take good footwear and a strong torch. Aboriginal paintings exist at both ends and a two-hour tour ( 08-9191 5355; www.bungoolee.com.au; adult/child $50/20) is available.
Not to be missed, magnificent Geikie Gorge ( Apr-Dec) is 22km north of Fitzroy Crossing. The self-guided trails are sandy and hot, but the DEC ( 08-9191 5121; 1hr tour adult/child $30/7.50; various cruises from 8am May-Oct) runs daily cruises. Local Bunuba guides introduce indigenous culture and bush tucker on the amazingly informative cruises run by Darngku Heritage Tours ( 0417 907 609; www.darngku.com.au; adult/child 2hr $65/55, 3hr $80/65, half-day $160/$128; Apr-Dec) . A shorter one-hour cruise (adult/child $30/5) operates during the shoulder season (April and October to December).
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Fitzroy Crossing to Halls Creek
Gooniyandi, Bunuba, Walmatjarri and Wangkajungka people populate the small settlement where the Great Northern Hwy crosses the mighty Fitzroy River. There's little reason to stay other than its good access to the Devonian Reef national parks. Check out Mangkaja Arts (see boxed text, Click here ) with its unique acrylics, and the exquisite glass and ceramics of Dr Sawfish ( 8.30am-4.30pm Mon-Fri, shorter hours Sat & Sun) , next to the tyre guy (whom you'll probably need).
Camping and rooms are available at the atmospheric Crossing Inn ( 08-9191 5080; www.crossinginn.com.au; Skuthorpe Rd; unpowered/powered sites $26/30, r from $180; ) and across the river at the upmarket Fitzroy River Lodge ( 08-9191 5141; www.fitzroyriverlodge.com.au; Great Northern Hwy; camping per person $15, tent d $155, motel d $199, meals $20-34; ) , which also offers decent counter meals. There's a new, well-stocked supermarket, and the visitor centre ( 08-9191 5355; www.sdwk.wa.gov.au; 8.30am-4.30pm Mon-Fri year round, plus 9am-1pm Sat in dry season) and bus stop are just off the highway.
One of the Kimberley's best-kept secrets is the vast subterranean labyrinth of Mimbi Caves , 90km southeast of Fitzroy Crossing. Located within Mt Pierre Station, on Gooniyandi land, the caves house a significant collection of Aboriginal rock art and some of the most impressive fish fossils in the southern hemisphere. Aboriginal-owned Girloorloo Tours (adult/child $80/40; Tue-Sat Apr-Sep) operates trips, including an introduction to local Dreaming stories, bush tucker and traditional medicines. Book through Fitzroy Crossing or Halls Creek visitor centres.
Nearby Larrawa Station ( 08-9191 7025; Great Northern Hwy; sites $20, s with/without meals $120/70) , halfway between Fitzroy Crossing and Halls Creek, makes a pleasant overnight stop, with hot showers, basic camp sites, and shearers rooms. Another 30km towards Halls Creek brings Yiyilli with its Laarri Gallery (see boxed text, Click here ).
On the edge of the Great Sandy Desert, Halls Creek is a small town with communities of Kija, Jaru and Gooniyandi people. The excellent visitor centre ( 08-9168 6262; www.hallscreektourism.com.au; Great Northern Hwy; 8am-5pm; ) books tours to the Bungles and tickets for Mimbi Caves. Check email next door at the Community Resource Centre ( 8.15am-3.45pm Mon-Fri) and across the highway, Yarliyil Gallery (see boxed text, Click here ) is definitely worth a look.
The Kimberley Hotel ( 08-9168 6101; www.kimberleyhotel.com.au; Roberta Ave; r from $172, restaurant mains $16-42; ) is your best lunch option and you can find a bed there or at Best Western ( 08-9168 9600; www.bestwestern.com.au; d $260; ) . There's a caravan park, but you're better off heading out of town.
Skippers flies from Fitzroy Crossing and Halls Creek to Broome, and Greyhound passes through daily.
OFF THE BEATEN TRACK
### Duncan Road
Snaking its way east from Halls Creek before eventually turning north and playing hide and seek with the Northern Territory border, Duncan Rd is the Kimberley's 'other' great outback driving experience. Unsealed for its entire length (445km), it receives only a trickle of travellers compared to the GRR, but those who make the effort are rewarded with stunning scenery, beautiful gorges, tranquil billabongs and breathtakingly lonely camp sites.
Technically it's no harder than the Gibb, and while there are several creek and river crossings, the fords are concrete lined and croc free. It also makes a nice loop if you've come down the Great Northern Hwy to Purnululu and want to return to Kununurra and/or the NT. There are no services on the entire Duncan, so carry fuel for at least 500km and watch out for road trains. Enquire at Halls Creek or Kununurra visitor centres about road conditions.
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Wyndham
pop 900
A gold-rush town fallen on leaner times, Wyndham is scenically nestled between rugged hills and Cambridge Gulf, some 100km northwest of Kununurra. Sunsets are superb from the spectacular Five Rivers Lookout on Mt Bastion (325m) overlooking the King, Pentecost, Durack, Forrest and Ord Rivers entering Cambridge Gulf.
A giant 20m croc greets visitors entering town, but you might see the real thing if Wyndham Crocodile Farm ( 08-9161 1124; Barytes Rd; feeding time 11am) is open. The port precinct also contains a small museum ( 08-9161 1857; Old Courthouse, Port Precinct; 10am-3pm daily Dry) and the Wyndham Town Hotel ( 08-9161 1202; O'Donnell St; d $143, meals $18-38; ) with its legendary meals and overpriced rooms.
In town, Five Rivers Cafe ( 08-9161 2271; 12 Great Northern Hwy; meals $6-16; 6am-3pm daily, from 7am Sat & Sun ) serves up great coffee, breakfasts and barra burgers, while laid-back Wyndham Caravan Park ( 08-9161 1064; Baker St; unpowered/powered sites $25/30, donga d $70; ) offers grassy, shady camp sites.
Greyhound drops passengers 56km away at the Victoria Hwy junction. Internet is available at the Telecentre (CRC; 08-9161 1166; www.wyndham.crc.net.au; 26 Koojarra Rd; 8am-4pm Mon-Fri; ) , and Tuesday/Wednesdays' mail-run flights might get you to Kununurra.
For a taxi, call 0408 898 638.
WORTH A TRIP
### PARRY LAGOONS NATURE RESERVE
This beautiful Ramsar-listed wetland, 15km from Wyndham, teems in the Wet with migratory birds arriving from as far away as Siberia. There's a bird hide and boardwalk at Marlgu Billabong (4WD) and an excellent view from Telegraph Hill . Back on the highway, steep steps lead down to the Grotto , a deep, peaceful pool in a small gorge, perfect for a quiet dip.
Surrounded by nature reserve, tranquil Parry Creek Farm ( 08-9161 1139; www.parrycreekfarm.com.au; unpowered/powered sites $34/37, r $125, cabins $210; ) , with grassy camp sites, attracts hordes of wildlife. Comfy rooms and air-con cabins are connected by a raised boardwalk above a billabong for easy bird spotting. The licensed cafe serves excellent baked barramundi, wood-fired pizzas and other gourmet delights.
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Kununurra
pop 6000
Kununurra, on Miriwoong country, is a relaxed town set in an oasis of lush farmland and tropical fruit and sandalwood plantations, thanks to the Ord River irrigation scheme. With good transport and communications, excellent services and well-stocked supermarkets, it's every traveller's favourite slice of civilisation between Broome and Darwin.
Kununurra is also the departure point for most of the tours in the East Kimberley, and with all that fruit, there's plenty of seasonal work. Note that there's a 90-minute time difference with the NT.
1 Sights & Activities
Across the highway from the township, Lily Creek Lagoon is a mini-wetlands with amazing bird life, boating and freshwater crocs. Lake Kununurra (Diversion Dam) has pleasant picnic spots and great fishing. Groups could consider hiring their own 'barbie' boat from Kununurra Self Drive Hire Boats ( 0409 291 959; Lakeside Resort; per hr from $88) .
Self-guided two- or three-day canoe trips run from Lake Argyle along the scenic Ord River to Kununurra, overnighting at designated riverside camp sites. Canoes, camping equipment and transport are provided, while you supply your own food and sleeping bag. You can choose to paddle the whole way back, bail out along the way, or take an extra day.
Don't miss the excellent Waringarri Aboriginal Arts centre ( Click here ) on Speargrass Rd, opposite the road to Kelly's Knob , a popular sunset viewpoint.
Mirima National Park NATIONAL PARK
(per car $11) A stunning area of rugged sedimentary formations like a mini-Bungle Bungles. The eroded gorges of Hidden Valley are home to brittle red peaks, spinifex, boab trees and abundant wildlife. Several walking trails lead to lookouts, and early morning or dusk are the best times for sighting fauna.
Red Rock Art Gallery GALLERY
( 08-9169 3000; 50 Coolibah Dr; 10am-4pm Mon-Fri) If you're lucky, you might see indigenous artists in action at this excellent gallery showcasing ochres from the East Kimberley.
Kununurra Historical Society Museum MUSEUM
(Coolibah Dr; admission by gold-coin donation) Old photographs and newspaper articles document the history of Kununurra, including the story of a wartime Wirraway aircraft crash and subsequent recovery mission. The museum is opposite the country club exit.
Big Waters CANOEING
( 1800 650 580; www.bigwaters.com.au; 3 days $185) Self-guided overnight canoe trips on the Ord River.
Go Wild CANOEING, ADVENTURE SPORTS
( 1300 663 369; www.gowild.com.au; 3-day canoe trips $180) Guide yourself down the Ord by canoe on a three-day trip, or join a group caving ($200), abseiling (from $150) or bushwalking (from $40).
Yeehaa Trail Rides HORSE RIDING
( 0417 957 607; yeehaa7@hotmail.com; Boab Park, Old Darwin Rd; per hr from $60) Various-length bush rides and tuition to suit all levels.
DON'T MISS
### Purnululu National Park & Bungle Bungle Range
Looking like a packet of half-melted Jaffas, the World Heritage–listed Purnululu National Park (per car $11; Apr-Dec) is home to the incredible ochre and black striped 'beehive' domes of the Bungle Bungle Range.
The distinctive rounded rock towers are made of sandstone and conglomerates moulded by rainfall over millions of years. Their stripes are the result of oxidised iron compounds and algae. To the local Kidja people, _purnululu_ means sandstone, with Bungle Bungle possibly a corruption of 'bundle bundle', a common grass. Whitefellas only 'discovered' the range during the mid-1980s.
Over 3000 sq km of ancient country contains a wide array of wildlife, including over 130 bird species. Kungkalahayi Lookout has a fine view of the range. Look for tiny bats high on the walls above palm-fringed Echidna Chasm (a one-hour return walk) in the north, but it's the southern area comprising aptly named Cathedral Gorge (a 45-minute return walk) that's most inspiring. Remote and pristine Piccaninny Gorge is best experienced as an overnight round trip (30km return); check with the park's visitor centre for details. The restricted gorges in the northern park can only be seen from the air.
Rangers are based here April to December and the park is closed outside this time. The turn-off is 53km south of Warmun and you'll need a high-clearance 4WD for the 52km twisting, unsealed road to the visitor centre. There are five deep, permanent creek crossings, so allow 2½ hours. Kurrajong Camp Site ( May-Sep) and Walardi Camp Site ( Apr-Dec) have fresh water and toilets (sites per person $11). Book online via the DEC (Click here ), allowing at least 48 hours' notice. Alternatively, Mabel Downs Station (Bungle Bungle Caravan Park; 08-9168 7220; www.bunglebunglecaravanpark.com.au; tent sites/powered sites $30/45, safari tents with/without en suite $ 225/120) offers camping just 1km from the highway (outside the park). Don't expect much privacy: tents are jammed between choppers and ridiculously long trailers. Various tours are available.
#### Tours
Most Kimberley tour operators include Purnululu in multi-day tours. See Click here for tours operating from Kununurra. You can also pick up tours at Warmun Roadhouse, Halls Creek and Mabel Downs. Helicopters will get you closer than fixed-wing flights.
East Kimberley ( 08-9168 2213; www.eastkimberleytours.com.au; tours from $180) Has a wide range of tours from both Kununurra and Warmun.
Sling Air ( 1800 095 500; www.slingair.com.au; 18/30/48min flights $225/299/495) Runs helicopter flights from Bellburn airstrip in the park, as well as fixed-wing flights from Warmun and Kununurra.
Bungle Bungle Expeditions ( 08-9168 7220; www.bunglebungleexpeditions.com.au; bus day/overnight $250/695, helicopter from $250) Various 4WD bus and helicopter tours run from the caravan park on Mabel Downs, near the highway.
T Tours
Kununurra Cruises CRUISE
( 08-9168 1718; www.thebbqboat.com.au; adult/child $95/45) Popular sunset 'BBQ Dinner' cruises on Lily Creek Lagoon and the Ord River. BYO drinks.
Triple J Tours CRUISE
( 08-9168 2682; www.triplejtours.net.au; adult/child one way $165/125, return $150/115) Triple J cruises along the 55km Ord River between Kununurra and Lake Argyle Dam.
Shoal Air SCENIC FLIGHTS
( 08-9169 3554; www.shoalair.com.au; per person from $295) Various flights around the Bungles, Cambridge Gulf, Kalumburu and majestic Mitchell and King George Falls.
4 Sleeping
There's a great variety of accommodation to choose from, and the more it costs, the more of a discount you'll get in the Wet. Watch out for mozzies if you're camping near the lake.
Hidden Valley Tourist Park CARAVAN PARK $
( 08-9168 1790; www.hiddenvalleytouristpark.com; 110 Weaber Plains Rd; unpowered/powered sites $24/30, cabin d $125; ) Under the looming crags of Mirima National Park, this excellent little park has nice grassy sites and is popular with seasonal workers. The self-contained cabins are good value.
Kimberley Croc Backpackers HOSTEL $
( 1300 136 702; www.kimberleycroc.com.au; 120 Konkerberry Dr; dm $27-33, d $89-125; ) Close to the action, this slick, modern YHA has a large pool and BBQ area and excellent kitchen facilities. It also runs the nearby Kimberley Croc Lodge (dm per week $160) for seasonal workers.
Freshwater APARTMENTS $$
( 1300 729 267; www.freshwaterapartments.net.au ; 19 Victoria Hwy; studio/1-/2-/3-bedroom apt $218/249/304/399; ) At Freshwater, Kununurra's newest rooms feature exquisite fully self-contained units with exotic open-roofed showers.
Lakeview Apartments APARTMENTS $$
( 08-9168 0000; www.lakeviewapartments.net; 31 Victoria Hwy; 1-/2-/3-bedroom apt $230/280/380; ) Across from Lily Creek Lagoon, these spacious, self-contained apartments have all mod cons, fully equipped kitchens, free wi-fi and cable. There's a weekend minimum two-night stay.
5 Eating
The big resorts all have restaurants offering similar dining experiences. There are two well-stocked supermarkets and several takeaways. Most places keep shorter hours during the Wet, and you'll struggle finding lunch after 2pm.
o Wild Mango CAFE $
( 08-9169 2810; 20 Messmate Way; breakfasts $9-23, lunches $6-13; 7.30am-4pm Mon-Fri, 8am-1pm Sat & Sun; ) S The hippest, healthiest feed in town, with curry wraps, mouth- watering pancakes, chai smoothies, real coffee, gelato and free wi-fi. The entrance is in Konkerberry Dr.
Kimberley Asian Cuisine ASIAN $
( 08-9169 3698; 75 Coolibah Dr; mains $7-22; 10am-2pm & 5-10pm daily) Ask any local and they'll tell you this quality Asian (next to the visitor centre) is one of the best feeds in town.
Ivanhoe Cafe CAFE $$
( 0427 692 775; Ivanhoe Rd; mains $11-20; 8am-4pm Tue-Fri, to 2pm Sat & Sun) Grab a table under the leafy mango trees and tuck into tasty wraps, salads and burgers, all made from fresh, local produce.
o PumpHouse MODERN AUSTRALIAN $$$
( 08-9169 3222; www.ordpumphouse.com.au; Lakeview Dr; lunches $18-30, dinners $33-42; 11.45am-1.45pm & 6pm-late Wed-Fri, from 8am Sat & Sun, dinner only Tue; ) Idyllically situated on Lake Kununurra, the PumpHouse creates succulent dishes featuring quality local ingredients. Watch the catfish swarm should a morsel slip off the verandah. Or just have a beer and watch the sunset. There's an excellent wine list to enjoy and free wi-fi.
7 Shopping
Artlandish INDIGENOUS ART
( 08-9168 1881; www.aboriginal-art-australia.com; cnr Papuana St & Konkerberry Dr; 9am-4.30pm Mon-Fri, to 1pm Sat) Features a stunning collection of Kimberley ochres and Western Desert acrylics to suit all price ranges.
Kununurra Markets MARKET
(Whitegum Park; 8am-noon Sat dry season) The Kununurra Markets are located in the park opposite the visitor centre; stalls feature local crafts and produce.
Bush Camp Surplus OUTDOOR EQUIPMENT
( 08-9168 1476; cnr Papuana St & Konkerberry Dr) The best camping gear between Broome and Darwin.
8 Information
There are ATMs near the supermarkets and a 24-hour laundromat at the BP roadhouse (Messmate Way) . Several cafes have free wi-fi; otherwise try the library ( 08-9169 1227; Mangaloo St; from 8am, closed Sun; ) or CRC ( 08-9169 1868; Coolibah Dr; per hr $6; 8am-5pm Mon-Fri, 9am-1pm Sat; ) .
DEC Office ( 08-9168 4200; Lot 248) Ivanhoe Rd; 8am-4.30pm Mon-Fri) Parks information and permits.
Visitor Centre ( 1800 586 868; www.visitkununurra.com; Coolibah Dr; 8.30am-4.30pm Mon-Fri, 9am-1pm Sat & Sun Apr-Oct, shorter hours Nov-Mar) Check here for accommodation, tours, seasonal work and road conditions.
WORTH A TRIP
### LAKE ARGYLE
Enormous Lake Argyle, where barren red ridges plunge spectacularly into the deep blue water of the dammed Ord River, is Australia's second-largest reservoir. Holding the equivalent of 18 Sydney Harbours, it provides Kununurra with year-round irrigation, and important wildlife habitats for migratory waterbirds, freshwater crocodiles and isolated marsupial colonies. You can drive across the dam wall, take a boat tour ( 08-9168 7687; www.lakeargylecruises.com; adult/child morning $70/45, afternoon $155/90, sunset $85/50) or just amble nearby. Lake Argyle Village ( 08-9168 7777; www.lakeargyle.com; Lake Argyle Rd; unpowered/powered sites $28/35, cabins $139-199, units from $299; ) offers a range of accommodation and incredible views, especially from its infinity pool. Nearby, the original Argyle Homestead ( 08-9167 8088; adult/child $4/1; 8am-4pm Apr-Oct) has been turned into a museum.
8 Getting There & Around
Airnorth flies to Broome and Darwin daily, and to Perth on Saturday. Skywest departs for Perth daily, Broome thrice weekly and Darwin on Monday.
Greyhound has daily buses to Darwin ($191, 13 hours) and Broome ($237, 13 hours) that stop at the BP roadhouse. Destinations include Halls Creek ($86, four hours), Fitzroy Crossing ($181, seven hours), Derby ($212, 10 hours) and Katherine ($129, eight hours).
Avis ( 08-9168 1999) , Budget ( 08-9168 2033) and Thrifty ( 1800 626 515) rental cars are available.
For a taxi, call 13 10 08.
Understand
Perth & West Coast Australia
Perth & West Coast Australia Today
An expanding number of multibillion-dollar mines, a well-preserved lifestyle with all the bells and whistles (house, boat, beach) and a feeling of confidence borne of isolation.
History
Lawlessness, hardship, good times, and the rebirth of Fremantle after a yacht race loved by the wealthy. Western Australia has seen it all.
Local Produce & Wineries
Taste test your way around Western Australia's expanding network of wineries, breweries and local food producers.
Boom town: Mining & the Environment
How demand by Asia's biggest economies is shaping the economic, demographic and physical landscapes of Western Australia.
Indigenous Art in Western Australia
Understanding the key styles of Western Australian indigenous art, and where to see the best examples throughout the state.
Perth & West Coast Australia Today
Welcome to the engine room of the Australian economy, a boom town where nature's resources are driving ongoing growth and expansion ( Click here ). Perth is rapidly developing into an international city – further enhancing the population's existing independent streak – and the urban landscape is being transformed by heritage restorations and audacious town planning. And in the remote mining regions that drive the economy, there are glimmers of hope that the benefits of this latest fiscal gold rush may be slightly more equitably spread.
#### Best on Film
Rabbit-Proof Fence (2002) Three Aboriginal girls trek through the WA desert to be reunited with their families.
Japanese Story (2003) A touching film that's set in the Pilbara and equal parts romance and thriller.
Gallipoli (1981) Young men from rural WA enlist to fight as Anzac soldiers in the ill-fated Gallipoli campaign.
Mad Bastards (2010) Shot in the Kimberley and featuring Indigenous issues and a great soundtrack.
#### Best in Print
Cloudstreet (Tim Winton, 1991) A chronicle of post-WWII working-class families sharing a house in Perth.
Sand (John Kinsella and Robert Drewe, 2010) Poetry and prose exploring the role of sand in the Australian psyche.
Tales from Outer Suburbia (Shaun Tan, 2008) Beautifully illustrated short stories – for kids – with quirky reimaginings of Australian suburbia.
That Deadman Dance (Kim Scott, 2011) Novel exploring the 19th-century interactions between settlers, whalers and the indigenous Noongar people of Albany.
### A Confident Western Capital
Just a few decades ago, Perth was definitely in the shadow of east-coast Australia's major cities, but, fuelled by the energy and economics of the mining boom, it's now a contemporary city on the rise. There's an almost tangible confidence and verve to the city's population, keen to look westwards for both recreation and reward. Bali is firmly entrenched as the state's favourite holiday destination – it's even emerging as a residential option for FIFO ('fly in, fly out') mining workers – and the 21st-century mega economies of China, India and Indonesia are huge markets for WA's resources and agricultural sectors.
Evidence of the city's impetuous growth includes newly sprawling suburbs, with oversized homes squeezed onto compact plots, and front gardens punctuated with shiny boats, flash utes, and other blokey indicators of ongoing injections of mining money. With so many cars in circulation, transport to these emerging satellite suburbs can be slow going, and the need for ongoing investment to keep Perth's much-admired rail system up to scratch is another hot topic. A $1-billion light-rail system to link Perth's northern suburbs to the CBD is projected to open in 2018. Other major civic works in progress include Perth's City Link Project and the development of Elizabeth Quay to _finally_ reintroduce the CBD to the river (see boxed text, Click here ).
Another 'finally' moment is the restoration of many of the heritage buildings along St George's Terrace in the city's west end that were proudly constructed during much earlier mining booms. The emergence of new eating and drinking precincts and boutique hotels is an overdue dynamic in a city blighted sometimes in recent history by showy modern architecture.
### Spreading the Success?
As in other parts of Australia, Aboriginal communities in WA struggle on, many mired in disadvantage, and a form of unspoken segregation between white Australians and Aboriginal Australians appears to exist.
Divisions persist, but the search for petroleum and gas has brought mining companies and Aboriginal groups to the negotiating table in deals brokered, both successfully and unsuccessfully, for mining companies to set up shop on traditional Aboriginal lands.
In the far north region of the Kimberley, one of the biggest planned developments is a $35-billion liquefied natural gas (LNG) project at James Price Point near Broome. Following the striking of a $1.5-billion compensation deal with the Kimberley Land Council (KLC) – representing members of the local Aboriginal Goolarabooloo and Jabirr Jabirr peoples – other members of the Goolarabooloo people have lodged a claim with the Western Australia Supreme Court to overturn the state government's compulsory acquisition of the site. Opponents of the acquisition contend that the KLC was placed under 'improper pressure' by the state government, and the ongoing legal machinations are powerful proof that negotiations between traditional Aboriginal landowners, the government and resource companies are seldom straightforward.
The rise of Indigenous recruitment agencies has increased the number of Aboriginal workers in the resources sector. The mine owners benefit from a reduced need for costly FIFO workers, and the local Aboriginal population benefits from education and employment opportunities.
### Football Crazy
Western Australia has two teams in the AFL: the Fremantle Dockers and the West Coast Eagles. The Dockers ( often just 'Freo') were only founded in 1995 but have already built a very strong following. They've traditionally enjoyed a working-class underdog image, but with another strong finals showing in 2012, the underdog moniker is starting to look slightly out of date. With key players like skipper Matthew Pavlich, an AFL premiership crown can't be too far away. Watch this space.
Founded in 1986, the West Coast Eagles currently play at Subiaco Oval (aka Patersons Stadium), but when – or maybe if – a new stadium is built across the river at Burswood, they'll be moving there for the 2018 season. Like expansion teams in other codes – come on down, the Melbourne Storm NRL team – they've enjoyed considerable success in their short history, and have already won three premierships, the last in 2006. Like Freo, the Eagles also reached the finals in the 2012, but just missed out on a Grand Final berth.
Now if only they could get started on that new footie stadium...
Population: 2.19 million
Population growth: 3.1%
Area: 2,529,875 sq km
GDP: AU$2.17 billion
GDP growth: 4.3%
Unemployment: 3.5%
History
Today Western Australia (WA), the largest state in the country, is also the most sparsely populated, being home to less than 10% of the population.
Many of the first ships to bring convicts to WA were whalers. Human cargo would be unloaded and then the ships continued whaling.
The story of Western Australia's history is one of hardship, boom, bust, and boom again. Human history started some 40,000 years ago, when the first people are thought to have arrived – although some argue that this could have occurred as long as 65,000 years ago.
Dirk Hartog is considered the first European explorer to land on the shores of WA (as a record of his journey he displayed a pewter plate on an island in Shark Bay in 1616, now known as Dirk Hartog Island).
The British set up a military base in Albany, in the south of the state, in 1826. Perth was then founded in 1829, when Captain James Stirling declared all surrounding land property of King George IV.
In 1829 immigrants led by Stirling arrived in the territory of the Noongar people, sparking controversy between the two groups. Conflict with the indigenous population continued, notably in the Battle of Pinjarra (1834), when some 25 Aboriginal people and one European were killed.
WA began its economic transformation with the discovery of gold in the 1880s and the inception of the nickel boom in the early 1960s, albeit thwarted by the two world wars and the Depression. Riches from the mines at Mt Newman, Tom Price and Kalgoorlie, among several others, dovetailed into the economic bubble of the 1980s, which burst when WA Inc (as the dealings among select businessmen and state politicians came to be known) was discovered to have lost $600 million in public money. Ever enterprising, it was not long, however, before the state was soon back on its feet, enjoying untrammelled economic mining growth and development by 2010.
## First Arrivals
People first arrived on the northern shores of Australia at least 40,000 years ago. As they began building shelters, cooking food and telling each other tales, they left behind signs of their activities. They left layers of carbon – the residue of their ancient fires – deep in the soil. Piles of shells and fish bones mark the places where these people hunted and ate. And on rock walls across WA they left paintings and etchings, some thousands of years old, which tell their stories of the Dreaming, that spiritual dimension where the earth and its people were created, and the law was laid down.
Contrary to popular belief, these Aboriginal people, especially those living in the north, were not entirely isolated from the rest of the world. Until 6000 years ago, they were able to travel and trade across a bridge of land that connected Australia to New Guinea. Even after white occupation, Aboriginal people of the northern coasts regularly hosted Macassan fishermen from Sulawesi, with whom they traded and socialised.
When European sailors first stumbled on the coast of 'Terra Australis', the entire continent was occupied by hundreds of Aboriginal groups, living in their own territories and maintaining their own distinctive languages and traditions. The fertile Swan Valley around Perth, for example, is the customary homeland of about a dozen groups of Noongar people, each speaking a distinctive dialect.
The prehistory of Australia is filled with tantalising mysteries. In the Kimberley, scholars and amateur sleuths are fascinated by the so-called Bradshaw paintings. These enigmatic and mystical stick figures are thousands of years old. Because they look nothing like the artwork of any other Aboriginal group, the identity of the culture that created them is the subject of fierce debate.
Meanwhile there are historians who claim the Aboriginal people's first contact with the wider world occurred when a Chinese admiral, Zheng He, visited Australia in the 15th century. Others say that Portuguese navigators mapped the continent in the 16th century.
The founding of Perth is most famously depicted in George Pitt Morison's painting _The Foundation of Perth_ (1829). It is often erroneously credited as an authentic record of the ceremony rather than a historical reconstruction.
## Early Dutch Exploration
These are intriguing theories. But most authorities believe that the first man to travel any great distance to see Aboriginal Australia was a Dutchman named Willem Janszoon. In 1606, he sailed the speedy little ship _Duyfken_ out of the Dutch settlement at Batavia (modern Jakarta) to scout for the Dutch East India Company, and found Cape York (the pointy bit at the top of Australia), which he thought was an extension of New Guinea.
Ten years later, another Dutch ship, the _Eendracht_ , rode the mighty trade winds across the Atlantic, bound for the 'spice islands' of modern Indonesia. But the captain, Dirk Hartog, misjudged his position, and stumbled onto the island (near Gladstone) that now bears his name. Hartog inscribed the details of his visit onto a pewter plate and nailed it to a post. In 1697, the island was visited by a second Dutch explorer, named Willem de Vlamingh, who swapped Hartog's plate for one of his own.
Other Dutch mariners were not so lucky. Several ships were wrecked on the uncharted western coast of the Aboriginal continent. The most infamous of these is the _Batavia_ . After the ship foundered in the waters off modern Geraldton in 1629, the captain, Francis Pelsaert, sailed a boat to the Dutch East India Company's base at Batavia. While his back was turned, some demented crewmen unleashed a nightmare of debauchery, rape and murder on the men, women and children who had been on the ship. When Pelsaert returned with a rescue vessel, he executed the murderers, sparing only two youths whom he marooned on the beach of the continent they knew as New Holland. Some experts believe the legacy of these boys can be found in the sandy hair and the Dutch-sounding words of some local Aboriginal people. The remains of the _Batavia_ and other wrecks are now displayed at the Western Australian Museum in Geraldton and in the Fremantle Shipwreck Galleries, where you can also see de Vlamingh's battered old plate.
The Dutch were businessmen, scouring the world for commodities. Nothing they saw on the dry coasts of this so-called 'New Holland' convinced them that the land or its native people offered any promise of profit. When another Dutchman named Abel Tasman charted the western and southern coasts of Australia in 1644, he was mapping not a commercial opportunity but a maritime hazard.
Built by convicts, the Fremantle Arts Centre was once a lunatic asylum and then a poorhouse, or 'women's home'. Today this Gothic building is a thriving arts centre well worth a visit.
## The British (Finally) Claim the West Coast
Today the dominant version of Australian history is written as though Sydney is the only wellspring of Australia's identity. But when you live in WA, history looks very different. In Sydney, white history traditionally begins with Captain James Cook's epic voyage of 1770, in which he mapped the east coast. But Cook creates little excitement in Albany, Perth or Geraldton – places he never saw.
Cook's voyage revealed that the eastern coastline was fertile, and he was particularly taken with the diversity of plant life at the place he called 'Botany Bay'. Acting on Cook's discovery, the British government decided to establish a convict colony there. The result was the settlement of Sydney in 1788 – out of which grew the great sheep industry of Australia.
By the early 19th century, it was clear that the Dutch had no inclination to settle WA. Meanwhile, the British were growing alarmed by the activities of the French in the region. So on Christmas Day 1826, the British army warned them off by establishing a lonely military outpost at Albany, on the strategically important southwestern tip of the country.
## The Founding of Perth
The challenge to Aboriginal supremacy in the west began in 1829, when a boatload of free immigrants arrived with all their possessions in the territory of the Noongar people. This group was led by Captain James Stirling – a swashbuckling and entrepreneurial naval officer – who had investigated the coastal region two years earlier. Stirling had convinced British authorities to appoint him governor of the new settlement, and promptly declared all the surrounding Aboriginal lands to be the property of King George IV. Such was the foundation of Perth.
Stirling's glowing reports had fired the ambitions of English adventurers and investors, and by the end of the year, 25 ships had reached the colony's port at Fremantle. Unlike their predecessors in Sydney, these settlers were determined to build their fortunes without calling on government assistance and without the shame of using convict labour.
Kim Scott's _Benang_ (1999), which won the Miles Franklin Award in 2000, is a confronting but rewarding read about the assimilation policies of the 20th century and the devastating effect they had on Aboriginal Australia.
## Frontier Conflict
As a cluster of shops, houses and hotels rose on the banks of the Swan River, settlers established sheep and cattle runs in the surrounding country. This led to conflict with the Aboriginal people, following a pattern which was tragically common throughout the Australian colonies. The Aboriginal people speared sheep and cattle – sometimes for food, sometimes as an act of defiance. In the reprisals that resulted, people on both sides were killed, and by 1832 it was clear that the Aboriginal people were organising a violent resistance. Governor Stirling declared that he would retaliate with such 'acts of decisive severity as will appal them as people for a time and reduce their tribe to weakness'.
In October 1834 Stirling showed he was a man of his word. He led a punitive expedition against the Noongar, who were under the leadership of the warrior Calyute. In the Battle of Pinjarra, the governor's forces shot, according to one report, around 25 Aboriginal people and suffered one fatality themselves. This display of official terror had the desired effect. The Noongar ended their resistance and the violence of the frontier moved further out.
## The Deployment of Convicts
Aboriginal resistance was not the only threat to the survival of this most isolated outpost of the British Empire. The arid countryside, the loneliness and the cost of transport also took their toll. When tough men of capital could make a fortune in the east, there were few good reasons to struggle against the frustrations of the west, and most of the early settlers left. Two decades on, there were just 5000 Europeans holding out on the western edge of the continent. Some of the capitalists who had stayed began to rethink their aversion to using cheap prison labour.
In 1850 – just as the practice of sending British convicts to eastern Australia ended – shiploads of male convicts started to arrive in Fremantle harbour.
## Exploration & Gold
Meanwhile, several explorers undertook journeys into the remote Aboriginal territories, drawn in by dreams of mighty rivers and rolling plains of grass 'further out'. Mostly their thirsty ordeals ended in disappointment. But the pastoralists did expand through much of the southwestern corner of WA, while others took up runs on the rivers of the northwest and in the Kimberley.
Perhaps the most staggering journey of exploration was undertaken by an Aboriginal man called Wylie and the explorer Edward Eyre, who travelled from South Australia, across the vast, dry Nullarbor Plain, to Albany.
By the 1880s, the entire European population of this sleepy western third of Australia was not much more than 40,000 people. In the absence of democ racy, a network of city merchants and large squatters exercised political and economic control over the colony.
The great agent of change was gold. The first discoveries were made in the 1880s in the Kimberley and the Pilbara, followed by huge finds in the 1890s at Coolgardie and Kalgoorlie, in hot, dry country 600km inland from Perth. So many people were lured by the promise of gold that the population of the colony doubled and redoubled in a single decade. But the easy gold was soon exhausted, and most independent prospectors gave way to mining companies who had the capital to sink deep shafts. Soon the miners were working not for nuggets of gold but for wages. Toiling in hot, dangerous conditions, these men banded together to form trade unions, which remained a potent force in the life of WA throughout the following century.
Largely set in WA, _Gallipoli_ (1981, directed by Peter Weir, screenplay by David Williamson) is an iconic Australian movie exploring naivety, social pressure to enlist and, ultimately, the utter futility of this campaign.
## The Great Pipeline to Kalgoorlie
The year 1890 also saw the introduction of representative government, a full generation after democracy had arrived in the east. The first elected premier was a tough, capable bushman named John Forrest, who borrowed courageously in order to finance vast public works to encourage immigrants and private investors. He was blessed with the services of a brilliant civil engineer, CY O'Connor. O'Connor oversaw the improvement of the Fremantle harbour, and built and ran the state's rail system. But O'Connor's greatest feat was the construction of a system of steam-powered pumping stations along a mighty pipeline to drive water uphill, from Mundaring Weir near Perth to the thirsty goldfields around distant Kalgoorlie.
By the time Forrest opened the pipeline, O'Connor was dead. His political enemies had defamed him in the press and in parliament, falsely accusing him of incompetence and corruption. On 10 March 1902, O'Connor rode into the surf near Fremantle and shot himself. Today, the site of his anguish is commemorated by a haunting statue of him on horseback, which rises out of the waves at South Beach.
Ironically, just as the water began to flow, the mining industry went into decline. But the 'Golden Pipeline' continues to supply water to the mining city of Kalgoorlie, where gold is once again being mined, on a Herculean scale unimaginable a century ago. Today you can visit the No 1 Pump Station at Mundaring Weir and follow the Golden Pipeline Heritage Trail as a motorist from Perth to Kalgoorlie, where you can visit the rather astonishing Super Pit.
## The Stolen Generations
At the turn of the century, the lives of many Aboriginal people became more wretched. The colony's 1893 Education Act empowered the parents of white schoolchildren to bar any Aboriginal child from attending their school, and it was not long before Aboriginal people were completely excluded from state-run classrooms. The following decade, the government embarked on a policy of removing so-called 'half-caste' children from their parents, placing them with white families or in government institutions. The objective of the policy was explicit. Full-blood Aboriginal people were to be segregated, in the belief that they were doomed to extinction, while half-caste children were expected to marry whites, thereby breeding Aboriginal people out of existence. These policies inflicted great suffering and sorrow on the many Aboriginal people who were recognised in the 1990s as 'the stolen generations'.
## Wars & the Depression
On 1 January 1901, WA and the other colonies federated to form the nation of Australia. This was not a declaration of independence. This new Australia was a dominion within the British Empire. It was as citizens of the empire that thousands of Australian men volunteered to fight in the Australian Imperial Force when WWI broke out in 1914. They fought in Turkey, Sinai and in Europe – notably on the Somme. More than 200,000 of them were killed or wounded over the terrible four years of the war. Today, in cities and towns across the state you will see war memorials that commemorate their service.
Though mining, for the time being, had ceased to be an economic force, farmers were developing the lucrative WA wheat belt, which they cultivated with the horse-drawn stump-jump plough, one of the icons of Australian frontier farming. At the same time, a growing demand for wool and beef and the expansion of dairying added to the state's economic growth.
Nevertheless, many people were struggling to earn a living – especially those ex-soldiers who were unable to shake off the horrors they had endured in the trenches. In 1929, the lives of these 'battlers' grew even more miserable when the cold winds of the Great Depression blew through the towns and farms of the state. So alienated did West Australians feel from the centres of power and politics in the east that, in 1933, two-thirds of them voted to secede from the rest of Australia. Although the decision was never enacted, it expressed a profound sense of isolation from the east that is still a major factor in the culture and attitudes of the state today.
In 1939, Australians were once again fighting a war alongside the British, this time against Hitler in WWII. But the military situation changed radically in December 1941 when the Japanese bombed the American fleet at Hawaii's Pearl Harbor. The Japanese swept through Southeast Asia and, within weeks, were threatening Australia. Over the next two years they bombed several towns in the north of the state, including Broome, which was almost abandoned.
It was not the British but the Americans who came to Australia's aid. As thousands of Australian soldiers were taken prisoner and suffered in the torturous Japanese prisoner-of-war camps, West Australians opened their arms to US servicemen. Fremantle was transformed into an Allied naval base for operations in the Indian Ocean, while a US submarine-refuelling base was established at Exmouth. In New Guinea and the Pacific, Americans and Australians fought together until the tide of war eventually turned in their favour.
When _Australia II_ won the America's Cup in 1983, Australian Prime Minister Bob Hawke opined, 'Any boss who sacks a worker for not turning up today is a bum'.
## Postwar Prosperity
When the war ended, the story of modern Western Australia began to unfold. Under the banner of 'postwar reconstruction', the federal government set about transforming Australia with a policy of assisted immigration, designed to populate Australia more densely as a defence against the 'hordes' of Asia. Many members of this new work force found jobs in the mines, where men and machines turned over thousands of tonnes of earth in search of the precious lode. On city stock exchanges, the names of such Western Australian mines as Tom Price, Mt Newman and Goldsworthy became symbols of development, modernisation and wealth. Now, rather than being a wasteland that history had forgotten, the west was becoming synonymous with ambition, and a new spirit of capitalist pioneering. As union membership flourished, labour and capital entered into a pact to turn the country to profit. In the Kimberley, the government built the gigantic Ord River Irrigation Scheme, which boasted that it could bring fertility to the desert – and which convinced many Western Australians that engineering and not the environment contained the secret of life.
There was so much country, it hardly seemed to matter that salt was starting to poison the wheat belt or that mines scoured the land. In 1952 the British exploded their first nuclear bomb on the state's Monte Bello Islands. And when opponents of the test alleged that nuclear clouds were drifting over Australia, the government scoffed. The land was big – and anyway, we needed a strong, nuclear-armed ally to protect us in the Cold War world.
Once bankrupt and convicted of corporate fraud, Alan Bond's wealth was estimated at $265 million by _Business Review Weekly_ in 2008.
This spirit of reckless capitalism reached its climax in the 1980s when the state became known as 'West Australia Inc' – a reference to the state in operation as a giant corporation in which government, business and unions had lost sight of any value other than speculation and profit. The embodiment of this brash spirit was an English migrant named Alan Bond, who became so rich that he could buy anything he pleased. In 1983 he funded a sleek new racing yacht called _Australia II_ in its challenge for the millionaire's yachting prize, the America's Cup. Equipped with a secret – and now legendary – winged keel, the boat became the first non-American yacht to win the race. It seemed as though everyone in Australia was cheering on the day Bond held aloft the shining silver trophy.
But in the 1990s, legal authorities began to investigate the dealings of Alan Bond, and of many other players in West Australia Inc. Bond found himself in court and spent four years in jail after pleading guilty to Australia's biggest corporate fraud.
### WESTERN AUSTRALIA IN BLACK & WHITE
Like other Aboriginal Australians in the rest of the country, the 70,000 or so who live in WA are the state's most disadvantaged group. Many live in deplorable conditions; outbreaks of preventable diseases are common, and infant-mortality rates are higher than in many developing countries. Indigenous employment in the resources sector is slowly increasing, but the mining boom has not alleviated indigenous social and economic disadvantage to any large degree.
In 1993, the federal government recognised that Aboriginal people with an ongoing association with their traditional lands were the rightful owners, unless those lands had been sold to someone else.
Despite this recognition, the issue of racial relations in WA remains a problematic one, and racial intolerance is still evident in many parts of the state.
## The State Today
WA's mining boom of the early 21st century continues to make the state one of the most dynamic parts of the country. The populations of Perth and key mining areas like the Plibara are growing faster than east-coast Australia, with many of the state's total population of 2.4 million originally born overseas. There are substantial South African and British communities in Perth, and many New Zealanders and Irish immigrants are taking advantage of employment opportunities in the mining and resources sector. In the case of the Kiwis, they are the ultimate in mobile FIFO ('fly in, fly out') workers, some making the seven-hour flight back home to New Zealand between contracts.
Despite occasional warnings of a slow-down in the Chinese and Indian economies fuelling the mining boom, there's still plenty of optimism in the resources sector. However, the benefits are not spread equally, and for many Perth and WA residents not earning a mine worker's salary, the high costs of accommodation and eating out can be a struggle. WA's high prices, the global financial crisis and a strong Australian dollar have all conspired to put a dampener on the tourism sector, with the north of the state particularly hard hit.
With the huge economies of Asia in close proximity – Indonesia and Vietnam are also being touted as the next countries to drive growth in the mining and agricultural sectors – WA's future remains inexorably linked to the resources under the state's red earth. Huge new developments are planned for the Kimberley region, and even areas around Exmouth and Ningaloo are potentially being dragged into a mining way of life.
Welcome to Australia's biggest environmental battleground of the 21st century.
Timeline
40,000 years ago
First humans arrive on the shores of Australia.
Up to 6000 years ago
Aboriginal communities from northwestern Australia trade and interact with Macassan fishermen from Sulawesi.
1616
Dutch explorer Dirk Hartog lands on an island in Shark Bay, marking his visit with a pewter plate on which he inscribed a record of his visit.
1629
Debauchery, rape and murder break out while the _Batavia_ is shipwrecked at the Houtman Abrolhos Islands. All crew but two are subsequently executed at senior merchant Francisco Pelsaert's behest.
1697
Willem de Vlamingh replaces Hartog's plate with his own.
1826
The British army establishes a military post in Albany, on the southern coast.
1829
Led by Captain James Stirling, a boatload of free immigrants land in the territory of the Noongar people.
1829
Governor Stirling declares all surrounding Aboriginal lands to be the property of King George IV. Perth is founded.
1834
The Battle of Pinjarra occurs after Stirling leads a punitive expedition against the Noongar. It is thought that 25 Aboriginal people are shot, with Stirling's camp suffering one fatality.
1840–41
An Aboriginal man called Wylie and explorer Edward Eyre make a staggering journey across the Nullarbor Plain to Albany.
1850
Shiploads of male convicts start to arrive in Fremantle. They go on to build key historical buildings such as Fremantle prison, Government House and Perth Town Hall.
1860s
With no democracy, a network of city merchants and squatters exercises control over the colony.
1880s–90s
Gold changes everything. The first discoveries are in the Kimberley and the Pilbara, followed by massive finds in Coolgardie and Kalgoorlie.
1890
The state's first trade unions are formed by three men. Unions exert a substantial influence for the following century.
1890
Representative government is formed. Bushman John Forrest is the first elected premier.
1893
Inception of the Education Act, which allows white parents to bar Aboriginal children from schools. What follows is a policy of removal of 'half-caste' children from their parents.
1901
WA and the other colonies are federated to form the nation of Australia.
1902
Following false accusations of incompetence and corruption, CY O'Connor, engineer of the great pipeline from Perth to Kalgoorlie, takes his own life at a Fremantle beach.
1914
Over 200,000 are killed or wounded in WWI.
1933
Two-thirds of the voting population votes to secede from the rest of the country. Although never enacted, secession remains topical.
1939
WWII begins. Several towns in WA's north, including Broome, are bombed during the war. Fremantle is turned into an Allied naval base, and a US submarine-refuelling base is established at Exmouth.
1963
Development of the gargantuan Ord River Irrigation Scheme to fertilise the desert.
1967
Australia's Indigenous Aboriginal people are recognised as Australian citizens and granted the right to vote.
1970
The Indian Pacific train completes its first trans-continental journey from Sydney to Perth.
1979
The Skylab space station crashes in the state's remote southeastern sector. Remnants are now at the Esperance Museum.
1980s
The state becomes known as WA Inc, a reference to its image as a giant corporation intent on speculation and profit.
1983
'Bondie' (Alan Bond) funds the racing yacht _Australia II,_ which wins the America's Cup with its secret winged keel. Bond is later jailed for corporate fraud.
1987
Sleepy Fremantle is transformed for Australia's first defence of America's Cup. Australia loses 5-0 to the United States.
1990s
Aboriginal rock art (the Bradshaw paintings), featuring distinctive stick-like images, possibly the earliest figurative painting, is found in the Kimberley. The stolen generations are formally recognised.
1995
The Fremantle Dockers join the Australian Football League.
1998
One of Australia's most infamous trade union battles is waged in Fremantle between the Maritime Union and Patrick Corporation (a stevedore company).
2000s
Unparalleled economic growth due to the mining boom.
Local Produce & Wineries
Regional produce and local wines are the highlights of Western Australia (WA), and leisurely, outdoor eating is best experienced in the vineyard restaurants of the Margaret River, the Porongurups, Denmark and the Swan Valley. Select spots up north – Geraldton, Broome, Kununurra, Exmouth – include a few local gems.
The Wine Industry Association of Western Australia (www.winewa.asn.au) runs wine courses for consumers and the industry.
Regional produce includes marron (small freshwater crayfish unique to the southwest), crayfish (rock lobster, from up north), McHenry Hohnen beef (Margaret River) and barramundi (the Kimberley). Much of WA's best produce is also available at supermarkets and delicatessens. Look out for Browne's iced coffee and yoghurts, Harvey Fresh products – especially its fresh orange juice – and excellent chilli mussels.
Perth's leading chefs celebrate the region's produce by showcasing Manjimup truffles, Mt Barker chicken and Shark Bay scallops. Top-end spots in the central city include Restaurant Amusé, Print Hall and Greenhouse, Mt Lawley has Must Winebar and Jackson's, and Nahm Thai is in Northbridge. Excellent midrange cafes and bistros like Duende, Cantina 663 and Canvas abound in Perth and Fremantle. Regional dining highlights include The Studio Bistro near Yallingup, Pepper & Salt in Denmark, and Albany's York Street Cafe.
Across the state you can easily pay too much for pathetic pasta or a boring burger, and unfortunately lax service and attention to detail is often prevalent both in Perth and regional WA.
### WA COOKBOOKS & COOKING CLASSES
» Wine and Food by Kate Lamont. Winemaker and chef Kate Lamont unpretentiously matches food with wine – chapters are helpfully organised into champagne, light whites, robust whites, dessert wines etc.
» Whole Food by Jude Blereau. A straightforward cookbook devoted to unprocessed food. Blereau has been promoting whole food in Perth for the last two decades or so.
» Degustation by Alain Fabrègues. This mini-shrine to French degustation is produced by the chef at the Loose Box, a renowned dining destination in Mundaring.
» Must Eat by Russell Blaikie. A nicely done French-style working cookbook that prises out the best of the region's produce – Cone Bay barramundi, Mt Barker chicken, Jarrahdene free-range pork.
» Seek hands-on inspiration with a cooking class at Wildwood Valley near Yallingup or Foragers Field Kitchen near Pemberton.
The best value can usually be found at the top end, and then budget spots like farmers markets and Northbridge's Asian eateries.
Tipping is not required in WA.
## Local Beer
WA's leading working-class beers are Emu Bitter (EB) and Swan Draught. They're both pretty bland, so focus instead on exploring the craft-beer scene. In Fremantle, and the southwest in particular, local microbreweries abound, and the Swan Valley is also a top spot.
In Fremantle, visit the Sail & Anchor and the Monk for blackboards full of ever-changing brews. Freo also has the iconic Little Creatures, now owned by a multi-national company but still tasting great with its hoppy Pale Ale.
In the Swan Valley, the best craft breweries are Feral Brewing Company and Mash Brewing, and Mash also has locations in Bunbury and Rockingham.
Continuing south, the Margaret River region is emerging as a craft-beer hot spot – see our picks on Click here – and Denmark's Boston Brewing Company and Pemberton' Jarrah Jacks are also worth visiting. In Albany, there's the excellent Tanglehead Brewery at the White Star Hotel, and good beers and ciders are crafted at the Cidery in Bridgetown.
Up north, the only craft brewery you'll find is Matso's in Broome. EB and Swan are surprisingly difficult to find, and Carlton, XXXX and Tooheys dominate the mainstream market.
Australian beer has a higher alcohol content than British or American beers. Standard beer is around 5% alcohol (midstrength is around 3.5%, light 2% to 3%).
BYO – bringing your own beer or wine to the restaurant – is a widely accepted and budget-friendly practice.
## Wine & the Cellar Door
Wine is a big deal, with the focus firmly on the quality end of the market. For example, the Margaret River region produces only 3% of Australia's grapes but accounts for over 20% of the country's premium wines.
The first wineries began in the southwest in the 1960s, and Vasse Felix was a notable early player. Because the southwest has always focused on low-yield, quality output, it wasn't as influenced by the problems of oversupply that beset the Australian wine industry in 2005 and 2006. Fortuitous combinations of rain and warm weather also produced consistently excellent Margaret River vintages from 2007 to 2011.
Aside from Margaret River, other key winery regions are the Swan Valley, the Great Southern (Frankland, the Porongurups, Denmark, Mt Barker) region, Pemberton, and the Peel and Geographe regions. These all uphold WA's reputation as a world-class wine producer.
### Margaret River
WA's best wineries are in Margaret River, 250km (3½ hours' drive) southwest of Perth. The climate is defined by cooling ocean breezes, producing Margaret River's distinctively elegant and rich wines.
Margaret River also produces many blends of semillon and sauvignon blanc grapes. These very popular fruity wines are not Margaret River's very best, but they are often the most affordable. Cape Mentelle, Cullen Wines and Lenton Brae all make good examples. Cullen Wines is also renowned for its organic and sustainable approach to winemaking.
### MARGARET RIVER'S FOUNDING FIVE
Five top wineries compose the cornerstone of Margaret River.
» Cape Mentelle Makes consistently excellent cabernet sauvignon and a wonderful example of sauvignon blanc semillon.
» Cullen Wines (Click here ) Still in the family, producing superb chardonnay and excellent cabernet merlot while adhering to sustainable winemaking principles.
» Leeuwin Estate (Click here ) Stylish cellar door, a highly regarded restaurant, and put chardonnay on the map in Australia with its Art Series.
» Moss Wood Makes a heady semillon, a notable cabernet sauvignon and a surprising pinot noir.
» Vasse Felix (Click here ) Must-see winery with a renowned restaurant.
### Swan Valley
The Swan Valley may once have aspired to take on mighty Margaret River, but now the region's true merit lies in its proximity to Perth and its small clutch of winery-restaurants – not the wines per se. It's hotter than down south, so leisurely outdoor-dining opportunities are better. You can also travel from Perth along the Swan River to the Sandalford Winery.
Houghton Wines is the area's best winery, and the Houghton Classic White, a blend of white-wine grapes that tastes like a mix of tropical, zesty fruits, is the Swan Valley's most ubiquitous wine. Others of note include Lamont Wines and Sandalford. Best for lunch are Riverbank Estate and Lamont's (tapas only).
### Peel & Geographe Regions
Because the Peel region starts about 70km south of Perth, it's often hot, dry and rugged. Much like the Swan Valley, wine here is not generally considered of great significance. Millbrook Winery, relatively close to Perth, is excellent for lunch, with a verandah right beside the vines.
Further south, in the slightly cooler Geographe region, are wineries of varying quality, and many people come to visit Capel Vale. This winery has a 30-year history of winemaking excellence, particularly with chardonnay, shiraz and, more recently, merlot. Willow Bridge Estate also produces well-priced wines, with its whites attracting attention.
Wine for Dudes ( Click here ) has excellent wine tours led by a winemaker. It also visits craft breweries around Margaret River.
### Great Southern & Pemberton
The Great Southern region will never challenge Margaret River's pre-eminence among wine-touring regions – Margaret River is so spectacularly beautiful – but it nevertheless produces good-quality wines. Wine tourism here is not as developed, and that can be a good thing. Shiraz, cabernet sauvignon, riesling and sauvignon blanc do especially well.
The region stretches from the southeast town of Frankland, further southeast to Albany, and then west again to Denmark. Mt Barker, in the middle, is 350km southeast of Perth. The Great Southern's wines are full of flavour and power, and have a sense of elegance – try the peppery shiraz.
In Frankland, Alkoomi is still a family-run business, and produces great cabernet sauvignon and riesling. Ferngrove produces an honest chardonnay, an excellent shiraz and a brilliant cabernet sauvignon–shiraz blend called 'the Stirlings'. Frankland Estate is one of the key wineries that has helped revitalise riesling.
There are more wineries southwest of Frankland, in Mt Barker, and among the nearby Porongurup range. Riesling and shiraz are consistently great performers here; also try the lean, long-flavoured cabernet sauvignon. Two of the best are Forest Hill (try its cabernet sauvignon) and Plantagenet Wines, the area's best winery.
Further south, in Denmark and Albany, are some of Australia's most esteemed wine names. Howard Park, the area's standout, has superb cabernet sauvignon, riesling and chardonnay. West Cape Howe is a straightforward winery that's excellent value, and Wignall's Wines is noted for its pinot noir.
For information and tasting notes about Western Australian wines, and to shop online for reds and whites, visit www.mrwines.com.
Travelling east of Margaret River in the direction of the Great Southern wine region, you'll hit the Pemberton–Manjimup area (280km due south of Perth). Pemberton is a beautiful, undulating area home to forests of the area's famous karri trees, and its cool-ish climate produces cooler wine styles – pinot noir, merlot and chardonnay, in particular. Excellent producers in Pemberton are Salitage Wines and Smithbrook Wines. Salitage is a large, stylish winery and the wines back it up. Try one of the winery tours. Smithbrook Wines has excellent merlot.
### ESSENTIAL CELLAR-DOOR STOPS
A second set of wineries that remain standouts:
» Devil's Lair Small, cosy, stylish cellar door with top-of-the-line chardonnay and cabernet.
» Happs Impressive wines, including the Three Hills range.
» Pierro Powerful chardonnay and sauvignon blanc.
» Voyager Estate (Click here ) Great wines, and an elegant cellar door and restaurant.
» Xanadu (Click here ) Broad range, decent cellar door and restaurant.
Boom Town: Mining & the Environment
If you fly into Perth, you'll notice one thing straight away. The fly-in, fly-out 'FIFO' lifestyle is not only ubiquitous but now the norm. Large clutches of workers nonchalantly board their flights to remote mines and oil and gas plants every few hours. Some will be wearing their fluorescent orange or yellow 'high-vis' vests, required attire on site and perhaps an understated badge of honour at the airport.
The 'four weeks on, one week off' fly-in, fly-out schedule on the mines is referred to as the 'divorce roster'.
## How It All Got Started
Really, mining is old news – this is a frontier land founded on mining money. Although in the 1800s Western Australia (WA) was once quietly focused on acquiring more modest fortunes from wheat, meat and wool, gold was discovered in Coolgardie in 1892, and in Kalgoorlie in 1893. And so the transformation to riches began. Today, gold mining is still going strong, albeit with incrementally diminishing returns. In Kalgoorlie you can visit the Super Pit, an open-pit gold mine the size of 35 football fields sunk 360m into the ground. Copper, nickel, oil and gas are also a steady source of state income, with uranium mining (slated for Wiluna, in the midwest) a current aspiration.
But iron ore is today's multi-billion-dollar blockbuster industry. Karara mine in the midwest, for example, sits on just under $100 billion worth of iron ore. All this magnetite dug up out of the ground, later to become iron ore, is expected to generate $3 billion per year in export revenue for the next 30 years. Most of it will go to China.
Of course, foreign investment is big business. And while such major investment has now been criticised for exposing the state to the twisting fortunes of the Chinese economy, the boom would never have occurred without it. For an iron-ore mine, for example, about $1 billion must be available up front just to develop the extraction machinery. These biscuits are just too big for the Australian economy alone.
## Life on the Mines
The source of the state's affluence remains outside many travellers' field of view. Take the Pilbara gold-mining town of Telfer, for instance, considered the most remote town in WA. Life here is altogether different to that in the leafy western suburbs of Perth. For Telfer is less traditional country town (with main street, two quiet pubs, maybe a community town hall) and more giant mine plus attendant camp, purpose-built for its hundreds of workers.
### The Birth of the Mobile Workforce
In efforts to accommodate a work force that periodically grows and shrinks, Telfer has been dismantled and rebuilt a few times by mining companies over the years. But then in the mid-1990s it was discovered that it was cheaper to simply fly the entire work force in and out rather than continually build and reconstruct permanent accommodation. Under the new plan, those flown in would work for a sustained period of time (say four weeks), then have a week or two off back home – in Perth or over east. The company would then be able to draw from a broader, more skilled labour force, and workers would no longer need to contemplate the unattractive lifestyle of living permanently in the middle of nowhere. As this business model was adopted across the state, the FIFO work culture was born.
_Field Guide to the Birds of Australia_ is full colour, splendidly detailed, accessible and portable. This endlessly fascinating reference, Pizzey and Knight's claim to fame, is in its 8th edition.
### Setting Up Camp
The FIFO lifestyle is perhaps no more apparent than in Karratha, once a sleepy, nondescript town but today infamous for its bulging FIFO population, expensive food and severe accommodation shortages. Woodside, a major oil and gas producer, has set up camp here, exploring for gas off the north coast. The pace of expansion was so speedy, in fact, that there wasn't time to build brick-and-tile homes for the workers. And so today in Karratha, bolted on to the original small town centre, are a number of suburbs composed of 'dongas' – makeshift, moveable, one-man accommodation units. A typical donga in Gap Ridge, the main suburb, has a single bed, a TV, a shower and a toilet carved into a shipping-container-like box-home. Meals are taken in the 'wet mess' (much like a mess hall).
Karratha locals have for some time been voicing concerns that an entire FIFO population parties in their town without regard for the community. Places like Gap Ridge are home to an almost entirely young, moneyed, male population, and this has created a pattern of influx and change in Karratha that is echoed in other mining towns across the state. Many labourers are away from home and family, and have considerable funds to sink into beer and good times.
Such social shifts have not gone unnoticed by politicians, including Premier Colin Barnett. One initiative rolled out since the peak of the boom is 'Royalties for Regions' – putting money back into regional areas like Karratha, which had not been able to easily build much-needed infrastructure despite the boom. Mobile-phone coverage is now being expanded on the remote highways.
Tim Flannery's _The Future Eaters_ is a highly readable overview of evolution in Australasia, covering the last 120 million years of history, with thoughts on how the environment has shaped Australasia's human cultures.
### Work Hard, Play Hard
Drinking has long been part of Australian culture, but FIFO workers off the clock focus particularly keenly on playing hard. Throughout the global financial crisis (or 'GFC' in Australian parlance), letting off steam over a few beers simply continued apace for many. But by late 2012, dropping iron-ore and nickel prices had started to reduce the number of nights out on the town: jobs had been shed. And it is perhaps those who hold the mantra 'work hard, play hard' most closely to their hearts who have been found to be most vulnerable to shakes in the economy. Many young workers have limited education and have been earning big sums from a young age. For some, the upkeep of their lifestyle (jet skis, cars, houses) has always been contingent on a mining salary that did not waver. When it does, there may be no Plan B.
## You're In or You're Out
Aboriginal Australian employment is very low within the mining industry. Some argue that training programs for Aboriginal Australians – attempts to settle Australia's most disadvantaged into the western working life – have not proved effective. Mining magnate Andrew 'Twiggy' Forrest (whom Forbes labelled Australia's richest man in 2010) in 2008 boldly promised support for 50,000 jobs for Aboriginal Australians. This government-backed program is also one of the most high-profile attempts by a key mining figure to not only change employment patterns but also speak frankly about the lack of opportunity afforded to Aboriginal communities across the state. Just how the 50,000 jobs will be effectively taken up in the long term is yet to be determined, and that will be the tricky bit. By late 2012, fours years after the program was developed, some 10,000 positions had been taken up.
It is now more widely acknowledged that the gap between the resource boom–driven 'haves' and 'have-nots' is real and ever increasing, with signs of economic strain creeping up the social strata. The tension between income and cost of living – strongly driven by the high cost of housing – has become so tight that some middle-class workers employed on good salaries struggle to pay the rent. Foreign financial investment is gargantuan, and it will likely be here for some years to come. But patterns of job losses, however intermittent, are causing many to wonder aloud how long the good times will last.
In _The Weather Makers_ , Tim Flannery argues lucidly and passionately that there is an immediate need to address the implications of a global change in climate that is damaging all life on earth and endangering our very survival. An accessible read.
## The Environmental Flashpoints
Enter James Price Point, an expanse of wilderness along the Kimberley coast 60km north of Broome. A multinational consortium and the WA state government are proposing a liquefied natural gas (LNG) station here – the biggest in the world.
James Price Point has become a leading symbol of tensions between the growing financial fortunes of the state and the less easily quantified value of a pristine, untouched landscape. Not only are mining interests, traditional land owners, politicians and environmentalists in fierce disagreement with each other but also divisions within these groups run deep. For locals in the relatively small community of nearby Broome, for instance, 'whose side you're on' is often common knowledge, and this lack of anonymity is a further source of strain.
For the state premier Colin Barnett, successful extraction of the gas at James Price Point would not just award him a badge of honour. It would mark the zenith of the state's contemporary achievements, and he would be leading the charge. In May 2012, in response to noisy but peaceful protestors, over 150 riot police were flown up from Perth to protect the site and quell the clamour.
The approval process for extraction of the gas is lengthy and complex. In July 2012 the state's Environmental Protection Authority (EPA), an independent statutory body that provides environmental advice to government, flashed up a green light of approval, subject to a series of restrictions and amendments that included which areas of land should remain untouched (there are dinosaur tracks in evidence) and when gas could be piped out (not at night during in the whales' migratory and breeding season, please).
Four members of the EPA board who helped develop the initial assessment were stood aside due to conflicts of interest. Two had superannuation shares in Woodside; one had worked for BP, one of the joint-venture partners of the project; and another had worked for a related state government department. (In many respects, WA is – and always has been – a 'small town'.) This left just one member standing: the chairman, Paul Vogel. That initial environmental approval for development of the world's largest LNG station was granted by one individual has been a source of consternation for many. Some claim that the environmental-assessment process was not rigorous enough, and that too much about the area remains unknown. Many others, though, see a seemingly endless expanse of coastline and red dirt and believe that, while the financial fruits of development would be expansive, environmental and cultural costs would be limited.
Aside from its dinosaur fossils, it is thought that the area is a playground for spinner and snubfin dolphins, dugongs and breeding bilbies. Humpback whales breed and calve along the coastline, and the rainforest backing the coast harbours a multitude of plant species. Not least, this is traditional Aboriginal land. Negotiating a native title deed this size would mark a historic achievement.
Keep your eyes peeled for the banded anteater, also known as the numbat. Tiny, light-footed and incredibly shy, the numbat is a solitary creature who will venture outside its neatly delineated territory only to find a mate. Singular dietary requirement: termites.
### Elsewhere on the Land
But WA's environmental flashpoints are by no means limited to James Price Point. Aside from climate change and greenhouse-gas emissions – issues not unique to WA, of course – ground water has been utilised very freely for decades. Alternative water sources, using desalination plants, have been in place for some time. Old-growth forests, with their thousand- year-old karri trees, were logged until the 1990s. Today scientists cite lowered rainfall in the southwest as the result of deforestation. Other controversial sites slated for mining include the Burrup Peninsula on the Dampier Archipelago, also the location of a multitude of petroglyphs (rock art), archaeological wonders thought to date from the last ice age. Although disruption to the works began in the 1960s, in 2007 Woodside had several petroglyphs gingerly removed and fenced off in a separate area to better facilitate development. Some argue that the works are not discrete: disruption of one petroglyph compromises the entire site. Elsewhere in the state, four uranium mines are under consideration.
Head to Ningaloo Reef around April to June to swim alongside many-metres-long, remarkably docile whale sharks.
Much like other major cities in Australia, Perth is subject to suburban sprawl. Because the boom has driven much property development, the city now tails out across 100km, densely studded with so-called affordable housing. The environmental effects of the lifestyle out here are not immediately apparent but may nevertheless prove significant. Many housing estates are divorced from public-transport routes, so people must always drive for their litre of milk, and the roads are becoming increasingly congested. Many have long been calling for more high-density housing in and near the city of Perth.
For detailed directions on where and how to surround yourself with wildflowers, see the Wildflower Society of Western Australia's website (www.members.ozemail.com.au/~wildflowers).
## But Still Booming
Stoushes over the environment are nothing new here. The argument over whether a resort should be developed at Ningaloo, up north, was particularly fierce in the early 2000s (so far development has not gone ahead). And the state is not naive about the environmental dangers of mining. In 2006 and 2007, dangerously high levels of lead were detected after Esperance locals sighted a number of dead birds around the township. Lead had been emitted by local industry, and the Esperance Port Authority has been convicted on lead-contamination charges.
_Boomtown 2050_ , by landscape architect Richard Weller, is a nicely packaged book about how a rapidly growing town like Perth could be developed – sustainably.
But today the stakes seem higher. LNG exploration at James Price Point is a $30-billion project. The boom has spawned a handful of mega-rich mining magnates whose influence extends beyond resources and into politics and the media. Gina Rinehart, daughter of the late iron-ore magnate Lang Hancock, in 2012 became the largest shareholder in Fairfax Media. Much of the state's population has capitalised on opportunities afforded by the resources boom, and tougher times spent sweating over every utilities bill seem a distant memory. What's more, many of these same people have long said goodbye to steady nine-to-five jobs and embraced a more cosmopolitan lifestyle thanks to financial return from the mines; for them to maintain this lifestyle, such returns must continue to materialise. And yet behind all these competing interests, the fact remains that every new mine or gas plant much reach deep into pristine wilderness.
### NINGALOO'S CLOSE SCRAPE
Some locals still sport 'Save Ningaloo' bumper stickers on their cars. No one seems to pay much attention to the faded stickers these days, but they're a reminder of one of the most high-profile and fiercely contested environmental campaigns the state has seen. 'Save Ningaloo', with its thousands of protestors, successfully blocked development of a massive marina resort (slated for 2003) on a loggerhead-turtle nesting ground. Comprising 280km of coral reef, and visited by species such as manta rays, whale sharks, dugongs, humpback whales and turtles, Ningaloo is one of the last healthy major reef systems in the world.
The area has nevertheless remained a site of interest for property developers and the resources sector. In late 2012 BHP Billiton submitted a proposal to the state government to explore for LNG some 5km from Ningaloo's perimeter. Regardless of whether exploration goes ahead, the condition of this World Heritage–listed reef will remain precarious and controversial.
Locals are fond of wryly mentioning the increasing numbers of educated Irish now coming to toil as FIFO workers. At first glance it seems to be a modern echo of colonial days, but for many it's a reminder that the economic climate is altogether better in WA than overseas. Many Western Australians still feel lucky.
ENvironmental Battles Waged & Continued
1970s
Environmentalists take on and defeat the Albany whaling industry.
1980s
Clashes with loggers over the old-growth jarrah, karri and wandoo forests in the southwest.
2000s
Development of a $200-million marina resort at Ningaloo Reef is prevented.
Today
Controversy over a liquefied natural gas (LNG) refinery at the Kimberley's James Price Point.
Indigenous Art in Western Australia
Experiencing the Indigenous art of Western Australia (WA) creates an indelible link for travellers to this land of red dirt and desert expanses. Ancient rock art echoes across the centuries, traditional designs and motifs inspire modern artists, and indigenous tour operators inform with stories of spirituality, bush tucker and country.
The Western Desert Mob (www.westerndesertmob.com.au) is a coalition of artists cooperatives of the Ngaanyatjarra lands of Western Australia. Mediums include _punu_ , the traditional art of woodcarving.
## Indigenous Art
### Rock Art
Some Aboriginal rock paintings are believed to date back between 18,000 and 60,000 years and provide a record of changing environments and lifestyles over the millennia. For the local Indigenous people, rock-art sites are a major source of traditional knowledge – their historical arch-ives in place of a written form.
The earliest hand or grass prints were followed by a naturalistic style, with large outlines of people or animals filled in with colour. Then came the dynamic style, in which motion was often depicted (a dotted line, for example, to show a spear's path through the air). In this era the first mythological beings appeared, with human bodies and animal heads. Following this were simple human silhouettes, and then the more recent x-ray style, displaying the internal organs and bones of animals.
### WHERE TO SEE ROCK ART
» Mulkas Cave, near Wave Rock and Hyden
» Around Esperance with Kepa Kurl ( 08-9072 1688; www.kepakurl.com.au; Museum Village)
» The Wandjina and Gwion Gwion images of the Kimberley
» Mitchell Falls in the Kimberley
» Mt Elizabeth Station on the Gibb River Road
### Art of the Kimberley
The art of the Kimberley is perhaps best known for its images of the Wandjina, a group of ancestral beings who came from the sky and sea and were associated with fertility. They controlled the elements and were responsible for the formation of the country's natural features.
Wandjina images are found painted on rock as well as on more recent contemporary media; some of the rock images are more than 7m long. They generally appear in human form, with large black eyes, a nose but no mouth, a halo around the head (representative of both hair and clouds) and a black oval shape on the chest.
Each Wandjina traditionally has its own custodian family, and to ensure good relations between the Wandjina and the people, the images have to be retouched annually.
One of the other significant styles of painting found in the Kimberley is that of the Gwion Gwion figures (also named the Bradshaw images after the first non-Indigenous person who saw them). The Gwion Gwion figures are generally small and seem to be of ethereal beings depicted engaged in ceremony or dance. It is believed that they pre-date the Wandjina paintings, though little is known of their significance or meaning.
### BEST NORTHERN GALLERIES
» Gecko Gallery ( 08-9192 8909; www.geckogallery.com.au; 9 Short St, Broome; 10am-6pm Mon-Fri, to 2pm Sat & Sun dry season, shorter hours in wet season)
» Short Street Gallery ( 08-9192 2658; www.shortstgallery.com.au; 7 Short St, Broome; 10am-5pm Mon-Fri, to 2pm Sat)
» Mowanjum Art & Culture Centre ( 08-9191 1008; www.mowanjumarts.com; Gibb River Road, Derby; 9am-5pm daily dry season, closed Sat & Sun wet season)
» Waringarri Aboriginal Arts Centre ( 08-9168 2212; www.waringarriarts.com.au; 16 Speargrass Rd, Kununurra; 8.30am-4.30pm Mon-Fri, dry season 10am-2pm Sat)
» Red Rock Art Gallery ( 08-9169 3000; 50 Coolibah Dr, Kununurra; 10am-4pm Mon-Fri)
### Western Desert Painting
Western Desert painting, also known as dot painting, is probably the most well known of indigenous painting styles. It partly evolved from 'ground paintings', which formed the centrepiece of dances and songs. These were made from pulped plant material, with designs made on the ground. While dot paintings may look random and abstract, they depict Dreaming stories and can be read in many ways, including as aerial landscape maps. Many paintings feature the tracks of birds, animals and humans, often identifying the land's ancestral beings. Subjects may be depicted by the imprint they leave in the sand – a simple arc depicts a person (as that is the print left by someone sitting cross-legged), a coolamon (wooden carrying dish) is shown by an oval shape, a digging stick by a single line, and a campfire by a circle. Men or women are identified by the objects associated with them: digging sticks and coolamons for women, spears and boomerangs for men. Concentric circles usually depict Dreaming sites, or places where ancestors paused in their journeys.
While these symbols are widely used, their meaning in each painting is known only by the artist and the people closely associated with them – either by clan or by the Dreaming – since different clans apply different interpretations to each painting. In this way sacred stories can be publicly portrayed, as the deeper meaning is not revealed to uninitiated viewers.
## Buying Aboriginal Art Ethically
By buying authentic items you are supporting indigenous culture and helping to ensure that traditional and contemporary expertise and designs continue to be of economic and cultural benefit to indigenous individuals and communities. Unfortunately, some of the so-called indigenous art sold as souvenirs is ripped off, consisting of appropriated designs illegally taken from indigenous people or just plain fake, and sometimes made overseas by underpaid workers. Artworks should have a certificate of authenticity. Note that haggling is not part of Aboriginal culture.
The best place to buy art is either directly from the communities that have art collectives, or from galleries and outlets that are owned and operated, or supported by indigenous communities. You can then be sure that the items are genuine and that the money you spend goes to the right people. However, some indigenous artists continue to be paid small sums for their work, only to find it being sold for much higher prices in commercial galleries in cities that don't have the interest of the communities producing the art as their priority.
To negate this, it's vital to do some research. The Australian Commercial Galleries Association (www.acga.com.au) lists galleries considered to observe ethical practices. Another excellent organisation is Solid Arts, with its online portal (www.solidarts.com.au) offering support for indigenous artists and ethical considerations to keep in mind when purchasing indigenous art.
### BEST SOUTHERN GALLERIES
» Art Gallery of Western Australia (www.artgallery.wa.gov.au; Perth Cultural Centre; 10am-5pm Wed-Mon) Perth.
» Indigenart (www.mossensongalleries.com.au; 115 Hay St; 10am-5pm Mon-Fri, 11am-4pm Sat) Perth.
» Japingka (www.japingka.com.au; 47 High St; 10am-5.30pm Mon-Fri, noon-5pm Sat & Sun) Fremantle.
» Tunbridge Gallery (www.tunbridgegallery.com.au; 101 Bussell Hwy; 10am-5pm Mon-Sat, to 3pm Sun) Margaret River.
» Kepa Kurl Art Gallery (www.kepakurl.com.au; cnr Dempster & Kemp Sts; 10am-4pm Mon-Fri & market Sun) Esperance.
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### Accommodation
Accommodation in Western Australia ranges from camping grounds to high-end hotels. Perth's accommodation is generally more expensive, although Margaret River, Broome, the Coral Coast and Pilbara mining towns come very close. For simplicity, reviews in this book use the same price categories throughout the state.
Over summer (December to February) and around school and public holidays, prices are at their highest. Outside these times discounts and lower walk-in rates can be found. One exception is the far north, where the wet season (November to March) is the low season and prices can drop by as much as 50%.
Accommodation in the Pilbara can be hard to find, due to the fly-in, fly-out (FIFO) mining phenomenon. Camping is often the best option.
### BOOK YOUR STAY ONLINE
For more accommodation reviews by Lonely Planet authors, check out <http://hotels.lonelyplanet.com>. You'll find independent reviews, as well as recommendations on the best places to stay. Best of all, you can book online.
#### B&Bs
Bed and breakfast (B&B) options range from rooms in heritage buildings to a bedroom in a family home. A full cooked breakfast is not the norm. Tariffs for couples are typically in the $150 to $250 range but can be much higher for exclusive properties. For online information, try www.australianbedandbreakfast.com.au, www.babs.com.au or www.ozbedandbreakfast.com.
#### Camping & Caravan Parks
For many travellers, touring with a tent or campervan is the consummate WA experience. In the outback and up north you often won't even need a tent. Check with visitor centres before heading out to confirm locations of free roadside stops. Many stops have been phased out immediately north of Perth but are more frequent further away from the city.
Designated camp sites in national parks cost $7/2 per adult/child with no or basic facilities. Sites with showers (including unpowered caravan sites) cost $9/2. You'll also need to pay entrance fees for many national parks, but only when you enter the park. If you're exploring several parks, pick up a four-week national-park holiday pass ($40). Some national-park camp sites can be booked online. See www.dec.wa.gov.au/campgrounds.
At WA's ubiquitous holiday parks, prices for two people range from $25 (unpowered tent sites) to $40 (powered caravan sites). Many caravan parks are phasing out unpowered sites because they are less profitable. Most holiday parks offer accommodation, from simple chalets to flasher motel units.
Pick up the free _Caravanning, Camping and Motorhoming in WA_ at visitor centres or see www.caravanwa.com.au.
#### Dongas
Commonly found in the outback, especially in mining towns, the donga is basically a prefab tin room (usually air-conditioned) with a single bed, TV and small fridge.
#### Farmstays & Station Stays
The Gascoyne and Pilbara areas are popular spots for station stays, and at some you may be asked to pitch in. Accommodation is either in the main homestead (B&B style, with dinner on request) or in adjacent self-contained cottages. Other farms provide budget options in outbuildings or former shearers' quarters. Search for 'Farmstay' online at www.tacawa.com.au.
#### Hostels
Prices for dorm beds range from $23 to $35, private rooms from $65 to $90. Staff can often help in securing seasonal work.
Some hostels, especially in Perth, are popular as short-term accommodation for FIFO workers, changing the traditional travellers' vibe.
A Youth Hostel Association (YHA; www.yha.com.au) or Hostelling International (HI; www.hihostels.com) annual membership (in Australia $42) gives a 10% discount at participating hostels. Sign up at the first YHA you stay in.
VIP Backpackers (www.vipbackpackers.com) also offers discounts in participating WA hostels. A 12-month membership ($47) offers discounts on accommodation and some transport, tours and activities. Join online, or at VIP hostels.
#### Hotels & Motels
Full-service hotels are rare outside of Perth, and coastal properties tend to be resort-style, with standalone cottages or apartments. Rates vary widely, but there are benefits in booking early, directly with the properties, or at the last minute, on accommodation-booking websites.
In rural areas, book ahead, as motels are used by government workers and tour groups.
#### Pubs
You can sometimes rent a single room at a country pub for not much more than a hostel dorm. If you're a light sleeper, never book a room above the bar. Some pubs also have separate motel-style accommodation.
#### Rental Accommodation
The ubiquitous holiday flat resembles a motel unit but has cooking and often laundry facilities. They're often rented on a weekly basis, and nightly prices are higher for shorter stays. For listings of holiday homes, see www.stayz.com.au.
For self-contained accommodation, many of the places reviewed in this book will suit; with full kitchens, they're a good option to save money by not eating out. Check out the listings flagged as 'cottage', 'chalet', and 'apartment'.
In cities a good alternative is a serviced apartment. Number Six has apartments around Perth, Fremantle and Margaret River, and others are also listed in this book. See boxed text on Click here for tips to offset high accommodation prices, especially in Perth.
### SLEEPING PRICE RANGES
The following price ranges refer to the cheapest double room per night.
$ less than $150
$$ $150 to $250
$$$ more than $250
### Customs Regulations
For comprehensive information on customs regulations, contact the Australian Customs Service ( 02-6275 6666; www.customs.gov.au) .
On arrival, declare all goods of animal or plant origin, as it's vital to protect Australia's unique environment and agricultural industries. If you fail to declare quarantine items, you risk an on-the-spot fine of over $200 or even prosecution and imprisonment. For more information contact the Australian Quarantine and Inspection Service (AQIS; www.daff.gov.au/aqis) .
Duty-free allowances:
» Alcohol – 2.25L
» Cigarettes – 50
» Other goods – up to $900 value; or items for personal use that you will be taking with you when you leave.
### GST REFUNDS
The goods and services tax (GST) is a flat 10% tax on all goods and services with the exception of basic food items (milk, bread, fruits and vegetables etc). By law the tax must be included in the quoted or shelf price, so all prices in this book are GST inclusive.
If you purchase goods with a minimum value of $300 from any one supplier (on the same invoice) no more than 30 days before you leave Australia, you are entitled under the Tourist Refund Scheme (TRS) to a refund of any GST paid. The scheme only applies to goods you take with you as hand luggage or wear onto the plane or ship. You can collect your refund at the airport up to 30 minutes before departure. At Perth airport, the refund counter is just after passport control. For more information, contact the Australian Customs Service.
### Discount Cards
The most common discount card for accommodation, transport and some attractions is the International Student Identity Card (ISIC; www.isic.org) , issued to full-time students aged 12 years and over. See the International Student Travel Confederation (ISTC; www.istc.org) . ISTC also has an International Youth Travel Card (IYTC or Go25), for people between 12 and 26 years of age who are not full-time students. Benefits are equivalent to the ISIC.
### Electricity
### Embassies & Consulates
The principal diplomatic representations to Australia are in Canberra, but many countries are represented in Perth by consular staff.
Remember that while in Australia you are bound by Australian laws. Your embassy will not be sympathetic if you end up in jail after committing a crime locally, even if such actions are legal in your own country.
Canada ( 08-9322 7930; www.canadainternational.gc.ca; 267 St Georges Tce, 3rd fl)
France ( 0406 654 254; www.ambafrance-au.org; 4/105 Broadway, Nedlands)
Germany ( 08-9221 2941; www.canberra.diplo.de; 2 The Esplanade, Level 18, Exchange Plaza)
Irish Embassy ( 02-6214 0000; www.embassyofireland.au.com; 20 Arkana St, Yarralumla, Canberra, ACT)
Netherlands ( 08-9486 1579; http://australia.nlembassy.org; 1139 Hay St)
New Zealand Embassy ( 02-6270 4211; www.nzembassy.com; Commonwealth Ave, Yarralumla, ACT)
UK ( 08-9224 4700; www.fco.gov.uk; 77 St Georges Tce, Level 26, Allendale Sq)
USA ( 08-9202 1224; http://perth.usconsulate.gov; 16 St Georges Tce, 4th fl)
### Gay & Lesbian Travellers
In general Australians are open-minded about homosexuality and, in WA, gays and lesbians are protected by anti-discrimination legislation and share an equal age of consent with heterosexuals (16 years).
Perth has the state's only gay and lesbian venues and its small scene is centred on Northbridge. It's very unlikely you'll experience any problems, although the further away from the main centres, the more likely you are to experience overt homophobia.
Useful resources:
Gay & Lesbian Community Service of WA ( 08-9420 7201; www.glcs.org.au; 2 Delhi St) Information and counselling line.
Gay & Lesbian Tourism Australia (GALTA; www.galta.com.au) Has a handful of WA members offering accommodation and tours.
Q Pages (www.qpages.com.au) Gay and lesbian business directory and what's-on listings.
### Health
Australia is a healthy country for travellers. Malaria and yellow fever are unknown, cholera and typhoid are unheard of, and animal diseases such as rabies and foot-and-mouth disease have yet to be recorded. The standard of hospitals and health care is high.
Few travellers should experience anything worse than an upset stomach or a bad hangover.
#### Before You Go
Bring medications in their original, clearly labelled, containers. A signed and dated letter from your physician describing your medical conditions and medications, including generic names, is also a good idea. If carrying syringes or needles, be sure to have a physician's letter documenting their medical necessity.
### REQUIRED VACCINATIONS
Proof of yellow-fever vaccination is required from travellers entering Australia within six days of having stayed overnight or longer in a yellow-fever-infected country. For a full list of these countries, see the World Health Organization (www.who.int/ith) or the Centers for Disease Control & Prevention (www.cdc.gov/travel) .
#### Insurance
If your health insurance doesn't cover you for medical expenses abroad, consider getting extra insurance – check www.lonelyplanet.com for more information. Find out in advance if your insurance plan will make payments directly to providers or reimburse you later for overseas health expenditures.
#### Availability & Cost of Health Care
Health insurance is essential for all travellers. While health care in Australia is of a high standard and not overly expensive by international standards, considerable costs can build up and repatriation is extremely expensive.
Australia's health-care system is a mixture of privately run medical clinics and hospitals alongside a government-funded system of public hospitals. The Medicare system covers Australian residents for some health-care costs. Visitors from countries with which Australia has a reciprocal health-care agreement (New Zealand, the UK, the Netherlands, Sweden, Finland, Norway, Italy, Malta, Ireland, Slovenia and Belgium) are eligible for benefits to the extent specified under the Medicare program. If you are from one of these countries check the details before departure. In general the agreements provide for any episode of ill health that requires prompt medical attention. For further details see www.humanservices.gov.au and search for 'reciprocal'.
Over-the-counter medications are widely available at pharmacies. These include painkillers, antihistamines for allergies and skin-care products.
Some medications readily available over the counter in other countries are only available in Australia by prescription. These include the oral contraceptive pill, most medications for asthma and all antibiotics. If you take medication on a regular basis, bring an adequate supply and ensure you know the generic name, as brand names may differ.
#### Infectious Diseases
##### Bat Lyssavirus
This disease is related to rabies and some deaths have occurred after bites. The risk is greatest for animal handlers and vets. Rabies vaccine is effective, but the risk to travellers is very low.
##### Dengue Fever
Also known as 'breakbone fever', because of the severe muscular pains that accompany the fever, this viral disease is spread by a species of mosquito that feeds primarily during the day. Most people recover in a few days, but more severe forms of the disease can occur, particularly in residents who are exposed to another strain of the virus (there are four types) in a subsequent season.
##### Giardiasis
Giardiasis is widespread in the waterways around Australia. Drinking untreated water from streams and lakes is not recommended. Water filters, and boiling or treating water with iodine, are effective in preventing the disease. Symptoms consist of intermittent bad-smelling diarrhoea, abdominal bloating and wind. Effective treatment is available (tinidazole or metronidazole).
##### Meningococcal Disease
This disease occurs worldwide and is a risk with prolonged, dormitory-style accommodation. A vaccine exists for some types of this disease, namely meningococcal A, C, Y and W. No vaccine is presently available for the viral type of meningitis.
##### Ross River Fever
The Ross River virus is widespread throughout Australia and is spread by mosquitoes living in marshy areas. In addition to fever the disease causes headache, joint and muscular pains and a rash, before resolving after five to seven days.
##### Sexually Transmitted Diseases
STDs occur at rates similar to those in most other Western countries. Always use a condom with any new sexual partner. Condoms are readily available in chemists and through vending machines in many public places including toilets.
##### Viral Encephalitis
Also known as the Murray Valley encephalitis virus, this is spread by mosquitoes and is most common in northern Australia, especially during the wet season (November to April). This potentially serious disease is normally accompanied by headache, muscle pains and light sensitivity. Residual neurological damage can occur and no specific treatment is available. However, the risk to most travellers is low.
### Insurance
Sign up for a travel-insurance policy covering theft, loss and medical problems.
Some policies exclude designated 'dangerous activities' such as scuba diving, parasailing, or even bushwalking. Ensure your policy fully covers you for activities of your choice. Check you're covered for ambulances and emergency medical evacuations by air.
Worldwide travel insurance is available at www.lonelyplanet.com/travel_services.
### Internet Access
Internet cafes are located across WA but are becoming less prevalent with the growth of smartphones and other internet-enabled mobile devices. Many backpacker hostels and public libraries offer connections. In smaller towns visit the Community Resource Centre. The cost ranges from around $5 an hour in Perth to $10 an hour in locations that are more remote.
The best bets for free wi-fi connections are public libraries and cafes. Wi-fi is becoming more prevalent in accommodation; it's sometimes free in hostels but is often charged for in caravan parks and hotels.
### Legal Matters
Police have the power to stop your car and see your licence (you're required to carry it), check your vehicle for roadworthiness, and compel you to take a breath test for alcohol.
First-time offenders in possession of small amounts of illegal drugs are likely to receive a fine rather than go to jail, but a conviction may affect your visa status. If you remain in Australia after your visa expires, you will officially be classified as an 'overstayer' and could face detention and expulsion, and be prevented from returning to Australia for a period of up to three years.
### Maps
Tourist-information offices usually have serviceable town maps. For more detailed information, the Royal Automobile Club of WA (RACWA; www.rac.com.au) has road maps available (including downloadable route maps). UBD publishes a handy _South West & Great Southern _ book.
Hema Maps (www.hemamaps.com.au) Best for the north, especially the dirt roads.
Landgate (www.landgate.wa.gov.au) State-wide maps and topographical maps for bushwalking.
### PRACTICALITIES
» Key newspapers are the _West Australian_ or the _Australian_ , a national broadsheet, from Monday to Saturday, and the _Sunday Times_ on Sunday.
» TV networks include the ad-free ABC, multicultural SBS, and commercial TV stations Seven, Nine and Ten.
» Tune in to the ABC on the radio – pick a program and frequency from www.abc.net.au/radio.
» DVDs sold in Australia can be watched on players accepting region 4 DVDs (the same as Mexico, South America, Central America, New Zealand, the Pacific and the Caribbean). The USA and Canada are region 1 countries, and Europe and Japan are region 2.
» The metric system is used for weights and measures.
» Smoking is banned on public transport and airplanes, in cars carrying children, between the flags at patrolled beaches, within 10m of a playground and in government buildings. It's also banned within bars and clubs but permitted in al-fresco or courtyard areas.
### Money
All prices in this books are in Australian dollars, unless otherwise stated.
#### ATMs
Bank branches with 24-hour ATMs attached can be found state-wide. In the smallest towns there's usually an ATM in the local pub. Most ATMs accept cards from other banks and are linked to international networks.
#### Cash
The Australian dollar is made up of 100 cents; there are 5c, 10c, 20c, 50c, $1 and $2 coins, and $5, $10, $20, $50 and $100 notes.
Cash amounts equal to or in excess of the equivalent of A$10,000 (in any currency) must be declared on arrival or departure.
Changing foreign currency or travellers cheques is usually no problem at banks throughout WA.
#### Credit & Debit Cards
Visa and MasterCard are widely accepted and a credit card is essential (in lieu of a large deposit) for car hire. Any debit cards connected to the international banking network (Cirrus, Maestro, Plus and Eurocard) will work. Diners Club and Amex are not as widely accepted.
### Photography
Purchase memory cards, batteries and DV tape in larger cities and towns as they're cheaper than in the remote areas. Most photo labs have self-service machines to make your own prints and burn CDs and DVDs.
### Public Holidays
New Year's Day 1 January
Australia Day 26 January
Labour Day First Monday in March
Easter (Good Friday and Easter Monday) March/April
Anzac Day 25 April
Foundation Day First Monday in June
Queen's Birthday Last Monday in September
Christmas Day 25 December
Boxing Day 26 December
### Safe Travel
#### Environmental Hazards
##### Heat Exhaustion & Heatstroke
Heat exhaustion occurs when fluid intake does not keep up with fluid loss. Symptoms include dizziness, fainting, fatigue, nausea or vomiting. On observation the skin is usually pale, cool and clammy. Treatment consists of rest in a cool, shady place and fluid replacement with water or diluted sports drinks.
Heatstroke is a severe form of heat illness that occurs after fluid depletion or extreme heat challenge from heavy exercise. This is a true medical emergency: heating of the brain leads to disorientation, hallucinations and seizures. Heatstroke is prevented by maintaining an adequate fluid intake to ensure the continued passage of clear and copious urine, especially during physical exertion.
##### Hypothermia
Hypothermia is a significant risk, especially during the winter months in southern parts of Australia. Early signs include the inability to perform fine movements (such as doing up buttons), shivering and a bad case of the 'umbles' (fumbles, mumbles, grumbles, stumbles). The key elements of treatment include changing the environment to one where heat loss is minimised, changing out of any wet clothing, adding dry clothes with windproof and waterproof layers, adding insulation and providing fuel (water and carbohydrate) to allow shivering, which builds the internal temperature. In severe hypothermia, shivering actually stops – this is a medical emergency requiring rapid evacuation in addition to the above measures.
### SCHOOL HOLIDAYS
The Christmas season is part of the summer school holidays (mid-December to late January), when transport and accommodation are often booked out, and there are long, restless queues at tourist attractions. There are three shorter school-holiday periods during the year that change slightly from year to year. Generally, they fall in mid-April, mid-July and late September to mid-October.
#### Animal Hazards
Australia is home to some seriously dangerous creatures. On land there are poisonous snakes and spiders, while the sea harbours deadly box jellyfish and white pointer sharks. The saltwater crocodile spans both environments.
In reality you're unlikely to see these creatures in the wild, much less be attacked by one. Far more likely is a hangover after a big night, or getting sunburnt after not wearing sunscreen.
##### Box Jellyfish & Other Marine Dangers
There have been fatal encounters between swimmers and box jellyfish on the northern coast. Also known as the sea wasp or 'stinger', they have venomous ten- tacles that can grow up to 3m long. You can be stung any time, but from November to March you should stay out of the water unless you're wearing a 'stinger suit' (available from sporting shops).
If you are stung, first aid consists of washing the skin with vinegar to prevent further discharge of remaining stinging cells, followed by rapid transfer to a hospital; antivenin is widely available.
Marine spikes from sea urchins, stonefish, scorpion fish, catfish and stingrays can cause severe local pain. If this occurs, immediately immerse the affected area in water as hot as is tolerable. Keep topping up with hot water until the pain subsides and medical care can be reached. The stonefish is found only in tropical Australia; antivenin is available.
##### Crocodiles
In northwest WA, saltwater crocodiles can be a real danger. They live around the coast, and are also found in estuaries, creeks and rivers, sometimes a long way inland. Observe safety signs or ask locals whether an inviting waterhole or river is croc-free before plunging in. The last fatality caused by a saltwater crocodile was in 1987, and attacks occurred in 2006 and 2012.
##### Insects
For four to six months of the year you'll have to cope with flies and mosquitoes. Flies are more prevalent in the outback, where a humble fly net is effective. Repellents may also deter them.
Mozzies are a problem in summer, especially near wetlands in tropical areas, and some species are carriers of viral infections. Keep your arms and legs covered after sunset and use repellent.
The biting midge (sandfly) can be found in WA's northern coastal areas. Locals often appear immune, but it's almost a rite of passage for those heading north to be covered in bites. Cover up at dusk.
Ticks and leeches are also common. For protection, wear loose-fitting clothing with long sleeves. Apply 30% DEET on exposed skin, repeated every three to four hours, and impregnate clothing with permethrin.
##### Sharks
In 2012 there were six major shark attacks in WA, five of them fatal, and most of them involved surfers at more remote beaches. Around popular coastal and city beaches, shark-spotting methods include spotter planes, jet skis and surf lifesavers, and at the time of writing, the WA government had also launched a $20-million program to track, identify and mitigate (ie kill) sharks that are considered to pose an imminent threat. A shark cull was also being discussed, a controversial proposal given that great white sharks are a protected species. See boxed text on Click here for guidelines on how best to avoid a shark attack.
##### Snakes
There are many venomous snakes in the Australian bush, the most common being the brown and tiger snakes. Unless you're interfering with one, or accidentally stand on it, it's extremely unlikely you'll be bitten.
Australian snakes have a reputation that is justified in terms of the potency of their venom, but unjustified in terms of the actual risk to travellers and locals. They are endowed with only small fangs, making it easy to prevent bites to the lower limbs (where 80% of bites occur) by wearing protective clothing (such as gaiters) around the ankles when bushwalking.
The bite marks are small and preventing the spread of toxic venom can be achieved by applying pressure to the wound and immobilising the area with a splint or sling before seeking medical attention. Application of an elastic bandage (you can improvise with a T-shirt) wrapped firmly, but not so tightly circulation is cut off, around the entire limb – along with immobilisation – is a life-saving first-aid measure.
##### Spiders
The redback is the most common poisonous spider in WA. It's small and black with a distinctive red stripe on its body. Bites cause increasing pain at the site followed by profuse sweating and generalised symptoms. First aid includes application of ice or cold packs to the bite and transfer to hospital. White-tailed (brown recluse) spider bites may cause an ulcer that is very difficult to heal. Clean the wound thoroughly and seek medical assistance.
Hospitals have antivenin on hand for all common snake and spider bites, but it helps to know what it was that bit you.
### TAP WATER & OTHER WATER SOURCES
Tap water is universally safe to drink in WA. Increasing numbers of streams, rivers and lakes, however, are being contaminated by bugs that cause diarrhoea, making water purification essential. The simplest way of purifying water is to boil it thoroughly. Consider purchasing a water filter; it's very important when buying a filter to read the specifications, so that you know exactly what it removes from the water and what it doesn't. Simple filtering will not remove all dangerous organisms, so if you cannot boil water it should be treated chemically. Chlorine tablets will kill many pathogens, but not some parasites like giardia and amoebic cysts. Iodine is more effective in purifying water and is available in tablet form. Follow the directions carefully and remember that too much iodine can be harmful.
#### Other Hazards
##### Bushfires
Bushfires are a regular occurrence in WA and in hot, dry and windy weather, be extremely careful with any naked flame. Even cigarette butts thrown out of car windows can start fires. On a total fire ban day it's forbidden even to use a camping stove in the open.
Bushwalkers should seek local advice before setting out. When a total fire ban is in place, delay your trip until the weather improves. If you're out in the bush and you see smoke, even a long distance away, take heed – bushfires move fast and change direction with the wind. Go to the nearest open space, downhill if possible. A forested ridge is the most dangerous place to be during a bushfire.
##### Crime
Western Australia is a relatively safe place to visit, but you should still take reasonable precautions. Don't leave hotel rooms or cars unlocked, and don't leave valuables unattended and visible in cars.
In recent years there has been a spate of glassings (stabbings with broken glass) at Perth venues. If you see trouble brewing, it's best to walk away. Take due caution on the streets after dark, especially around hot spots such as Northbridge. There have also been reports of drinks being spiked with drugs in Perth pubs and clubs. Authorities advise women to refuse drinks offered by strangers in bars and to drink bottled alcohol rather than that in a glass.
##### Driving
Australian drivers are generally a courteous bunch, but rural 'petrolheads', inner-city speedsters and drink drivers can pose risks. Open-road dangers can include include wildlife, such as kangaroos (mainly at dusk and dawn); fatigue, caused by travelling long distances without the necessary breaks; and excessive speed. Driving on dirt roads can also be tricky for the uninitiated.
##### Outback Travel
If you're keen to explore outback WA, it's important not to embark on your trip without careful planning and preparation. Travellers regularly encounter difficulties in the harsh outback conditions, and trips occasionally prove fatal.
##### Swimming
Popular beaches are patrolled by surf life-savers and flags mark out patrolled areas. Even so, WA's surf beaches can be dangerous places to swim in, if you aren't used to the often heavy surf. Undertows (or 'rips') are the main problem. If you find yourself being carried out by a rip, just keep afloat; don't panic or try to swim against the rip, which will exhaust you. In most cases the current will stop within a couple of hundred metres of the shore and you can then swim parallel to the shore for a short way to get out of the rip and swim back to land.
On the south coast, freak 'king waves' from the Southern Ocean can sometimes break on the shore with little or no warning, dragging people out to sea. In populated areas there are warning signs; in other areas, be extremely careful.
People have been paralysed by diving into waves in shallow water and hitting a sandbar; check the depth of the water before you leap.
### Telephone
The two main telecommunications companies are Telstra (www.telstra.com.au) and Optus (www.optus.com.au) . Both are also major players in the mobile (cell) market, along with Vodafone (www.vodafone.com.au) , Virgin (www.virginmobile.com.au) and 3 (www.three.com.au) .
Local calls from private land lines cost 15c to 30c, while local calls from public phones cost 50c; both allow for unlimited talk time. Calls to mobile phones attract higher rates and are timed.
Although the whole of WA shares a single area code ( 08), once you call outside of the immediate area or town, it is likely that you are making a long-distance call. STD calls (Subscriber Trunk Dialling – a long-distance call within Australia) can be made from public phones and are cheaper during off-peak hours, generally between 7pm and 7am.
Phonecards can be purchased at newsagents and post offices for a fixed dollar value (usually $10, $20, $30 etc) and can be used with any public or private phone by dialling a toll-free access number and then the PIN number on the card. Call rates vary, so shop around. Some public phones also accept credit cards.
#### Mobile Phones
Australia's GSM and 3G mobile networks service more than 90% of the population but leave vast tracts of the country uncovered, including much of inland WA. Perth and the larger centres get good reception, but outside these centres it's haphazard or nonexistent, especially in the north. Of the mobile telcos, Telstra has the best coverage for both voice and internet services.
Australia's digital network is compatible with GSM 900 and 1800 (used in Europe), but is generally not compatible with the US or Japanese systems. All the main service providers offer prepaid mobile services for short-term access.
### A BIT OF PERSPECTIVE
Despite the recent increase in fatal shark attacks in WA, statistically it's still very unlikely that visitors will be attacked. Blue-ringed octopus deaths are even rarer – only two in the last century – and there's only ever been one confirmed death from a cone shell. Jellyfish kill about two people annually, but you're stil 100 times more likely to drown.
On land, snakes kill one or two people per year (about the same as bee stings, or less than a thousandth of those killed on the roads). There hasn't been a recorded death from a tick bite for over 50 years, nor from spider bites in the last 20.
#### Phone Codes
» 0011 International calling prefix (the equivalent of 00 in most other countries).
» 61 Australia's country code.
» 08 Area code for all of WA. If calling from overseas, drop the initial zero.
» 04 All numbers starting with 04 (such as 0410, 0412) are mobile phone numbers. If calling from overseas, drop the initial '0'.
» 190 Usually recorded information calls, costing from 35c to $5 or more per minute (more from mobiles and payphones).
» 1800 Toll-free numbers; can be called free of charge from anywhere in the country, though they may not be accessible from certain areas or from mobile phones.
» 1800-REVERSE (738 3773) or 12 550 For reverse-charge (collect) calls from any public or private phone.
» 13 or 1300 Cost of a local call. The numbers can usually be dialled Australia-wide, but may be applicable only to a specific state or STD district.
Note: 1800, 13 or 1300 numbers can't be dialled from outside Australia.
### Tourist Information
For general statewide information, try the WA Visitor Centre in Perth.
Around WA, tourist offices with friendly staff (often volunteers) provide local knowledge including info on road conditions.
### RESPONSIBLE INDIGENOUS TRAVEL
There are a range of protocols for visiting indigenous lands, but it's always courteous to make contact prior to your visit. In many cases you must acquire a permit to enter, so check with local Indigenous Land Councils and police stations before visiting.
Some indigenous sites are registered under heri-tage legislation and have conditions attached, or may be visited only with permission from their traditional custodians or in their company. Don't touch artworks, as the skin's natural oils can cause deterioration. Dust also causes problems – move thoughtfully at rock-art sites and leave your vehicle some distance away. Respect the wishes of indigenous custodians by reading signs carefully, keeping to dedicated camping areas and staying on marked tracks. Remember that rock art and engravings are manifestations of sacred beliefs and laws.
When interacting with Indigenous Australians, you'll generally find them polite and willing to share their culture with you – but it must be on their terms. Show respect for privacy and remember that your time constraints and priorities may not always be shared. In some areas, English is not a first language, but in others many people speak English fluently. Body language and etiquette often vary: the terms 'thank you', or 'hello' and 'goodbye', may not be used in some areas, or direct eye contact may be avoided. So take note of local practices: take them as they come and follow the cues. Some Aboriginal communities are 'dry'. There may be rules relating to the purchase and consumption of alcohol, or it may be forbidden altogether.
### Travellers with Disabilities
Disability awareness in WA is excellent. Legislation requires that new accommodation meets accessibility standards, and discrimination by tourism operators is illegal. Many of the state's key attractions provide access for those who have limited mobility, and an increasing number of places are addressing the needs of visitors who have visual or aural impairments. It's advisable to contact attractions in advance to confirm the facilities that are available.
Useful contacts:
Association for the Blind of WA ( 1800 847 466, 08-9311 8202; www.abwa.asn.au)
Easy Access Australia (www.easyaccessaustralia.com.au) Available from bookshops and detailing accessible transport, accommodation and attraction options.
National Information Communication & Awareness Network (Nican; 02-6241 1220, TTY 1800 806 769; www.nican.com.au) National directory with information on access issues, accessible accommodation, sporting and recreational activities, transport and specialist tour operators.
National Public Toilet Map (www.toiletmap.gov.au) Over 2300 public and private toilets, including those with wheelchair access.
People with Disabilities WA (PWdWA; 08-9485 8900, 1800 193 331; www.pwdwa.org) Website detailing WA's major disability service providers.
Tourism WA (www.westernaustralia.com) Website highlighting all accessible listings (accommodation, restaurants, tours etc).
WA Deaf Society ( 08-9441 2677, TTY 08-9441 2655; www.wadeaf.org.au)
### Visas
All visitors to Australia need a visa – only New Zealand nationals are exempt, and even they receive a 'special category' visa on arrival. Visa application forms are available from Australian diplomatic missions overseas, travel agents or the website of the Department of Immigration and Citizenship ( 13 18 81; www.immi.gov.au) .
#### eVisitor
Many European passport holders are eligible for an eVisitor, which is free and allows visitors to stay in Australia for up to three months. eVisitors must be applied for online and they are electronically stored and linked to individual passport numbers, so no stamp in your passport is required. It's advisable to apply at least 14 days prior to the proposed date of travel to Australia. Applications are made on the Department of Immigration and Citizenship website.
#### Electronic Travel Authority (ETA)
Passport holders from eight countries that aren't part of the eVisitor scheme – Brunei, Canada, Hong Kong, Japan, Malaysia, Singapore, South Korea and the USA – can apply for either a visitor or business ETA. ETAs are valid for 12 months, and allow stays of up to three months on each visit. Apply online at www.eta.immi.gov.au.
#### Tourist Visas
Short-term tourist visas have largely been replaced by the eVisitor and ETA. However, if you are from a country not covered by either, or you want to stay longer than three months, you'll need to apply for a visa. Tourist visas cost $105 and allow single or multiple entry for stays of three, six or 12 months and are valid for use within 12 months of issue.
#### Visa Extensions
If you want to stay in Australia for longer than your visa allows, you'll need to apply for a new visa (usually a tourist visa 676) through the Department of Immigration and Citizenship at www.immi.gov.au/visitors/tourist. Apply at least two or three weeks before your visa expires.
#### Work & Holiday Visas (462)
Nationals from Bangladesh, Chile, Indonesia, Iran, Malaysia, Thailand, Turkey and the USA between the ages of 18 and 30 can apply for a work and holiday visa prior to entry to Australia. It allows the holder to enter Australia within three months of issue, stay for up to 12 months, leave and re-enter Australia any number of times within that 12 months, undertake temporary employment to supplement a trip, and study for up to four months.
#### Working Holiday Maker (WHM) Visas (417)
Young visitors (those aged 18 to 30) from Belgium, Canada, Cyprus, Denmark, Estonia, Finland, France, Germany, Hong Kong, Ireland, Italy, Japan, Korea, Malta, the Netherlands, Norway, Sweden, Taiwan and the UK are eligible for a WHM visa, allowing visits of up to one year and casual employment.
The emphasis of this visa is on casual and not full-time employment, so you're only supposed to work for any one employer for a maximum of six months. A first WHM visa must be obtained prior to entry to Australia and can be applied for at Australian diplomatic missions abroad or online (www.immi.gov.au/visitors/working-holiday). You can't change to a WHM visa once you're in Australia, so apply up to 12 months before your departure to Australia.
### Women Travellers
WA is generally a safe place for women travellers, although the usual sensible precautions apply. Avoid walking alone late at night in major cities and towns, and always keep enough money aside for a taxi home. The same applies to outback and rural towns with unlit, semi-deserted streets between you and your temporary home. Lone women should be wary of staying in basic pub accommodation unless it appears safe and well managed.
Lone hitching is risky for everyone, but women especially should consider taking a male companion.
### Work
If you come to Australia on a tourist visa then you're not allowed to work for pay – working for approved volunteer organisations in exchange for board is OK. If you're caught breaching your visa conditions, you can be expelled from the country and banned for up to three years.
#### Seasonal Work
WA is experiencing a labour shortage and a wealth of opportunities exist for travellers (both Australian and foreign) for paid work year-round.
In Perth, plenty of temporary work is available in tourism and hospitality, administration, IT, nursing, childcare, factories and labouring. Outside Perth, travellers can easily get jobs in tourism and hospitality, plus a variety of seasonal work. Some places have specialised needs; in Broome, for example, there is lucrative work in pearling, on farms and boats.
Industry | Time | Region(s)
---|---|---
grapes | Feb-Mar | Denmark, Margaret River, Mt Barker, Manjimup
apples/pears | Feb-Apr | Donnybrook, Manjimup
prawn trawlers | Mar-Jun | Carnarvon
bananas | Apr-Dec | Kununurra
bananas | year-round | Carnarvon
vegies | May-Nov | Kununurra, Carnarvon
tourism | May-Dec | Kununurra
flowers | Sep-Nov | Midlands
lobsters | Nov-May | Esperance
#### Information
Backpacker accommodation, magazines and newspapers are good resources for local work opportunities.
Useful websites:
Australian Jobsearch (www.jobsearch.gov.au) Government site offering a job database.
Career One (www.careerone.com.au) General employment site, good for metropolitan areas.
Centrelink (www.centrelink.gov.au) The Australian government employment service has information and advice on looking for work, training and assistance.
Gumtree (http://perth.gumtree.com.au) Great classified site with jobs, accommodation and items for sale.
Harvest Trail (http://jobsearch.gov.au/HarvestTrail) Specialised recruitment search for the agricultural industry, including a 'crop list' detailing what you can pick and pack, when and where.
Job Shop (www.thejobshop.com.au) WA-based recruitment agency specialising in jobs for WA as well as the Northern Territory.
MyCareer (www.mycareer.com.au) General employment site, good for metropolitan areas.
Seek (www.seek.com.au) General employment site, good for metropolitan areas.
Travellers at Work (www.taw.com.au) Excellent site for working travellers in Australia.
West Australian (www.thewest.com.au) WA's main newspaper advertises jobs online.
#### Volunteering
Lonely Planet's _Volunteer: A Traveller's Guide to Making a Difference Around the World_ provides useful information about volunteering. Organisations that take on volunteers include the following.
Conservation Volunteers Australia (CVA; 03-5330 2600, 1800 032 501; www.conservationvolunteers.com.au) A nonprofit organisation focusing on practical conservation projects such as tree planting, walking-track construction, and flora and fauna surveys. Most projects are either for a weekend or a week and all food, transport and accommodation is supplied in return for a contribution to help cover costs ($40 per day, $208 for four nights).
Department of Environment and Conservation (DEC; www.dec.wa.gov.au) Current and future opportunities at national parks all over WA. Online, click on the Community & Education tab and then Volunteer Programs. Opportunities vary enormously, from turtle tagging at Ningaloo Marine Park to feral-animal control at Shark Bay. Working with the dolphins at Monkey Mia is a popular program (contact: monkeymiavolunteers@westnet.com.au).
Willing Workers on Organic Farms (WWOOF; 03-5155 0218; www.wwoof.com.au) Work four to six hours each day on a farm in return for bed and board, often in a family home. Almost all places have a minimum stay of two nights. Not all places are farms – you might help out at a pottery or do the books at a seed wholesaler. Most placements have a connection to alternative lifestyles.
Earthwatch Institute ( 03-9682 6828; www.earthwatch.org) Offers volunteer 'expeditions' focusing on conservation and wildlife.
Go Volunteer (www.govolunteer.com.au) National website that lists volunteer opportunities.
i-to-i (www.i-to-i.com) Volunteer holidays in Australia, focused on conservation.
Responsible Travel (www.responsibletravel.com) Volunteer travel opportunities.
STA (www.statravel.com.au) Click on 'Experiences' and go to the volunteer link.
Transitions Abroad (www.transitionsabroad.com) Listings of volunteer opportunities.
Volunteering Australia (www.volunteeringaustralia.org) Support, advice and volunteer training.
Transport
## Getting There & Away
Unless you're coming by land from other states in Australia, chances are you'll be touching down in Perth. Western Australia's (WA's) capital is considerably closer to Southeast Asia than it is to Australia's east coast – it's actually closer to Jakarta than to Sydney.
Flights, tours and rail tickets can be booked online at www.lonelyplanet.com/bookings.
### Entering the Country
Global instability has resulted in increased security in Australian airports, in both domestic and international terminals. Customs procedures may be a little more time-consuming but are still straightforward.
### CLIMATE CHANGE & TRAVEL
Every form of transport that relies on carbon-based fuel generates CO2, the main cause of human-induced climate change. Modern travel is dependent on aeroplanes, which might use less fuel per kilometre per person than most cars but travel much greater distances. The altitude at which aircraft emit gases (including CO2) and particles also contributes to their climate change impact. Many websites offer 'carbon calculators' that allow people to estimate the carbon emissions generated by their journey and, for those who wish to do so, to off set the impact of the greenhouse gases emitted with contributions to portfolios of climate-friendly initiatives throughout the world. Lonely Planet off sets the carbon footprint of all staff and author travel.
### Air
#### Airports & Airlines
If you're coming to Australia from Europe, Asia or Africa you'll find it quicker to fly directly to Perth Airport (PER; 08-9478 8888; www.perthairport.com) . If you do fly to the east coast first, there are frequent connecting flights to Perth from major cities. Port Hedland has international flights to/from Bali, while Port Hedland and Broome both welcome interstate flights.
##### Airlines Flying to & from WA
All flights listed here are to Perth, unless otherwise specified, and all phone numbers are for dialling from within Australia.
Air Asia (D7; 1300 760 330; www.airasia.com) Budget flights from Kuala Lumpur and Denpasar (Bali).
Air Mauritius (MK; 1300 332 077; www.airmauritius.com) Flies from Mauritius.
Air New Zealand (NZ; 13 24 76; www.airnz.com.au) Flies from Auckland.
Airnorth (TL; 1800 627 474; www.airnorth.com.au) Destinations include Perth, Broome, Darwin, Kununurra, Karratha and Port Hedland.
Cathay Pacific (CX; 13 17 47; www.cathaypacific.com) Flies from Hong Kong.
Emirates (EK; 1300 303 777; www.emirates.com) Flies from Dubai.
Garuda Indonesia (GA; 08-9214 5101; www.garuda-indonesia.com) Flies from Denpasar and Jakarta.
Jetstar (JQ; 13 15 38; www.jetstar.com) Runs cheapies from Sydney, Melbourne, Brisbane, Cairns, Adelaide and the Gold Coast. International routes include Jakarta and Denpasar.
Malaysia Airlines (MH; 08-9263 7043, 13 26 27; www.malaysiaairlines.com) Flies from Kuala Lumpur.
Qantas (QF; 13 13 13; www.qantas.com.au) Direct flights from Hong Kong and Singapore. Flies between Perth and all Australian state capitals (excluding Hobart), as well as Cairns, Alice Springs and Uluru (Ayers Rock). Also flies from Kalgoorlie to Adelaide and Perth, and from Melbourne to Broome year round, and from Sydney and Brisbane to Broome during school holidays.
Qatar Airways (QR; 1300 340 600; www.qatarairways.com) Flies from Doha.
Singapore Airlines (SQ; 13 10 11; www.singaporeair.com.au) Flies from Singapore.
Skywest (XR; 1300 660 088; www.skywest.com.au) Regional and international destinations from Perth including Darwin, Melbourne and Denpasar. Bali to Port Hedland on weekends.
South African Airways (SA; 1300 435 972; www.flysaa.com) Flies from Johannesburg.
Thai Airways International (TG; 1300 651 960; www.thaiairways.com) Flies from Bangkok.
Tiger Airways (TR; 03-9335 3033; www.tigerairways.com) From Melbourne and Singapore.
Virgin Australia (DJ; 13 67 89; www.virginaustralia.com) Links Perth to other Australian state capitals, except Canberra and Hobart. International destinations include Denpasar and Phuket.
### Land
The nearest state capital to Perth is Adelaide, 2560km away by the shortest road route. To Melbourne it's at least 3280km, Darwin is around 4040km and Sydney 3940km. Despite the vast distances, sealed roads cross the Nullarbor Plain from the eastern states to Perth, and then up the Indian Ocean coast and through the Kimberley to Darwin.
#### Bus
The only interstate bus is the daily Greyhound ( 1300 473 946; www.greyhound.com.au) service between Darwin and Broome ($361, 27½ hours), via Kununurra, Fitzroy Crossing and Derby.
#### Car, Motorcycle & Bicycle
Driving to Perth from any other state is a _very_ long journey, but it's a great way to see the country. Be aware that there are strict quarantine restrictions on fruit and vegetables when crossing the border into WA.
#### Hitching
Hitching is never entirely safe – we don't recommend it. Hitching to or from WA across the Nullarbor is definitely not advisable, as waits of several days are not uncommon.
People looking for travelling companions for driving to WA from Sydney, Melbourne, Adelaide or Darwin frequently leave notices in backpacker hostels. See also car-share websites ( Click here ).
#### Train
The only interstate rail link is the famous Indian Pacific, run by Great Southern Rail ( 13 21 47; www.greatsouthernrail.com.au) , which travels 4352km to Perth from Kalgoorlie (10 hours), Adelaide (two days), Broken Hill (2¼ days) and Sydney (three days). From Port Augusta to Kalgoorlie the seemingly endless crossing of the virtually uninhabited centre takes well over 24 hours, including the 'long straight' on the Nullarbor – at 478km this is the longest straight stretch of train line in the world. You can take 'whistle-stop' tours of some towns on the way.
Flexible one-way adult fares for the full journey are $783 (reclining seat), $1700 (sleeper cabin) and $2178 ('gold service', including meals). Substantial discounts are available off the seat-only price for backpackers, students, children and pensioners, and non-cancellable 'Ready Rail' and 'Rail Saver' fares also offer significant discounts.
Cars can be transported between Perth and Sydney, Melbourne and Adelaide – a good alternative to driving across the Nullarbor Plain in both directions. Note that service is usually around 40% cheaper _from_ Perth, than _to_ Perth.
## Getting Around
The distances between key WA towns are vast, especially in the north.
### Air
Unless you have unlimited time, consider internal flights.
#### Airlines Flying Within WA
Airnorth (TL; 1800 627 474; www.airnorth.com.au) Routes include Perth– Kununurra, Karratha–Port Hedland, Karratha–Broome, Port Hedland–Broome and Broome–Kununurra.
Cobham ( 1800 105 503; www.cobham.com.au) Flies between Perth and Kambalda.
Qantas ( 13 13 13; www.qantas.com.au; 55 William St) WA destinations include Kal-goorlie, Paraburdoo, Newman, Exmouth, Karratha, Port Hedland and Broome.
Skippers Aviation ( 1300 729 924; www.skippers.com.au) Flies three routes in both directions: Perth– Leonora–Laverton, Perth–Wiluna–Leinster, Perth–Mt Magnet–Meekatharra, Perth–Carnarvon, Perth–Geraldton–Carnarvon and Perth–Kalbarri–Monkey Mia. Of most relevance to the mining industry. Also flies Broome–Fitzroy Crossing–Halls Creek.
Skywest (XR; 1300 660 088; www.skywest.com.au) Flies to Perth, Busselton, Albany, Esperance, Geraldton, Exmouth, Port Hedland and Kalgoorlie.
Alliance Airlines ( 1300 780 970; www.allianceairlines.com.au) Mine-industry services linking Broome and Karratha, but also can be booked by the public.
Virgin Australia (DJ; 13 67 89; www.virginaustralia.com) Flies from Perth to Broome, Karratha, Port Hedland, Christmas Island and the Cocos Islands.
### Bicycle
Bicycle helmets are compulsory in WA, as are white front lights and red rear lights for riding at night.
If you're coming specifically to cycle, bring your own bike. Check with your airline for costs. Within WA you can load your bike onto a bus to skip the boring bits of the country. Book well ahead so that you and your bike can travel on the same vehicle.
Suffering dehydration is a very real risk in WA and can be life-threatening. It can get very hot in summer, so take things slowly until you're used to the heat. A prudent plan is to start riding every day at sunrise, relax in the shade – bring your own shelter – during the heat of the day and then ride a few more hours in the afternoon. Always wear a hat and plenty of sunscreen, and drink _lots_ of water.
Outback travel needs to be planned thoroughly, with the availability of drinking water the main concern. Those isolated water sources (bores, tanks, creeks) shown on your map may be dry or undrinkable, so you can't always depend on them. Also don't count on getting water from private mine sites as many are closed to the public. Bring necessary spare parts and bike-repair knowledge. Check with locals (start at the visitor centres) if you're heading into remote areas, and always let someone know where you're headed before setting off.
Useful contacts for information on touring around WA, including suggested routes, road conditions and cycling maps:
Bicycle Transportation Alliance ( 08-9420 7210; www.btawa.org.au)
Cycle Touring Association of WA (www.ctawa.asn.au)
### Bus
WA's bus network could hardly be called comprehensive, but it offers access to substantially more destinations than the railways. All long-distance buses are modern and well equipped with air-con, toilets and videos.
#### Main Companies
Greyhound ( 1300 473 946; www.greyhound.com.au) North of Geraldton, Greyhound is the main provider, with services from Perth to Broome via Geraldton, Carnarvon, Karratha and Port Hedland, and from Broome to Darwin, via the Great Northern Hwy. Multiday passes allow you to stop along the route.
Integrity Coach Lines ( 1800 226 339; www.integritycoachlines.com.au) Weekly buses between Perth and Port Hedland via the Great Northern Hwy, and also from Perth to Lancelin, Cervantes, Geraldton and Exmouth.
South West Coach Lines ( 08-9261 7600; www.veoliatransportwa.com.au) From Perth to all the major towns in the southwest – your best choice for Margaret River.
Transwa ( 1300 662 205; www.transwa.wa.gov.au) The state government's transport service, operating mainly in the southern half of the state. Main routes include Perth–Augusta, Perth–Pemberton, Perth–Albany (three different routes), Perth–Esperance (two routes), Albany– Esperance, Kalgoorlie– Esperance, Perth–Geraldton (three routes) and Geraldton–Meekatharra.
### Car & Motorcycle
Providing the freedom to explore off the beaten track, travelling by vehicle is the best option in WA. With several people travelling together, costs can be contained and, if you don't have major mechanical problems, there are many benefits.
The climate is good for motorcycles for much of the year, and many small trails into the bush lead to perfect camping spots. Bringing your own motorcycle into Australia requires valid registration in the country of origin and a Carnet de Passages en Douanes, allowing the holder to import their vehicle without paying customs duty or taxes. Apply to the motoring organisation/association in your home country. You'll also need a rider's licence and a helmet. A fuel range of 350km will cover fuel stops up the centre and on Hwy 1 around the continent. The long, open roads are really made for large-capacity machines above 750cc.
The Royal Automobile Club (RAC; 13 17 03; www.rac.com.au) has useful advice on state-wide motoring, including road safety, local regulations and buying/selling a car. It also offers car insurance to members, and membership can secure discounts on car rentals and motel accommodation.
Also popular are car-share sites, especially for securing a lift to Broome, Perth, Denmark and Darwin. See the following websites: www.findalift.com.au, www.needaride.com, www.coseats.com, www.gumtree.com.au.
### 4WD DRIVING TIPS
We don't need to see more 4WDs on tow trucks: the victims of a dirt-road rollover, a poorly judged river crossing, or coming to grief when meeting the native fauna on the road. Here are some tips to help keep you from riding upfront in a tow truck:
» Before heading off-road, check the road conditions at www.mainroads.wa.gov.au.
» Recheck road conditions at each visitor centre you come across – they can change quickly.
» Let people know where you're going, what route you're taking and how long you'll be gone.
» Don't drive at night: it's safer to stop in the mid-afternoon to avoid wildlife.
» Avoid sudden changes in direction – 4WDs have a much higher centre of gravity than cars.
» On sand tracks, reduce tyre pressure to 140kpa (20psi) and don't forget to reinflate your tyres once you're back on the tarmac.
» When driving on corrugated tracks, note that while there is a 'sweet spot' speed where you feel the corrugations less, it's often too fast to negotiate a corner – and rollovers often happen because of this.
» When crossing rivers and creeks, always walk across first to check the depth – unless you're in saltwater crocodile territory, of course!
#### Driving Licence
You can use your own home country's driving licence in WA for up to three months, as long as it carries your photo for identification and is in English. Alternatively, arrange an International Driving Permit (IDP) from your home country's automobile association and carry it along with your licence.
#### Fuel
Fuel (predominantly unleaded and diesel) is available from service stations. Liquefied petroleum gas (LPG) is not always stocked at more remote roadhouses – if your car runs on gas it's safer to have dual fuel capacity.
Prices vary wildly in WA, even between stations in Perth. For up-to-date fuel prices, visit the government fuel-watch website (www.fuelwatch.wa.gov.au).
Distances between fill-ups can be long in the outback, but there are only a handful of tracks where you'll require a long-range fuel tank or need to use jerry cans. However, if you are doing some back-road explorations, always calculate your fuel consumption, plan accordingly and carry a spare jerry can or two. Keep in mind that most small-town service stations are only open from 6am to 7pm and roadhouses aren't always open 24 hours. On main roads there'll be a small town or roadhouse roughly every 150km to 200km.
Always carry two spare tyres and at least 20L of water.
#### Hire
Competition between car-rental companies in Australia is fierce, so rates vary and special deals come and go. The main thing to remember when assessing your options is distance – if you want to travel widely, you need to weigh up the price difference between an unlimited kilometres deal and one that offers a set number of kilometres free with a fee per kilometre over that set number.
Local firms are always cheaper than the big operators – sometimes half the price – but cheap car hire often comes with restrictions on how far you can take the vehicle away from the rental centre.
Some, but not all, car- rental companies offer one-way hires, so research this option before you arrive. It's worth investigating and combining with an internal flight if you're travelling to somewhere like Exmouth, Broome or Esperance. A significant premium is usually charged. There are sometimes good deals for taking a car or campervan from, say, Broome back to Perth, but you'll need to contact local rental companies closer to the time of rental.
You must be at least 21 years old to hire from most firms – if you're under 25 you may only be able to hire a small car or have to pay a surcharge. A credit card will be essential.
Renting a 4WD enables you to safely tackle routes off the beaten track and get out to more remote natural wonders. Note that many 'normal' rental cars aren't allowed off main roads, so always check insurance conditions carefully, especially the excess, as they can be onerous. Even for a 4WD, the insurance offered by most companies does not cover damage caused when travelling 'off-road', which basically means anything that is not a maintained bitumen or dirt road.
Avis ( 13 63 33; www.avis.com.au)
Backpacker Car Rentals ( 08-9430 8869; www.backpackercarrentals.com.au) Good-value local agency.
Bayswater Car Rental ( 08-9325 1000; www.bayswatercarrental.com.au) Local company with four branches in Perth and Fremantle.
Britz Rentals ( 1800 331 454; www.britz.com) Hires out fully equipped 4WDs fitted out as campervans, popular on the roads of northern WA. Britz has offices in all the state capitals, as well as Perth and Broome, so one-way rentals are possible.
Budget ( 1300 362 848; www.budget.com.au)
Campabout Oz ( 08-9477 2121; www.campaboutoz.com.au) Campervans, 4WDs and motorbikes.
Hertz ( 13 30 39; www.hertz.com.au)
Mighty Cars & Campers ( 1800 670 232; www.mightycampers.com.au)
Thrifty ( 1300 367 227; www.thrifty.com.au)
Wicked Campers ( 1800 246 869; www.wickedcampers.com.au) Check the website for good last-minute discounts.
#### Insurance
In Australia, third-party personal-injury insurance is always included in the vehicle registration cost. This ensures that every registered vehicle carries at least minimum insurance. You'd be wise to extend that minimum to at least third-party property insurance as well – minor collisions with other vehicles can be surprisingly expensive.
If you're bringing your own car from within Australia, take out the most comprehensive roadside assistance plan you can. It's not a matter of if your car will break down, but when. Having the top cover will offset your recovery costs considerably.
For hire cars, establish exactly what your liability is in the event of an accident. Rather than risk paying out thousands of dollars if you do have an accident, you can take out your own comprehensive insurance on the car, or (the usual option) pay an additional daily amount to the rental company for an 'insurance excess reduction' policy. This brings the amount of excess you must pay in the event of an accident down from between $2000 and $5000 to a few hundred dollars.
Be aware that if you're travelling on dirt roads you may not be covered by insurance. Also, most companies' insurance won't cover the cost of damage to glass (including the windscreen) or tyres. Always read the small print.
#### Purchase
If you're planning a stay of several months that involves lots of driving, buying a second-hand car will be much cheaper than renting. But remember that reliability is all-important. Breaking down in the outback is very inconvenient (and potentially dangerous) – the nearest mechanic can be a very expensive tow-truck ride away!
You'll probably get any car cheaper by buying privately through the newspaper (try Saturday's _West Australian_ ) rather than through a car dealer. Buying through a dealer can include a guarantee, but this is not much use if you're buying a car in Perth for a trip to Broome. Online, see www.carpoint.com.au and www.drive.com.au to buy a car.
There are local regulations to comply with when buying or selling a car. In WA a vehicle has to have a compulsory safety check and obtain a road-worthiness certificate (RWC) before it can be registered in the new owner's name – usually the seller will indicate whether the car already has a RWC. Stamp duty has to be paid when you buy a car; as this is based on the purchase price, it's not unknown for the buyer and the seller to agree privately to understate the price.
To avoid buying a lemon, you might consider forking out some extra money for a vehicle appraisal before purchase. The RAC ( 13 17 03; www.rac.com.au) offers this kind of check in Perth and other large WA centres for around $198/220 for members/nonmembers; it also offers extensive advice on buying and selling cars on its website.
The beginning of winter (June) is a good time to start looking for a used motorbike. Local newspapers and the bike-related press have classified advertisement sections.
Fremantle has a number of secondhand-car yards, including a cluster in North Fremantle on the Stirling Hwy, while in Perth there's the Traveller's Auto Barn ( 1800 674 374; www.travellers-autobarn.com.au; 365 Newcastle St, Northbridge) .
#### Road Conditions
WA is not criss-crossed by multilane highways; there's not enough traffic and the distances are too great to justify them. All the main routes are well surfaced and have two lanes, but not far off the beaten track you'll find yourself on unsealed roads. Anybody seeing the state in reasonable detail can expect some dirt-road travelling. A 2WD car can cope with the major ones, but for serious exploration, plan on a 4WD.
Driving on unsealed roads requires special care – a car will perform differently when braking and turning on dirt. Under no circumstances exceed 80km/h on dirt roads; if you go faster you won't have enough time to respond to a sharp turn, stock on the road, or an unmarked gate or cattle grid. Take it easy and take time to see the sights.
It's important to note that when it rains, some roads flood. Flooding is a real problem up north because of cyclonic storms. Exercise extreme caution at wet times, especially at the frequent yellow 'Floodway' signs. If you come to a stretch of water and you're not sure of the depth or what could lie beneath it, pull up at the side of the road and walk through it (excluding known saltwater-crocodile areas, such as the Pentecost River crossing on the Gibb River Road!). Even on major highways, if it has been raining you can sometimes be driving through 30cm or more of water for hundreds of metres at a time.
Mainroads ( 13 81 38; www.mainroads.wa.gov.au) provides statewide road-condition reports, updated daily (and more frequently if necessary).
#### Road Hazards
Travelling by car within WA means sometimes having to pass road trains. These articulated trucks and their loads (consisting of two or more trailers) can be up to 53.5m long, 2.5m wide and travel at around 100km/h. Overtaking them is tricky – once you commit to passing there's no going back. Exercise caution and pick your time, but don't get timid mid-manoeuvre. Also, remember that it is much harder for the truck driver to control their giant-sized vehicle than it is for you to control your car.
WA's enormous distances can lead to dangerous levels of driver fatigue. Stop and rest every two hours or so – do some exercise, change drivers or have a coffee. The major routes have rest areas and many roadhouses offer free coffee for drivers; ask for maps from the RAC that indicate rest stops.
Cattle, emus and kangaroos are common hazards on country roads, and a collision is likely to kill the animal and cause serious damage to your vehicle. Kangaroos are most active around dawn and dusk, and they travel in groups. If possible plan your travel to avoid these times of the day. If you see a roo hopping across the road in front of you, slow right down – its friends are probably just behind it.
It's important to keep a safe distance behind the vehicle in front, in case it hits an animal or has to slow down suddenly. If an animal runs out in front of you, brake if you can, but don't swerve unless it is safe to do so. You're likely to survive a collision with an emu better than a collision with a tree or another vehicle.
#### Road Rules
Driving in WA holds few surprises, other than those that hop out in front of your vehicle. Cars are driven on the left-hand side of the road (as in the rest of Australia). An important road rule is 'give way to the right' – if an intersection is unmarked, you must give way to vehicles entering the intersection from your right.
The speed limit in urban areas is generally 60km/h, unless signposted otherwise. The state speed limit is 110km/h, applicable to all roads in non-built-up areas, unless otherwise indicated. The police have radar speed traps and speed cameras, often in carefully concealed locations.
Oncoming drivers who flash their lights at you may be giving you a warning of a speed camera ahead – or they may be telling you that your headlights are not on. It's polite to wave back if someone does this. Don't get caught flashing your lights yourself, as it's illegal.
Seat belts are compulsory, and not using them incurs a fine. Children must be strapped into an approved safety seat. Talking and text-ing on a mobile phone while driving is illegal.
Drink-driving is a serious problem in WA, especially in country areas, and random breath tests are used to reduce the road toll. If you're caught driving with a blood-alcohol level of more than 0.05%, expect a hefty fine, a court appearance and the loss of your licence.
### Local Transport
Perth has an efficient, fully integrated public-transport system called Transperth ( 13 62 13; www.transperth.wa.gov.au) covering public buses, trains and ferries in a large area that reaches south to include Fremantle, Rockingham and Mandurah. Larger regional centres, including Bunbury, Busselton and Albany, have limited local bus services.
Taxis are available in most of the larger towns.
### Tours
The WA Visitor Centre in Perth has a wide selection of brochures and suggestions for tours all over the state. The tours listed here are only a selection of what's available. Prices given are rates per person in twin share; there's usually an extra supplement for single accommodation. Students and YHA members often get a discount.
The hop-on, hop-off bus options are a popular way for travellers to get around in a fun, relaxed atmosphere. Some adventure tours include serious 4WD safaris, taking travellers to places that they simply couldn't get to on their own without large amounts of expensive equipment.
AAT Kings Australian Tours ( 1300 228 546; www.aatkings.com.au) A long-established and professional outfit offering a wide range of fully escorted bus trips and 4WD adventures. At the time of writing it offered 17 tours in WA, ranging from a five-day Perth to Monkey Mia trip ($1825) to a 20-day Perth to Darwin 'Western Discovery' ($8075).
Adventure Tours ( 1800 068 886; www.adventuretours.com.au) A wide range of WA tours, many with an off-the-beaten-track focus for active and adventurous travellers. Accommodation may include hostels and camping, and tour options include Perth to Broome ($2555, 14 days) and Monkey Mia, Kalbarri and the Pinnacles ($645, four days).
Outback Spirit ( 1800 688 222; www.outbackspirittours.com.au) Luxury all-terrain explorations including a Western Wildflowers Discovery tour ($5595, 15 days) and Pilbara, Karijini and Ningaloo Reef ($5995, 12 days).
Red Earth Safaris ( 1800 501 968; www.redearthsafaris.com.au) Operates a six-day Perth to Exmouth minibus tour ($745) with a two-day return trip ($200).
### Train
The state's internal rail network, operated by Trans-wa ( 1300 662 205; www.transwa.wa.gov.au) , is limited to the _Prospector_ (Perth to Kalgoorlie), the _AvonLink_ (Perth to Northam) and the _Australind_ (Perth to Bunbury). Transperth's local train network reaches as far south as Mandurah.
Behind the Scenes
### SEND US YOUR FEEDBACK
We love to hear from travellers – your comments keep us on our toes and help make our books better. Our well- travell ed team reads every word on what you loved or loathed about this book. Although we cannot reply individually to postal submissions, we always guarantee that your feedback goes straight to the appropriate authors, in time for the next edition. Each person who sends us information is thanked in the next edition – and the most useful submissions are rewarded with a free book.
Visit lonelyplanet.com/contact to submit your updates and suggestions or to ask for help. Our award-winning website also features inspirational travel stories, news and discussions.
Note: We may edit, reproduce and incorporate your comments in Lonely Planet products such as guidebooks, websites and digital products, so let us know if you don't want your comments reproduced or your name acknowledged. For a copy of our privacy policy visit lonelyplanet.com/privacy.
## OUR READERS
Many thanks to the travellers who used the last edition and wrote to us with helpful hints, useful advice and interesting anecdotes:
Roger Bailye, Christian Cantos, Jane Coffey, Lena Lise Ibsen, Paul Joyce, Karen Mein, John O'Connor, John O'Gorman
## AUTHOR THANKS
#### Brett Atkinson
Huge thanks to the keen and professional staff at WA's visitor centres who smoothed the way for information gathering, allowing me to focus on the vital task of taste testing the craft breweries of Margaret River. In Perth, thanks to Amanda Keenan for the pre-trip hit list. Special thanks to my fellow scribe Steve Waters, and also to the LP in-house team, especially Maryanne Netto for her support. Final thanks to Carol for holding the fort back home in Auckland.
#### Steve Waters
Thanks to Karen from RACWA for not hanging up, Mick for the tow, Leonie and Nev for beer and watermelons, Dave and Thuman of Djarindjin for the sand rescue, Travis for the drive shaft, John in the Subie for the WD40, Colleen and Karen for dinner and great conversation, Trace and Heath, Brodie, Abbidene, Meika and Kaeghan for everything, Roz, Megan and Batty for caretaking, Friz and Ian for putting up with me, and the Bung-Bung crew for, well, Bung-Bung!
## ACKNOWLEDGMENTS
Cover photograph: Camel caravan, Broome, George Steinmetz/Corbis
## THIS BOOK
This is the 7th edition of Lonely Planet's _Perth & West Coast Australia _ guidebook. Brett Atkinson was the coordinating author, joined by coauthor Steve Waters. Rebecca Chau contributed the Boomtown: Mining & the Environment essay. Michael Cathcart wrote the History chapter, with additions and updates by Brett Atkinson. The previous edition was written by Peter Dragicevich, Steve Waters and Rebecca Chau. This guidebook was commissioned in Lonely Planet's Melbourne office, and produced by the following:
Commissioning Editor Maryanne Netto
Coordinating Editors Victoria Harrison, Sarah Koel
Coordinating Cartographer Peter Shields
Coordinating Layout Designer Kerrianne Southway
Managing Editor Barbara Delissen
Senior Editors Andi Jones, Martine Power
Managing Cartographers Corey Hutchison, Diana Von Holdt
Managing Layout Designer Chris Girdler
Assisting Cartographers Valeska Cañas, Csanad Csutoros, Xavier Di Toro
Assisting Layout Designer Mazzy Prinsep
Assisting Editors Susie Ashworth, Trent Holden
Cover Research Naomi Parker
Internal Image Research Aude Vauconsant
Thanks to Ryan Evans, Larissa Frost, Mark Griffiths, Genesys India, Jouve India, Trent Paton, Kirsten Rawlings, Raphael Richards, Gerard Walker
Ebook thanks to Shahara Ahmed, Anita Banh, Andrew Bigger, Sally Darmody, Julie Dodkins, Mark Germanchis, Craig Kilburn, Corine Liang, Chris Love, Wayne Murphy, Jared O'Loughlin, Kirsten Rawlings, Jacqui Saunders, Matt Swaine, Chris Tsismetzis, the team at Textech.
### Our Story
A beat-up old car, a few dollars in the pocket and a sense of adventure. In 1972 that's all Tony and Maureen Wheeler needed for the trip of a lifetime – across Europe and Asia overland to Australia. It took several months, and at the end – broke but inspired – they sat at their kitchen table writing and stapling together their first travel guide, Across Asia on the Cheap. Within a week they'd sold 1500 copies. Lonely Planet was born.
Today, Lonely Planet has offices in Melbourne, London and Oakland, with more than 600 staff and writers. We share Tony's belief that 'a great guidebook should do three things: inform, educate and amuse'.
OUR WRITERS
###### Brett Atkinson
Coordinating Author; Perth & Fremantle, Around Perth, Margaret River & the Southwest Coast, South Coast Brett's previous visits to Western Australia had involved museum- and bar-hopping in Fremantle, and taking on the mighty Nullarbor Plain. This time he expanded his WA horizons by immersing himself in Perth's restaurants and cafes, 'researching' craft breweries in the Swan Valley, and jumping from beach to forest and back to beach throughout Margaret River and the southwest. As a New Zealander, he's used to weird and wonderful wildlife but still thinks WA's quirky combo of woylies, numbats and whale sharks is something special. Brett's based in Auckland, and has covered more than 45 countries as a guidebook author and travel and food writer. See www.brett-atkinson.net for what he's been eating recently, and where he's travelling to next.
###### Steve Waters
Around Perth, Monkey Mia & the Central West, Coral Coast & the Pilbara, Broome & the Kimberley While researching the previous edition of this book, Steve descended into rental-car hell, so this trip he drove 15,000km in his own Subaru L-series, which took a hammering on the Tanami and almost drowned getting into Purnululu. Driving lights dropped off, shockers, tyres and drive shafts all broke. At least it only caught fire once. Slept in, eaten on, buried in Dampier Peninsula pindan, covered in Pilbara dust, pulled over by Cervantes cops, from Kununurra to Perth, the Subie kept going. Steve's also co-authored previous editions of _Australia_ , _Indonesia_ and _Great Adventures_ ; while not on the road, he frequents Lonely Planet's Melbourne office.
Read more about Steve at: lonelyplanet.com/members/stevewaters
###### CONTRIBUTING AUTHORS
Rebecca Chau wrote the Boomtown: Mining & the Environment chapter. Rebecca first started learning about WA back in the '80s, when she started school in Albany, south of the state. After growing up on this land crinkled by beaches and coveted by whales, she moved to Perth, and later became a commissioning editor for Lonely Planet. Also an author on the previous editions of this guide, she heads back to WA a couple of times a year. She has long followed the mining boom with fascination.
Dr Michael Cathcart wrote the History chapter. Michael teaches history at the Australian Centre, the University of Melbourne. He is well known as a broadcaster on ABC Radio National and has presented history programs on ABC TV. His most recent book is _The Water Dreamers_ (2009), a history of how water shaped the history of Australia.
Published by Lonely Planet Publications Pty Ltd
ABN 36 005 607 983
7th edition – July 2013
ISBN 9781741799521
© Lonely Planet 2013 Photographs © as indicated 2013
All rights reserved. No part of this publication may be copied, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, recording or otherwise, except brief extracts for the purpose of review, and no part of this publication may be sold or hired, without the written permission of the publisher. Lonely Planet and the Lonely Planet logo are trademarks of Lonely Planet and are registered in the US Patent and Trademark Office and in other countries. Lonely Planet does not allow its name or logo to be appropriated by commercial establishments, such as retailers, restaurants or hotels. Please let us know of any misuses: lonelyplanet.com/ip.
Although the authors and Lonely Planet have taken all reasonable care in preparing this book, we make no warranty about the accuracy or completeness of its content and, to the maximum extent permitted, disclaim all liability arising from its use.
# Quick Links
### A
Aarli
Aboriginal Art & Craft Gallery
About Bike Hire
Above Bored
Acacia Chalets
Ace Subiaco
Air
Aiyana Retreat
Albany Convict Gaol
Albany Discovery Inn
Albany Entertainment Centre
Albany Harbourside
Alimento
Alkoomi Wines
All Seasons Karratha
Allison Tentland
Ambar
Amble Inn
Amplifier
Anchorage Caravan Park
Angies Cafe
Annalakshmi
Aquarium of Western Australia
Aristocat II
Aristos
Army Museum of WA
Art Gallery of Western Australia
ArtGeo Cultural Complex
Artlandish
Artézen
Ashbrook
Aspects of Kings Park
Astor
Astro Tours
Atlas Divine
Augusta Historical Museum
Aussie Bight Expeditions
Aussie Off Road Tours
Australasian Diving Academy
Australia Day Skyworks
Australian Sailing Museum
Avalon Homestead
Avon River Festival
Avon Valley Gourmet Food & Wine Festival
Avon Valley Vintage Festival
Awesome International Festival for Bright Young Things
Azuki
### B
BHP Billiton
Bali Hai Resort & Spa
Balthazar
Bannister Suites Fremantle
Barn Hill Station
Batavia Coast Dive Academy
Bay Lodge
Bay Merchants
Bayview Backpackers YHA
Baywatch Manor YHA
Beach House at Bayside
Beaches of Broome
Beachlands Holiday Park
Beachside Apartment Hotel
Beatty Park Leisure Centre
Beer Nuts
Bell Tower
Benesse
Bennet Brook Railway
Best Western Georgiana Molloy
Best Western Pemberton Hotel
Bettyblue Bistro
Big Day Out
Big River Ranch
Big Waters
Bill Campbell Secondhand Book Seller
Billabong Backpackers Resort
Bird Hide
Birds
Bivouac Canteen & Bar
Black Swan
Blackwood River
Blackwood River Canoeing
Blackwood River Houseboats
Blessing of the Fleet
Blue Bay Apartments
Blue Ginger
Blue Waters Lodge YHA
Blue Wren Travellers' Rest YHA
Boab Festival
Boab Inn
Bodkin's Bootery
Books & Stuff
Boranup Drive
Boranup Gallery
Boston Brewery
Boucla
Brass Monkey
Bridgetown Riverside Chalets
Bridgetown Hotel
Brig Amity
Brighton Hotel
Broome Adventure Company
Broome Beach Resort
Broome Bird Observatory
Broome Camel Safaris
Broome Museum
Broome Race Round
Bunbury Glade Caravan Park
Bunbury Regional Entertainment Centre
Bunbury Regional Art Galleries
Bunbury Wildlife Park
Burlong Pool
Burnside Organic Farm
Bush Camp Surplus
Bush Flight
Bushtucker Tours
Busselton Drive-In Outdoor Cinema
Busselton Jetty
### C
Cabin Fever
Cable Beach
Cable Beach Backpackers
Cable Beach General Store
Cafe 55
Cafe Moka
Cafe Yasou
Café 140
Calgardup & Giants Caves
Camelot Outdoor Cinema
Cannery Arts Centre
Cantina 663
Canvas
Cape Arid National Park
Cape Dive
Cape Howe Cottages
Cape Le Grand National Park
Cape Leeuwin Lighthouse
Cape Wine Bar
Capricorn Holiday Park
Capricorn Kayak Tours
Capricorn Seakayaking
Captain Cook Cruises
Captain Cook Cruises
Caravan Park
Carnarvon Central Apartments
Casella's
Catch
Cathedral of St Francis Xavier Church
CaveWorks & Lake Cave
Caversham Wildlife Park
Caves Caravan Park
Celestine Retreat
Cervantes Country Club
Cervantes Holiday Homes
Cervantes Lodge & Pinnacles Beach Backpackers
Challenge Stadium
Chamber of Commerce Building
Charles Hotel
Chart & Map Shop
Charter 1
Cheeky Sparrow
Chutney Mary's
Cicerello's (Fremantle)
Cicerello's (Mandurah)
Cinema Paradiso
CinéfestOZ
City Beach
City Sightseeing Perth Tour
City Waters
Clearwater Motel Apartments
Coalmine Beach
Coco's Thai
Coffee Cat
Cola Café & Museum
Comfort Hotel Perth City
Connor's Mill
Coogee Beach Holiday Park
Cooke Point Caravan Park
Coolibah Lodge
Coorinja
Coral Bay Ecotours
Coral Coast Tourist Park
Coral Coast Tours Driving Tour
Corrugated Lines
Cossack Budget Accommodation
Cottesloe Beach
Cottesloe Beach Hotel
Courthouse Gallery
Courthouse Markets
Culinary HQ
Cullen Wines
Customs House
Cycle Centre
### D
DEC Campsites
Dampier Transit Caravan Park
Dancing Goat
Dear Friends
Deck Treasures
Deckchair Gourmet
Dekked Out Adventures
Denham Seaside Tourist Village
Denmark Bakery
Denmark Hotel
Denmark Ocean Beach Holiday Park
Denmark Rivermouth Caravan Park
Denmark Tavern
Denmark Wine Lovers Tour
Department of Education Hostel
Derby Bus Service
Desert Rose
Devilles Pad
Diamond Forest Cottages
Diamond Tree Lookout
Dinosaur World
Discovery Coach Tour
Discovery Holiday Parks – Perth
Dive Shed
Diver's Tavern
Divido
Diving
Dog Rock
Dog Rock Motel
Dolphin Retreat YHA
Dongara Backpackers
Dongara Hotel Motel
Dongara Tourist Park
Donnelly River Cruises
Down Under
Driftwood Apartments
Duende
Dunsborough Beachouse YHA
Dunsborough Central Motel
Durack House
Dwellingup Adventures
### E
E Shed Markets
Eagles Heritage
Earl of Spencer
Eco-Discovery Tours
Edge of the Forest
Eight Nicholson
Eighty Mile Beach Caravan Park
El Público
Elba
Elizabeth's Bookshop
Ellensbrook Homestead
Ellington Jazz Club
Emperor's Crown
Empire Retreat
Emu Beach Holiday Park
Endeavour Tavern
Environs Annual Art Auction
Esperance B&B by the Sea
Esperance Diving & Fishing
Esperance Island Cruises
Esperance Museum
Esplanade Hotel (Fremantle)
Esplanade Hotel (Port Hedland)
Exmouth Cape Holiday Park
Exmouth Holiday Accommodation/Ray White
Exmouth Ningaloo Caravan & Holiday Resort
Exmouth Shopping Centre
Ezra Pound
### F
Faversham House
Fenwick 3 Cinemas
Feral Brewing Company
Festival of Voice
Finlay's Fresh Fish BBQ
Fins Cafe
Fish & Whistle
Fishing
Five Bar
Flaming Hot Takeaways
Flipside (Fremantle)
Flipside (Perth)
Floreat Beach
Fly by Night Musicians Club
Flying Scotsman
Foragers
Foragers Field Kitchen
Foreshore Backpackers
Forest Fresh Marron
Forest Heritage Centre
Fothergills of Fremantle
Found
Four Aces
Fraser's
Freemasons Hotel
Fremantle Arts Centre
Fremantle Colonial Accommodation
Fremantle Festival
Fremantle Grammar School
Fremantle Indigenous Heritage Tours
Fremantle Markets
Fremantle Prison
Fremantle Trails
Fremantle Train Station
Fremantle Tram Tours
Freshwater
Funcats
Future Shelter
### G
G-Spot Xtreme
Gantheaume Point & Dinosaur Prints
Garden City
Gecko Bike Hire
Gecko Gallery
Geisha
Geraldton Regional Art Gallery
Gimme Fest
Gino's
Gloucester Motel
Go Health Lunch Bar
Go Wild
Gold Rush Buildings
Golden Sun Cruises
Gomboc Gallery
Good Fortune Roast Duck House
Gorges Café
Grand Cinemas
Grand Mercure
Great Ocean Drive
Greenhouse
Greenhouse
Green's & Co
### H
HMAS Sydney II Memorial
Hacienda Crab Shack
Hall's Cottage
Hamelin Bay Holiday Park
Hamersley Gorge
Harvest
Harvest Tours
Have a Chat General Store
Helvetica
Hidden Valley Tourist Park
His Majesty's Theatre
Holberry House
Holy Smoke!
Hopetoun Motel & Chalet Village
Horizontal Falls Seaplane Adventures
Hospitality Inn
Hotel Northbridge
Hotel Rottnest
Hotham Valley Railway
Houghton
Hoyts
Hula Bula Bar
Hyde Park
### I
Il Lido
Imperial Inn
Indigenart
Indigenous Tours WA
Injidup Spa Retreat
Island View Esperance
Ivanhoe Cafe
### J
Jackson's
Japingka
Jarrah Jacks
Jarrahcorp
Jetty
Jewel Cave
Jezebelle
Jila Gallery
John St Cafe
Joonjoo Botanical Trail
Juicy Beetroot
Jules Cafe
Jus Burgers
### K
Kakulas Sister
Kalbarri Abseil
Kalbarri Adventure Tours
Kalbarri Air Charter
Kalbarri Backpackers
Kalbarri Boat Hire
Kalbarri Motor Hotel
Kalbarri Reef Villas
Kalbarri Sandboarding
Kalbarri Wilderness Cruises
Kalbarri Wildflower Centre
Kalgan Queen
Karratha Sushi Bar
Karrinyup
Kepa Kurl Eco Cultural Discovery Tours
Kimberley Adventure Tours
Kimberley Asian Cuisine
Kimberley Birdwatching
Kimberley Bookshop
Kimberley Camping & Outback Supplies
Kimberley Croc Backpackers
Kimberley Dreamtime Adventure Tours
Kimberley Entrance Caravan Park
Kimberley Klub
Kimberley School of the Air
Kimberley Wild Expeditions
Kings Ningaloo Reef Tours
Kings Park & Botanic Garden
Kings Park Festival
Kingston Barracks Youth Hostel
KiteWest
Kitsch
Knee Deep in Margaret River
Kombi Cafe
Kujurta Buru
Kulcha
Kullari NAIDOC Week
Kununurra Cruises
Kununurra Historical Society Museum
Kununurra Markets
### L
La Cholita
Lake Monger
Lake Warden Wetland System
Lakeside
Lakeview Apartments
Lamont's
Lancelin Caravan Park
Lancelin Lodge YHA
Laneways
Laundry Cafe
Lazy Susan's Comedy Den
Ledge Point Holiday Park
Leederville Hotel
Leeuwin Estate
Lestok Tours
Lesueur National Park
Liberté
Lighthouse Bay
Lime 303
Little Creatures
Little Lagoon
Little Starfish
Little Willy's
Llewellin's
Lobster Shack
Loose Box
Love in Tokyo
Luna
Luna on SX
Lurujarri Dreaming Trail
Luxe
### M
M on the Point
Magabala Books
Makanikai Kiteboarding
Malcolm Douglas Wilderness Park
Maleeya's Thai Cafe
Mama Tran
Mammoth Cave
Mandurah Boat & Bike Hire
Mandurah Ferry Cruises
Mandurah Ocean Marina Chalets
Mandurah Performing Arts Centre
Mango Festival
Mangrove Boardwalk
Mantaray's Bar & Brasserie
Mantra
Mantra on Hay
Marapikurrinya Park
Margaret River Chocolate Company
Margaret River Regional Wine Centre
Margaret River Wine Region Festival
Margaret River Backpackers
Margaret River Bakery
Margaret River Dairy Company
Margaret River Farmers Market
Margaret River Gourmet Escape
Margaret River Lodge YHA
Margaret River Tours
Margaret Riviera
Margies Big Day Out
Marima Cottages
Marine Park
Market Days
Marudi Designs
Mash (Fremantle)
Mash (Margaret River)
Matso's Broome Brewery
Matsuri
Maya
Mechanics Institute
Medina Executive Barrack Plaza
Melbourne
Metro City
Metropolis Fremantle
Mettams Pool
Middleton & Emu Beaches
Middleton Beach Holiday Park
Midwest Surf School
Millhouse Cafe
Mills Charters
Mills Records
Mirima National Park
Miss Maud
Moingup Springs
Mojo's
Monkey Mia Dolphin Resort
Montebello Island Safaris
Moondyne Festival
Moonlight Cinema
Moore & Moore
Morby Cottage
Morel's Orchard
Morries Anytime
Motor Museum
Motor Museum of WA
Mot's Cafe
Mount Trio Bush Camping & Caravan Park
Mountford
Mounts Bay Waters
Mrs Browns
Mrs Jones
Mt Melville & Mt Clarence
Mundaring Weir Hotel
Museum Village
Must
Must Winebar
My Place
### N
NIB Stadium
Naked Fig
Nambung National Park
Namh Thai
Nannup Bridge Cafe
Nannup Music Festival
National Park Campgrounds
Naturaliste Charters
Naturally Walpole Eco Tours
Nelsons of Bridgetown
New Edition
New Norcia Bakery
Newcastle Gaol
Newport Hotel
Newtown House
Ngilgi Cave
Ningaloo Club
Ningaloo Ecology Cruises
Ningaloo Health
Ningaloo Kayak Adventures
Ningaloo Kite & Board
Ningaloo Lodge
Ningaloo Marine Interactions
Ningaloo Reef Dive
Ningaloo Reef Resort
Ningaloo Whaleshark-N-Dive
Noble Grape Guesthouse
Noodlefish
Norfolk Hotel
Nornalup Riverside Chalets
Norval Gallery
Novotel Ningaloo Resort
Number Six
### O
Observatory Guesthouse
Ocean Beach Backpackers
Ocean Beach Hotel
Ocean Blues
Ocean Park
Ocean Restaurant
Ocean West
Oceanic Cruises
Oceanside Village
Old Blythewood Homestead
Old Brewery
Old Broome Guesthouse
Old Butter Factory Museum
Old Derby Gaol
Old Farm at Strawberry Hill
Old Firestation Backpackers
Old Geraldton Gaol Craft Centre
Old German Consulate
Old Pearler Restaurant
Old Picture Theatre Holiday Apartments
Old Railway Station Museum
Oliver Hill Train & Tour
One Tide Charters
One Tree Bridge & Glenoran Pool
One World Backpackers
Onshore Cafe
Opera Under the Stars
Orana Cinemas
Ospreys Beach Chalet
Out & About
Out of Sight!
Oyster Stacks
### P
Parklife
Patersons Stadium
Patrick Taylor Cottage
Peak Charles National Park
Peel Zoo
Pelican Feeding
Pelican Shore Villas
Pelican's Nest
Pemberton Backpackers YHA
Pemberton Discovery Tours
Pemberton Hiking & Canoeing
Pemberton Pool
Pemberton Tramway
Pemberton Wine Centre
Pengo's Cafe
Pension of Perth
Pensione Hotel
Peoples Park Caravan Village
Pepper & Salt
Perth Arena
Perth City YHA
Perth Concert Hall
Perth Cup
Perth Institute of Contemporary Arts
Perth International Arts Festival
Perth Map Centre
Perth Mint
Perth Royal Show
Perth Zoo
Perugino
Pier 21
Pier Hotel
Pigeonhole
Pilbara Holiday Park
Pinnacles Caravan Park
Pinnacles Edge Resort
Pinocchio
Pirates
Planet
Porongurup Range Tourist Park
Porongurup Village Inn, Shop & Tearooms
Port Denison Holiday Units
Port Hedland Yacht Club
Port Mill B&B
Port Smith Caravan Park
Potshot Hotel Resort
Pretty Pool
Prideau's
Prince of Wales
Princess Royal Fortress
Print Hall
Priory Hotel
Providore
Provincial
Public Sculptures
Pump Hill Farm Cottages
PumpHouse
Punurrunha
### Q
Quaalup Homestead
Queens
Quest Harbour Village
Quod & Aboriginal Burial Ground
### R
Ralph Bower Adventureland Park
Raven Wines
Ray White
Ray White Kalbarri Accommodation Service
Reading Cinema
Record Finder
Red Earth Arts Festival
Red Rock Art Gallery
Red Sun Camels
Red Teapot
Reddell Beach
Reef Cafe
Reefs & Wrecks
Reefwalker Adventure Tours
Regal Apartments
Regal Theatre
Remedy
Residency Museum
Rest Point Holiday Village
Restaurant Amusé
Revolutions
Richardson
Riva
RiverBank Estate
Riverbend Caravan Park
Riverglen Chalets
Riversedge Cafe
Riverside Retreat
Riverview on Mount Street
Rockingham Wild Encounters
Roebuck Bay Caravan Park
Roebuck Bay Hotel
Rose & Crown
Rosemount Hotel
Rottnest Adventure Tour
Rottnest Air Taxi
Rottnest Bakery
Rottnest Island Authority Cottages
Rottnest Lodge
Rottnest Museum
Rottnest Voluntary Guides
Round House
Rustico
### S
STS Leeuwin II
Sadie's
Sail & Anchor
Sail Ningaloo
Sal Salis
Salitage
Salt Store
Saltdish
Sampey Meats
Samson Beach Bistro
Samson Beach Caravan Park
Samson Beach Chalets
Samson House
Samudra
Sandalford
Sayers
Sayers Sister
Scarborough Beach
Seashells Cafe
Seashells Resort
Seashells Yallingup
Sebel
Secret Garden
Sensational Heights
Settler's Tavern
Shark Bay Coaches & Tours
Shark Bay Hotel
Shark Bay Scenic Flights
Shark Bay World Heritage Discovery Centre
Shinju Matsuri Festival of the Pearl
Ships of the Desert
Shoal Air
Shoalwater Islands
Short Street Gallery
Silver Star
Skydive Express
Snags & Sons
Somerville Auditorium
Source Foods
Southbound
Southern End
Spinifex Hotel
Squid Lips
St John Brook Conservation Park
St John's Anglican Church
St Mark's (Old Picton) Church
Staircase to the Moon
State Theatre Centre
Stella Bella
Stimulatte
Stirling Range Retreat
Subiaco Arts Centre
Subiaco Hotel
Summadayze
Sun Pictures
Sunmoon Boutique Resort
Sunset Bar & Grill
Sunset Beach Holiday Park
Surf Sail Australia
Surfing
Surfpoint
Surfschool (Lancelin)
Surfschool (Perth)
Swan Jet
Swan Valley Tours
Swanbourne Beach
### T
Taka
Taku Japanese Kitchen
Tarangau Caravan Park
Tarts
Taste & Graze
Taunton Farm Holiday Park
Taylor's Beach Bar & Cafe
Telstra Drug Aware Pro
Terrace Central B&B Hotel
The Art Place
The Bakery
The Beaufort St Merchant
The Bird
The Brisbane
The Cidery
The Clifton
The Cove
The Goose
The Grosvenor
The Happy Wife
The Lily
The Monk
The Moon
The Outram
The Peninsula
The Pourhouse
The Sebel Residence
The Studio Bistro
The Terrace Hotel
The Trustee
Thompson Estate
Thurlby Herb Farm
Tides Garden Bar
Tiger, Tiger
Timber & Heritage Park
Tingle All Over YHA
Tom's Kitchen
Toodyay Agricultural Show
Toodyay International Food Festival
Top Deck Cafe
Topolinis Caffe
Torndirrup National Park
Toun Beach Cafe
Town Beach Cafe
Town Hall (Albany)
Town Hall (Fremantle)
Tradewinds
Tram Rides
Travelodge Perth
Trigg Beach
Trigg Retreat
Triple J Tours
Tuart Forest
Tunbridge Gallery
Turquoise Bay
Turquoise Coast Enviro Tours
Two Feet & A Heartbeat
Two Peoples Bay
Ty-Jarrah
### U
Universal
### V
Vancouver Arts Centre
Vancouver Cafe & Store
Vasse
Vasse Felix
Veggie Mama
Velvet Lounge
Venn Cafe & Bar
Vibe
Viet Hoa
Vintages
Vlamingh's Lookout
Voyager Estate
### W
WA Skydiving Academy
WACA
WOW Wilderness Ecocruises
Walpole Lodge
Walpole-Nornalup National Park
Wander Inn Backpackers
Wardan Aboriginal Centre
Waters Edge
Watershed Premium Wines
Waychinicup National Park
Weelaway
West Coast Blues 'n' Roots Festival
West Coast Dive Park
West Oz Active Adventure Tours
WestTreks
Western Australian Museum – Albany
Western Australian Museum – Maritime
Western Australian Museum – Perth
Western Australian Museum – Shipwreck Galleries
Western Australian Museum
Western Beach Lodge
Western Xposure
Whale Watching
Whale World Museum
Whalers Restaurant
Wharefinger Museum
Wharf Restaurant
Wheels & Doll Baby
Whisper
White Star Hotel
Whiteman Park
Who's Your Mumma
Wickham Retreat
Wild Mango
Wild Poppy
Wildsights
Wildwood Valley Cottages & Cooking School
William Topp
Willowleigh B&B
Wills Domain
Windmills Break
Windsurfer Beach Chalets
Windward Adventures
Wine & Truffle Co
Wine for Dudes
Witch's Hat
Wolfe Lane
Woodman Point Holiday Park
Woody Island Eco-Stays
Wula Guda Nyinda Aboriginal Cultural Tours
### X
X-Wray Cafe
Xanadu
### Y
Yallibiddi Café
Yallingup Beach Holiday Park
Yallingup Surf School
Yardie Homestead Caravan Park
Yeehaa Trail Rides
York Caravan Park
York Mill
York Street Cafe
### Z
ZeeBar
|
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The Ebbtide
Domestic Violence and the Draft: the NFL's Problem with Keeping the Hits on the Field
The NFL stands for many different things to different people. With the way our nation's most popular sport in heading, however, the most justifiable meaning of it should be 'Not For Ladies.'
Because let's be honest, when it comes to respect of women, the NFL's stance is almost nonexistent. The most obvious indicator of this?
Well, take a look at the draft.
Year after year, we see players with such high potential and sheer athleticism coming out of college, with teams drooling over what they can bring to a professional team. But what seems to be overlooked are the dozens of cases each year in which a potential first or second round pick drops down draft boards because of off-the-field issues. These "issues" have a name, and that name is domestic violence.
Football players are humans, with flaws just like the rest of us. It's tough to not put million dollar athletes on a pedestal when they are always in the limelight and seem perfect, but that's rarely the case.
"What concerns me is when I see something like (the Ray Rice elevator video), and kids see that and make the connection that 'a role model did this, so it must be okay,'" says Rachel David, a gender and women's studies instructor who has taught at Shoreline for 18 years. "On top of that, there's the cultural reaction to this. They hear people blaming the women, they hear excusing of his behavior."
We've seen it so many times before and the country is slowly becoming numb to it, that is a dangerous thing.
David brings an interesting point of view to the mental side of DV cases.
"When you grow up playing football, you're taught that when you experience pain, you swallow it and tough it out, no matter how hard it hurts. … And if you're not able to sympathize with your own pain over the years, then you won't be able to see others'," David offers.
"And on the field, they're taught to hurt others, without thinking about the outcome. That pulls into their personal life, where violence and aggression might become normalized."
We cannot keep letting the Ray McDonalds, the Greg Hardys and the Frank Clarks of the NFL become role models for the millions of wide-eyed, malleable young kids who are watching.
Don't believe me? Take a look at just this year's draft class.
Oklahoma Sooners running back Joe Mixon, a gifted athlete predicted to be a top-10 pick, fell to the second round before hearing the Cincinnati Bengals call his name. From the thunder of boos pouring out of the crowd on Philadelphia's Ben Franklin Parkway, one could assume that those fans had seen the viral video of Mixon breaking four bones in a young woman's face in 2014.
The 2016 Heisman trophy finalist Dede Westbrook, also out of OU, fell to Jacksonville in the fourth. Was this because of injury concerns? Production concerns? Maturity concerns? No, not really.
He just got arrested twice before even being recruited to a university. Once for throwing the mother of his two children to the ground during an argument, and again for punching the same woman as well as biting her arm.
These, ladies and gentlemen, are potential Rookie of the Year candidates, coming primetime to a television near you. And not only will they star in the NFL because they are such talented football players, but the brighter their star shines, the less light will be shed on their dark pasts. 'Tis the way of the world in today's NFL.
-Vaughn Drewien
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{"url":"http:\/\/www.physicsforums.com\/showthread.php?t=540872","text":"## Divergence of Energy-momentum Tensor\n\nHow do you prove that Maxwell's energy-momentum equation is divergence-free?\nI don't know whether or not I have to use Lagrangians or Eistein's tensor, or if there's a simlpler way of expanding out the tensor..\n\n\u2202$_{\\mu}$T$^{\\mu\\nu}$=0\n\nT$^{}\\mu\\nu$=F$^{}\\mu\\alpha$F$^{}\\nu$$_{}\\alpha$-1\/4F$^{}\\alpha\\beta$F$_{}\\alpha\\beta$$\\eta$$^{}\\mu\\nu$\n\n PhysOrg.com science news on PhysOrg.com >> 'Whodunnit' of Irish potato famine solved>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change>> Curiosity Mars rover drills second rock target\n I mean \u2202$_{\\mu}$T$^{\\mu\\nu}$=0 T$^{\\mu\\nu}$=F$^{\\mu\\alpha}$F$^{\\nu}$$_{\\alpha}$-1\/4F$^{\\alpha\\beta}$F$_{\\alpha\\beta}$$\\eta$$^{\\mu\\nu}$\n Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus Try writing $F_{\\mu\\nu} = \\partial_\\mu A_\\nu - \\partial_\\nu A_\\mu$ and using the commutativity of the derivatives.\n\n Tags divergence, energy, momentum, relativity, tensor","date":"2013-05-21 15:20:28","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\": 0.5747504830360413, \"perplexity\": 2736.0199318266887}, \"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-2013-20\/segments\/1368700132256\/warc\/CC-MAIN-20130516102852-00018-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
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Q: Add background music at specific time period in mp3 files using ffmpeg I want to add background music after every 5 seconds in .mp3 file using ffmpeg.
I have 2 audio files : input1.mp3 of 5 seconds and input2.mp3 of 4 minutes 04 seconds. I want to add input1.mp3 after every 5 seconds in input2.mp3 like after 0,5,10,15,20,... seconds.
I am using :
ffmpeg -i input1.mp3 -i input2.mp3 -filter_complex amix=inputs=2:duration=first:dropout_transition=3 OUTPUT.mp3
The command is working properly. How can I repeat the input1.mp3 after every 5 seconds to input2.mp3 ?
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//
// Generated by the J2ObjC translator. DO NOT EDIT!
// source: ./queryparser/src/java/org/apache/lucene/queryparser/xml/builders/package-info.java
//
/*!
@brief XML Parser factories for different Lucene Query/Filters.
*/
#include "J2ObjC_header.h"
#pragma push_macro("INCLUDE_ALL_OrgApacheLuceneQueryparserXmlBuildersPackage_info")
#ifdef RESTRICT_OrgApacheLuceneQueryparserXmlBuildersPackage_info
#define INCLUDE_ALL_OrgApacheLuceneQueryparserXmlBuildersPackage_info 0
#else
#define INCLUDE_ALL_OrgApacheLuceneQueryparserXmlBuildersPackage_info 1
#endif
#undef RESTRICT_OrgApacheLuceneQueryparserXmlBuildersPackage_info
#if __has_feature(nullability)
#pragma clang diagnostic push
#pragma GCC diagnostic ignored "-Wnullability"
#pragma GCC diagnostic ignored "-Wnullability-completeness"
#endif
#if __has_feature(nullability)
#pragma clang diagnostic pop
#endif
#pragma pop_macro("INCLUDE_ALL_OrgApacheLuceneQueryparserXmlBuildersPackage_info")
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