text:
import { Injector } from '@angular/core';
import {
  Action,
  props,
  ScannedActionsSubject,
  ActionsSubject,
  createAction,
} from '@ngrx/store';
import { Actions, ofType } from '../';
import { map, toArray } from 'rxjs/operators';

describe('Actions', function () {
  let actions$: Actions<AddAction | SubtractAction>;
  let dispatcher: ScannedActionsSubject;

  const ADD = 'ADD';
  const SUBTRACT = 'SUBTRACT';

  interface AddAction extends Action {
    type: 'ADD';
  }

  interface SubtractAction extends Action {
    type: 'SUBTRACT';
  }

  const square = createAction('SQUARE');
  const multiply = createAction('MULTYPLY', props<{ by: number }>());
  const divide = createAction('DIVIDE', props<{ by: number }>());

  // Class-based Action types
  const actions = [ADD, ADD, SUBTRACT, ADD, SUBTRACT];

  beforeEach(function () {
    const injector = Injector.create([
      {
        provide: ScannedActionsSubject,
        useClass: ScannedActionsSubject,
        deps: [],
      },
      { provide: ActionsSubject, useClass: ActionsSubject, deps: [] },
      { provide: Actions, useClass: Actions, deps: [ScannedActionsSubject] },
    ]);

    actions$ = injector.get(Actions);
    dispatcher = injector.get(ScannedActionsSubject);
  });

  it('should be an observable of actions', (done) => {
    const actions = [
      { type: ADD },
      { type: SUBTRACT },
      { type: SUBTRACT },
      { type: SUBTRACT },
    ];

    const iterations = [...actions];

    actions$.subscribe({
      next(value) {
        const change = iterations.shift();
        expect(value.type).toEqual(change?.type);
        done();
      },
    });

    actions.forEach((action) => dispatcher.next(action));
    dispatcher.complete();
  });

  it('should filter out actions', (done) => {
    const expected = actions.filter((type) => type === ADD);

    actions$
      .pipe(
        ofType(ADD),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    actions.forEach((action) => dispatcher.next({ type: action }));
    dispatcher.complete();
  });

  it('should filter out actions and ofType can take an explicit type argument', (done) => {
    const expected = actions.filter((type) => type === ADD);

    actions$
      .pipe(
        ofType<AddAction>(ADD),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    actions.forEach((action) => dispatcher.next({ type: action }));
    dispatcher.complete();
  });

  it('should let you filter out multiple action types with explicit type argument', (done) => {
    const expected = actions.filter(
      (type) => type === ADD || type === SUBTRACT
    );

    actions$
      .pipe(
        ofType<AddAction | SubtractAction>(ADD, SUBTRACT),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    actions.forEach((action) => dispatcher.next({ type: action }));
    dispatcher.complete();
  });

  it('should filter out actions by action creator', (done) => {
    actions$
      .pipe(
        ofType(square),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(['SQUARE']);
          done();
        },
      });

    [...actions, square.type].forEach((action) =>
      dispatcher.next({ type: action })
    );
    dispatcher.complete();
  });

  it('should infer the type for the action when it is filter by action creator with property', (done) => {
    const MULTYPLY_BY = 5;

    actions$
      .pipe(
        ofType(multiply),
        map((update) => update.by),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual([MULTYPLY_BY]);
          done();
        },
      });

    // Unrelated Actions
    actions.forEach((action) => dispatcher.next({ type: action }));
    // Action under test
    dispatcher.next(multiply({ by: MULTYPLY_BY }));
    dispatcher.complete();
  });

  it('should infer the type for the action when it is filter by action creator', (done) => {
    // Types are not provided for generic Actions
    const untypedActions$: Actions = actions$;
    const MULTYPLY_BY = 5;

    untypedActions$
      .pipe(
        ofType(multiply),
        // Type is infered, even though untypedActions$ is Actions<Action>
        map((update) => update.by),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual([MULTYPLY_BY]);
          done();
        },
      });

    // Unrelated Actions
    actions.forEach((action) => dispatcher.next({ type: action }));
    // Action under test
    dispatcher.next(multiply({ by: MULTYPLY_BY }));
    dispatcher.complete();
  });

  it('should filter out multiple actions by action creator', (done) => {
    const DIVIDE_BY = 3;
    const MULTYPLY_BY = 5;
    const expected = [DIVIDE_BY, MULTYPLY_BY];

    actions$
      .pipe(
        ofType(divide, multiply),
        // Both have 'by' property
        map((update) => update.by),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    // Unrelated Actions
    actions.forEach((action) => dispatcher.next({ type: action }));
    // Actions under test, in specific order
    dispatcher.next(divide({ by: DIVIDE_BY }));
    dispatcher.next(divide({ by: MULTYPLY_BY }));
    dispatcher.complete();
  });

  it('should filter out actions by action creator and type string', (done) => {
    const expected = [...actions.filter((type) => type === ADD), square.type];

    actions$
      .pipe(
        ofType(ADD, square),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    [...actions, square.type].forEach((action) =>
      dispatcher.next({ type: action })
    );

    dispatcher.complete();
  });

  it('should filter out actions by action creator and type string, with explicit type argument', (done) => {
    const expected = [...actions.filter((type) => type === ADD), square.type];

    actions$
      .pipe(
        // Provided type overrides any inference from arguments
        ofType<AddAction | ReturnType<typeof square>>(ADD, square),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    [...actions, square.type].forEach((action) =>
      dispatcher.next({ type: action })
    );

    dispatcher.complete();
  });

  it('should filter out up to 5 actions with type inference', (done) => {
    // Mixing all of them, up to 5
    const expected = [divide.type, ADD, square.type, SUBTRACT, multiply.type];

    actions$
      .pipe(
        ofType(divide, ADD, square, SUBTRACT, multiply),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    // Actions under test, in specific order
    dispatcher.next(divide({ by: 1 }));
    dispatcher.next({ type: ADD });
    dispatcher.next(square());
    dispatcher.next({ type: SUBTRACT });
    dispatcher.next(multiply({ by: 2 }));
    dispatcher.complete();
  });

  it('should support more than 5 actions', (done) => {
    const log = createAction('logarithm');
    const expected = [
      divide.type,
      ADD,
      square.type,
      SUBTRACT,
      multiply.type,
      log.type,
    ];

    actions$
      .pipe(
        // Mixing all of them, more than 5. It still works, but we loose the type info
        ofType(divide, ADD, square, SUBTRACT, multiply, log),
        map((update) => update.type),
        toArray()
      )
      .subscribe({
        next(actual) {
          expect(actual).toEqual(expected);
          done();
        },
      });

    // Actions under test, in specific order
    dispatcher.next(divide({ by: 1 }));
    dispatcher.next({ type: ADD });
    dispatcher.next(square());
    dispatcher.next({ type: SUBTRACT });
    dispatcher.next(multiply({ by: 2 }));
    dispatcher.next(log());
    dispatcher.complete();
  });
});

redpajama_set_name: RedPajamaGithub


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text:
\section{Introduction}
The molecular gas in our galaxy shows structure on a wide range of
scales. The largest structures detected in the molecular gas are
giant molecular clouds (GMCs), of which the largest have diameters
of $\sim 100 \, {\rm pc}$ and masses of more than $10^6 \, {\rm M}_{\sun}$.
High resolution studies of molecular clouds, however, reveal that
they have internal structure on all scales, and are typically
clumpy or filamentary. Direct imaging of CO in nearby
clouds reveals structure on all scales down to lengths of $\sim 0.01$ pc
and masses of $\sim 0.01 \, {\rm M}_{\sun}$ (Falgarone, Puget,
\& P\'erault 1992; Langer et al. 1995). Studies of the time variability
of absorption lines indicates the presence of structure in the
dense gas on scales down to lengths of $\sim 5 \times 10^{-5}$ pc and
masses of $\sim 5 \times 10^{-9} \, {\rm M}_{\sun}$ (Marscher, Moore
\& Bania 1993; Moore \& Marscher 1995).

In this hierarchy of sizes, however, not all scales are of equal
interest to astronomers. Stars form by gravitational collapse of
dense regions within molecular clouds; much interest is therefore
focused on the scale corresponding to the mass of protostars.
Surveys of nearby clouds (within 500 parsecs of the earth)
have focused attention on dense cores with typical diameters of
$\sim 0.1 \, {\rm pc}$, masses of $\sim 30 \, {\rm M}_{\sun}$,
and densities of $\sim 2 \times 10^4 \, {\rm cm}^{-3}$
(Myers, Linke, \& Benson 1983; Benson \& Myers 1989). In addition
to dense cores embedded within GMCs, our galaxy also contains
isolated dense clouds known as Bok globules (Bok \& Reilly 1947).
Neither dense cores nor Bok globules are spherical, as a general
rule. The projected axis ratio,
$q \equiv b/a$, of small Bok globules has an average value
$< \! q \! > \approx 0.6$ (Clemens \& Barvainis 1988, hereafter CB; Bourke,
Hyland, \& Robinson 1995; hereafter BHR). Embedded dense cores are similarly
flattened, with $ < \! q \! > \approx 0.5 - 0.6$ (Myers et al. 1991;
Tatematsu et al. 1993).

The projected axis ratios of globules and cores are of interest
because they place constraints on the intrinsic shapes of
these objects. The intrinsic shapes of isolated globules and embedded
cores are determined by a variety of physical processes. Globules
and cores are sculpted by the self-gravity of the gas which they
contain and by thermal pressure, turbulent pressure, and magnetic
pressure. Since star formation occurs in these dense regions,
their physical properties are further modified by outflows
and winds from the protostars which may be embedded within them.
Recent optical surveys of Bok globules (CB; BHR;
Hartley et al. 1986) and millimeter surveys of dense cores (Benson
\& Myers 1989; Loren 1989; Lada, Bally, \& Stark 1991; Nozawa et al.
1991) provide data sets of apparent axis ratios. As a cautionary note,
however, it should be pointed out that a core or globule is not
a solid, well-defined object with easily measurable axis ratios. It
is merely one scale in a hierarchy of structure. The shape of a dense core
as defined by the emission of one molecular line, moreover, will not be
precisely the same as its shape defined by the emission of a
different molecule. Readers are advised to regard the shapes measured
in surveys with a certain amount of skepticism.

Previous studies (David \& Verschueren 1987; Myers et al. 1991; Fleck 1992)
have placed constraints on the permitted intrinsic shapes of dense cores.
For instance, the mean apparent axis ratio $< \! q \! > \approx
0.5 - 0.6$ for cores is fully consistent
with a population of prolate objects, but only marginally
consistent with an oblate population (Myers et al. 1991;
Fleck 1992). More sophisticated analytic tools for examining
sets of axis ratios have now been developed by investigators
studying the intrinsic axis ratios of elliptical galaxies and
other stellar systems. For instance, starting with a nonparametric
estimate for the distribution $f(q)$ of apparent axis ratios,
it is possible to find an estimate for the distribution $N(\gamma)$
of intrinsic axis ratios, given the assumption that
the systems considered are either oblate or prolate
spheroids and are randomly oriented with respect
to the observer (Tremblay \& Merritt 1995; Ryden 1996).

Using this technique, one is able, for instance, to
test the hypothesis that all dense cores or Bok globules are
randomly oriented prolate objects.
A test of the randomly oriented prolate hypothesis, more stringent than simply looking
at the mean $< \! q \! >$, is
provided by examining the entire distribution $f(q)$.
I first compute an estimate $\hat f (q)$ for the distribution
of apparent axis ratios, then mathematically invert it to
find a estimated distribution ${\hat N}_P (\gamma)$ of intrinsic
axis ratios. The inversion is mathematically unique, but the
resulting function ${\hat N}_P$ is only physically meaningful
if it is non-negative for all values of $\gamma$.
If ${\hat N}_P$ dips below zero at a statistically
significant level, the initial hypothesis -- that the cores or
globules are randomly oriented prolate objects -- can be rejected.

Similarly, one can test the hypothesis that cores or globules
are randomly oriented oblate objects. The available kinematic information,
however, indicates that dense cores are not rotationally supported
oblate spheroids (Goodman et al. 1993). Large scale maps also show that
many dense cores are aligned with larger filamentary structures,
indicating that a prolate geometry is more likely in such cases
(Myers et al. 1991). Thus, it should not be surprising when the
randomly oriented oblate hypothesis turns out to be
emphatically rejected for samples of dense cores.

In section 2, I give a brief outline of the mathematical techniques
used to find the distribution of intrinsic axis ratios, given either
the prolate or oblate hypothesis -- a fuller description, for those
who desire it, is given
in Ryden (1996). In section 3, I apply these techniques
to Bok globules, and in section 4, I apply them to dense cores embedded
within molecular clouds. Generally speaking, for each data set considered,
the prolate hypothesis gives a better fit than does the oblate hypothesis,
given the assumption that the globules and cores are randomly oriented.
In section 5, I discuss the implications of this finding for the
origin and evolution of dense cores and globules.

\section{Methods}

I start with a sample $q_1$, $q_2$, $\dots$, $q_N$ measured axis ratios
for a sample of $N$ globules or dense cores.
The nonparametric kernel estimator for the underlying
distribution $f(q)$ is
\begin{equation}
{\hat f} (q) = {1 \over N h} \sum_{i=1}^N K \left( {q - q_i \over h}
\right) \ ,
\end{equation}
where $K$ is the kernel function. A discussion of kernel
nonparametric estimators, as applied to astronomical
problems, is given by Merritt \& Tremblay (1994), Vio et al. (1994),
and Merritt \& Tremblay (1995). For my purposes, I want
a smooth differentiable kernel, so I use a Gaussian:
\begin{equation}
K(x) = {1 \over \sqrt{2 \pi} } e^{-x^2/2}  \ .
\end{equation}
For a kernel width $h$, I adopt
\begin{equation}
h = 0.9 A N^{-0.2} \ ,
\end{equation}
where $A$ is the smaller of the standard deviation of the sample and
its interquartile range divided by $1.34$ (Silverman 1986; Vio et al. 1994).
For samples which are not strongly skewed, this formula for $h$ is
a good approximation to the value which minimizes the integrated
mean square error in $\hat f$. For the samples examined in this paper,
$0.06 < h < 0.10$.

Since $f(q)$ must be equal to zero for $q < 0$ and $q > 1$, reflective
boundary conditions are applied at the boundaries $q = 0$ and $q=1$
(Ryden 1996). The  use of reflective boundary conditions ensures
the proper normalization
\begin{equation}
\int_0^1 {\hat f} (q) dq = 1 \ .
\end{equation}
One drawback of reflective boundary conditions is that they compel
the slope of $\hat f$ to be equal to zero at the boundaries, which
might not be true of the actual distribution $f$. The shape of $\hat f$
within a distance $h$ of the boundaries should therefore be viewed
with skepticism.

If the globules or cores in the sample are all randomly oriented
oblate spheroids, then the estimated distribution ${\hat N}_O ( \gamma )$
for the intrinsic axis ratio $\gamma$ is given by the relation
\begin{equation}
{\hat N}_O ( \gamma ) = {2 \gamma \sqrt{1 - \gamma^2 } \over \pi }
\int_0^\gamma {d \ \over dq} \left( {\hat f} / q \right) {dq \over
\sqrt{\gamma^2 - q^2} } \ .
\end{equation}
If the globules or cores are assumed to be randomly oriented prolate spheroids,
then the estimated distribution ${\hat N}_P ( \gamma )$ for the
intrinsic axis ratio is
\begin{equation}
{\hat N}_P ( \gamma ) = {2 \sqrt{ 1 - \gamma^2 } \over \pi \gamma }
\int_0^\gamma {d \ \over dq} \left( q^2 {\hat f} \right) {dq \over
\sqrt{\gamma^2 - q^2} } \ .
\end{equation}
If ${\hat N}_O$ is negative for any value of $\gamma$, at a statistically significant level,
then I can reject the hypothesis that the sample is
drawn from a population of randomly oriented oblate objects. Either
they are not all oblate, or they are not randomly oriented. Having
a negative number of objects with a given value of $\gamma$ is
permissible from a purely mathematical viewpoint, but is
nonsensical from a physical viewpoint. Similarly,
if ${\hat N}_P$ drops below zero at a statistically significant level,
the randomly oriented prolate hypothesis can be rejected. The statistical significance
of excursions below zero is estimated by bootstrap resampling techniques
(Scott 1992; Merritt \& Tremblay 1994). From the original data set
$q_1$, $q_2$, $\dots$, $q_N$, I draw, with replacement, a new set
of $N$ data points. Using this bootstrap resampling of the original
data, I compute new estimates for $\hat f$, ${\hat N}_O$, and
${\hat N}_P$. After making a large number $n$ of these bootstrap estimates
(for this paper, I used $n=800$), confidence intervals can be placed
on the original estimates $\hat f$, ${\hat N}_O$, and ${\hat N}_P$.
At each value of $\gamma$, for instance, an upper limit can be placed
on ${\hat N}_O$ at the 99\% one-sided confidence level,
by finding the value of ${\hat N}_O$ such that
1\% of the bootstrap estimates lie above this value. If this
upper confidence limit drops below zero, then the hypothesis that
the objects are randomly oriented oblate spheroids can be rejected
at the 99\% confidence level. Similar analysis of ${\hat N}_P$ can
be used to test the hypothesis that the objects in the original
sample are randomly oriented prolate spheroids.

The confidence intervals derived from bootstrap resampling represent
only the error resulting from finite sample size. Additional errors
in the estimates $\hat f$, $\hat N_O$, and $\hat N_P$ will be
present as a result of errors in the measured values of $q$. If
a typical measurement error $\sigma_q$ is smaller than the smoothing length
$h$, then the effects of measurement error can be ignored. The
errors in the axis ratios of dense cores observed at millimeter wavelengths
are relatively small, if the effects of the beamwidth are correctly
subtracted (see section 4 below). However, the errors in the
published axis ratios for surveys of Bok globules (CB; BHR)
are significantly larger than $h$.
A further complication is added by the fact
that errors in $q$ are generally not Gaussian, so they cannot
simply be added in quadrature to the kernel width $h$. The presence of
non-Gaussian errors in the measurement of the axis ratio of nearly
circular objects can significantly affect the shape of $\hat f$ when
$q \sim 1$. This distortion of $\hat f$, in turn, can affect the
conclusions which are drawn about the intrinsic shapes of the
observed objects. A cautionary tale is related by Franx \& de Zeeuw
(1992), who deduced the intrinsic ellipticity $\epsilon$ of disk
galaxies from their observed axis ratios. Assuming Gaussian errors
in $q$, their best model had $\epsilon = 0.06$; however, the introduction
of non-Gaussian errors led to a best fitting model with $\epsilon = 0$.
In the following section, it will also be seen that the introduction of
non-Gaussian rounding errors distorts the distribution $\hat f (q)$ for
Bok globules.

\section{Isolated Bok Globules}

Bok globules are not, in general, spherical. Bok \& Reilly (1947) defined
globules as ``approximately circular or oval dark objects of small size'',
as contrasted to the ``wind-blown wisps of dark nebulosity'' which can
also be found in the interstellar medium of our galaxy. CB
constructed a catalog of small Bok globules
with declination $\delta > -36\deg$. They searched Palomar Observatory
Sky Survey (POSS) plates for isolated, opaque globules with diameters less
than $10'$. The axis ratio of the globules was explicitly not a
selection criterion. Their complete catalog contains 248 objects,
with a mean angular size of $4'$. The apparent axis ratio of each
globule was determined by approximating its shape as an ellipse,
and then measuring the minor and major axes of the fitted ellipse.
The axis ratios measured for the complete sample ranged from
$q = 1.00$ to $q = 0.14$, with a mean $< \! q \! > = 0.59$ and
standard deviation $\sigma_q = 0.23$.

To begin the analysis, I na\"{\i}vely take the values for the
axis length $a$ and $b$ published by CB,
and use the resulting values of $q = b/a$ to find the estimated
distribution ${\hat f} (q)$. The function $\hat f$ determined in
this way is shown as the solid line in the upper panel of Figure
1. In this Figure (and in every subsequent Figure in this paper),
the dashed lines indicate the 80\% confidence band and
the dotted lines show the 98\% confidence band, as determined
by bootstrap resampling. The estimated distribution ${\hat N}_O$ of
intrinsic axis ratios, given the randomly oriented oblate hypothesis, is shown in
the middle panel of Figure 1. The estimated distribution ${\hat N}_P$
of axis ratios, given the randomly oriented prolate hypothesis, is shown in the bottom panel. The
most striking aspect of the estimate $\hat f (q)$ found in this
manner is that it is bimodal. In addition to a broad maximum around
$q \sim 0.55$, there is a second peak at $q = 1$. Does this bimodality
indicate that there are two populations of globules, one flattened
and one nearly spherical? No. The peak at $q = 1$ is an artifact,
the result of rounding errors in $q$. CB, in measuring
the axis lengths of globules on the POSS plates, rounded $a$ and $b$
to the nearest millimeter, corresponding to $1{\farcm}12$ in
angular scale. Many of the globules in the survey are quite small;
42 out of 248 have $a \leq 2 \, {\rm mm}$. Consequently, rounding
of the axis lengths can have a large effect on the measured value
of $q$. For instance, a globule whose true size on the POSS plate
is $1.6 \, {\rm mm} \times 2.4 \, {\rm mm}$ will be tabulated as
being $2.0 \, {\rm mm} \times 2.0 \, {\rm mm}$. Its axis ratio will
be erroneously computed as $q = 1.00$ instead of its true value of
$q = 0.67$. A major effect of rounding errors is that small flattened
globules will be incorrectly classified as being circular.

The effect of the non-Gaussian rounding errors can be approximately
compensated for. To the values of $a$ and $b$ tabulated by
CB for each globule, I add an error term $\Delta$
drawn uniformly from the interval $ -0{\farcm}56 < \Delta < 0{\farcm}56$.
I then compute the new values of $q$ after the error terms are added on,
and compute ${\hat f} (q)$. After repeating this process 800 times, with
a different seed for the random number generator each time, I take
the average value of the 800 estimates $\hat f (q)$ as the new best
estimate of the underlying distribution $f (q)$, taking into
account the errors introduced by rounding the axis lengths $a$ and
$b$. The best estimate found in this way is given as the solid line
in the top panel of
Figure 2. The 80\% confidence bands (dashed lines) and the 98\% confidence bands
(dotted lines) include
both the errors due to finite sample size and the errors in
$q$ due to rounding.

Note that when the rounding errors are compensated for, the peak at
$q = 1$ disappears. The distribution $\hat f$ now has a single maximum
at $q = 0.6$. The mean value of $q$ is $< \! q \! > = 0.57$ and the
standard deviation is $\sigma_q = 0.22$. The derived values of ${\hat N}_O$,
given the oblate hypothesis, and ${\hat N}_P$, given the prolate hypothesis,
are shown in the middle panel and bottom panel of Figure 2. The oblate
hypothesis cannot quite be rejected at the 99\% one-sided confidence level,
but can be rejected at lower confidence levels. If the globules are
all oblate spheroids, then they must be quite flattened. Few or no
globules, if they are oblate, can have $\gamma \gtrsim 0.7$, and
the peak in ${\hat N}_O$ is at $\gamma \approx 0.25$. The observed
axis ratios, when corrected for rounding errors, are fully consistent
with the hypothesis that globules are all prolate objects with
random orientations. The
distribution ${\hat N}_P$ (bottom panel of Figure 2) is everywhere
positive, yielding a mean axis ratio $< \! \gamma \! > = 0.48$ and
standard deviation $\sigma_\gamma = 0.20$. The prolate hypothesis
yields a broader range of intrinsic axis ratios than does the
oblate hypothesis, with prolate globules ranging in shape from
filamentary structures with $\gamma \sim 0.1$ to nearly spherical
globules with $\gamma \sim 1$.

The catalog of CB in the northern sky
is complemented by that of BHR in the southern
sky. Starting with the comprehensive catalog of Hartley et al. (1986),
which lists dark clouds with $\Delta < - 33\deg$, BHR
selected highly opaque clouds with $a < 10'$. A total of 169 globules
met their selection criteria. The axis lengths of the selected
globules were measured from SERC Schmidt survey plates. Axis lengths
longer than $3'$ were rounded to the nearest arcminute; axis lengths
shorter than $3'$ were rounded to the nearest $0.5$ arcminute. This
rounding of axis lengths was sufficient to create significant errors
in the axis ratio $q$. Consequently, I computed the estimated distribution
function ${\hat f} (q)$ using the correction technique described
above. To axis lengths less than $3'$, I added an error $\Delta$
drawn uniformly from the interval $-0{\farcm}25 < \Delta < 0{\farcm}25$.
For axis lengths greater than $3'$, $-0{\farcm}5 < \Delta < 0{\farcm}5$.
The value of ${\hat f}$, including corrections for rounding errors,
is given in the upper panel of Figure 3. The 80\% and 98\% confidence bands
include the effects both of finite sample size and of rounding errors.

The BHR globules are slightly rounder on average than
the CB globules; $< \! q \! > = 0.61$ as compared
to $< \! q \! > = 0.57$. The standard deviation for each sample
is $\sigma_q = 0.22$. In addition, the $\hat f$ for the BHR
globules lacks the dip at $q \approx 1$ which is seen in
$\hat f$ for the CB sample. The difference in apparent shapes
for the CB sample and the BHR sample is a result of the
difference in their definitions of a Bok globule, and not
a reflection of differences in the properties of Bok globules
in the northern and southern hemispheres.

The oblate distribution ${\hat N}_O$ for the BHR sample is shown
in the middle panel of Figure 3; it is consistent with the hypothesis that
the globules are randomly oriented oblate spheroids. If so, however,
they must be intrinsically quite flat, with a mean and standard deviation
of $< \! \gamma \! > = 0.33$ and $\sigma_\gamma = 0.15$; few or no
globules can have $\gamma \gtrsim 0.7$. If, by contrast, the globules
are randomly oriented prolate spheroids, they will have a broader
range of intrinsic axis ratios, shown in the bottom panel of Figure 4.
Under the prolate hypothesis, the mean and standard deviation of
the intrinsic axis ratio are $< \! \gamma \! > = 0.52$ and $\sigma_\gamma
= 0.21$.

In conclusion, both the BHR and CB data sets show that the spherical
approximation is a poor one for Bok globules; they must be intrinsically
quite flat. The hypothesis that Bok globules are randomly oriented
oblate objects cannot be excluded. If the globules are oblate, however,
they must be quite flat, with a distribution peaking at $\gamma \sim 0.3$,
and equal to zero at $\gamma \gtrsim 0.7$. If the Bok globules are
randomly oriented prolate objects, they have a wider range of intrinsic
axis ratios. Still, there are few nearly spherical globules, even under
the prolate hypothesis. For the BHR sample, 21\% of prolate globules
have $\gamma \geq 0.7$; for the CB sample, only 14\% of the prolate
globules have $\gamma \geq 0.7$.

\section{Embedded Dense Cores}

Bok globules, according to Bok's original definition,
are relatively well-defined and isolated objects. The
CB and BHR catalogs of Bok globules contain only small globules. Their
upper size limit of $10'$ corresponds to a linear scale of $0.7 \,
{\rm pc}$ at a distance of $500 \, {\rm pc}$. Small Bok globules
are of interest to astronomers because their relative simplicity makes
them good laboratories for testing theories of star formation.
Most star formation in our galaxy, however, occurs not within
simple Bok globules but within the more complex environment of
large molecular clouds. The dense cores of molecular clouds
(with ``dense'' meaning $n \gtrsim 10^4 \, {\rm cm}^{-3}$)
can be traced using the emission lines of CS (Lada et al. 1991)
or NH$_3$ (Benson \& Myers 1989). Each emission line probes
a different density and temperature. Cores defined by
CS emission have a larger velocity dispersion, density,
and mass than the cores defined by NH$_3$ emission
(Zhou et al. 1989). However, Myers et al.
(1991), by mapping dense cores in the lines of NH$_3$,
CS, and C$^{18}$O, have demonstrated that the maps in
the different lines are similar (but not identical)
in position, orientation, and elongation. Thus, it
seems that the observed shapes of cores are not strongly
dependent on the particular emission line which is chosen
for the purpose of observation.

Benson \& Myers (1989) made a search for dense cores in the
$(J,K) = (1,1)$ rotation inversion line of NH$_3$. They
surveyed 149 positions selected to be in the center of
opaque regions on POSS plates. The dark clouds selected
in this manner are mainly nearby, with 119 of the 149 clouds
known to be less than $500 \, {\rm pc}$ away. Of the 149 regions
surveyed, 66 were detected in NH$_3$. Of the regions where
NH$_3$ was detected, 37 were mapped, and had their apparent axis ratios
measured. Of the mapped regions, 26 were identified as being dense cores
embedded within a larger molecular complex (type C),
5 were identified as being isolated globules (type G),
and 6 were classified as type M, intermediate between types C and G.
A Kolmogorov-Smirnov (KS) test comparing the 26 type C cores to the
11 type M and G cores reveals no significant difference in their
distribution of apparent axis ratios ($P_{\rm KS}
= 0.86$). For the purposes of my analysis,
therefore, I will lump all the mapped regions together, and
refer to them as ``dense cores''. In addition to the dense cores
selected from POSS plates,
Benson \& Myers provided maps and axis ratios for an additional
4 dense cores, selected for observation because they were in the
same position as an IRAS point source. Estimated masses of the
41 mapped dense cores lie in the range $0.5 \, {\rm M}_{\sun} < M <
760 \, {\rm M}_{\sun}$, with a median of $13 \, {\rm M}_{\sun}$.

The upper panel of Figure 4 shows the
estimated distribution ${\hat f} (q)$ for the distribution
of apparent axis ratios for all 41 dense cores mapped by Benson
\& Myers (1989). The mean apparent flattening ($< \! q \! > = 0.59$) for
this sample is comparable to the mean for the BHR and CB samples
of Bok globules. However, the Benson \& Myers dense cores are
notably lacking in nearly circular objects; the maximum axis
ratio in the entire sample is $q = 0.89$. The lack of nearly
circular objects is the classic indication that a population
cannot consist of randomly oriented oblate spheroids. Indeed,
the oblate hypothesis can be rejected at a very high confidence level --
the middle panel of Figure 4 shows that ${\hat N}_O$
dips far below zero for $\gamma \gtrsim 0.8$. So great is the
paucity of nearly circular cores that even the randomly oriented prolate hypothesis
can be rejected at the 99\% confidence level (see the bottom
panel of Figure 4). In short, the Benson \& Myers sample of dense
cores cannot be a population of randomly oriented axisymmetric
objects. Either they contain a significant number of triaxial cores
or there is a selection effect which excludes axisymmetric cores from the
sample when their axis of symmetry is close to the line of sight.
Compared to populations of axisymmetric objects, populations of
triaxial objects provide a better fit to samples with a lack
of apparently circular objects. This is because triaxial objects
appear to be nearly circular from only a very limited range of
viewing angles (Binggeli 1980; Binney \& de Vaucouleurs 1981).

Of the dense cores mapped by Benson \& Myers (1989), 21 have IRAS
point sources within one core diameter of the core's center. The
IRAS point sources are most plausibly explained as being
protostars or young stars embedded within the dense core.
It is not absurd to speculate that dense cores with embedded
IRAS sources could have different shapes, on average, than
cores without IRAS sources. For instance, cores of a particular
shape might be more efficient at collapsing to form stars. In
addition, an embedded protostar, in pouring out matter and radiation,
might change the shape of the core which encloses it. However,
it turns out that there is no significant difference between the
distribution of $q$ for the 21 cores with embedded IRAS sources and
the distribution for the 20 cores without IRAS sources. A KS
test comparing the two distributions yields $P_{\rm KS} = 0.9987$,
indicating a remarkably close similarity between the two distributions.
The similarity in axis ratios occurs in spite of the fact that
the cores with embedded sources have significantly larger radii,
masses, and line widths than the cores without sources (Benson
\& Myers 1989). Perhaps there is a preferred range of shapes for
NH$_3$ cores, which does not depend on the size of the core or
whether it contains an embedded protostar.

The dense cores mapped by Benson \& Myers exist lie within many
separate molecular clouds, with a wide range in galactic longitude.
To eliminate the variance which may exist between the cores of
different molecular clouds, with different physical and chemical
properties, it is useful to look at the population of dense cores
embedded within a single molecular cloud. Lada et al. (1991) studied
the dense cores of Lynds 1630 (alias Orion B), a molecular cloud
containing $\sim 10^5 \, {\rm M}_{\sun}$ of
gas (Maddalena et al. 1986), located $\sim 400 \, {\rm pc}$
away (Hilton \& Lahulla 1995).
Lada et al. mapped the cloud using the $J = 2 \to 1$ transition
of CS, using a beamwidth of $1{\farcm}8$ (corresponding to $0.21 \, {\rm pc}$).

Lada et al. (1991) identified individual ``clumps'' within Lynds 1630.
A clump was identified as a closed volume in position-velocity space,
containing CS emission at a $5\sigma$ level above the noise. The
entire region surveyed contained 42 clumps, as defined in this manner.
Shapes of individual clumps were determined by measuring the major
and minor axis lengths of the $5\sigma$ contours on the sky, subtracting
the beamwidth in quadrature. The majority of the clumps were unresolved,
but measured axis ratios were provided for 19 clumps with corrected major axis
length greater than the beamwidth ($2 a > 1{\farcm}8$). Virial masses
for these clumps lie in the range $8 \, {\rm M}_{\sun}  < M < 460
\, {\rm M}_{\sun}$, with a median of $104 \, {\rm M}_{\sun}$. Although 19
is not a large number, and consequently the derived error bands on
$\hat f$ and $\hat N$ are large, it is still interesting to compare
the shapes of the Lynds 1630 clumps to the more eclectic dense cores of Benson
\& Myers (1989). The 19 cores of Lada et al. (with a mean and standard
deviation in $q$ of $0.55 \pm 0.19$) have a distribution of apparent
shapes similar to that of the 41 dense cores of Benson \& Myers (with
a mean and standard deviation of $0.59 \pm 0.19$). A KS test comparing
the two distributions yields $P_{\rm KS} = 0.70$.
The nonparametric estimate ${\hat f} (q)$ for the Lada et al. clumps
is shown in the upper panel of Figure 5.
Because of the small number
of clumps, the oblate hypothesis cannot be excluded at the 99\%
one-sided confidence level (see the middle panel of Figure 5).
However, if the clumps are oblate and randomly oriented, then
they must all be quite flat, just as in the case of the Bok
globules studied by BHR and CB. The best-fitting function
${\hat N}_O$ peaks at $\gamma \sim 0.4$, and there can be
few or no oblate clumps with $\gamma \gtrsim 0.6$. Conversely,
the randomly oriented prolate hypothesis, as illustrated in the bottom panel of Figure 5,
is statistically more acceptable, and yields a broader range of
intrinsic axis ratios. The best-fitting function ${\hat N}_P$ yields
a mean axis ratio $< \! \gamma \! > = 0.46$ and a standard deviation
$\sigma_\gamma = 0.17$.

Another molecular cloud which has been surveyed for dense cores is
the $\rho$ Ophiuchus cloud. Its center is located at approximately
$b = 17\deg$, $l = 355\deg$ and is at a distance of $160 \, {\rm pc}$ from
the sun. Its total mass is estimated to be $\sim 3000 \, {\rm M}_{\sun}$
(Loren 1989). Thus, although smaller than Orion B, the $\rho$ Oph
cloud is closer, and can be mapped at higher resolution. Loren (1989)
mapped the $\rho$ Oph cloud using the $J = 1 \to 0$ transition of
$^{13}$CO. The telescope beamwidth was $2{\farcm}4$ FWHM, corresponding
to a spatial resolution of $0.11 \, {\rm pc}$.
The catalog of Loren (1989) contains 89 ``clumps'', located at
maxima of the emission in velocity-position space. Each clump
must be clearly separated from other clumps in order to be
included in the catalog. The masses estimated from
the integrated $^{13}$CO intensity lie in the range
$0.6 \, {\rm M}_{\sun} < M < 850 \, {\rm M}_{\sun}$, with a median
of $8.8 \, {\rm M}_{\sun}$. The major and minor axis lengths of
each clump are the FWHM along the principal axes, projected
onto the sky (the beamwidth is subtracted in quadrature).
The definition of a ``clump'' and of its major and minor axis lengths
thus differ from the definitions used by Lada et al. (1991); be
cautious in comparing the two different types of clump.

The estimated distribution ${\hat f} (q)$ for the
Loren clumps (upper panel of Figure 6) is marked by a
scarcity of objects with $q \gtrsim 0.8$. Of 89 clumps,
only 6 have $q > 0.8$. The distribution of $q$ for the
clumps of Loren (1989) is significantly different
at the 98\% confidence from that for
the dense cores of Benson \& Myers (1989); a K-S test yields
$P_{\rm KS} = 0.015$. The Loren clumps are flatter, on
average, than the Benson \& Myers cores, with a mean
and standard deviation in $q$ of $0.48 \pm 0.20$.
The difference between the clump shapes
found by Loren (1989) and those found by Lada et al. (1991)
is not statistically significant: $P_{\rm KS} = 0.41$.
Because of the lack of nearly circular clumps in the
Loren sample, the randomly oriented oblate hypothesis can be rejected
at the 99\% confidence level; see the middle panel of Figure 6.
The prolate hypothesis, however, is statistically acceptable,
as shown in the bottom panel of Figure 6. If the clumps
are randomly oriented prolate objects, they must be quite flat,
with $< \! \gamma \! > = 0.39$ and $\sigma_\gamma = 0.17$, and with
very few clumps having $\gamma > 0.7$.

The dense cores and clumps observed by the various surveys differ
somewhat in their definitions. Their masses, however, all lie
in the range $0.5 \, {\rm M}_{\sun} < M < 900 \, {\rm M}_{\sun}$, and
their characteristic density is $\sim 10^4 \, {\rm cm}^{-3}$.
Broadly speaking, the dense
cores and clumps are more readily explained by the prolate
hypothesis than by the oblate hypothesis. This conclusion results from
the lack of nearly circular objects in the samples. The cores
and clumps must be intrinsically quite nonspherical; if they
are randomly oriented prolate objects, the mean axis ratio
is approximately $\gamma \sim 0.4$.

In focusing solely on the
dense cores of molecular clouds, however, I have been neglecting
the larger structures within clouds. Molecular clouds show
substructure on all resolvable scales, including scales larger
and smaller than individual dense cores. The existence
of hierarchical structure on such a
broad range of scales has prompted investigators
to describe molecular clouds in terms of their fractal
dimension (Dickman, Horvath, \& Margulis 1990; Falgarone,
Phillips, \& Walker 1991). However, different
physical processes dominate at different length scales, which makes
it unlikely that the structure is a perfectly self-similar fractal.
To investigate the dependence of the shape of substructure
upon size, I can use the molecular survey of Nozawa et al. (1991),
who identified and cataloged substructures of different size
in their survey.

Nozawa et al. (1991) mapped an area
in the Ophiuchus region using the $J = 1 \to 0$ transition
of $^{13}$CO. The telescope beamwidth was $2{\farcm}7$ FWHM.
The area mapped ($b = 15\deg \to 33\deg$; $l =
355\deg \to 12\deg$) is north of the $\rho$ Ophiuchus main cloud
mapped by Loren (1989). Nozawa et al. picked out two types of
substructure in their survey. The larger substructures, which
they call ``clouds'', are defined as the regions enclosed by
the $3\sigma$ contours in the integrated $^{13}$CO map. The
map contains 23 clouds defined in this manner, with estimated
masses in the range $13 \, {\rm M}_{\sun} < M < 1200 \, {\rm M}_{\sun}$.
The median cloud mass was $76 \, {\rm M}_{\sun}$. The smaller
substructures, called ``cores'', are defined as maxima in the
integrated $^{13}$CO emission. Thus, each cloud contains at least
one core; the largest cloud contains 8 separate cores.
The total number of cores mapped by Nozawa et al. (1991)
is 51 (including 3 cores not well resolved at $2{\farcm}7$).
The axis ratios of the cores were estimated by finding the
contour at the half peak intensity level and fitting the
contour with an ellipse.
The estimated core masses lie in the range $3 \, {\rm M}_{\sun}
< M < 160 \, {\rm M}_{\sun}$, with a median mass of $13
\, {\rm M}_{\sun}$. The mass of each core is from 0.6\% to
48\% of the mass of the cloud in which it is embedded.

The ``cores'' in the $^{13}$CO map of Nozawa et al. (1991) are
slightly larger, on average, than the ``clumps'' in the $^{13}$CO
map of Loren (1989). The two populations, however, do not have
different distributions of axis ratios at a high
statistical confidence level. Comparison of the axis ratios of
the two populations, using a KS test, yields $P_{\rm KS} = 0.18$.
The most noticeable difference between the two populations is
that the cores of Nozawa et al. (1991) are rounder; they have
a mean and standard deviation in $q$ of $0.57 \pm 0.21$, as
compared to $0.48 \pm 0.20$ for the Loren (1989) clumps.

The best-fitting estimate ${\hat f} (q)$ for the cores of Nozawa
et al. (1991) is shown in the upper panel of Figure 7. Once again,
we see a dip in $\hat f$ as $q \to 1$. However, the dip is not
as deep or as wide as in the case of the Loren (1989) clumps, shown
in Figure 6. As a result, the randomly oriented oblate hypothesis cannot be rejected
at the 90\% confidence level for the Nozawa cores
(see the middle panel of Figure 7). If the oblate hypothesis is
true, however, the cores must be very flat, with ${\hat N}_O$ peaking
at $\gamma \sim 0.3$, and with few or no cores having $\gamma \gtrsim
0.6$. The prolate hypothesis gives a better fit to the observations
(see the bottom panel of Figure 7). If the Nozawa cores are randomly
oriented prolate objects, then the mean axis ratio is $< \! \gamma
\! > = 0.48$, with a standard deviation of $\sigma_\gamma = 0.19$.
The results for the {\it cores} of Nozawa et al. (1991) are thus
similar to the results found for other dense cores and for Bok
globules; the prolate hypothesis gives a better fit than the
oblate hypothesis, and if the oblate hypothesis is insisted
upon, then the cores must all be quite flat. But what can be
deduced about the shapes of the {\it clouds}, which are larger
than the cores?

The clouds in the catalog of Nozawa et al. (1991) are distinctly
different in shape from the smaller, denser cores which are
embedded within them. A KS test comparing the 23 clouds with the
48 resolved cores yields $P_{\rm KS} = 2 \times 10^{-3}$. The
clouds are generally elongated filaments, with a mean and standard
deviation in their axis ratio of $< \! q \! > = 0.39$ and $\sigma_q
= 0.17$. The most elongated cloud, with $q = 0.07$, is also the
most massive, with an estimated mass $M = 1200 \, {\rm M}_{\sun}$.
The estimated ${\hat f} (q)$ for the clouds, shown in the upper
panel of Figure 8, peaks at $q = 0.3$ and goes to zero at $q = 1$.
The severe lack of nearly spherical clouds means that the hypothesis
of randomly oriented oblate clouds can be strongly ruled out. The
99\% upper confidence band of ${\hat N}_O$
(seen in the middle panel of Figure 8) dips well below zero. The
roundest object in the sample of clouds has $\gamma = 0.7$. The
distribution of oblate objects which minimizes the number of apparently
circular objects is a population of infinitesimally thin disks ($\gamma = 0$);
this population, when placed at random orientations, produces a
distribution $f(q)$ which is uniform between $q = 0$ and $q=1$. The
probability that a sample of 23 infinitesimally thin disks, seen
at random angles, produces no projections with $q > 0.75$ is only
$P = (0.75)^{23} \approx 1.3 \times 10^{-3}$. Any other population
of oblate objects would produce an even smaller value of $P$.
The lack of nearly circular objects in the sample of clouds
can even be used to rule out the hypothesis that the clouds
are randomly oriented prolate objects. In the bottom panel of
Figure 8, showing ${\hat N}_P$, the one-sided 99\% confidence
level drops below zero for $\gamma > 0.84$. Thus, either the
clouds are intrinsically triaxial, or there is a selection effect
which eliminates prolate clouds whose axes of symmetry lie close
to the line of sight.

\section{Discussion}

Bok globules and dense molecular cloud cores, with densities
$n \gtrsim 10^4 \, {\rm cm}^{-3}$, are of particular interest
to astronomers because they are where stars form; see Myers (1985) and
Shu, Adams, \& Lizano (1987) for reviews. The assumption of
spherical symmetry in a star-forming dense core is seductive
from a theoretical viewpoint. It allows analytic calculations
of collapse, such as the self-similar isothermal solution of
Shu 1977), and permits numerical simulations with very high
resolution. However, the observations reveal that the spherical
assumption is a poor one. In the samples analyzed in this paper,
the mean apparent axis ratio ranges from $< \! q \! > = 0.48$
for the clumps observed by Loren (1989) to $< \! q \! > = 0.61$ for the Bok
globules cataloged by BHR. The intrinsic axis ratios are even
more elongated than the projected axis ratios. Under the prolate
hypothesis, the mean intrinsic axis ratio is $< \! \gamma \! > = 0.39$
for the Loren (1989) sample and $< \! \gamma \! > = 0.53$ for
the BHR sample.

For each of the samples analyzed, the prolate hypothesis (that all
cores and globules are randomly oriented prolate spheroids) yields
a better fit to the observed distribution of axis ratios than does
the oblate hypothesis. This conclusion agrees with other indications
that cores and globules are primarily prolate objects.
For instance, cores are unlikely to be rotating oblate
spheroids. In a sample of dense cores ($n
\gtrsim 10^4 \, {\rm cm}^{-3}$) studied by Goodman et al. (1993), only
29 of 43 had a statistically significant velocity gradient. The
measured gradients lie in the range $0.3 \to 4 \, {\rm km} \, {\rm
s}^{-1} \, {\rm pc}^{-1}$, with a typical ratio of rotational energy
to gravitational energy of only $\sim 0.02$. In addition, no
correlation was found between the rotation axis and the projected
short axis of the core, indicating that the cores are not rotationally
supported oblate objects. Moreover, a study of the few molecular clouds
with large velocity gradients (Arquilla \& Goldsmith 1986) shows
that clouds with significant gradients often have velocity fields
which are more complicated than would be produced by simple rotation.
If cores are shaped not by rotation but by anisotropic gravitational
fields (Fleck 1992), then the extremely elongated cores ($q \lesssim 0.3$)
must be prolate rather than oblate.
A study of the environment of dense cores offers hints that at least some
cores must be prolate. Of the 16 cores studied by Myers et al. (1991),
6 are observed to have their long axes aligned
with larger filamentary structures, which are almost certainly
prolate because of their extreme axis ratios ($q \sim 0.1$).

The tendency for dense cores to be embedded in long filaments
of lower density matter was noted by Schneider \& Elmegreen (1979),
who compiled a catalog of ``globular filaments'', defined as
long filamentary dark clouds with globule-like dense cores
spaced evenly along the filament. The distance between the
dense cores in a globular filament is equal to 3 times the
diameter of the cores. The work of Nozawa et al. (1991) confirms
the general picture of cores being prolate objects with
$q \sim 0.6$ embedded within larger, lower density,
more filamentary ($q \sim 0.4$) clouds. Although the long
axes of the dense cores tend to be aligned with the larger filaments
in which they are embedded (Myers et al. 1991), being embedded
within a larger structure does not greatly affect their shape.
Embedded cores have shapes similar to those of isolated globules.
Direct comparison of optically selected Bok globules
(BHR; CB) to dense cores detected at millimeter wavelengths
(Benson \& Myers 1989; Lada et al. 1991; Loren 1989; Nozawa et al. 1991)
is something that should only be done with caution. However,
the shapes of the embedded (type C) cores in the Benson \& Myers (1989)
sample are indistinguishable from the shapes of the isolated (type G) cores.

For all the samples of dense objects in this sample, whether they
are called globules, cores, or clumps, the best-fitting estimate
${\hat f} (q)$ dips below one as $q \to 1$. As a consequence,
${\hat N}_O ( \gamma )$ dips below zero, and the hypothesis that
the objects are randomly oriented oblate spheroids can be rejected
at some confidence level. For some samples -- the dense cores
of Benson \& Myers (1989) and the clouds of Nozawa et al. (1991) --
the best-fitting estimate ${\hat N}_P$ drops below zero.  For these
populations, we can reject the hypothesis of randomly oriented
prolate spheroids. Previously, I have concentrated on the implications
if the assumption of oblateness or prolateness is incorrect, and
the objects are actually triaxial. But what
if the other assumption I've made is incorrect, and the objects
in the sample are not randomly oriented? Neighboring cores on
a long filament, for instance, will tend to have their long
axes pointing in the same direction (Nozawa et al. 1991). This
correlation in the orientation angle will reduce the effective
number of independent viewing angles. Thus, the assumption of
independent random viewing angles is incorrect in this case,
and the error bands placed on $\hat f$, ${\hat N}_O$, and ${\hat N}_P$
by bootstrap resampling will be underestimates. Relaxing the
assumption that the orientations of cores are uncorrelated thus
makes it more difficult to rule out the hypotheses that the
cores are all oblate or all prolate.

It is not always obvious which assumption is incorrect when
a particular hypothesis is rejected. For instance, I rejected
the hypothesis that the clouds in the Nozawa et al. (1991) sample
are randomly oriented prolate spheroids. This rejection is based
on the lack of nearly circular clouds in the sample. Perhaps the assumption
of random orientations is incorrect, and prolate clouds whose
axis of symmetry lies close to the line of sight have been excluded
from the sample. An examination of the maps of the clouds (Nozawa et al.
1991) reveals, however, that the other assumption -- that the
clouds are intrinsically prolate, must be incorrect. In projection,
the clouds with the greatest apparent elongation are not ellipses,
but are arc-shaped. The major axis of the cloud, in some cases,
has a radius of curvature comparable to the axis length. This
curvature of filaments is also seen in the ``globular filaments''
of Schneider \& Elmegreen (1979). The long, filamentary clouds
must be intrinsically curved, which prevents them from appearing
exactly circular in projection from any angle.

On scales larger than dense cores, and with mean densities lower
than $n \sim 10^4 \, {\rm cm}^{-3}$, the distribution of molecular
gas is generally described as filamentary, wispy, or cobwebby, with
gas lying in long, curved filaments. Dense cores and Bok globules,
however, have less extreme axis ratios. It is not known which
forces are dominant in determining the shape of cores and globules.
It is possible, though, to state some forces which are not
greatly significant. Since the shape of cores and globules
is independent of whether they are embedded in larger structures
(Benson \& Myers 1989), external forces such as gravitational
tidal forces cannot determine the shapes in the majority of
cases. The shapes of cores also is independent of whether
they contain embedded protostars (Benson \& Myers 1989), so
outflows and radiation pressure from protostars cannot have
a significant effect on the overall shape of the core or
globule in which it is embedded. Since nearly all cores
are slowly rotating (Goodman et al. 1993), rotational flattening
does not play an important role. The dense cores are not
collapsing on a freefall timescale. The dynamical time for
a core with $n \sim 10^4 \, {\rm cm}^{-3}$ is $t_{\rm dyn} \sim
10^6 \, {\rm yr}$; the low efficiency of star formation in cores
and globules -- $\varepsilon \sim 0.3\%$ in the northern Ophiuchus
region, for instance (Nozawa et al. 1991) -- means that clouds
are contracting on timescales much longer than their dynamical
time. Thus, the ``pancaking'' effect of anisotropic collapse
(Lynden-Bell 1964; Lin, Mestel, \& Shu 1965)
is not what flattens cores and globules.

Dense cores and globules, it is generally proposed, are supported
by a combination of thermal pressure, turbulent pressure, and
magnetic pressure. For all but the smallest cores, the observed
line widths are greater than would be produced by thermal broadening
alone. Temperatures in dense cores and Bok globules are typically
$\sim 10 \, {\rm K}$. For $^{13}$CO, thermal velocities alone
produce a FWHM of $\Delta V = 0.13 \, {\rm km} \, {\rm s}^{-1}
( T / 10 \, {\rm K} )^{1/2}$. The observed width of $^{13}$CO
absorption lines is $\Delta v = 0.73 \to 2.24 \, {\rm km} \, {\rm s}^{-1}$
for the Lada et al. (1991) clumps and $\Delta v = 0.5 \to 1.8 \, {\rm km}
\, {\rm s}^{-1}$ for the Nozawa et al. (1991) cores. Supersonic
velocities are seen within Bok globules as well. When the BHR globules
were observed in NH$_3$ emission (Bourke et al. 1995),
the intrinsic linewidth in globules where
ammonia was strongly detected was $\Delta v = 0.28 \to 1.02 \, {\rm km} \,
{\rm s}^{-1}$, where thermal broadening would produce
$\Delta v = 0.16 \, {\rm km} \, {\rm s}^{-1}$ at a temperature
of $10 \, {\rm K}$. The additional broadening can be explained
as the result of turbulent motions within the globule or core
(Larson 1981). However, it seems that the shape of cores is
not crucially dependent upon the extent to which it is supported
by turbulence. Benson \& Myers (1989) found that the mean linewidth
for cores without embedded IRAS sources is $\Delta v = 0.27 \,
{\rm km} \, {\rm s}^{-1}$ is significantly narrower than the
mean width for cores with embedded sources, $\Delta v = 0.45 \,
{\rm km} \, {\rm s}^{-1}$, despite the fact that their kinetic
temperatures are all $\sim 10 \, {\rm K}$. Although the cores
with sources contain a higher fraction of turbulent
kinetic energy, their distribution of apparent shapes is
indistinguishable from that of cores without sources.

Magnetic forces can also play a significant role in determining
the structure of dense cores (McKee et al. 1993). Although measuring magnetic
fields in molecular clouds is a tricky business, available
measurements indicate that magnetic pressure and turbulent
pressure are of comparable importance in supporting cores
against collapse (Myers \& Goodman 1988). The presence of
magnetic flux is certainly capable of influencing the size and
shape of gaseous clumps. As an example, consider the scenario in
which dense cores form by gravitational condensation along a
filament -- a proposed method for the formation of globular
filaments (Schneider \& Elmegreen 1979; Elmegreen 1985). The
filament will break into globules whose separation is equal
to the wavelength $\lambda_m$ of the most rapidly growing
instability. In the absence of a magnetic field, $\lambda_m
= 5.4 D$, where $D$ is the initial diameter of the filament (Chandrasekhar
\& Fermi 1953).
If the filament is aligned with a magnetic flux, however,
$\lambda_m$ will be increased. In the real interstellar
medium, where the geometry of the magnetic field and the
gas distribution is far more complicated, the shape of
dense cores and Bok globules is determined by nonlinear
magnetohydrodynamic turbulence whose study will require
sophisticated numerical simulations. It is possible that the observed
shapes of Bok globules and dense cores will act as constraints
on future studies. It is also possible that the characteristic
distribution $f (q)$ which is observed, peaking at $q \sim 0.4 \to 0.6$
and falling below $f = 1$ as $q \to 1$, is a generic result
for a wide range of initial conditions and evolutionary histories.

\acknowledgments
I thank R. Barvainis, D. Clemens, R. Fleck, R. Pogge, and
K. Sellgren for their advice and assistance, and the onymous referee,
N. Evans, for his exceptionally helpful report.
This work was supported by NSF grant AST-9357396.

redpajama_set_name: RedPajamaArXiv


Our attention, when we think about women mainly, focuses on their beauty. It is, however, not possible for a person to feel beautiful if their health is not good. Over the years, women's healthcare has been improved greatly. The availability of specialized healthcare for women is not only because they are female but mainly because of the biology of their bodies. Science has proven that women's bodies are a marvel that needs to be taken care of the best way at all times. Let us focus on some of the issues that good women's healthcare should focus on.
Knowing the specific details of a medical problem is the best way one can be sure they will get the best care. For any woman seeking to get quality healthcare, the facility you get services from must have top class disease diagnosing equipment. Among these crucial machines are scanners. In most of the times, healthcare facilities will provide a list of all the medical scans that are available for patients. The woman's body is very delicate and getting the right problem detected is as good as having the best medical care.
Both the aged and young males are affected by almost similar health problems. However, the health problems affecting the young females are different from those that affect the older women. There are more health complications facing the young and maturing women compared to those that face the old ones. This means that the young women need quite different attention from those that are older.
Another very crucial part when it comes to women's healthcare is the mental health. One fact about women Is that they are emotional and will be affected more by the happenings around them than men. The emotional part has a direct connection to the overall health of a person. There is need for a women's healthcare facility to dedicate a department that deals with the mental health of the patients. All the other medical attention that a patient gets would be rendered useless if the mental health of the patient is not good.
Cancer is the last issue that needs to be taken care of when dealing with women's healthcare. According to studies, women are affected by more than ten types of cancer. The most common among the ten types of cancer affecting women are the breast and cervical cancer. Provision of screening services for the different types of cancer should be provided by any facility that offers women's healthcare. Provision of screening services does not necessarily mean that the facility offers treatment services but helping the women detect any problems they might be having helps a lot.


text:
NGC 779 é uma galáxia espiral barrada (SBb) localizada na direcção da constelação de Cetus. Possui uma declinação de -05° 57' 51" e uma ascensão recta de 1 horas, 59 minutos e 42,6 segundos. Ela foi descoberta em 10 de Setembro de 1785 por William Herschel.

Ver também
Astronomia extragaláctica
Lista de galáxias
Lista de objectos NGC
New General Catalogue

Ligações externas

NGC 0779
Constelação de Cetus
Galáxias espirais barradas

redpajama_set_name: RedPajamaWikipedia


If you thought the wrestlers looked realistic in WWE 2K15, it appears they will look even better for the upcoming WWE 2K16 video game.
From WrestleMania 31 weekend, WWE posted a photo diary of Rusev being scanned for the WWE 2K16 video game. This time, 2K Games is using 96 cameras to capture the likeness of your favourite wrestlers. This is up from WWE 2K15 where the cameras were only focused on wrestlers' faces.
The scanning process for WWE 2K16 is evidence that they are also in the middle of taking photos of everyone again. Some people speculated they could have just used the same character models in WWE 2K15. Rusev was already scanned for WWE 2K15, so him being scanned again shows they want to improve the look of the character models.
It will be interesting to see if 2K Games were able to scan the wrestlers they missed for WWE 2K15. They missed out on the likes of Brock Lesnar, The Rock, Undertaker and Vince McMahon. All four of them were at WrestleMania 31. It remains to be seen if 2K Games managed to get them all to be scanned for WWE 2K16.


text:
Q: Как реализовать этот метод на чистом js $('#el').bind('click change input', function(e){

});

то есть повесить много событий на один элемент ?

A: function doSomething() {
  ...
}

var el = document.getElementById('el')
['click', 'change', 'input'].forEach( function(event) {
  el.addEventListener(event, doSomething(), false);
});

A: function yourFunc() {}

const elem = document.getElementById('el');
elem.addEventListener('click', yourFunc);
elem.addEventListener('change', yourFunc);
elem.addEventListener('input', yourFunc);

redpajama_set_name: RedPajamaStackExchange


text:
Orpine is a common garden plant, but you can also find it growing wild in nature. It's a good edible plant to know because of its long harvest season and its appealing crispness.
Orpine can thrive in many different landscapes. You can find it in forests and ditches, but it also fares well in dry conditions in rocky soil. Because its thick, succulent leaves allow it to retain water in full sun, it can flourish on the dry edges of woods, in salt marshes, or on south-facing slopes and hills where the sun's strong rays desiccate most other plant life.
Salt marshes, deciduous forests, coniferous forests, towns, hedges, roadsides, grasslands.
When to Find It
You can pick the leaves from April until October, and the flowers from June until October.
Leaves: April, May, June, July, August, September, October.
Flowers: June, July, August, September, October.
How to Spot It
The orpine you find in nature has often crossbred with cultivated varieties, so it may vary slightly in shape and color. A succulent and fleshy plant that typically grows to be 30-80 cm tall, it is matte green in color with round or teardrop leaves that have soft teeth at the edges. On tall plants, the leaves grow individually up the stem, while on more bushy specimens they huddle in small, rounded bunches. The small flowers grow in large, broccoli-like flower heads that can vary in color from white to purple.
How to Pick It
Pick the leaves being careful not to damage the rest of the plant. Cut or clip off the flowers.
On the palate
Orpine is juicy, and eating its young leaves feels similar to biting into a crisp apple. Mildly acidic, it tastes of cucumber and asparagus. If you pick orpine near the beach, it will also have a salty flavor. Older plants have a distinct bitterness and their texture is mealy, like beans.
Orpine has no particular scent.
Orpine can tolerate only short, gentle cooking before it loses its juicy crispness. When cooked, the plant takes on a mild flavor of artichoke, with a smoky aftertaste. The young leaves are so fresh and crisp that they're best eaten raw as a garnish or in salads. The old leaves can be blanched or quickly sautéed. Otherwise, add them to hot dishes just before serving. The flowers are best enjoyed raw, but they can be briefly cooked over low heat.
You can use orpine as a crisp and fresh ingredient in places where you'd otherwise use leafy greens. If you'd like to preserve its gentle taste, keep it separate from ingredients with pronounced flavors, and use it in simple preparations where it can stand out. Orpine pairs well with flatfish, shellfish, potatoes, olive oil, cucumber, veal, poultry, and salad. You can pickle the flowers.
Cover the orpine with a moist cloth and store in a sealed bag or airtight container inside the crisper drawer of your refrigerator, where the leaves will stay fresh for up to one week. The flowers won't keep for more than three to five days.
Sea asters can be substituted for orpine.
Risk of misidentifying the plant
There is no risk of mistaking the plant for another dangerous or undesirable plant.
Ingredient used in
Orpine sautéed in butter with smoked fish and buckwheat Enteromorpha intestinalis
Yogurt dip with wild herbs and roots Enteromorpha intestinalis
Herb pesto with nuts Enteromorpha intestinalis
Alternative ingredient in
Sea sandwort tzatziki Enteromorpha intestinalis
Elm seed sandwich Enteromorpha intestinalis

redpajama_set_name: RedPajamaCommonCrawl


text:
Tar Heels blow by the Hurricanes
Published 5:10 am Sunday, October 7, 2007
By The Daily News
By By AARON BEARD, AP Sports Writer
CHAPEL HILL — Butch Davis' latest reclamation project took a major step in the right direction.,
The coach's old team is still trying to find its way back to elite status.
Brandon Tate scored on a long end-around in a spurt of 27 points to start the game and Connor Barth kicked four field goals to help North Carolina hold off Miami 33-27 on Saturday, giving Davis his first ACC win against a program he once built into a national champion.
Anthony Elzy ran for 95 yards and a score for the Tar Heels (2-4, 1-2 Atlantic Coast Conference), who turned in a dominating performance to take a 27-0 lead at halftime then hung on as the Hurricanes (4-2, 1-1) twice rallied to within a touchdown in the second half.
Davis had played down his first game against the Hurricanes earlier in the week and said after the game that beating Miami didn't make the victory anymore special.
Finally finishing off an opponent made Davis' day.
The Tar Heels had struggled to do that this season, from a 34-31 loss on a final-play field goal at East Carolina to a 22-20 loss to Virginia and last week's 17-10 loss at Virginia Tech. This time, they put together big plays when they needed them in the second half: a punt-forcing sack from Hilee Taylor to end a Miami drive near midfield late in the third quarter; a 49-yard catch-and-run from Tate on the ensuing possession; and two fourth-quarter field goals from Barth that kept Miami in catch-up mode.
Davis took over at Miami in 1995 and inherited a program hindered by NCAA sanctions that limited scholarships for his first three seasons. He gradually brought the Hurricanes back to the prominence they had enjoyed under Jimmy Johnson, going 51-20 over six seasons, while winning three Big East Conference titles and four bowl games.
His last team went 11-1 and finished ranked No. 2 nationally in 2000 after winning the Sugar Bowl. Then, after Davis left to coach the NFL's Cleveland Browns, his former players went unbeaten in 2001 and won a national title under Larry Coker.
Davis' new team got off to a fast start against Miami and Shannon, who was a player and an assistant under Davis.
But Miami did everything it could to get back in the game, with Darnell Jenkins scoring on a 97-yard touchdown catch that made it 27-20 late in the third quarter and Javarris James scoring on a short run to set up an onside kick with about a minute left. But the Hurricanes couldn't overcome the halftime deficit or four interceptions from Kyle Wright — including one at North Carolina's 3-yard line with about 6 minutes left and Miami trailing 33-20.
North Carolina played as close to perfect as it possibly could in the opening half. Elzy ran past and through Miami defenders. Barth, who kicked the winning field goal on the final play to upset fourth-ranked Miami here as a freshman in 2004, nailed a pair of kicks, including a 51-yarder. The Tar Heels' special teams came up with a blocked punt that led to a touchdown, and Tate scored on a 54-yard run down the left sideline — thanks to Hakeem Nicks blocking two defenders — for the 27-0 lead with 9:59 left in the half.
The Tar Heels ultimately hung on by holding off several Miami spurts, including Jenkins' long TD catch from Wright that was the second-longest in Miami history and the longest allowed by North Carolina in its history.
But Barth kicked 20- and 35-yard field goals, setting a school record with 19 consecutive made kicks, that pushed the lead to 33-20 with 10:55 left.
North Carolina finished with a season-high 183 yards rushing, with quarterback T.J. Yates adding a touchdown on a keeper in the second quarter. Yates threw for 218 yards.
NORTH CAROLINA 33, MIAMI 27
Miami 0 0 20 7 — 27
North Carolina 13 14 0 6 — 33
NC—Elzy 39 run (Barth kick), 10:33.
NC—FG Barth 33, 4:23.
NC—FG Barth 51, :27.
NC—Yates 1 run (Barth kick), 11:25.
NC—Tate 54 run (Barth kick), 9:59.
Mia—Wright 1 run (Zampogna kick), 12:38.
Mia—Shields 4 pass from Wright (kick failed), 8:06.
Mia—Jenkins 97 pass from Wright (Zampogna kick), 4:22.
NC—FG Barth 35, 14:12.
Mia—James 1 run (Zampogna kick), 1:17.
A—59,000.
Mia NC
Rushes-yards 36-109 46-183
Passing 302 218
Punts-Avg. 5-30.0 4-49.3
Fumbles-Lost 2-0 2-1
Penalties-Yards 4-35 8-56
RUSHING—Miami, G.Cooper 13-77, James 10-27, Wright 13-5. North Carolina, Elzy 25-95, Tate 2-64, J.White 3-19, Houston 4-13, Little 1-9, Team 2-(minus 7), Yates 9-(minus 10).
PASSING—Miami, Wright 17-33-4-302. North Carolina, Yates 15-23-0-218.
RECEIVING—Miami, Shields 5-80, Leggett 5-61, Jenkins 3-110, G.Cooper 3-24, Farr 1-27. North Carolina, Nicks 5-76, Elzy 4-39, Tate 3-54, Dailey 2-38, Quinn 1-11.
Memorial Day ceremony held in Washington
Mary Lou Alligood
Susan Jane Mish
EMS expansion "biggest driver" behind tax increase


Specifies constants defining a group of Amazon S3 users who can be granted permissions to Amazon S3 buckets and objects. This enumeration contains all the valid Amazon S3 group grantees.
Grants anonymous access to any Amazon S3 object or bucket.
Grants access to buckets or objects to anyone with an Amazon AWS account.
Grants access to Amazon S3 log delivery so that an S3 bucket can receive server access logs.
Gets the group grantee's URI.
Gets the GroupGrantee enumeration value with the specified Amazon S3 group URI (eg.
Grants anonymous access to any Amazon S3 object or bucket. Any user will be able to access the object by omitting the AWS Key ID and Signature from a request.
Amazon highly recommends that users do not grant the AllUsers group write access to their buckets. If granted, users will have no control over the objects others can store and their associated charges.
Grants access to buckets or objects to anyone with an Amazon AWS account. Although this is inherently insecure as any AWS user who is aware of the bucket or object will be able to access it, users may find this authentication method useful.
Grants access to Amazon S3 log delivery so that an S3 bucket can receive server access logs. Turning on server access logging for an Amazon S3 bucket requires that the bucket receiving the logs is granted permission for the log delivery group to deliver logs.
For internal use only. Group grantees have preset identifiers that cannot be modified.
Gets the GroupGrantee enumeration value with the specified Amazon S3 group URI (eg. http://acs.amazonaws.com/groups/global/AllUsers). Returns null if an invalid Amazon S3 group URI is specified.
The GroupGrantee object represented by the given Amazon S3 group URI string. Returns null if the string isn't a valid Amazon S3 group URI.


Inglot Brow and Concealer palette..
Recently purchased this palette during the mother's day special sale on Inglot website. I bought some concealer pans and some brow products..
Here are swatches of the same..
I haven't tried the concealers yet since I find them too creamy for Summer.. Will give them a try as we enter Fall and Winter later this year.. I am enjoying using the brow products though.. I use the brow wax first.. comb through the brow and then use the powders to fill them in..


IMF Executive Board Completes Third Review Under Argentina's Stand-By Arrangement, Approves US$10.8 Billion Disbursement - April 2019 English | Español.
The last Article IV Executive Board Consultation was on December 18, 2017. Listed below are items related to Argentina.


text:
Beauty in the eye of the beholder
Posted on December 22, 2015 by deborahjones2012
Revelations in New York, stars made at The Australian Ballet, Alina Cojocaru in Brisbane and more …
The Australian Ballet dubbed its 2015 season A Year of Beauty. Giselle, Swan Lake, Cinderella and Frederick Ashton's The Dream were on the program, lovely ballets all, but essentially teasers for the main event – the new Sleeping Beauty, staged by artistic director David McAllister with opulent designs by Gabriela Tylesova. On the other side of the world an even grander production was unveiled. American Ballet Theatre's Alexei Ratmansky sought to return The Sleeping Beauty to something close to its original form and style.
The Australian Ballet's The Sleeping Beauty, designed by Gabriela Tylesova
In Brisbane, Queensland Ballet staged Greg Horsman's smaller-scaled interpretation (originally made for Royal New Zealand Ballet in 2011) and a visiting company, Russian National Ballet Theatre, toured Australia and New Zealand extensively with (inevitably) Swan Lake but also Beauty. The AB's new Storytime Ballet venture for very young children was launched this year with, yes, The Sleeping Beauty (a miniature clocking in at well under an hour).
I thus had my own Year of Beauty in 2015 with 10 performances in all – two casts of the Ratmansky, four of McAllister's, two of Horsman's and just one Russian National Ballet Theatre (more than enough, alas) and one Storytime Ballet: The Sleeping Beauty.
This Beauty bounty inevitably drew me back to DVDs of productions including those by The Royal Ballet, Bolshoi Ballet and The Australian Ballet. Their stagings of Sleeping Beauty could be looked at anew, particularly in light of Ratmansky's discoveries, and encouraged repeated returns to the complete score (the 2012 version by the Bergen Philharmonic Orchestra conducted by Neeme Järvi for Chandos is superb) although none of the versions I saw used all the music, as no one does. A little-admired four-hour 1999 Mariinsky version aiming for authenticity has been dropped from the repertoire. These days companies want – and need – to bring The Sleeping Beauty in under three hours. At American Ballet Theatre the reason was stated bluntly in the program: "The ballet has, however, had to be cut somewhat to fit within the union-defined time limitation."
Gillian Murphy as Princess Aurora for ABT. Photo: Gene Schiavone.
It's worth quoting in length from David Nice's scene-by-scene analysis that accompanies the Chandos recording to see the kind of thing that's lost. In the second entr'acte (the first is rarely heard at all), "the note C is sustained by the strings, principally the violins, for exactly one hundred bars. This is time suspended: the 'sleep' chords … and the themes of the Lilac Fairy and Carabosse pass and dissolve. Few if any productions observe the full symbolic duration of this hypnotic spell – Aurora is usually heard to sleep for a mere forty or so years." Not that Petipa used every bit of the music Tchaikovsky wrote for his ballet either. Pragmatism reigned then as now.
All the productions I saw were traditional ones underpinned by Petipa's 1890 staging for St Petersburg's imperial Ballet. It and other ballets were recorded in the Stepanov system of notation and came to the West in the luggage of Nicholas Sergeyev, a regisseur who managed to exit Russia not long after the revolution of 1917. Diaghilev's 1921 production The Sleeping Princess was based on these notations as was The Royal Ballet's of 1939, staged by Sergeyev and also called The Sleeping Princess although claiming to be more true to Petipa's original than Diaghilev's Ballets Russes version (with which Sergeyev was also closely associated). When revived in 1946 – and famously winning over New York in 1949 – the ballet was now The Sleeping Beauty and contained some new choreography.
The Beauty staged by the RB to celebrate its 75th anniversary in 2006 had further changes: it was billed as being produced by Monica Mason and Christopher Newton after Ninette de Valois and Nicholas Sergeyev with additional choreography by Frederick Ashton, Anthony Dowell and Christopher Wheeldon. That list in itself tells the story of how ballet is translated and transformed down the ages. The Australian Ballet's 1993 recording has choreography by Petipa, "reproduced by Monica Parker from the Nicholas Sergeyev notation" with direction and additional choreography by Maina Gielgud.
Sarah Lane and Herman CornejoŽ in Alexei Ratmansky's The Sleeping Beauty. Photo: Rosalie O'Connor.
The versions are very similar when it comes to the overall story arc and key passages but have many different details that give an individual stamp. Not all of them are improvements, as Ratmansky's painstaking research into how The Sleeping Beauty would have looked in 1890 makes clear.
The choreographer made a close study of the Stepanov notations and created a revelatory version for ABT and La Scala, who shared the eye-watering cost, reported to be in the vicinity of $US6 million. The money was well spent: this was indisputably the dance event of the year. I saw it in New York in May following its premiere in California. The production was extraordinarily sumptuous, flooding the Metropolitan Opera stage with so many dancers and supernumeraries that at some points there were more than 100 people on stage.
Even so, Ratmansky used fewer people than were in Petipa's original, with its hordes of children, pages, courtiers, cavaliers and minor royalty to attend upon their majesties, each carefully arranged according to rank. The Sleeping Beauty is not only a fairy tale celebrating the victory of good over evil. It depicts a formal, long-established power structure as the embodiment of harmony. Its traditions and ceremonies imply continuance and order. In such a world Carabosse's exclusion from Aurora's christening, the event that initiates the action, puts a great tear in the social fabric. Ratmansky shows that in a healing gesture she is invited to Aurora's wedding. It makes perfect sense, even if in the vast congregation at the end of the ballet Carabosse was seen only fleetingly.
And that's the thing about Ratmansky's version. It feels right dramatically and musically at every point.
A brief moment in the Rose Adagio perfectly illustrates how ballet can shift from its original intention into a kind of never-never land of whispers only partly heard. Aurora steps forward on her left foot, on pointe, then lowers her heel to the floor. She bends forward in an arabesque penchée, inclines her head and upper body towards the audience, bends her right arm and holds it close to her chest. Her right hand is seen to touch her left cheek, or perhaps is held near her face without obscuring it. Aurora does this four times, and sometimes the four Princes kneel behind her, all together or else one by one. Sometimes she leans on each Prince as she passes (as in the Grigorovich version for the Bolshoi), sometimes not. Sometimes she gives the Princes a glance, sometimes not. What exactly is she doing here, in this very specific sequence of body and head inclines?
Diana Vishneva with violin pages. Photo: Gene Schiavone.
Ratmansky tells us. Aurora is listening to a group of little pages as they play violins. In the Grigorovich staging, filmed in 1989, we can see youngsters dancing in the background while holding violins; in the RB version, young boys stand in the background plucking mandolins in a haphazard and desultory fashion. So the idea there should be some young people on stage with stringed instruments has survived, sometimes, in some form, but not their reason for being there. It may seem odd to single out a sequence that lasts less than 20 seconds but it always looked meaningless to me; Ratmansky turns the light on.
It was also delightful to see the Precious Stones music of the third act danced by the rarely seen fairies of Gold, Silver, Sapphire and Diamond (in McAllister's and Horsman's productions the Prologue fairies are drafted in for these dances). The Sapphire music is, excitingly, in the tricky metre of 5/4, written this way because Petipa was thinking of a five-faceted stone. In 1946 the RB introduced the now-familiar characters of Florestan and his sisters to replace the jewel fairies, with choreography by Ashton.
Study of the Stepanov notations revealed a quality of movement that has changed dramatically since Petipa's time although Ratmansky also examined many other sources to fill gaps. For guidance on upper-body style Ratmansky consulted Ballets Russes material, including film shot in Australia by Melbourne eye specialist and ballet enthusiast Ringland Anderson that McAllister was able to make available. In Ratmansky's version there are no extreme extensions. Legs are held softly, there is extensive use of the demi-pointe and lines are more rounded. With less height comes more speed and time for intricate footwork. The ballet sparkles as much as it intrigues. A delightful aspect is the low retiré position in pirouettes, sometimes not much above the ankle. In supported pirouettes the men use one arm only to guide the ballerina rather than paddling her around, and there are many other surprises, such as the double air turn for the Prince that ends with a landing on one foot. A beguiling airiness prevails.
The production includes some elements from The Sleeping Princess and later versions of the ballet that are now considered standard, including fish dives in the grand pas de deux and the arms raised en couronne as Aurora pauses, balancing on pointe, in between greeting each suitor (said to be a Fonteyn innovation). Interestingly, the very poor production from Russian National Ballet Theatre is more faithful to Petita in both those respects although quite chaotic in others. I couldn't help thinking, though, that the Russian Aurora I saw, Elizaveta Lobacheva, perhaps didn't attempt the balances in the Rose Adagio as we know them because the taped music offered no room to move. (I saw her Odette-Odile too; she's a very proficient dancer.)
David McAllister's staging experience was quite limited before he took on the task of bringing a new Sleeping Beauty into his company's repertoire to replace Stanton Welch's 2005 production. It was a courageous move on his part, pulled off remarkably well. I have a handful of reservations about aspects of the storytelling but audiences have responded strongly and a long life seems assured. It needs to stick around: this Beauty cost the royal sum of $2 million or thereabouts, although more than 70 per cent of the budget came from about 2000 ballet-lovers, making donations big and small. Some gave individual gifts of more than $50,000, others put in $100. It was an impressive fund-raising feat.
Lana Jones in David McAllister's production of The Sleeping Beauty for The Australian Ballet. Photo: Jeff Busby
While the drain on the AB coffers wasn't particularly great for such a large-scale production, the many people who donated would have a right to feel very cheated if it wasn't a stayer. My prediction: when the AB vacates the Joan Sutherland Theatre at the Sydney Opera House for some months in 2017 to allow replacement of the ageing theatre machinery it will presumably perform elsewhere in the city and will need popular repertoire to entice the audience to follow. If it can get the Capitol – and I stress I have no information on this – the larger stage and the big, ornate auditorium would be perfect for this Sleeping Beauty.
I digress. As I wrote just after the Melbourne premiere in September, Gabriela Tylesova's design "is almost absurdly beautiful. Tylesova revels in saturated colours, flounces upon ruffles, embellishments, beads, crystals and feathers. There are columns, chandeliers and romantic vistas." It is a sumptuous fantasia at one with Tchaikovsky's magical score and I enjoyed it greatly each time I saw it, or at least most of it. I still think McAllister and dramaturg Lucas Jervies have muddled and muddied certain details of the story but McAllister was able to field strong casts and gave several dancers a career-defining break.
The AB seems to have hit the mark with Storytime Ballet: The Sleeping Beauty. Hordes of tutu-wearing, wand-waving little ones packed the Drama Theatre of the Sydney Opera House to see a vastly simplified version of the ballet, helped along with clear, clever narration. The dancing from young Australian Ballet School graduates and members of the AB's education ensemble was a touch on the careful side as they negotiated bits and pieces of Petipa on the small stage. (For the first time ever I regretted the absence of the White Cat and Puss-in-Boots from Act III; I think the children would have adored them.) The real fun came from panto-like interaction between narrator Catalabutte and an enthusiastic audience that was thrilled to warn of Carabosse's appearance at Aurora's birthday party – "Behind you! Look behind you!!" – and helped rouse the slumbering palace with lusty wake-up shouts.
Storytime Ballet: The Sleeping Beauty. Photo: Jeff Busby
Queensland Ballet's production, which I saw in October, is a great success. Greg Horsman made it for relatively small forces and his cuts and conflations are done with a keen eye to clarity and logic. The world he creates is coherent and consistent in tone. Everything makes sense in a world that's perhaps not terribly grand but zesty and imaginative. Among the pleasant innovations is the presence at the christening of four young princes who will grow up to become Aurora's suitors; the garland dance arranged for gardeners and their girls, making it happy and relaxed; and a youthful, glamorous Carabosse who has the ability to turn into a dragon.
Russian National Ballet Theatre toured New Zealand and Australia for three months, offering more than 100 performances divided between Swan Lake and The Sleeping Beauty. They performed in a variety of venues, from modestly sized arts centres in small cities to large theatres such as Melbourne's Regent and Sydney's State. In October I saw The Sleeping Beauty in the Big Top at Sydney's Luna Park, not the most atmospheric venue for grand classical ballet but RNBT was taking whatever venues it could. There was a set of the most meagre kind (well, an unchanging backcloth really), recorded music, far too few dancers and the story told in such broad strokes as to be incomprehensible.
It was depressing to see how basic everything was. The Princess Florine made no attempt to emulate the flutterings of the Bluebird with whom she was dancing, thus eliminating all charm and meaning; Carabosse, shorn of attendants, dashed about the stage manically and confusingly; the hunt scene appeared to be happening within the castle confines; and so on. RNBT's ability to have so many dates on this tour is evidence, however, that there is audience demand for the ballet classics that is not being met by local companies, and that Russian companies, no matter how inadequate, can still pull a crowd.
While I greatly admired Ratmansky's production, the first-cast Aurora of Gillian Murphy felt rather too modern for this staging despite the care taken to rein in her 21st-century facility. Her Prince, Marcelo Gomes, was a wonderfully charismatic figure. Although Sarah Lane, a soloist I saw at the second New York performance, was not as technically assured as Murphy she was warm, youthful and had lovely rapport with her Prince, the superlative Herman Cornejo. He bounded through the fleet, delicate, precise footwork with much ease and charm.
Chi Cao and Alina Cojocaru for Queensland Ballet. Photo: David Kelly
At Queensland Ballet there was the gift of Alina Cojocaru as guest artist. She is rightly thought to be among the very best, if not the best, Aurora of the moment. As I wrote at the time: "She radiates light and joy from a tiny body that gives the impression not only of being buoyed by the music but indivisible from it. Her dancing is brilliant, each moment etched with great precision, yet everything feels as if it is the inspiration of that moment. Most potent of all is her warm generosity, seen in abundant, open-hearted gestures and an intense gaze that encompasses the entire theatre."
QB's second-cast Aurora was the newish principal artist Yanela Piñera, who came to Brisbane from National Ballet of Cuba. She dances on a grand scale, making the Act III pas de deux a glittering highlight in concert with principal Hao Bin, who recently announced his retirement and will be missed in a company with few experienced leading men.
The AB ended its Year of Beauty on a high note by promoting three dancers who had made debuts in Sydney as Aurora and Prince Désiré. At the Melbourne premiere principals Lana Jones and Kevin Jackson gave stately performances that matched the grandeur of the setting. Two months later, on the smaller Joan Sutherland Theatre stage in Sydney, there was a more intimate feel, at least in the performances I attended.
Brett Chynoweth was made a senior artist (the second-highest rank) after his soaring, heartfelt Prince Désiré. There was a felicitous pairing with senior artist Natasha Kusch as Aurora – though both are relatively small they make an abundant impression with legs like rapiers, exquisitely articulated feet and loads of height and speed. This was an incredibly important opportunity for Chynoweth, who has rarely been cast in leading classical roles (although he danced a very fine Prince in The Nutcracker in 2014). In Beauty he radiated passion from every pore and his Act II solo, marked by pillowy elevation and immaculate airborne turns, was a glorious expression of longing.
Robyn Hendricks's first Aurora also won her a promotion to senior artist. She was a slightly mysterious young woman in whom you could see the queen she is destined to be. The watchfulness and engagement with her suitors created a whole, interesting, individual character and the elegance and quiet sophistication of her dancing spoke of great things ahead. Principal Adam Bull partnered her securely although he was not looking in peak physical form – a little tired at year's end perhaps.
Benedicte Bemet in rehearsal with Kevin Jackson. Photo: Kate Longley
McAllister astutely gave coryphée Benedicte Bemet the inestimable support of principal Kevin Jackson, who has been on fire all year, for her debut as Aurora. It could be the start of a very fruitful relationship following the retirement earlier this year of Jackson's most frequent partner, Madeleine Eastoe. The possibilities for Bemet would appear to be boundless. Her Aurora rates as the most exciting debut I've seen in more than 40 years of ballet-watching. At just 21 she brought the authentic glow of youth and promise to the stage. She was so entirely at one with the role that all the technical requirements and difficulties simply disappeared. Every step was part of her journey from innocent to prospective bride to woman on the brink of maturity.
Usually one has a sympathetic butterfly or two as the dancer approaches the climactic balances and promenades of the Rose Adagio but not here. Bemet was absolutely in the moment and so was her audience. The balances were astonishing – the audience went wild – and they were part of a story. There was purity, radiance and joy in Bemet's dancing. She was enchanting; a promotion to soloist swiftly came her way.
I haven't even got started on the many exquisite fairies and Bluebirds, the merits or otherwise of various Carabosses and Catalabuttes, the conducting and many other aspects of this endlessly fascinating ballet. But enough, I think, for now.
This entry was posted in Dance and tagged Adam Bull, Alexei Ratmansky, Alina Cojocaru, Anthony Dowell, Benedicte Bemet, Benedicte Bernet, Bergen Philharmonic Orchestra, Bolshoi Ballet, Brett Chynoweth, Christopher Newton, David McAllister, David Nice, Elizaveta Lovacheva, Frederick Ashton, Gabriela Tylesova, Gillian Murphy, Greg Horsman, Hao Bin, Herman Cornejo, Kevin Jackson, La Scala, Lana Jones, Lucas Jervies, Maina Gielgud, Marcelo Gomes, Marius Petipa, Monica Mason, Natasha Kusch, Neeme Järvi, Nicholas Sergeyev, Ninette de Valois, Queensland Ballet, Ringland Anderson, Robyn Hendricks, Russian National Ballet Theatre, Sarah Lane, The Australian Ballet, The Royal Ballet, The Sleeping Beauty, The Sleeping Princess, Yanela Piñera by deborahjones2012. Bookmark the permalink.


Sara has always had a passion for movement, adventure, and exploration. Growing up in the little community of Pie Town, New Mexico she never missed an opportunity to climb and swing in the trees, scramble through boulders and caves, or ride her bike over homemade wooden ramps. Sara has since become an avid traveler and outdoor adventurer, a lover of foreign language and culture studies, a dancer and a dedicated yogi. She found AcroYoga while interning in ecotourism and sustainability in Costa Rica. She immediately fell in love with the practice and its endless possibilities for human connection, playfulness, and creative expression.
Sara sees AcroYoga as empowering and transformative, and is continuously inspired by the way it brings people together, finding strength in themselves and in one another. She loves to see the joyful surges of energy people experience when they first learn to balance and fly, to go places they have never gone before, and achieve things they may have never thought possible. In her practice, and teaching she strives to share the incredible moments of bliss that are found through yoga, AcroYoga, dance, or any other movement practice with people around the globe. Sara also loves to perform, and when she is not teaching, she is dreaming up new adventures, performance pieces, and ways to share her passions with all that she comes into contact with.
Sara believes that in life we are all students as we are all teachers, and that in each day, in each experience we are forever learning and sharing with those around us. It is through this sharing process that we as individuals and communities can find true freedom, growth and progression.