text:
\section{Introduction}

Wrinkling is a frequent response of soft surfaces or thin sheets to lateral stresses or stress mismatches.
Commonly, it represents a stable or metastable energy minimum of an elastically deformed structure.
In thin films of common fluids, such as free-standing films of soap solutions, or low viscosity liquids on an
elastic substrate, a lateral compression and reduction of the film area can be easily compensated by local
film thickness changes. Thus, these films do never wrinkle or buckle. In fluid films with internal structures
such as smectic free-standing films or lipid membranes, the situation is different. A reduction of the film
extension requires structural reorganizations which may be slow compared to the compression rate, and wrinkles
may form to compensate lateral compressions that occur sufficiently fast.

Owing to their internal molecular layer structure, some smectic phases can form stable freely suspended
films with submicrometer thickness and up to several centimeters in lateral extension. Smectic A and C phases
exhibit fluid-like characteristics with regard to flow in the film plane.
Such films have many features in common with soap films, and they can be prepared, similar to the latter,
in the form of bubbles \citep{Oswald1987,Stannarius1997,Stannarius1998}.
At first glance, freely floating smectic bubbles appear very similar to soap bubbles, but they differ from
the latter qualitatively in some dynamic properties
\citep{May2012,May2014}, as a consequence of the layered molecular arrangement.

Any reduction of the local film surface requires the growth of the film thickness to conserve the volume
of the smectic material. The related reorganization of smectic layers is achieved in the films by the formation
of so-called  islands, viz. spots with additional molecular layers on the film that are enclosed by dislocation
arrays \citep{Oswald1987,May2014,May2012,Daehmlow2018}.
Such a structural rearrangement represents a comparably slow process, it requires up to several hundred
milliseconds.
Thus, on short time scales these free-standing films are not able to respond to external forcing by thickness adaption.
They retain a roughly constant surface area. When exposed to fast geometrical shape transformations,
they behave more similar to thin elastic sheets than like fluid films.
An effective demonstration of a wrinkle formation should be achieved by the rapid reduction of the area of
a rectangular frame supporting such films. However, this is technically very challenging.
As we have shown, very rapid shape changes can be observed in freely floating smectic films
and bubbles \citep{May2014}. We describe in this manuscript that
a fast and efficient response of the smectic film to such changes is the formation of bulges and
tubuli or wrinkles. Thereby, the film surface remains
roughly constant, yet the local deformations result in a reduction of the effective lateral extension of the film
(shortly referred to as 'film area' in the following).
In the present paper, we characterize this unique dynamic wrinkling and we describe the spontaneous formation of
bulges and tubuli (as shown in Figs.~\ref{fig:1},\ref{fig:1a}). A model is derived that gives a qualitative explanation of the main features of the instability.

We performed most of the experiments in microgravity
during parabolic flights, a few studies were carried out in the ground lab at
normal gravity.
\begin{figure
\center
\includegraphics[width=0.8\columnwidth]{wrinkles1.pdf}
\caption{Freely floating smectic bubble with homogeneous film thickness of 50 nm
that is axially compressed by air flow.
Thereby, it develops a wrinkled structure normal to the compression direction. The right hand image was recorded 50 ms after the left one.
The bubble was produced under normal gravity, thus the pinch-off is asymmetric and
the bottom part develops a typical invagination.
}
	\label{fig:1}
\end{figure}

\begin{figure
\center  \includegraphics[width=0.8\columnwidth]{13y175.jpg}
	\caption{Detail of a freely floating smectic bubble near the invagination at one end, with wrinkles and tubular extrusions that form during shape relaxation. Extrusions of the bubble can point inwards or outwards (see arrows). Wrinkles appear, for example, when the bubble is rapidly compressed in one or two directions. The image width is approximately 1~mm.}
	\label{fig:1a}
\end{figure}

\section{Wrinkling mechanisms}

Before describing the experiment and data analysis, we give a short introduction into wrinkling
mechanisms of thin elastic or fluid membranes:
Wrinkles in soft matter systems can be of very different types, static and dynamic.
Examples of static structures are skin wrinkles \citep{Cerda2003}, drying fruit and vegetable peels, or stiff
surface layers on shrinking elastic supports. They are quasi-static responses to stress balances.
The latter also applies to curtains or drapes, where the spontaneous crinkles
reflect a compromise between gravitation energy and bending stiffness. Those structures represent
stable or metastable energy minima.

Mechanically induced static layer undulations have also been discovered in smectic liquid crystals confined to thin sandwich cells with fixed boundary conditions. One example is the classical Helfrich-Hurault instability \citep{Helfrich1970,Bevilacqua2005}. It can occur in thin cells under dilation strain when the cell thickness is increased by external forcing.
Layer undulations relieve smectic layer dilation, the elastic energy necessary for layer thickness changes competes with the elastic energy of director distortions induced by layer curvature. Wavelengths of those patterns are typically in the nanometer range. A similar instability can be produced in a rigid cell by means of electric or magnetic fields.
These are conservative equilibrium patterns as well, representing free energy minima.

On the other hand, dynamic wrinkles can form, e. g. during a collapse of fluid bubbles
in a gaseous environment. When a hemispherical bubble of highly viscous material sessile above a bulk bath ruptures,
it can develop well-ordered wrinkles. The driving forces are gravitation and lateral confinement by the bubble
geometry \citep{Debregeas1998,daSilveira2000,Aumaitre2013}. The formation of wrinkles of fluid interfaces have also been described
during the impact of droplets onto a viscous liquid \citep{Li2017} and for droplets rising in a liquid \citep{Uemura2010}.
A related phenomenon is the buckling of viscous fluid filaments \citep{Merrer2012,Salili2016}.

The structures described here are also of dynamical origin. They belong to the
class of transient pattern forming instabilities. The smectic films undergo a rapid change from an initially
flat to an undulated shape. Thereby, a broad band of modes with different wavelengths becomes
unstable, and the mode with the fastest growth rate dominates the periodicity of
the pattern. We note that the area of the film-air interface does not change noticeably during this wrinkling process,
we can disregard any forces related to surface tension. The thickness of the films is typically
in the range of a few dozen nanometers, much smaller than the observed wavelengths. Therefore we can
treat the film as a quasi-twodimensional (2D) fluid sheet, surrounded by air on both sides.
Because of the absence of sublayers with differing stiffnesses, and the absence of rigid boundaries at the film surfaces, the wrinkles described in our experiment are homogeneous across the films.

\section{Experimental setup and materials}

Films were prepared from a room temperature smectic C mixture with 50 vol\% of 2-(4-n-Hexyloxyphenyl)-5-n-octylpyrimidine and 50 vol\% of 5-n-Decyl-2-(4-n-octyloxyphenyl) pyrimidine. The smectic C range is between 20 and 53$\,^\circ$\,C. We created the bubbles by a technique described earlier \cite{May2012},
sketched in Fig. \ref{fig:geo}:
The two coaxial circular rings are wetted with the smectic substance, then brought in contact. After their slow separation with a stepper motor, a catenoid shaped smectic film is formed. Since the catenoid exists as an
equilibrium film shape only up to a maximum ring separation of $D_{\rm crit}\approx 1.3254~R$ (with the inner
radius $R$ of the supporting rings), the catenoid collapses at this critical separation and leaves a freely floating, elongated bubble, as sketched in Fig.~\ref{fig:geo}.
With rings between 20 mm and 25 mm radius, the bubbles have radii of a few millimeters.
The catenoid collapse usually also leaves two circular films in the support rings which perform damped oscillations
to equilibrium.

\begin{figure
\centering\includegraphics[width=0.8\columnwidth]{catenoid1.pdf}
\caption{Experimental geometry: two support rings and the catenoid before pinch-off (left) and the satellite bubble plus remnant films after pinch-off (right). The dashed rectangle sketches the maximum field of view of the side view camera. Most of the images shown in this paper are smaller clips of this field of view,
focusing on details.}
\label{fig:geo}
\end{figure}

Experiments were performed in microgravity during parabolic flights at NOVESPACE (Bordeaux)
with an Airbus 310, as well as in the ground lab under normal gravity. In both situations, bubbles form, but their properties differ in detail. Microgravity leads to a symmetric pinch-off of the upper and lower film parts, producing initially symmetric bubbles and a pair of films at the catenoid holders oscillating in antiphase. Those films periodically create air flow along the central axis that affects the bubble, squeezing
and stretching it.

In normal gravity, the pinch-off is asymmetric, the bubbles usually pinch off at their upper end first. The initial bubble shapes,
the relative phase of the film oscillations as well as the symmetry are affected. One problem with
experiments under normal gravity is that the bubbles tend to leave the observation window rather fast.

The bubbles were observed with two high-speed cameras, providing a side view and a bottom view. Within this study, exclusively the side views recorded with a Phantom v710 camera (operated at 5,000 to 10,000 fps) were evaluated.
We illuminated the bubbles with monochromatic parallel light, using a blue high-power LED with wavelength 460 nm.
The thickness of the smectic film was measured with a standard interference technique
developed for spherical smectic bubbles \citep{Stannarius1999}.
All films studied had submicrometer thicknesses, bubble diameters were in the millimeter to centimeter range.

Wavelengths of the wrinkles were determined from 2D Fourier Transforms of the optical images.
We selected for evaluation only film regions oriented normal to the viewing direction.

\section{Results and discussion}

\subsection{Shape dynamics}

As seen in Fig.~\ref{fig:1} and sketched in Fig.~\ref{fig:geo}, the bubbles have an elongated shape after pinch-off. They gradually
transform into spheres with minimal
surface during a period of several hundred milliseconds. This scenario has been analyzed in detail before \citep{May2012,May2014}.
On short time scales, however,
the smectic films behave like membranes with zero surface tension and fixed surface area.
During the shape transformations, the films permanently experience local compressions and dilations.
Air flow around the bubbles advects the smectic film material and permanently forces the films to reorganize locally.
The main reason for this air flow in our experiments
is the oscillation of the two remnant films at the support rings (Fig.~\ref{fig:geo}).
It depends in a complex fashion on the amplitude and phase of the two oscillating films.

The 2D flow in the smectic film by these friction forces can become locally divergent.
Positive divergence either leads to local film thinning (rupture of some layers),
or to the rupture of the whole film \citep{May2014}.
In smectic C films, film rupture may even induce a reduction of the soft tilt angle \citep{Trittel2017}.
Negative divergence compresses the film region.
When the surface area of the film cannot be reduced quickly enough by island formation \citep{May2014,Daehmlow2018}, the films need to buckle out of the plane.

In addition, bubbles that are far from the equilibrium sphere shape can undergo complex shape transformations.

They can, for example, develop invaginations at their ends, whereby a part of the bubble is pushed inwards (cf. Figs.~\ref{fig:1},\ref{fig:1a}).
In all these cases, the film may be subject to lateral compression. The response of the films is diverse and it depends upon
the speed of the compression and on details of the film structure: If the compression is sufficiently slow,
then the film remains flat and forms islands \citep{Daehmlow2018}. Fast lateral compression of a smectic film
cannot be compensated by this mechanism.
If the film is uniformly thick, or if it contains only very few islands, periodic wrinkling is the dominant response
that reduces the lateral extension without changing the film surface.
If, however, the film thickness is inhomogeneous because many islands already exist, then the film can respond primarily by a local out-of-plane bulging of these islands as described in the next section.
At higher compression rates, if bulging does not provide sufficient area reduction, it is accompanied by
wrinkling of the background film.

\subsection{Bulges and tubuli}

Details of a bubble that is randomly speckled with islands of a few dozen micrometers diameter are shown in Fig.~\ref{fig:bulges}. These islands were formed previously during the collapse of a catenoid with inhomogeneous
film thickness.
This film reacts to the lateral compression with an extrusion of bulges at the centers of islands. Arrows point at two
selected features (islands/bulges) to visualize the axial contraction of the bubble. The open arrows indicate the
expected positions of the second feature if the film had not contracted.
The total axial contraction of the bubble in the displayed region amounts to about 10\%, with a maximum
shrinkage rate of about 2 - 3 \% per millisecond.
The time stamps given in the images refer to the first image in the sequence, which was taken 37 ms after pinch-off.

\begin{figure
	\centering
	\includegraphics[width=1.0\columnwidth]{Fig4.pdf}
		\caption{Formation of bulges during the lateral compression of a bubble consisting of an inhomogeneously thick film, observed in normal gravity. The film has a background
thickness of about 23 $\pm 3$ nm, islands of larger film thicknesses are seen as dark spots on the bubble.
Times are given respective to the first image. The 12.5 ms image shows a larger part of the bubble. Whitened corners in some images mask the regions outside the observation window. We note that the whole bubble slightly spins counterclockwise (when seen from above), thus the features on the front continuously move to the right. Explanation of the arrows see text.}
	\label{fig:bulges}
\end{figure}

The islands represent 'germs', and bulges are formed in their centers (Fig.~\ref{fig:bulges}).
Even though it seems natural that any film thickness inhomogeneity breaks the translation symmetry and thus acts as a local generator of deformations, it appears counterintuitive at first glance that the extrusions appear in the thicker parts (islands) of the film: The energy
per area necessary to bend the smectic film is proportional to the film thickness (see next section), and islands are thus stiffer than the surrounding background film. Apparently
it should be easier to bend the thin background film rather than islands.
A potential reason for the observed phenomenon is the line tension created by the dislocations surrounding an island
\citep{Geminard1997}. It contributes an additional lateral compression force.
This also explains the experimental observation that smaller islands are more probable to form bulges.
The typical lateral extensions of the bulges are determined by the island sizes.
The maximum diameters of bulges are of the order of the island diameters.

The bulges form at a time scale of a few milliseconds, much faster than new islands can be generated.
Figure \ref{fig:bulges} shows a typical image sequence of a contracting section of a bubble (in the first 15 ms).
As long as the compression continues, the bulges grow and they can form tubuli which may even pinch off.
When the exposed region stretches again, bulges disappear.
This is seen in the second, bottom part of Fig.~\ref{fig:bulges}, for the following 10 milliseconds.

In flat film regions, the islands can bulge to both sides. Even the small excess pressure of a few Pascal inside the bubbles does not affect the preference direction of the bulges noticeably, they can grow inward and outward.
However, the local
mean curvature of the film breaks the symmetry and defines such a preference direction for bulging.
Bulges grow outwards in regions where the local bubble surface is convex, which is the common situation.
But they can also grow inwards where the local bubble surface is concave.
This is exemplarily seen in Fig. \ref{fig:1a}.

\subsection{Wrinkles}

The homogeneity of the films or the existence of islands depend upon the history. It is difficult to produce
catenoid films that are completely uniform. Film inhomogeneities anneal only if the film is given sufficient
time for equilibration (up to minutes). Then, one can obtain bubbles which initially contain little or no islands.

In bubbles of uniform film thickness, the film response to lateral compression is completely different from that
of inhomogeneous bubbles, as shown in Fig.~\ref{fig:wrinkles}.
The overall bubble geometry and shape dynamics in this example are very similar to those in Fig.~\ref{fig:bulges}, except that there are practically no islands on the film. This bubble section undergoes an axial contraction, and
wrinkles form, with a preferential orientation perpendicular to the contraction direction. The first frame shown
was taken 42.4 ms after pinch-off.
As in Fig.~\ref{fig:bulges}, arrows point at two selected features of the film to visualize the axial contraction of the bubble.
The open arrows indicate the expected positions of the second feature if the film had not contracted.
The axial contraction of the bubble in the displayed region amounts to about 10\%, with a maximum
shrinkage rate comparable to that of the bubble in Fig.~\ref{fig:bulges}.

 \begin{figure
	\centering
	\includegraphics[width=1.0\columnwidth]{Fig5.pdf}
		\caption{Formation of wrinkles during the lateral compression of an almost homogeneously thick film. The
bubble has a background film thickness of about 32 nm. The images show a selected area of the bubble surface.
Times are given respective to the first image. The 25 ms image shows a larger part of the bubble. Whitened corners mask the regions
outside the observation window. Arrows mark selected features, in order to collate film regions in subsequent images (see text and Fig.~\ref{fig:bulges}).}
	\label{fig:wrinkles}
\end{figure}

The film undulations can be directly seen in microscopic images at the sides of the bubble. Figure \ref{fig:side} shows a zoomed-in detail of the fully developed wrinkles.

 \begin{figure
	\centering
	\includegraphics[width=0.6\columnwidth]{r01a_191a.jpg}
		\caption{Detail of the wrinkle structure in side view (zoom of the 25 ms image in Fig.~\ref{fig:wrinkles}).}
	\label{fig:side}
\end{figure}

When the contraction stress ceases, the wrinkles gradually disappear again (Fig.~\ref{fig:wrinkles}, bottom row). They can reappear
at a subsequent new contraction. During wrinkling, the surface area stays practically constant, and the orientation of the wrinkles
is directly coupled to the contracting direction.

\begin{figure
	\centering
	\includegraphics[width=0.8\columnwidth]{ffts.pdf}
	\includegraphics[width=0.7\columnwidth]{Fig7b.pdf}
	\caption{Wrinkles of an axially compressed bubble (top images), Fourier Transforms (middle) and vertical cross section profiles of the Fourier Transforms. The contraction stops after approximately 20 ms. Then,
the region expands again, the peak shifts back to lower wave numbers.}
	\label{fig:fft}
\end{figure}

Quantitatively, it is possible to measure the spectrum of the wrinkles by means of Fourier Transform (FT) of the optical images
of certain bubble regions. In order to avoid distortions, it is recommendable to choose regions where the viewing direction
is normal to the film. Figure \ref{fig:fft} shows three snapshots of wrinkles and the corresponding intensity of the 2D
FT power spectrum. It is obvious from the spectra that the wrinkles show a high degree of orientational ordering. From the
plot of the 2D cross sections of these spectra along the symmetry axis (vertical in the images) the graphs in the bottom image of
Fig.~\ref{fig:fft} were obtained. It is evident that the spectrum develops a characteristic peak around the wave number $q_{\max}\approx 300$/mm. This corresponds to wave lengths of about $20~\mu$m of the wrinkles. Furthermore it is evident that the wave length decreases
with time. This is the consequence of the material-fixed position of the wrinkles. The number of wrinkles in a certain film region
remains approximately constant, and the maximum of the spectrum shifts to shorter wavelengths (larger $q$) as a consequence of the lateral
compression of the structure.

\begin{figure
 \center  \includegraphics[width=1.0\columnwidth]{Fig8.pdf}
	\caption{Local contraction of the diameter of the freely floating bubble leads to axial wrinkles.
The dark corners are outside the observation window. Image heights are 2~mm. }
	\label{fig:quer}
\end{figure}

Another scenario where wrinkles can form is the radial contraction of a tubular bubble section, as seen in Fig.~\ref{fig:quer}.
Here, the wrinkles are generated with a preferential axial direction respective to the bubble.
In that geometry, the compression arises from
the local shrinkage of the bubble circumference.
Typical wavelengths appear to be slightly larger than in the former, tangential patterns.
Often, the shape transformations of bubbles involve more complex scenarios, where both the axial contraction
and the diameter shrinkage occur concurrently. In that case, less ordered patterns are observed. A typical example
is that of Fig.~\ref{fig:1a} where wavelengths with different orientations are superimposed.

\begin{figure
	\centering
	\includegraphics[width=1.0\columnwidth]{Fig9.pdf}
		\caption{Bubble with a background film thickness of 16 nm, observed in microgravity:
 Bulges form only in the contracting parts. In the second image, taken 8 ms after the first one, shallow wrinkles form at the bottom end where the axial compression rate is strongest. The bottom image is a zoomed view of this region.
 After another 38 ms, the wrinkles disappeared and the bulges gradually shrink (right image). }
	\label{fig:bulges2}
\end{figure}
Figure \ref{fig:bulges2} shows a bubble of more exotic shape during a phase when it is compressed in the central and lower parts while being only little deformed in the upper part. Here, we find the combination of both deformations,
bulges and wrinkles.
Even though islands are uniformly distributed across the surface of this bubble, bulges are formed almost exclusively in the contracting central and lower regions. Islands in the top part, less exposed to lateral film area contraction, remain flat.
In the bottom part of the bubble, the axial compression is so strong that it cannot be compensated by
bulging. Therefore, wrinkles are created in addition. The third image was taken during a phase where the
film shape reorganization has slowed down considerably, the wrinkles have vanished and the bulges gradually disappear.

\section{Dynamic wrinkling model}

The model developed in this section is intended to describe the simple structures shown in Figs.~\ref{fig:wrinkles}, to \ref{fig:bulges2}.
The complex air flow plays a decisive role in the present system.
In order to demonstrate the principal mechanism without providing a deeper quantitative analysis, we base our model on some crude approximations.

\begin{figure
\centering\includegraphics[width=0.5\columnwidth]{wrinkle.pdf}
\caption{Film geometry and definition of the coordinates.}
\label{fig:wrinklegeo}
\end{figure}

The model considers a rectangular film area of a given fixed width $B$ and initial length $L_0=L(t=0)$. This area be compressed uniaxially
by opposing forces $\vec F_s$ along $z$ and $-z$, resp. (see Figure \ref{fig:wrinklegeo}).
The detailed nature of these compression forces is not relevant for the pattern selection.
In the axially contracting bubbles,
it is generated by pressure acting on the upper and lower caps of the bubble and by friction of the
axially streaming surrounding air. The response of the
film is the formation of $N$ wrinkles with initial wavelength $\lambda_0=L_0/N$ and amplitude $a(t)$.
Small deformations are approximated by the harmonic ansatz $X(z)=a\sin q z$, with $q=2\pi/\lambda$.
The initial wavelength is
$q_0=2\pi N/L_0$. During the compression, the number of wrinkles remains roughly conserved (wrinkles are material-fixed)
and their wavelength decreases. Since we are interested in the initial wavelength selection process, we can safely
consider
the wavelengths to be approximately constant, $q\approx q_0$, the temporal variation does not exceed $\approx$10\%.

The driving force per width of the rippled film region is $f_s=F_s/B$.
This force performs a mechanical work $W_s$, which is in part stored in the deformation of the smectic
film ($W_{\rm b}$). The other part, $W_{\rm f}$, is dissipated primarily by the redisplacement of air near the
 film during the growth of the undulation amplitude.
We thus set $W_{\rm f}=W_{\rm s}-W_{\rm b}$.
The mechanical work of the driving external forces performed on the film during compression is
$W_s(t) = f_s B (L_0-L(t))$.
From the relation $L_0=\int_0^L {\sqrt{1+(dX/dz)^2}} dz$, one finds $L_0\approx (1+a^2q^2/4)L$,
thus
$$ W_{\rm s} = \frac{f_s B L}{4} a^2 q^2 .$$
The reduction of the lateral film area (at given amplitudes $a$ of the undulation) is more effective
for shorter waves, this will provide a suppression of the long-wavelength tail of the
unstable mode band.

Bending of smectic membranes is related to a free energy density contribution of the form
\begin{equation}
\label{eq2}
w_{\rm b}  = \frac{1}{2} K (X'')^2.
\end{equation}
The main contribution to this term is the splay deformation of the director $\vec n(z)$,
 %
\begin{equation}
\label{eq2a}
w_{\rm b}  \approx w_{\rm elast}  = \frac{1}{2} K_{11} (\nabla \vec n)^2
\end{equation}
which in the
smectic A phase is linearly coupled to layer undulations
$$ \quad (\nabla \vec n) =\frac{d n_z}{d z}=-\frac{d^2 X}{d z^2}$$
in our geometry.
Other potential contributions to the smectic layer bending elasticity \cite{Santangelo2005,Fujii2011} might add to that. For example,
the layer compression modulus may lead to some minor corrections, but the splay term remains to be the dominant one.
Integrated over the wrinkled region, one obtains (with the averages $\overline{\sin^2 qz}=\overline{\cos^2 qz}=1/2$)
\begin{equation}
\label{eq2b}
W_{\rm b}  = \frac{K L B h}{4}  a^2 q^4 ,
\end{equation}
where $h$ is the film thickness.
This model is strictly correct only for a smectic A film, and the elastic deformations are more complicated in the smectic C bubbles
studied here. But since we are interested primarily in the qualitative elucidation of the instability mechanism, this detail is
of secondary importance. The functional dependence on $a$ and $q$ in Eq.~(\ref{eq2b}) will not be different in our smectic C films.
Experiments with wrinkling smectic A bubbles would be advantageous for the modeling, but earlier experiments \cite{May2014} proved that it is much more difficult to obtain oscillating smectic A bubbles. They are much more vulnerable to bursting than the smectic C films investigated in our experiments.

Now, we need to relate the growth rate of the undulation to the flow of air from the crests to the valleys of the undulation wave, and consequently to the pressure profile $p(z)$ along the film.
We adapt a concept used in earlier descriptions of transient pattern formation in thin films,
 e. g. \cite{Vrij1968}, and relate the pressure gradient profile with the air flow $j_z$ along the film
($z$ direction) by the equation
\begin{equation}
j_z = -C p'(z),
\end{equation}
where $C$ is a geometrical constant that describes the complex flow processes redistributing
the air along the bulging film on both sides. The quantitative determination of this constant is not straightforward,
but one can make the reasonable assumption that it is roughly the same for all wavelengths.
The related pressure modulation has the same periodicity
as the film deflection, $p=p_0 \sin q z$.
The local film deformation changes according to
\begin{equation}
\dot X = \frac{d j_z}{d z}=  - C p''(z) .
\end{equation}
This yields the relation between the growth of the deformation amplitude and the pressure
amplitude
\begin{equation}
\dot a = Cq^2 p_0,  \quad p= \dot a  C^{-1} q^{-2} \sin qz .
\label{eq:4}
\end{equation}
The energy dissipated in this process is
\begin{equation}
W_{\rm f}= \int_0^L p dV = B\int_0^L p X dz .
\label{eq:0}
\end{equation}

Inserting Eq.~(\ref{eq:4}) into the equation~(\ref{eq:0}) for the dissipated energy $W_{\rm f}$, we find
\begin{equation}
W_{\rm f}=  B\int_0^L C^{-1} q^{-2} \sin^2(qz) a \dot a \,dz,
\end{equation}
and averaging $\overline{\sin^2 qz}=1/2$ yields
\begin{equation}
W_{\rm f}=  \frac{BL}{2C q^2} a\dot{a}.
\end{equation}
We arrive
at the dispersion relation
\begin{equation}
\dot a = {(f_s q^2-K h q^4)\cdot \frac{C}{2} q^2}a= (f_s q^4- K h q^6)\frac{C}{2}a,
\end{equation}
which describes exponential growth of an unstable mode band between $q=0$ and $q_c = \sqrt{f_s/(Kh)}$.
Short wavelength wrinkles are suppressed by the bending elasticity of the smectic layers, large wavelength wrinkles
grow very slowly, thus there exists an optimum growth rate for an intermediate wave length.
The fastest growing mode is
\begin{equation}
q_{\max} = \sqrt{\frac{2}{3} \frac{f_s}{Kh}},
\end{equation}
with the maximum growth rate
\begin{equation}
s_{\max}=\frac{2C}{27}\frac{f_s^3}{K^2h^2}.
\label{smax}
\end{equation}
Thinner films develop wrinkles faster than thicker ones.
An estimate of $f_s$, with available material parameters and experimental data,
$K\approx 10$~pN, $h\approx 20$~nm, and $q_{\max}=300$~mm$^{-1}$, yields reasonable 3~nN/m.
For quantitative predictions on the growth rates, one would need a guess of the geometrical constant $C$.
On the basis of the experimental data and Eq.~(\ref{smax}), we arrive at an estimate of $C\approx 10^{-3}$m$^5$~N$^{-1}$s$^{-1}$ .

We summarize these results as follows:
A lateral compression of the film that is faster than the time scale necessary
to reorganize the film thickness (i. e. island growth) leads to a growth of ripples within a certain
mode band. The wrinkles are aligned with the wave vector along the compression forces.
The fastest growing mode depends upon the bending rigidity of the film, the wave
number becomes smaller with larger $K$. The wave number also decreases with film
thickness, because the energy needed to buckle the film linearly increases with
film thickness.
An in-plane compressing force $f_s$ is the essential ingredient
for the development of the wrinkling instability. It needs to exceed a threshold
set by $K h$ in order to achieve the formation of an unstable mode band with sufficiently quick
growth rates. The larger the compression force $f_s$, the shorter wavelengths of the wrinkles are expected.
The forces $F_s$ can arise from pressure onto the upper and lower caps of the elongated bubbles, from
friction of a convergent air flow near the film surface, or axial contraction of the bubble (Fig.~\ref{fig:quer}).
Their quantitative determination is complicated and was not attempted within this study.
The film surface is unchanged during wrinkling.
The undulations are material-fixed, thus the dominant wavelength shortens during contraction proportional to $L/L_0$.
When the area stretches again, the wavelength grows again and the pattern vanishes.

\section{Conclusions and summary}

We have demonstrated that smectic freely floating bubbles can exhibit a novel type of spontaneously formed dissipative pattern,
the wrinkling of thin films. It occurs as a transient instability when elongated bubbles are compressed axially
or when a tube-like bubble section contracts. The patterns form only when the films are exposed to strong, fast compression
stresses in the film plane. The film surface area remains approximately unchanged. When the compression stresses cease or
transform into dilation, the wrinkles and bulges disappear again. Typical timescales for growth and disappearance are few milliseconds.
Typical wavelengths are in the range of a few dozen micrometers. It is obvious that this phenomenon cannot be observed in conventional soap
films which can respond to lateral compression by practically instantaneous thickness growth and film area reduction. The observed
phenomenon is a peculiarity of the smectic structure.

The second phenomenon described here is the extrusion of bulges from the plane in films that contain islands. Here, the analysis
of the instability mechanism in detail and the description of the quantitative relations between island sizes,
line tensions, external compression forces and bulge sizes still remains a challenge.
A better spatial resolution in the experiment will be required for that.

A key ingredient of our experiment are the oscillating drum-like smectic membranes that remain at the catenoid holders and that
produce strong air flows in axial direction, distorting the freely floating bubbles. More quantitative experimental data might be
obtained when the bubbles are exposed to well-controlled acoustic excitation fields. This could be a challenging future task.
The obvious reason that dynamic wrinkles have not been described before is that practically all earlier investigations of smectics,
with few exceptions, have been performed either in sandwich cells with rigid interfaces or in thin free-standing films spanned across
fixed supports. A desirable improvement of the experimental investigation of wrinkles of smectic films would be the study of
laterally compressed planar films. Several technical problems have to be solved for such an experiment. It would allow to
compare smectic C and smectic A phases using polarizing microscopy, and to identify the coupling of
the c-director dynamics to layer undulations.

Other structured fluid films like lipid membranes or Newton black films should exhibit a similar instability when exposed to sufficiently fast
lateral compressions.
Apart from the general relevance of this unique phenomenon in freely suspended fluid films, the analysis of wrinkles may provide
quantitative access to material parameters of smectic LCs that are otherwise very difficult to measure.

\section*{Acknowledgments}

This study was performed with financial support from DLR within Project OASIS-Co (50WM1430 and 50WM1744) and from DFG (STA 425/40-1). Participation of Robert G\"opfert and Vincent Nathow in the ground lab measurements is gratefully acknowledged.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


The fragrance of this aromatic candle is inspired by Istanbul, Ankara. A bare land, due to the hard, and at times, extreme continental climate with snowy winters and dry scorching summers.
Luxury candle in a glass made with the tradition of the best Valencian ceramics that embraces the opium flower.
Traces of amber, musk, vanilla, resins and unusual woods, often accompanied by spices and exotic flowers are the essence of oriental candle perfumes. They are sweet, sensual, intoxicating and intense. They are perfect for special occasions and cold seasons.


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Phileas Fogg, as self-composed as if the judgment did not in the least concern him, did not even lift his eyebrows while it was being pronounced. Just as the clerk was calling the next case, he rose, and said, "I offer bail." Fix saw them leave the carriage and push off in a boat for the steamer, and stamped his feet with disappointment. Eleven o'clock was striking; Mr. Fogg was an hour in advance of time.
The rascal is off, after all!" he exclaimed. "Two thousand pounds sacrificed! He's as prodigal as a thief! I'll follow him to the end of the world if necessary; but, at the rate he is going on, the stolen money will soon be exhausted. The detective was not far wrong in making this conjecture. Since leaving London, what with travelling expenses, bribes, the purchase of the elephant, bails, and fines, Mr. Fogg had already spent more than five thousand pounds on the way.Phileas Fogg, as self-composed as if the judgment did not in the least concern him, did not even lift his eyebrows while it was being pronounced. Just as the clerk was calling the next case, he rose, and said, "I offer bail." Fix saw them leave the carriage and push off in a boat for the steamer, and stamped his feet with disappointment. Eleven o'clock was striking; Mr. Fogg was an hour in advance of time.
The rascal is off, after all!" he exclaimed. "Two thousand pounds sacrificed! He's as prodigal as a thief! I'll follow him to the end of the world if necessary; but, at the rate he is going on, the stolen money will soon be exhausted. The detective was not far wrong in making this conjecture. Since leaving London, what with travelling expenses, bribes, the purchase of the elephant, bails, and fines, Mr. Fogg had already spent more than five thousand pounds on the way.
Cincinnati Homes is a leading property company in Nigeria with property listings for sale, rent and lease. We offer Nigerian property seekers an easy way to find details of property in Nigeria like homes, houses, lands, office spaces and other commercial property.
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text:
import db from '../core/database'
export default function (router) {
  router.get('/Quizzes/', function (req, res) {
    db.quiz.findAll({
      attributes: [
        'id',
        'name',
        'isActive',
        [db.fn('COUNT', db.col('Questions.id')), 'QuestionCount']
      ],
      include: [{model: db.question, attributes: []}],
      group: ['Quiz.id', 'Quiz.name', 'Quiz.isActive']
    }).then((quizzes) => {
      res.json({success: true, quizzes})
    })
  })

  router.get('/Quizzes/:id/Questions', function (req, res) {
    db.question.findAll({
      where: {
        QuizId: req.params.id
      }
    }).then((questions) => {
      res.json({success: true, questions})
    })
  })
  // Allows us to post our question and have it save to the database.
  router.post('/Quizzes/:quizId/Questions', function (req, res) {
    if (req.body.id) {
      db.question.update({id: req.body.id, title: req.body.title,
                    questionMarkdown: req.body.questionMarkdown,
                    QuizId: req.params.quizId
                    }, {where: {id: req.body.id}}).then((result) => {
                      res.json({success: true, id: req.body.id})
                    }).catch((error) => {
                      res.json({success: false, error})
                    })
    } else {
      db.question.create({id: req.body.id, title: req.body.title,
                  questionMarkdown: req.body.questionMarkdown,
                  QuizId: req.params.quizId
                  }).then((result) => {
                    res.json({success: true, id: result.id})
                  }).catch((error) => {
                    res.json({success: false, error})
                  })
    }
  })

  router.post('/Quizzes', function (req, res) {
    if (req.body.id) {
      db.quiz.update({id: req.body.id, name: req.body.name,
                    isActive: req.body.isActive}, {where: {id: req.body.id}}).then((result) => {
                      res.json({success: true, id: req.body.id})
                    }).catch((error) => {
                      res.json({success: false, error})
                    })
    } else {
      db.quiz.create({id: req.body.id, name: req.body.name,
                  isActive: req.body.isActive}).then((result) => {
                    res.json({success: true, id: result.id})
                  }).catch((error) => {
                    res.json({success: false, error})
                  })
    }
  })
}

redpajama_set_name: RedPajamaGithub


Lulav Forest won the 2015 Sukkahville Design Competition in Toronto.
Inspired by the protection and shelter provided by trees and forests, Lulav Forest is a symbolic forest that provides relief from the sun and a place to rest in the clearing of Nathan Philips Square. Composed of modules, Lulav Forest mimics the traditional formation of lulav bundles, bundles of three plant species the ancient Jews used to construct sukkahs. Lulav Forest features five modular "lulav components" bent into shape with woven tensioned elements. Arranged in multiple directions, the lulav modules reinterpret the Lulav ritual to reflect God's omnipresence.


Our investment in the latest laminating equipment means we can laminate and mount large format prints. We can laminate with both gloss or matt laminate, and mount onto boards too, no matter how big or small the laminating job is. Please contact us for more information.


Familiar and exotic animals disembark from the Ark as the floodwaters recede! Noah can supervise as you assemble this durable extra thick 200-piece cardboard jigsaw puzzle. A great value with bright, sturdy packaging that will withstand many uses! Made in the USA.


text:
Q: Why is Process Explorer reporting activity in non-existent dedicated GPU memory? I've been playing around with Process Explorer on a laptop of mine with Windows 7, 4 GB of RAM, and an onboard GPU(ATI Radeon 6480g as part of the A4 APU). Oddly enough, Process Explorer reports 1.5GB of system GPU memory--all's fine here.
Also included is 512 MB of "dedicated" memory that I'm not aware of the origin of--the card does not contain dedicated memory.

I've seen a few oddities with this card such as Bitcoin miners seeing both the APU (which maxes out CPU usage) and a Winterpark device actually using OpenCL, and the fact that it's reported as dual GPUs to some legacy OpenCL applications.
With that said, playing texture or shader heavy 3D games will, as expected, increase the usage of the dedicated memory--the GPU system memory remains nearly constant.
The GPU should only be getting 512MB of shared memory, which is reported as 1.5GB on the GPU tab.
I'm currently not having problems except for weird resource reporting in some applications, so I'm only asking so far on the basis of curiosity.

A: In Process Explorer, GPU Dedicated Memory represents the actual physical memory that is on the graphics card itself (memory chips are on the graphics card). I see that you have APU so I can't tell you exactly if there are specific memory chips for it or not since I haven't got the chance to get my hands on one.
GPU System Memory is actually the part of your system memory (RAM) that is assigned to be available to the graphics card in order to increase its memory capacity. Windows Vista and newer often use this for storing the previews of application windows when they are not active. Also I believe Windows also stores some other graphical assets in there.
There is nothing wrong about applications reporting that your computer has two OpenCL interfaces because it actually does have two OpenCL interfaces.
One is the OpenCL support of the built in GPU. This is done through graphical drivers. The other is the OpenCL support of the CPU. This is done through the CPU/APU drivers.
As far as I know, some AMD based APUs running OpenCL through the CPU/APU interface should make use of the combined power of both the CPU and GPU. This is not supported on every APU.

A: *

*Are you sure that Radeon hd 6480g embedded in A4 is the only GPU on your system? Several high-end notebook PC's have a discrete GPU as well

*You can try alternative system monitoring tools to gain more information.  (Sorry, I don't have any Windows boxes right now)

*

*http://sites.amd.com/us/game/downloads/amd-system-monitor/Pages/overview.aspx

*http://www.ozone3d.net/gpu_caps_viewer/

*Process Explorer from Windows Sysinternals

*Maybe this one as well? RAMMap, ibid

*Btw, this is how those numbers are calculated

*

*http://msdn.microsoft.com/en-us/library/windows/hardware/ff538322

*What's wrong with your Bitcoin miners?  OpenCL is an API for utilizing both CPU and GPU in an unified manner (but legacy OpenCL apps just assumed all the OpenCL devices were GPU)

redpajama_set_name: RedPajamaStackExchange


It might be early August, and it might be 100 degrees outside, but in the Daily Record/Sunday News sports department, none of that matters.
In what has become an annual tradition, both Penn State and the YAIAA held their football media days on Thursday, which generally means the sports department kidnaps the photo department and scrambles to get all of the photos, videos, helmet photos, rosters, stats and schedules that we'll need for the whole year. All 22 of the York-Adams high schools send players and coaches to the York Expo Center for a media frenzy, while almost 200 media members trekked to State College to interact with new coach Bill O'Brien and his Nittany Lions. It's a busy day for all involved, but it means the fall sports season is really here.
But with any annual event, we're challenged to bring a new twist to our coverage. A way to make it more exciting than rehashing the same stories and photos and videos from last year. And media days are packed with reporters shoving mics and cameras in front of players, who are caught like deer in headlights, making it tough to get them to open up or show some personality.
Thursday, our crew came up with some awesome twists. Somewhat unintentionally, we ended up turning the cameras on ourselves, and the results are fairly hilarious. Click the jump for a pair of videos that are more than worth your while.
High school sports reporter John Clayton went out on a limb last month when West York held a parade to honor its state champion baseball team. In search of a cool video opportunity, he put his FlipCam in the hands of the players themselves to document the parade in their honor. The resulting video added a really unique layer to our coverage that helped elevate the story.
They're not traditional news report videos by any means. And they might not be examples of award-winning journalism. But you know what? They're a lot of fun, and they bring an energy to the players and reporters alike that brightens the entire package. When those chances come along, we have to jump on them.


on Setting up a UPS solution, to enable clean shutdown of vital network components.
This post is about setting up the software that will be responsible for cleanly shutting down servers and workstations.
We have to decide which machine/s is/are going to be used to launch our script (which in turn is run by what APC call a command file).
Currently I've got an old laptop I pulled out of the rubbish about 5 years ago, with Windows XP running on it.
It's got just enough battery capacity to stay alive for long enough to receive the event from the NMC (Network Management Card) and run my .dll that issues the shutdown sequence.
A couple of EeePC 901's have also recently been made redundant, and I may use one of those with Windows 7 installed at some stage.
Currently all of my workstations and servers that don't have batteries, I.E. notebooks are VM's running on ESXi.
Oh… or servers that have their entire file system loaded into volatile memory, so if they are powered off, I.E. cold shutdown, there is no possible corruption of the file system.
What you can also do is host the PCNS (PowerChute Network Shutdown) on a VM, because once the shutdown of ESXi has been initiated, there is no stopping the sequence, and the VM's will all be cleanly shutdown.
Or better still, use more than one machine to host PCNS, as they will operate on a first in first served basis.
As you'll see here the NMC's firmware and PCNS are quite extensible.
The above document is recommended reading if your planning on setting up an APC UPS and want to automate clean shutdowns.
Without reading, the comms can get a little confusing.
v2.2.4 linked to from here, which has additional documentation.
v3.0.0 linked to from here, which has additional documentation.
Both of which were linked to from here, which has additional manuals etc.
The PCNS service needs to be run as a local Administrator as the default Local System account doesn't have sufficient rights.
In saying all that, William Tournas from APC recommended I use PCNS 2.2.1 for Windows XP.
Additional 2.2.1 resources are found here.
If using vMA with PCNS 3.0, you go through a Web UI configuration wizard once installed.
If using PCNS with Windows, the configuration is part of the install.
If it's not, you'll need to open those ports on your firewall.
VMware provide vMA (vSphere Management Assistant) a CentOS VM image.
You'll have to have the same ports open, as PCNS will be listening on them.
Once again, if these ports are not open, you'll have to find which script is being used to set up the rules.
This script would call a script that sets up the rules and one that tears them down.
I'm going to be making a post about how I set up my firewall (iptables) rules for the netfilter module on our notebooks at some stage soon.
If I haven't already done this and you need more help, just sing out.
ESXi.pdf linked to from here linked to from here.
I think this also applies to PCNS 3.0 and ESXi 4.1 which I tried out.
I read somewhere that the PCNS needs to have the same credentials as the NMC, so just be aware of this.
I made a couple of posts there.
goes through a whole lot of issues and work-arounds with PowerChute.
For example, discuss's the correct way to run the command file, PowerOff.bat in our case.
The APC PCNS receives an event from the AP9606 (that's the NMC (Network Management Card)) fitted to the UPS.
The script is launched by APC PCNS from a Windows or Linux box.
I read that PCNS will always shutdown the windows machine it's running on.
PowerChute has an option to 'run this command' but it's limited to 8.3 paths and won't accept command line parameters.
that runs the shutdown script with the parameters – but that could shut down other ESXi boxes as well if required.
I was keen to use PowerShell to perform the shutdowns, as I'd read it was quite capable and also VMware supplied a large set of management cmdlets.
If running PowerOffUPSGuests.ps1 from command shell rather than from a batch file.
You need to add the PowerCLI snapin.
Following are the PowerShell scripts I used.
First we had to create our password file to use to log in to vSphere.
See this post for how this was done.
REM VMware would have used the Export-Console cmdlet to export the name of the PowerShell snap-in PowerCLI uses.
REM Invoke the command with the call operator (The ampersand).
Write-Host "Waiting $seconds Seconds. "
Write-Host "Waiting %seconds Seconds. "
Write-Host "Putting $hostName into maintenance mode. "
I had a hunch that it was due to the read only restriction I had heard about.
So as it turned out, VMware has removed write access from PowerCLI to ESXi, in 4.0 onwards I think.
that I would execute using PowerShell.
First command needs to shutdown my fileserver.
Used Burp suite to diagnose the http frames being sent received from/to vSphere client/ESXi.
I haven't used this tool before, but it gave very good visibility of the messages being sent/received.
to point to 127.0.0.1:8080 This is where the Burp proxy listens on by default.
In Burp, you will also need to add another proxy listener to the proxy->options tab.
Check support invisible proxying for non-proxy-aware clients.
The in-app help has good documentation on this.
Set redirect to host to the ESXi host name.
Select the generate CA-signed per-host certificates radio button.
I also made sure the new proxy rule was the only one running.
When Burp captures each frame, you can forward each one onto any one of the other tools in the suite.
This is a really nice tool.
My PowerOffUPSGuests.ps1 was about to significantly change too.
so needed to Let PowerShell know about the .net 4 CLR.
By default PS 2.0 is only aware of the .net 2.0 framework.
This works for PowerShell, but not for PowerGUI (obviously) which I was using for debugging.
So If you still need PowerGUI you'll have to add the registry hacks explained in the links above.
Remember to remove them once finished as they take affect system wide.
I also had some trouble with later versions of C# than 2.0 when compiling on the fly in PowerShell.
Although I was specifying the language.
Found a workaround this bug here.
We'll go over the library code in the third part of this series.
# add the assembly that does the work.
I was unsure whether we were going to be able to get ESXi to cleanly shutdown it's guest VM's.
As I'd had some trouble with this previously.
I was thinking about writing a WCF service and client to shutdown windows guests for now.
The service being on the machine that needed to be cleanly shutdown.
Could use something like the following command line in the service.
I was sure there was a better way though.
——try put host into maintenance mode, set timer.
set it to something really small, so it runs the command file sooner.
Set the time that's required for the command file to complete to 5 minutes.
Although I don't think it matters that much, as long as there's enough time to start the execution of the PowerShell script.
Once the script is running, we don't care how long PCNS thinks it should wait, as it's non blocking.
What is needed for ESXi to shut down all machines cleanly?
Graceful shutdown work around for ESXi guests.
Also it's important to make sure the root user of ESXi has the Administrator Role.
What is needed for Windows VM's to shutdown cleanly?
First ascertain whether or not your VM is/isn't being shutdown cleanly.
The scripts that may play a part in the shutting down of the Windows VM's.
You can see for the shutdown script, that it actually does nothing.
I just created a shutdown.bat with the following in it.
This cleared up any errors I was getting in my Windows7 logs.
What is needed for Linux VM's to shutdown cleanly?
View the relevant log that contains shutdown info.
My Debian wheezy server wasn't getting shutdown cleanly.
Had some trouble with the NZ repo for those packages, they were corrupt.
So renamed /etc/apt/apt.conf so apt-get wasn't using my cached packages from apt-cacher.
The scripts that may play a part in the shutting down of the Linux VM's.
Mine didn't appear to do much, but my server was being shutdown cleanly now.
Shout out if anythings unclear.
This entry was posted on July 26, 2011 at 20:29 and is filed under GNU/Linux, Microsoft, PowerShell, Projects, UPS, Virtualisation.	You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
This is a well done article that I have bookmarked for future reading. Have a great day.
Everyone lovess what you guys tend to be up too. This kind of clever work and coverage!


Brand agency Bamboo has made its first venture into consumer products with the launch of frozen and bottle-aged cocktails brand Pontoon to the UK market.
The ingredients of the new pre-mixed drinks include Ketel One vodka, Somerset Cider Brandy, bitters, infusions, syrups and fresh hand pressed juices.
According to Bamboo, its bottle-aged cocktails can be drunk immediately or cellared; like a fortified wine. The products are designed to be stirred over ice until cold, strained into a cocktail or rocks glass and garnished with citrus zest.
The bottled range, which is priced at £6.99 for a 100ml bottle and £29.99 for 500ml, consists of No.17 Angelica, a vodka-based herbal drink, No.51 Medici, a "New Orleans decanter cocktail", No.31 Widow's Kiss and No.32 Erskine, a British take on a Boulevardier.
The frozen cocktail pouches, which are £5.99 for 100ml or £24.99 for 500ml, comprise No.12 Cosmopolitan, a version of the classic, No.14 Dusk, a peach and green tea fruit martini, No.54 Gotham, a blood orange Manhattan and No.63 Tommy's, the modern Margarita.


text:
Aspidura – rodzaj węża z podrodziny zaskrońcowatych (Natricinae) w rodzinie połozowatych (Colubridae).

Zasięg występowania
Rodzaj obejmuje gatunki występujące endemicznie na Sri Lance.

Systematyka

Etymologia
 Aspidura:  aspis, ασπιδος aspidos "tarcza"; ουρα oura "ogon".
 Haplocercus:  haploos "prosty, równy"; κερκος kerkos "ogon" . Gatunek typowy: Haplocercus ceylonensis .

Podział systematyczny
Do rodzaju należą następujące gatunki:
 Aspidura brachyorrhos
 Aspidura ceylonensis
 Aspidura copei
 Aspidura deraniyagalae
 Aspidura desilvai
 Aspidura drummondhayi
 Aspidura guentheri
 Aspidura ravanai
 Aspidura trachyprocta

Przypisy

Bibliografia

Połozowate

redpajama_set_name: RedPajamaWikipedia


The Circuit Court of Cook County is the largest of the 24 judicial circuits in Illinois and one of the largest unified court systems in the world. It has more than 400 judges who serve the residents of Cook County within the City of Chicago and its surrounding suburbs.
Cook County has several court locations, you can find information here about court locations and directions. If you are have to go to court in Cook County, be sure you know the correct location where the case will be heard.
The Probate Division of Cook County hears matters concerning wills and the administration of estates. It is located on the 18th Floor of the Richard J. Daley Center, 50 W. Washington Street, Chicago. Click here for more information about the Probate Division, including the local rules and other resources.
The Clerk of the Circuit Court of Cook County maintains the court records for Cook County. You can find information about cases in Cook County, including court dates and locations here.


text:
Q: Etale cohomology can not be computed by Cech It can be proven that if in a quasicompact scheme $X$ any finite subset is contained in an affine open subset then for any sheaf $\mathcal{F}$ on $X$ its Cech cohomology $\hat{H_{et}^{\bullet}}(X,\mathcal{F})$ is naturally isomorphic to etale cohomology $H^{\bullet}_{et}(X,\mathcal{F})$.
Is there a counterexaple for an arbitrary scheme? The assumptions of the theorem I cited fail, for instance for Hironaka's example of a threefold with two points not contained in any affine open subset but does it give a counterexample?

A: Čech cohomology fails for the plane with the doubled origin, $\mathbb A^2_{00}=\mathbb A^2\cup_{\mathbb A^2-0}\mathbb A^2$, with cohomology in the structure sheaf: $\check{H}^2(\mathbb A^2_{00};\mathcal O)=0\ne H^2(\mathbb A^2_{00};\mathcal O)$. Čech cohomology fails for both the Zariski and étale cohomologies.
Mayer-Vietoris shows that the punctured plane $\mathbb A^2-0$ has nontrivial cohomology in degree 1. Similarly, if we take any open subset of $\mathbb A^2$ that contains the origin, the same group appears in its first cohomology. Mayer-Vietoris pushes that into degree 2: $H^2(\mathbb A^2_{00};\mathcal O)=H^1(\mathbb A^2-0;\mathcal O)$. (In other words, if we push forward from the punctured plane to the affine plane $j\colon \mathbb A^2-0\hookrightarrow A^2$, then $R^1j_*\mathcal O$ is nontrivial and concentrated on the origin.)
The Čech cohomology for a particular cover amounts to pretending that the open sets of that cover and all of their $n$-fold intersections are acyclic for the sheaf. For a manifold and the constant sheaf, there do exist such "good covers" (eg, convex balls on a Riemannian manifold) and they are cofinal. For a separated scheme, affines are acyclic, so if intersections of affines are affine, then a single cover by affines computes quasi-coherent cohomology. This is why separated often appears as a hypothesis in cohomology (although it could be reduced to "semi-separated," ie, affine diagonal).
If $U\to X$ is a cover and $U^n$ is the $n$-fold fiber product over $X$, then the Čech complex is:
$$F(U)\to F(U^2)\to F(U^3)\to\cdots$$
This defines $\check{H}^*(U\to X;F)$. For any cover, the derived version of this computes the full cohomology:
$$RF(U)\to RF(U^2)\to RF(U^3)\to\cdots$$
This gives the Čech-to-cohomology spectral sequence: $E_1^{pq}=H^q(U^p;F)\Rightarrow H^{p+q}(X;F)$ and $E_2^{pq}=\check{H}^p(U\to X;R^qF)$). The edge map is the comparison from Čech cohomology to real cohomology and the groups off of the edge are obstructions to Čech cohomology working. Of course, we are not interested in a single cover, but in the limit over all covers.
For any cohomology class there exists a cover such that the restriction to the cover kills the class. Refining by that cover moves that class off of $E_1^{p,0}=H^p(U;F)$ to at least $E_1^{(p-1),1}$. If $p=1$ then it has moved into Čech cohomology. That is why first Čech is always correct in the limit over all covers. But there is no guarantee that a cycle can be moved all the way to the Čech edge $E^{0,p}$.
Indeed, this cannot be done in the example from the beginning: the second cohomology of the affine plane with the doubled origin with coefficients in the structure sheaf. Switching back to the language of ordinary spaces, our cover must have two open sets, each containing one of the two origins; their intersection is punctured in codimension 2 and thus has cohomology. Moreover, it is essentially the same cohomology, independent of the choice of cover. It cannot be killed by refining the cover, only by leaving the cover the same and introducing an auxiliary cover of the intersection, ie, Verdier's theory of hypercovers, a small change to Čech cohomology that always works. I have identified a cycle in $E_1^{1,1}$ that I claim obstructs Čech cohomology from being correct in this example. I have shown that it survives the limit of all covers. I have not shown that it survives to $E_2$, let alone $E_\infty$. For proofs of such pathologies, see the literature on hypercovers.

A: Let $k$ be an algebraically closed field. Glue two copies of $\text{Spec}(k[[x]])$ along $\text{Spec}(k((x)))$. This gives a scheme $X = U \cup V$ such that any etale covering of $X$ can be refined by the Zariski covering $X = U \cup V$. (Hint: use that $k[[t]]$ is strictly henselian.) Thus the etale Cech cohomology is the usual Cech cohomology. For a constant sheaf with value an abelian group $A$ we get $\check{H}^i_{et}(X, A) = 0$ for $i > 0$. On the other hand, if $A$ is finite of order invertible in $A$ then we have $H^2_{et}(X, A) \cong A$ as you can see by using the Cech to cohomology spectral sequence and using the fact that $H^1_{et}(U \cap V, A) \cong A$ as abelian groups (noncanonically).
Currently I am blanking on a separated example. If I remember, I will post another answer.
Edit: In the paper by Stefan Schoer, "Geometry on totally separably
closed schemes", the author conjectures that for separated and quasi-compact schemes etale Cech cohomology should agree with etale cohomology. (See remarks at the top of page 540.) He even conjectures it should suffice if the diagonal is affine. I have no idea how reasonable this conjecture is.


On March 18, 2016, I joined Lize Mogel, Neil Freeman, and Heidi Neilson at the Center for Book Arts for the first in a three-part series of discussions about "Map as Metaphor." I took some liberty with the theme and spoke instead about "Maps as Media" (besides, media are kind-of etymologically related to metaphors anyway). I drew segments of my talk from this "Gaps in the Map" essayI wrote, but never published, last fall, and I talked a lot about my student's map-work in our 2010-13 "Urban Media Archaeology" studio and the more recent "Maps as Media" studio. You can find my slides and text here.


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How do we prepare youth with the scientific literacy necessary for the 21st century?
In the Spring of 1986, British astrophysicist and science writer, John R. Gribbin wrote an alarming article following extensive research for the New Scientist. One particular paragraph stood out: "By the end of the next century, the "greenhouse effect" may increase temperatures worldwide to levels that have not been reached for at least 100,000 years. And the effects on sea level and on agriculture and other human activities are likely to be so profound that we should be planning for them now."
Gribbin was among a few scientists alerting us on climate change during an era when environmental issues were not a matter of significance. In those days, the topic of ecological sustainability was too complicated for the average person to comprehend. Policy-makers and educational institutions hardly paid attention to the potential threat of global warming.
Fast forward to 2020, the subjects of the environment and sustainability remain a rarity for most of the global education system. Public schools are particularly affected by the sluggish update of current curriculums. Bringing education programs up to date with the three pillars of sustainability - economic, environmental and social has proven to be unnecessarily challenging.
As a child during the 80s and 90s, watching the news headline with my Nigerian parents, I was attuned to the tragic consequences of Chernobyl and numerous oil spills, notably the pollution caused by Shell Oil Co in Ogoni. Like many other youths, I lacked a proper understanding of our future's most pressing climate issues.
How do we teach the youth to sustain and protect our ecosystem with a curriculum developed for the 20th century?
Many students have insufficient knowledge of how our daily habits and toxic pollutants impact the ecosystem. Despite numerous youth networks raising awareness and advocating environmental-focused agendas, overall, the new generation lacks the competence of creating or articulating concrete methods to preserve and sustain the ecosystem.
Teaching sustainability could tackle this knowledge gap by adopting green education into the national school curriculum. As a new multidisciplinary field, synonymous to environment or sustainability education, green education programmes equip students with the degree of scientific literacy necessary to preserve the planet.
Unfortunately, attempts to reform school curriculums have proven challenging for varied reasons, especially the lack of competence, budget and coordination between academics, policy-makers and teachers obstruct school curriculum updates. Nonetheless, some nations, particularly Nordic countries, have managed to integrate green education into their existing national curriculum by investing in developing relevant competencies and coordinating interdisciplinary stakeholder meetings.
Take Sweden for an example. Swedish schools integrate sustainability across all education levels. Higher education institutions, such as the Stockholm School of Economics, also organises specialist programmes for more senior business people.
Developing a sophisticated degree of scientific literacy for students is a prerequisite to achieving the United Nations' proposed sustainable development goals
Conveying information about sustainability that is easily understandable for all is necessary for competence building. Together with several associations, think-tanks and international institutions, the United Nations campaign for sustainable development has transformed the complicated matter of sustainability to easily relatable milestones affecting all world citizens.
To engage in the decision-making process with private and public organisations and provide creative sustainability solutions, students - both junior and senior need to be equipped with the necessary attitudes and comprehension. As a result of organisations going green, new businesses and jobs emerge. People with green education are likely to foster global partnerships and work together in concerted efforts to save the planet.
We are responsible for increasing the new generation's employability by ensuring that education program specialists integrate environmental sustainability and ethical principles for ecological and social change. Green education provides the degree of scientific literacy necessary for the most severe threats that humanity faces in the 21st century and beyond.
Rita Isiba is the founder of Aphropean Partners and Frontiers of Dialogue Forum in Austria. She is also an Associate Partner of Funkensprung, a chain of hubs for creativity, entrepreneurship and networking scattered across Vienna. As an engagement specialist, trainer and facilitator, she supports organisations with a need to prepare for international business development assignments with a focus on Africa and Europe. Rita Isiba resides in Vienna with her partner and daughter. She is also active on LinkedIn, where she shares her views of organisational culture and business trends impacting growth.

redpajama_set_name: RedPajamaCommonCrawl


We made it home all in one piece. Sunday was spent cleaning all the stuff that needs to go back into the camper. We packed up in the morning, so there was still dew on the camper. Because of this, when we get home, we have to open it back up in the drive way and let the sun dry it the rest of the way before we pack it up and take it back to storage. So, we did that and I had to get the lawn mowed.
Today it was back to work for me. Jennifer picked up Austin, who we left at the kennel while we were camping. Jennifer also went and got her hair done. She goes to a hair stylist at the RDV Sportsplex, a private gym across the street from where I work. She likes it because she can drop the kids off at the kids gym across the hall for a couple of hours while she's at the hair stylist. It would be great to take them there more often, but memberships to the RDV are too expensive. EA offers subsidized memberships for me and Jennifer, but they don't for the kids. Not sure why when there's more and more people with families working at EA. Hopefully they will change that one of these days.
REMOTE POSTING – FERNANDINA BEACH, FL.: It rained all night long. The girls slept right through it, but Jennifer and myself were tossing all night lon slept right through it, but Jennifer and myself were tossing all night long. At one point the wind started whipping, but we weathered the storm.
In the morning the girls got up at their normal 6:30 time and it was still raining. Every once in a while it would slow down to a sprinkle and I was able to get some charcoal lit for our breakfast. We cooked up egg and bacon English muffins heated up in a pie iron over the hot coals.
It was still raining and the girls were getting stir crazy, so we decided to get everyone into the Sequoia and head into Jacksonville. I looked up a children's museum with directions on the Internet using my phone. And off we went. It was a cute place. It was just a locally owned joint with several went. It was a cute place. It was just a locally owned joint with several areas like a pretend bank and post office. It had a dress up area and stage which Abby enjoyed.
We let the girls play around for a couple of hours and then we headed over to Dave & Busters. D&B is an arcade/restaurant which they have in Texas, which we haven't been to since leaving Austin. The best way to describe it is a Chuck E Cheese for adults. The girls had fun and won several toys playin a Chuck E Cheese for adults. The girls had fun and won several toys playing all the games that gave away tickets.
Believe it or not the sun had come out in the afternoon and dried up the camp. As the sun started to set, we had a quick snack for dinner and headed over to Fort Clinch for a candle light tour of the fort. The tour was very interesting. A soldier with a thick Irish accent answered the door to the fort and led us around the various areas. He stayed in character pretending to be a corporal in the Union army who captured and completed the fort during the Civil War. As I said, it was all very interesting. It was so hot inside the various buildings and it's amazing that people could live in the South without air conditioning. That's why our camper has it and I don't leave home without it. home without it.
REMOTE POSTING – FERNANDINA BEACH, FL.: We headed out on our first non-Disney excursion in the camper today: Fort Clinch State Park. It's just north of Jacksonville and was about a two and a half hour trip from Orlando. It's as far north as you can go in Florida without crossing over into Georgia. The campground is right along the Atlantic coast with the beach within walking distance.
Unfortunately, It's been raining almost the whole time, which is pretty unusual for Florida. Usually it rains for an hour max and then the sun comes back out. We did have a little break in the clouds and walked along the beach. We also rode our bikes down to the actual fort itself, but got there right as it was closing. We also got there right as the clouds decided to let the rain out again. It was a very soaking mile-long bike trek back to the camp site. We were still able to cook out on the grill even through the sprinkles. After dinner it was a couple of games of Chutes and Ladders inside the camper with the girls and it was time for bed. Hopefully it won't be as rainy tomorrow.


Like many other college students around the country this time of the semester, I found myself procrastinating on the pile of work I had to do. Instead of reading my Theology assignment or finishing my math homework, I pulled up the familiar comfort of Netflix on my computer and bundled up in a blanket on my bed. Scrolling through Netflix in search of something interesting and entertaining to watch, I stumbled upon a new Netflix original "Insatiable," and my curiosity forced me to press play. This led to five episodes watched over the period of a week, before I gave in and accepted that the show is frankly terrible and almost painful to watch.
"Insatiable" explores the life of a young girl, Patty Bladell (Debby Ryan), who was once obese but has now lost "the weight," due to an altercation with a homeless man. Patty is now hungry for revenge on her bullies, no matter what it takes. Though its creators claim the series is a satire, it is entirely riddled with issues ranging from poorly portrayed stereotypes to negative coverage of relevant social issues.
For starters, the depiction of extremely negative body-imaging throughout the series hits home for many young women today. The portrayal of Patty Bladell as angry, negative and having an extreme hatred for her body only helps nourish the negative mindset surrounding young women's bodies in today's society. It fosters the idea that if you aren't model-thin, your life can't be happy and full. Though it is unfortunately true that the overweight youth of today often face bullying and torment from classmates, it is not true to say that larger or curvier women cannot love their bodies or live happy lives. Furthermore, instead of allowing the newly skinny Bladell to simply be happy and, for lack of better words, to kill her bullies with kindness, the creators decided to make her intent on revenge. Often her revenge attempts are violent and deeply twisted, including an attempt to set a sleeping man on fire.
The series also tackles increasingly relevant topics, such as sexual assault and homophobia. Much like the damaging attempt at satirizing fat shaming, the creators entirely missed the mark on these two topics. Instead of creating satire, the writers seem to have created a narrative bashing every topic of controversy and relevance in today's society, making a complete mockery of the victims of these issues by misplacing these topics in humorous situations. The show is, simply put, a disgrace and a tragic attempt at satire writing.
Satire is an extremely difficult type of writing to master and can come across very wrong when done poorly, as evidenced by "Insatiable." The writers of this show should have taken a second look at the script before pushing it to production. The presentation of such controversial and difficult topics comes across more as a tragic attempt at a comedic representation than a true satire, and it seems as though I'm not the only one that feels this way. The show received a measly 11 percent and one star on Rotten Tomatoes, along with a mass of seething reviews. Even the original trailer received much controversial feedback, and many thought the show's release would be canceled. Ultimately, "Insatiable" is a terrible satirization of topics which should be handled with extreme care, as well as a failure to show the true importance of issues such as homophobia, sexual assault and fat-shaming. Despite the unfavorable reactions to the first season of the series, a second season has been announced and is in the process of production. Unfortunately, I can't say I'll be making it through the rest of season one, much less an additional season of such an unsuccessful satire.


SimpleGifts with Billy McLaughlin combines violin, celtic whistle, piano, acoustic guitar and percussion with angelic three-part female vocals to deliver a "modern Old World" sound in Christmas carols and hymns.
SimpleGifts, an ensemble led by award-winning musician McLaughlin, stays close to the heart of Christmas. With exceptional set and lighting design and an impeccable sound-system, SimpleGifts puts community celebration ahead of commercialization – pulling the audience into the sublime side of traditional repertoire in a truly meaningful Christmas event.
Crossings is thrilled to bring the popular SimpleGifts show back to Zumbrota for the ninth year running.
With little or no media attention, SimpleGifts is arguably the most successful holiday-themed project in the state celebrating exclusively traditional hymns and carols interpreted in modern arrangements. Fueled by passionate grassroots fans since 2001, the tour includes more than a dozen appearances between Thanksgiving and Christmas Eve in the Twin Cities metro or within close proximity.
Music from the group's five critically acclaimed CD releases will be featured. Familiar classics audiences may hear include "O Little Town of Bethlehem," "Hark the Herald Angels Sing," and "Little Drummer Boy," while lesser-known songs offer fresh perspectives on the holidays.
Members include Torie Redpath, Amy Courts, Heather Moen (Garborg), Billy Oehrlein, Laura MacKenzie and Billy McLaughlin.


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Click to Take the FREE Probability Crash-Course
A Gentle Introduction to Expectation-Maximization (EM Algorithm)
By Jason Brownlee on November 1, 2019 in Probability
Maximum likelihood estimation is an approach to density estimation for a dataset by searching across probability distributions and their parameters.
It is a general and effective approach that underlies many machine learning algorithms, although it requires that the training dataset is complete, e.g. all relevant interacting random variables are present. Maximum likelihood becomes intractable if there are variables that interact with those in the dataset but were hidden or not observed, so-called latent variables.
The expectation-maximization algorithm is an approach for performing maximum likelihood estimation in the presence of latent variables. It does this by first estimating the values for the latent variables, then optimizing the model, then repeating these two steps until convergence. It is an effective and general approach and is most commonly used for density estimation with missing data, such as clustering algorithms like the Gaussian Mixture Model.
In this post, you will discover the expectation-maximization algorithm.
Maximum likelihood estimation is challenging on data in the presence of latent variables.
Expectation maximization provides an iterative solution to maximum likelihood estimation with latent variables.
Gaussian mixture models are an approach to density estimation where the parameters of the distributions are fit using the expectation-maximization algorithm.
Discover bayes opimization, naive bayes, maximum likelihood, distributions, cross entropy, and much more in my new book, with 28 step-by-step tutorials and full Python source code.
Update Nov/2019: Fixed typo in code comment (thanks Daniel)
A Gentle Introduction to Expectation Maximization (EM Algorithm)
Photo by valcker, some rights reserved.
This tutorial is divided into four parts; they are:
Problem of Latent Variables for Maximum Likelihood
Expectation-Maximization Algorithm
Gaussian Mixture Model and the EM Algorithm
Example of Gaussian Mixture Model
A common modeling problem involves how to estimate a joint probability distribution for a dataset.
Density estimation involves selecting a probability distribution function and the parameters of that distribution that best explain the joint probability distribution of the observed data.
There are many techniques for solving this problem, although a common approach is called maximum likelihood estimation, or simply "maximum likelihood."
Maximum Likelihood Estimation involves treating the problem as an optimization or search problem, where we seek a set of parameters that results in the best fit for the joint probability of the data sample.
A limitation of maximum likelihood estimation is that it assumes that the dataset is complete, or fully observed. This does not mean that the model has access to all data; instead, it assumes that all variables that are relevant to the problem are present.
This is not always the case. There may be datasets where only some of the relevant variables can be observed, and some cannot, and although they influence other random variables in the dataset, they remain hidden.
More generally, these unobserved or hidden variables are referred to as latent variables.
Many real-world problems have hidden variables (sometimes called latent variables), which are not observable in the data that are available for learning.
— Page 816, Artificial Intelligence: A Modern Approach, 3rd edition, 2009.
Conventional maximum likelihood estimation does not work well in the presence of latent variables.
… if we have missing data and/or latent variables, then computing the [maximum likelihood] estimate becomes hard.
— Page 349, Machine Learning: A Probabilistic Perspective, 2012.
Instead, an alternate formulation of maximum likelihood is required for searching for the appropriate model parameters in the presence of latent variables.
The Expectation-Maximization algorithm is one such approach.
Want to Learn Probability for Machine Learning
The Expectation-Maximization Algorithm, or EM algorithm for short, is an approach for maximum likelihood estimation in the presence of latent variables.
A general technique for finding maximum likelihood estimators in latent variable models is the expectation-maximization (EM) algorithm.
— Page 424, Pattern Recognition and Machine Learning, 2006.
The EM algorithm is an iterative approach that cycles between two modes. The first mode attempts to estimate the missing or latent variables, called the estimation-step or E-step. The second mode attempts to optimize the parameters of the model to best explain the data, called the maximization-step or M-step.
E-Step. Estimate the missing variables in the dataset.
M-Step. Maximize the parameters of the model in the presence of the data.
The EM algorithm can be applied quite widely, although is perhaps most well known in machine learning for use in unsupervised learning problems, such as density estimation and clustering.
Perhaps the most discussed application of the EM algorithm is for clustering with a mixture model.
A mixture model is a model comprised of an unspecified combination of multiple probability distribution functions.
A statistical procedure or learning algorithm is used to estimate the parameters of the probability distributions to best fit the density of a given training dataset.
The Gaussian Mixture Model, or GMM for short, is a mixture model that uses a combination of Gaussian (Normal) probability distributions and requires the estimation of the mean and standard deviation parameters for each.
There are many techniques for estimating the parameters for a GMM, although a maximum likelihood estimate is perhaps the most common.
Consider the case where a dataset is comprised of many points that happen to be generated by two different processes. The points for each process have a Gaussian probability distribution, but the data is combined and the distributions are similar enough that it is not obvious to which distribution a given point may belong.
The processes used to generate the data point represents a latent variable, e.g. process 0 and process 1. It influences the data but is not observable. As such, the EM algorithm is an appropriate approach to use to estimate the parameters of the distributions.
In the EM algorithm, the estimation-step would estimate a value for the process latent variable for each data point, and the maximization step would optimize the parameters of the probability distributions in an attempt to best capture the density of the data. The process is repeated until a good set of latent values and a maximum likelihood is achieved that fits the data.
E-Step. Estimate the expected value for each latent variable.
M-Step. Optimize the parameters of the distribution using maximum likelihood.
We can imagine how this optimization procedure could be constrained to just the distribution means, or generalized to a mixture of many different Gaussian distributions.
We can make the application of the EM algorithm to a Gaussian Mixture Model concrete with a worked example.
First, let's contrive a problem where we have a dataset where points are generated from one of two Gaussian processes. The points are one-dimensional, the mean of the first distribution is 20, the mean of the second distribution is 40, and both distributions have a standard deviation of 5.
We will draw 3,000 points from the first process and 7,000 points from the second process and mix them together.
... # generate a sample X1 = normal(loc=20, scale=5, size=3000) X2 = normal(loc=40, scale=5, size=7000) X = hstack((X1, X2))
# generate a sample
X1 = normal(loc=20, scale=5, size=3000)
X = hstack((X1, X2))
We can then plot a histogram of the points to give an intuition for the dataset. We expect to see a bimodal distribution with a peak for each of the means of the two distributions.
# example of a bimodal constructed from two gaussian processes from numpy import hstack from numpy.random import normal from matplotlib import pyplot # generate a sample X1 = normal(loc=20, scale=5, size=3000) X2 = normal(loc=40, scale=5, size=7000) X = hstack((X1, X2)) # plot the histogram pyplot.hist(X, bins=50, density=True) pyplot.show()
# example of a bimodal constructed from two gaussian processes
from numpy.random import normal
# plot the histogram
pyplot.hist(X, bins=50, density=True)
Running the example creates the dataset and then creates a histogram plot for the data points.
The plot clearly shows the expected bimodal distribution with a peak for the first process around 20 and a peak for the second process around 40.
We can see that for many of the points in the middle of the two peaks that it is ambiguous as to which distribution they were drawn from.
Histogram of Dataset Constructed From Two Different Gaussian Processes
We can model the problem of estimating the density of this dataset using a Gaussian Mixture Model.
The GaussianMixture scikit-learn class can be used to model this problem and estimate the parameters of the distributions using the expectation-maximization algorithm.
The class allows us to specify the suspected number of underlying processes used to generate the data via the n_components argument when defining the model. We will set this to 2 for the two processes or distributions.
If the number of processes was not known, a range of different numbers of components could be tested and the model with the best fit could be chosen, where models could be evaluated using scores such as Akaike or Bayesian Information Criterion (AIC or BIC).
There are also many ways we can configure the model to incorporate other information we may know about the data, such as how to estimate initial values for the distributions. In this case, we will randomly guess the initial parameters, by setting the init_params argument to 'random'.
... # fit model model = GaussianMixture(n_components=2, init_params='random') model.fit(X)
model = GaussianMixture(n_components=2, init_params='random')
model.fit(X)
Once the model is fit, we can access the learned parameters via arguments on the model, such as the means, covariances, mixing weights, and more.
More usefully, we can use the fit model to estimate the latent parameters for existing and new data points.
For example, we can estimate the latent variable for the points in the training dataset and we would expect the first 3,000 points to belong to one process (e.g. value=1) and the next 7,000 data points to belong to a different process (e.g. value=0).
... # predict latent values yhat = model.predict(X) # check latent value for first few points print(yhat[:100]) # check latent value for last few points print(yhat[-100:])
# predict latent values
yhat = model.predict(X)
# check latent value for first few points
print(yhat[:100])
# check latent value for last few points
print(yhat[-100:])
Tying all of this together, the complete example is listed below.
# example of fitting a gaussian mixture model with expectation maximization from numpy import hstack from numpy.random import normal from sklearn.mixture import GaussianMixture # generate a sample X1 = normal(loc=20, scale=5, size=3000) X2 = normal(loc=40, scale=5, size=7000) X = hstack((X1, X2)) # reshape into a table with one column X = X.reshape((len(X), 1)) # fit model model = GaussianMixture(n_components=2, init_params='random') model.fit(X) # predict latent values yhat = model.predict(X) # check latent value for first few points print(yhat[:100]) # check latent value for last few points print(yhat[-100:])
# example of fitting a gaussian mixture model with expectation maximization
from sklearn.mixture import GaussianMixture
# reshape into a table with one column
X = X.reshape((len(X), 1))
Running the example fits the Gaussian mixture model on the prepared dataset using the EM algorithm. Once fit, the model is used to predict the latent variable values for the examples in the training dataset.
Your specific results may vary given the stochastic nature of the learning algorithm.
In this case, we can see that at least for the first few and last few examples in the dataset, that the model mostly predicts the correct value for the latent variable. It's a generally challenging problem and it is expected that the points between the peaks of the distribution will remain ambiguous and assigned to one process or another holistically.
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Section 8.5 The EM Algorithm, The Elements of Statistical Learning, 2016.
Chapter 9 Mixture Models and EM, Pattern Recognition and Machine Learning, 2006.
Section 6.12 The EM Algorithm, Machine Learning, 1997.
Chapter 11 Mixture models and the EM algorithm, Machine Learning: A Probabilistic Perspective, 2012.
Section 9.3 Clustering And Probability Density Estimation, Data Mining: Practical Machine Learning Tools and Techniques, 4th edition, 2016.
Section 20.3 Learning With Hidden Variables: The EM Algorithm, Artificial Intelligence: A Modern Approach, 3rd edition, 2009.
Gaussian mixture models, scikit-learn API.
sklearn.mixture.GaussianMixture API.
Maximum likelihood estimation, Wikipedia.
Expectation-maximization algorithm, Wikipedia.
Mixture model, Wikipedia.
In this post, you discovered the expectation-maximization algorithm.
Get a Handle on Probability for Machine Learning!
Develop Your Understanding of Probability
Bayes Theorem, Bayesian Optimization, Distributions, Maximum Likelihood, Cross-Entropy, Calibrating Models
Finally Harness Uncertainty in Your Projects
Probabilistic Model Selection with AIC, BIC, and MDL
A Gentle Introduction to Monte Carlo Sampling for Probability
7 Responses to A Gentle Introduction to Expectation-Maximization (EM Algorithm)
Ricardo November 1, 2019 at 10:32 am #
this part seems to contradict what follows it: " although it (EM) requires that the training dataset is complete"
oh, it refers to maximum likelihood, never mind
Jason Brownlee November 1, 2019 at 1:41 pm #
Daniel November 2, 2019 at 10:13 am #
Hi Jason, How are you? I hope finding you well!
I am confused, the first output list should be 0's right? And the second of ones, but they're inverted. Thank you in advance!
Jason Brownlee November 3, 2019 at 5:47 am #
The example shows the two different processes were identified, e.g. two class labels.
It was a typo to expect specific labels to be assigned. I have updated it. Thanks!
Alexander Ligthart December 4, 2019 at 3:45 am #
I would like to use a library with the EM algorithm for semi-supervised learning. However, I can't find an existing library in python. Do you know of an exiting one? There are plenty of papers on the subject (Rout et al. 2017, Hassan & Islam 2019) that use EM for semi supervised learning, but their code is not open.
alexander.ligthart@live.com
Jason Brownlee December 4, 2019 at 5:47 am #
Typically EM is implemented in service of another task.
e.g. Gaussian mixture models:
https://scikit-learn.org/stable/modules/mixture.html
How to Use ROC Curves and Precision-Recall Curves for Classification in Python
How and When to Use a Calibrated Classification Model with scikit-learn
How to Develop and Evaluate Naive Classifier Strategies Using Probability
5 Reasons to Learn Probability for Machine Learning
The Probability for Machine Learning EBook is where I keep the Really Good stuff.


text:
Home Newsroom News and press releases OSCE media freedom representative welcomes Ireland's decriminalization of defamation, calls for crime of 'blasphemy' to be abolished
OSCE Representative on Freedom of the Media
Media freedom and development, Decriminalization of defamation, Media laws
OSCE media freedom representative welcomes Ireland's decriminalization of defamation, calls for crime of 'blasphemy' to be abolished
VIENNA 12 January 2010
Media accreditation to OSCE events
OSCE Live
OSCE Representative on Freedom of the Media, Miklos Haraszti. (OSCE/Mikhail Evstafiev) Photo details
VIENNA, 12 January 2010 - The OSCE Representative on Freedom of the Media, Miklos Haraszti, welcomed today Ireland's amended Defamation Act which went into effect at the start of the year, but criticized the introduction of a new "blasphemy" provision.
The Defamation Act decriminalized speech offences, making Ireland the second Western European country after the United Kingdom to abolish criminal libel. In those countries, only civil courts are allowed to deal with offences like defamation and libel.
"I welcome Ireland's initiative. Decriminalization reform should be adopted by more countries which continue to treat journalistic mistakes as crimes, exerting a 'chilling effect' on critical journalism," Haraszti said. "Most European Union member states have long stopped using their criminal defamation or libel provisions, heeding the jurisdiction of the European Court of Human Rights in Strasbourg. Ireland made the logical and welcome next step by dropping those crimes from the books."
"As welcome as the Irish reform is, however, introducing a renewed version of the antiquated 'crime' of blasphemy is a step backward and sends the wrong signal to the international community."
Haraszti noted that the blasphemy provision, which penalizes statements that are "grossly abusive or insulting in relation to matters held sacred by any religion", is contrary to Ireland's stance in the UN Human Rights Council, where the country has consistently voted against motions that define "defamation of religion" as a crime.
"Defamation of religion is a concept that, if criminalized, restricts free dialogue in society as much as the other types of defamation which have now been repealed," Haraszti said. "Therefore, I call on the Irish authorities to also repeal this provision as quickly as possible."
Office of the OSCE Representative on Freedom of the Media
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Office: +43 1 51436 6813
Fax: +43 1 514 36 6802
jennifer.adams@osce.org
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