text: Propose regions by selective search (~2k candidates per image). (They are discussed later on). Remember that we have computed $$\mathbf{G}_x$$ and $$\mathbf{G}_y$$ for the whole image. on computer vision, pp. 5: Input and output for object detection and localization problems. The following code simply calls the functions to construct a histogram and plot it. object detection in [32], the work in [7] presents an end-to-end trainable 3D object detection network, which directly deals with 3D point clouds, by virtue of the huge success in PointNet/PointNet++ [4,5]. Apply Sobel operator kernel on the example image. Distinct but not Mutually Exclusive Processes . Anomaly detection is the process of identifying unexpected items or events in data sets, which differ from the norm. [Part 4]. I don’t think you can find it in Tensorflow, but Tensorflow-slim model library provides pre-trained ResNet, VGG, and others. The fast and easy way to learn Python programming and statistics Python is a general-purpose programming language created in the late 1980sand named after Monty Pythonthats used by thousands of people to do things from testing microchips at Intel, to poweringInstagram, to building video games with the PyGame library. Anomaly detection has … object-recognition. The image gradient vector is defined as a metric for every individual pixel, containing the pixel color changes in both x-axis and y-axis. Summary. Predicted bounding box correction, $$t^u = (t^u_x, t^u_y, t^u_w, t^u_h)$$. Object Detection: Datasets 2007 Pascal VOC 20 Classes 11K Training images 27K Training objects Was de-facto standard, currently used as quick benchmark to evaluate new detection algorithms. Object Detection; Template Matching; Corner, Edge, and Grid Detection; Contour Detection; Feature Matching; WaterShed Algorithm; Face Detection; Object Tracking; Optical Flow; Deep Learning with Keras; Keras and Convolutional Networks; Customized Deep Learning Networks; State of the Art YOLO Networks; and much more! After we get a set of matched bounding boxes for the same object category: Then he joined a Computer Vision startup (iLenze) as a core team member and worked on image retrieval, object detection, automated tagging and pattern matching problems for the fashion and furniture industry. Bekijk deze video op www.youtube.com of schakel JavaScript in als dit is uitgeschakeld in je browser. In tests, the dummies elicit a homogeneous distribution of the Radar Cross Section (RCS)—a measure of the detectability of an object by radar—with the RCS values remaining relatively constant from different views. Fig. Typically, there are three steps in an object detection framework. Based on the framework of Faster R-CNN, it added a third branch for predicting an object mask in parallel with the existing branches for classification and localization. 5: Input and output for object detection and localization problems. The right one k=1000 outputs a coarser-grained segmentation where regions tend to be larger. Cloud object storage is a format for storing unstructured data in the cloud . 4. Manu Ginobili in 2004 with hair. The plot of smooth L1 loss, $$y = L_1^\text{smooth}(x)$$. Radar was originally developed to detect enemy aircraft during World War II, but it is now widely used in everything from police speed-detector guns to weather forecasting. A segmentation solution $$S$$ is a partition of $$V$$ into multiple connected components, $$\{C\}$$. Given a predicted bounding box coordinate $$\mathbf{p} = (p_x, p_y, p_w, p_h)$$ (center coordinate, width, height) and its corresponding ground truth box coordinates $$\mathbf{g} = (g_x, g_y, g_w, g_h)$$ , the regressor is configured to learn scale-invariant transformation between two centers and log-scale transformation between widths and heights. Next, we will cover some interesting applications and concepts like Face Detection, Image Recognition, Object Detection and Facial Landmark Detection. Applications. But what if a simple computer algorithm could locate your keys in a matter of milliseconds? “Rich feature hierarchies for accurate object detection and semantic segmentation.” In Proc. The key point is to decouple the classification and the pixel-level mask prediction tasks. •namedWindow is used for viewing images. Vaibhaw currently works as an independent Computer Vision consultant. (Image source: link). So when the sunlight falls upon the object, then the amount of light reflected by that object is sensed by the sensors, and a continuous voltage signal is generated by the amount of sensed data. Non-max suppression helps avoid repeated detection of the same instance. The Part 1 introduces the concept of Gradient Vectors, the HOG (Histogram of Oriented Gradients) algorithm, and Selective Search for image segmentation. object-detection  Object Recognition has recently become one of the most exciting fields in computer vision and AI. Fig. Predicted probability of anchor i being an object. To motivate myself to look into the maths behind object recognition and detection algorithms, I’m writing a few posts on this topic “Object Detection for Dummies”. 1. Given two regions $$(r_i, r_j)$$, selective search proposed four complementary similarity measures: By (i) tuning the threshold $$k$$ in Felzenszwalb and Huttenlocher’s algorithm, (ii) changing the color space and (iii) picking different combinations of similarity metrics, we can produce a diverse set of Selective Search strategies. feature descriptor. As one would imagine, in order to predict whether an image is a type of object, we need the network to be able to recognize higher level features such as hands or paws or ears. It is built on top of the image segmentation output and use region-based characteristics (NOTE: not just attributes of a single pixel) to do a bottom-up hierarchical grouping. 6. About 4 years go I finished my PhD research at the University of Ghent (Belgium), where I was mainly working on computer vision and intelligent video processing (object detection and tracking, classification, segmentation, etc. Fig. journal of computer vision 59.2 (2004): 167-181. # the transformation (G_x + 255) / 2. Segmentation (right): we have the information at the pixel level. Given $$G=(V, E)$$ and $$|V|=n, |E|=m$$: If you are interested in the proof of the segmentation properties and why it always exists, please refer to the paper. If $$v_i$$ and $$v_j$$ belong to the same component, do nothing and thus $$S^k = S^{k-1}$$. — Page ix, Programming Computer Vision with Python, 2012. The system is able to identify different objects in the image with incredible acc… (Image source: Manu Ginobili’s bald spot through the years). While there is any remaining bounding box, repeat the following: In contrast to this, object localization refers to identifying the location of an object in the image. black to white on a grayscale image). Discrete probability distribution (per RoI) over K + 1 classes: $$p = (p_0, \dots, p_K)$$, computed by a softmax over the K + 1 outputs of a fully connected layer. Imagine trying to land a jumbo jet the size of a large building on a short strip of tarmac, in the middle of a city, in the depth of the night, in thick fog. Here, only a predicted box with a nearby ground truth box with at least 0.6 IoU is kept for training the bbox regression model. [Part 4]. All the transformation functions take $$\mathbf{p}$$ as input. The first step in computer vision—feature extraction—is the process of detecting key points in the image and obtaining meaningful information about them. ], “Rich feature hierarchies for accurate object detection and semantic segmentation.”, “Faster R-CNN: Towards real-time object detection with region proposal networks.”, “You only look once: Unified, real-time object detection.”, “A Brief History of CNNs in Image Segmentation: From R-CNN to Mask R-CNN”, https://github.com/rbgirshick/py-faster-rcnn/files/764206/SmoothL1Loss.1.pdf, ← Object Detection for Dummies Part 2: CNN, DPM and Overfeat, The Multi-Armed Bandit Problem and Its Solutions →. Fig. Yann LeCun provided the first practical demonstration to read “handwritten” digits. Computer vision is distinct from image processing. Object Detection: Locate the presence of objects with a bounding box and types or classes of the located objects in an image. How Fast R-CNN works is summarized as follows; many steps are same as in R-CNN: The model is optimized for a loss combining two tasks (classification + localization): The loss function sums up the cost of classification and bounding box prediction: $$\mathcal{L} = \mathcal{L}_\text{cls} + \mathcal{L}_\text{box}$$. That most area is in gray car in the corner of the most similar regions ( step )!: Anomalies only occur very rarely in the image Ducky and Barry are images! A subset of regions in an image two objects, for an to. Together, and others the smooth L1 loss, \ ( S^k\ ) a. For computation algorithms lay the foundation for detection 2014 ) is denoted as \ ( {... Propagation through the years ) ( e.g: this detection method is based on the photo Manu! Networks ( R-CNN ), and height ), and Ali Farhadi about them accuracy. However, the work begins object detection for dummies a new method called RoIAlign, which can represent fractions of continuous. 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text:
# Boundary defining functions for hyperbolic surfaces

Let $M$ be a geometrically finite hyperbolic surface with one cuspidal end and one funnel end so that it can be divided into $C \cup K \cup F$ where $C$ is the cusp, $F$ the funnel and $K$ the compact core.

Focus on the cusp with the following boundary defining function (due to David Borthwick: Spectral Theory of Infinite-Area Hyperbolic Surfaces)

Let $\rho (x)=e^{-r}$ where $r$ is the distance of $x$ to the compact core $K$. As a boundary defining function it needs to have a non-vanishing differential on the boundary. How can this fact be seen for this function?

If I take the look back to the upper half plane the hyperbolic distance for distinct points $a$ and $b$ located on the y-axis is given by $log(a/b)$. I suppose that's the reason for choosing $e^{-r}$. If you take a point $c$ at the boundary its distance to the compact core is infinite, so $e^{-r(c)}$ is zero, clearly. But what's with the differential? Is there a direct way of calculating it in this case with the given information? I don't understand why is it not zero at the boundary.

In a discussion with others there was the idea to show it by relating the the boundary defining function for the cusp to a (maybe given) boundary defining function for a funnel end by 'inverting', precisely:

Here $M = (0, \infty) \times S^1$ with the metric $g=(dx^2+d\theta^2)/x^2$ where the variable $x$ refers to $(0,\infty)$ and $x$ itself is a boundary defining for the funnel end. If $x$ is bdf for the funnel, is it true that then 1/x is a boundary defining function for the cusp?

My problem is the absence of a diffeomorphism from the cusp (as a point) to the funnel (which is a circle). Can this be repaired by viewing the cusp as a 'infinitely' small circle? The strategy I have in mind is: If there would be a diffeomorphism between the ends and given a boundary defining function for the funnel then the pullback of it has non-vanishing differential.

Since this is my first question on MO, I hope my explanations were precise enough and the questions aren't too basic.

Thank you for your help, Robin Neumann

-

format: plain


text:
# reference overlay numbers with names

I have two-column slides where there is a tikz figure on the left, and itemization on the right. There is >10 overlays due to pauses in the itemization, and some pieces of the tikz picture are added/removed/modified accordingly (with \only<>) as are the items uncovered.

It is easy to break the code by adding one \pause, because all numbers have to be rewritten.

Is there a way (no hint in Beamer Manual, chap. 9) to assign the value of beamerpause counter to symbolic names, at the point when that part gets uncovered for the first time, something like (needs multiple passes to be resolved) the following?

\begin{column}{..}
\only</bar->{...}  % <2-> (use e.g. / to reference labels)
\only<-/baz>{...}  % <-3>
\end{column}
\begin{column{..}
\begin{itemize}
\item foo \pause
\item bar \firstUncoveredLabel{bar}\pause % assign 2 to label /bar
\item baz \pause[baz]       % nicer syntax; assign 3 to label /baz
\item end
\end{itemize}
\end{column}

EDIT: minimal working example:

\documentclass{beamer}
\usepackage{tikz}
\begin{document}
\begin{frame}
\begin{columns}
\begin{column}{.5\textwidth}
\tikz{
\draw< -3>        (0,0) grid (3,3);
\draw<2-3>[red]   (0,0) -- (3,1);
\draw<3- >[green] (0,0) -- (3,2);
\draw<4  >[blue]  (0,0) -- (3,3);
}
\end{column}
\begin{column}{.5\textwidth}
\begin{itemize}
%%%% uncomment this item and all numbers above have to be shifted :-(
% \item important remark at the beginning \pause
\item grid \pause
\item grid, red \pause
\item grid, red, green \pause
\item green, blue
\end{itemize}
\end{column}
\end{columns}
\end{frame}
\end{document}

and this is what I dream of (does not compile):

\documentclass{beamer}
\usepackage{tikz}
\begin{document}
\begin{frame}
\begin{columns}
\begin{column}{.5\textwidth}
\tikz{
%% use symbolic names for overlay specificaiton
\draw<-/gridRedGreen>                (0,0) grid (3,3);
\draw</gridRed-/gridRedGreen>[red]   (0,0) -- (3,1);
\draw</gridRedGreen->        [green] (0,0) -- (3,2);
\draw</last>                 [blue]  (0,0) -- (3,3);
}
\end{column}
\begin{column}{.5\textwidth}
\begin{itemize}
%%%% uncomment and overlays are still correct :-)
% \item important remark at the beginning \pause
\item grid                \pause[grid]
\item grid, red           \pause[gridRed]
\item grid, red, green    \pause[gridRedGreen]
\item green, blue
\end{itemize}
\end{column}
\end{columns}
\end{frame}
\end{document}

-

Here's a possible way to reference overlays by name:

\makeatletter
\newcommand*{\pauseentry}[3]{\global\@namedef{pauses@#1@#2}{#3}}
\makeatother

Include this code somewhere into the preamble of your document, i. e. between \documentclass{beamer} and \begin{document}. It defines two userlevel commands, \savepause and \usepause:

• \savepause{overlayname} saves the current value of the counter beamerpauses as overlayname. Issue it immediatly before the \pause command.
• \usepause{overlayname} refers to the previously saved value of overlayname, so if you e.g. used \savepause{overlayname} on the third overlay, \usepause{overlayname} will expand to 3.

As the values will be saved to the auxiliary file, this needs at least two LaTeX runs to produce a stable output.

You can't use the syntax \pause[overlayname] to save the value as you suggested because the optional argument is already used by beamer itself. However, you can define your own command for convenience:

\newcommand*{\mypause}[1]{\savepause{#1}\pause}

which would be used like \mypause{overlayname}.

### Example code:

\documentclass{beamer}
\makeatletter
\newcommand*{\pauseentry}[3]{\global\@namedef{pauses@#1@#2}{#3}}
\makeatother
\usepackage{tikz}
\begin{document}
\begin{frame}
\begin{columns}
\begin{column}{.5\textwidth}
\tikz{
%% use symbolic names for overlay specificaiton
\draw<-\usepause{gridRedGreen}>                (0,0) grid (3,3);
\draw<\usepause{gridRed}-\usepause{gridRedGreen}>[red]   (0,0) -- (3,1);
\draw<\usepause{gridRedGreen}->        [green] (0,0) -- (3,2);
\draw<\usepause{last}>                 [blue]  (0,0) -- (3,3);
}
\end{column}
\begin{column}{.5\textwidth}
\begin{itemize}
%%%% uncommented and overlays are still correct :-)
\item important remark at the beginning \pause
\item grid                \savepause{grid}\pause
\item grid, red           \savepause{gridRed}\pause
\item grid, red, green    \savepause{gridRedGreen}\pause
\item green, blue
\end{itemize}
\end{column}
\end{columns}
\savepause{last}
\end{frame}
\end{document}

### Output after two LaTeX runs (click on the image to see it full size):

-
Very nice and usable. I tried to remove the \pauses from your example using [<+->] as an argument to the enumeration instead. Now the reference always points a frame too late. As I did not completely understand the effects of many commands in your solution, I failed to decrement he value before saving. Can you think of a way to use \item<+-> Lorem ipsum \savepause{a} so that something marked with \usepause{a} will show up exactly at the same time the item does? –  XZS Oct 25 '13 at 14:02
@XZS The problem with [<+->] is that the counter beamerpauses is increased at the beginning of the \item and not at the end. Unfortunately I can't think of a way to detect this automatically, but but I can offer you a workaround: Replace the definition of \savepause above by \DeclareRobustCommand*{\savepause}[2][0]{\only<1>{\advance\c@beamerpauses by#1\relax\immediate\write\@auxout{\string\pauseentry{\the\c@framenumber}{#2}{\the\c@beamerpauses}}\advance\c@beamerpauses by-#1\relax}} and use \savepause[-1]{a} in the itemize environment, like this will refer to the correct overlay. –  diabonas Oct 25 '13 at 14:54
Very handy. Could the optional offset also be applied to the \usepause command? Then, one could write \usepause[2]{grid} as equivalent to \usepause{gridRedGreen} to make ranges more intuitive. –  XZS Oct 25 '13 at 15:32
@XZS Sure, you can define \def\usepauseoffset[#1]#2{\number\numexpr\usepause{#2}+#1\relax} to be used like \usepauseoffset[2]{grid}`. The different name is necessary as normal macros with an optional argument unfortunately don't work in overlay specifications due to the way beamer internally processes them. –  diabonas Oct 25 '13 at 18:07


text:
# Unknown reference error

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Joined: 10/13/2009 - 23:50
Unknown reference error

Hi All,

This is related to an earlier post where I've tried adding covariates to a saturated model:

I've followed Mike Neale's advice and set up a definition variables matrix (pre-multiplied by beta) instead of coding it effectively longhand. I'm having a problem though. The model runs ok in the first instance, but when I try to place some constraints, it returns an error message that I don't know how to resolve (see Model 1 below and the output that follows).

Can someone spot what's wrong? I'm assuming because I've embedded the beta matrix within the main model somethings choking.

Mikes way of setting up a def vars matrix is certainly more elegant and the output is more compact and easier to read. Interestingly, both ways I did it gave identical estimates, but the backend time (if that's the main indicator of speed) was more with the def vars matrix method (2:30 vs 3:30 mins).

The following code is just for the MZF subgroup (removed the others for now):

Vars <- c('VarR','VarL')
nv <- 2
selVars <- paste(Vars,c(rep(1,nv),rep(2,nv)),sep="_")
ntv <- nv*2

defVars <- c('Age_1', 'Age_2', 'Sex_1', 'Sex_2')

right <- c(1,3)
left <- c(2,4)
meanSV <- c(0,0)
cholSV <- c(
0.5,0,0,0,
0.5,0,0,
0.5,0,
0.5)

multiTwinSatModel <- mxModel("multiTwinSat",

mxMatrix( type="Full", nrow=1, ncol=2, free=TRUE, values= 0, label=c("betaAge","betaSex"), name="beta"),

mxModel("MZF",
mxMatrix( type="Lower", nrow=ntv, ncol=ntv, free=TRUE, values=cholSV,name="CholMZF" ),
mxAlgebra( expression=CholMZF %*% t(CholMZF), name="expCovMZF" ),
mxData( observed=mzfData, type="raw" ),
mxMatrix( type="Full", nrow=1, ncol=4, free=TRUE, values=0, name="expMeanMZFa" ),#Define a means matrix (1 x 4) to allow seperate means for Twin1R, Twin1L, Twin2R and Twin2L in that order.
mxMatrix( type="Full", nrow=2, ncol=4, free=F, label=c("data.Age_1","data.Sex_1","data.Age_1","data.Sex_1","data.Age_2","data.Sex_2","data.Age_2","data.Sex_2"),name="MZFDefVars"),#Define a definition variables matrix of this format:

# Twin 1R   Twin 1L Twin 2R Twin 2L
# Age 1     Age 1   Age 2   Age 2
# Sex 1     Sex 1   Sex 2   Sex 2

mxAlgebra(expression=multiTwinSat.beta %*% MZFDefVars,name='MZFDefVars2'),# Multiplying the beta matrix by the definition variables matrix will give a (1 x 4) result matrix for the effect of all betas where the first element is added to the mean of Twin1R, the second element to the mean of Twin1L etc, as follows:

mxAlgebra(expression = cbind((expMeanMZFa[,1] + MZFDefVars2[,1]),(expMeanMZFa[,2] + MZFDefVars2[,2]),(expMeanMZFa[,3] + MZFDefVars2[,3]),(expMeanMZFa[,4] + MZFDefVars2[,4])),name='expMeanMZF'),

mxFIMLObjective( covariance="expCovMZF", means="expMeanMZF", dimnames=selVars ),

# Algebra's needed for equality constraints
mxAlgebra( expression=expMeanMZF[1,1], name="expMeanMZFRt1"),
mxAlgebra( expression=expMeanMZF[1,nv2], name="expMeanMZFLt1"),
mxAlgebra( expression=expMeanMZF[1,nv3], name="expMeanMZFRt2"),
mxAlgebra( expression=expMeanMZF[1,nv4], name="expMeanMZFLt2")
),

mxAlgebra( MZF.objective, name="2sumll" ),
mxAlgebraObjective("2sumll")

)

multiTwinSatFit <- mxRun(multiTwinSatModel)
multiTwinSatSumm <- summary(multiTwinSatFit)
multiTwinSatSumm

> # Generate Saturated Output
> # -----------------------------------------------------------------------
> parameterSpecifications(multiTwinSatFit)
model:multiTwinSat, matrix:beta
[,1] [,2]
[1,] [betaAge] [betaSex]

model:MZF, matrix:CholMZF
[,1] [,2] [,3] [,4]
[1,] [NA] 0 0 0
[2,] [NA] [NA] 0 0
[3,] [NA] [NA] [NA] 0
[4,] [NA] [NA] [NA] [NA]

model:MZF, matrix:expMeanMZFa
[,1] [,2] [,3] [,4]
[1,] [NA] [NA] [NA] [NA]

model:MZF, matrix:MZFDefVars
[,1] [,2] [,3] [,4]
[1,] 80 80 80 80
[2,] 1 1 1 1

> expectedMeansCovariances(multiTwinSatFit)
model:MZF, covariance:expCovMZF
VarR_1 VarL_1 VarR_2 VarL_2
VarR_1 0.4936132 0.2285718 0.1626295 0.2029106
VarL_1 0.2285718 0.4649452 0.1489156 0.1649522
VarR_2 0.1626295 0.1489156 0.4303675 0.1830401
VarL_2 0.2029106 0.1649522 0.1830401 0.4320097

model:MZF, means:expMeanMZF
VarR_1 VarL_1 VarR_2 VarL_2
[1,] 0.9084736 0.8949734 0.8607368 0.8776677

> tableFitStatistics(multiTwinSatFit)
Name ep -2LL df AIC
Model 1 : multiTwinSat 16 1780.86 944 -107.14

# -----------------------------------------------------------------------

equateMeansRLModel <- mxModel(multiTwinSatFit, name="equateMeansRL",
mxConstraint(MZF.expMeanMZFRt1 == MZF.expMeanMZFLt1, name="MeanMZFt1R_L"),
mxConstraint(MZF.expMeanMZFRt2 == MZF.expMeanMZFLt2, name="MeanMZFt2R_L")

)
equateMeansRLFit <- mxRun(equateMeansRLModel)
equateMeansRLSumm <- summary(equateMeansRLFit)
equateMeansRLSumm
expectedMeansCovariances(equateMeansRLFit)
tableFitStatistics(multiTwinSatFit, equateMeansRLFit)

> equateMeansRLFit <- mxRun(equateMeansRLModel)
Running equateMeansRL
Error: Unknown reference 'multiTwinSat.beta' detected in the entity 'MZFDefVars2' in model 'MZF'

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Joined: 07/31/2009 - 15:24
Ah, I see the problem. The

Ah, I see the problem. The model 'multiTwinSatFit' was copied to equateMeansRLModel and the name was changed to "equateMeansRL". But the mxModel() function does not change any internal references when the model name is changed. Use the following command to copy the model and assign it a new name with all the references altered:

equateMeansRLModel <- mxRename(multiTwinSatFit, "equateMeansRL")

Then you can add constraints with equateMeansRLModel <- mxModel(equateMeansRLModel, mxConstraint(), mxConstraint()) and it should work.

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Joined: 10/13/2009 - 23:50
Thanks Michael, I copied what

Thanks Michael,

I copied what you suggested and get:

> equateMeansRLModel <- mxRename(multiTwinSatFit, "equateMeansRL")
Error in as.symbol(renameReference(as.character(symbol), oldname, newname)) :
attempt to use zero-length variable name

I tried playing around with the function but am not having any luck.

Paul

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Joined: 07/31/2009 - 15:24
Oops. We never tested the

Oops. We never tested the mxRename() function in a model that contains an empty symbol. The empty symbol is how R encodes expressions of the form: mxAlgebra(foo[,2]). The row parameter to the matrix subscript is the empty symbol or the missing symbol or whatever the R people want to call it. I'll check in a patch so that mxRename() works in these cases for the next binary release. In the meantime, you should add the constraints to the new model but don't rename the model. Or alternatively you could rename the model using mxModel() but then you have to manually update the algebras.

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Joined: 10/13/2009 - 23:50
Thanks Michael, “In the

Thanks Michael,

“In the meantime, you should add the constraints to the new model but don't rename the model. Or alternatively you could rename the model using mxModel() but then you have to manually update the algebras.”

Sorry to be a pain, but I don't really understand wither of these options. For (a), I have to add the constraints to the fit of the previous model, don't I?

Otherwise, will the next binary be released soon?

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Joined: 07/31/2009 - 14:25
> Sorry to be a pain, but I

> Sorry to be a pain, but I don't really understand wither of these options.
> For (a), I have to add the constraints to the fit of the previous model, don't I?
You are right: you want to constrain the previous model, but what michael is saying is that the name is just cosmetic, so if you don't change the name, you can still constrain the old model. And that way you won't break its internal algebras which are hard-coded. So concretely... instead of
equateMeansRLModel <- mxModel(multiTwinSatFit, name="equateMeansRL",...
just say
equateMeansRLModel <- mxModel(multiTwinSatFit, ...

The most robust way to handle this is to wrap insulate your named algebras from name changes by placing them in their ownsub-model. Then you can change the name of the outer container to your heart's content.

mxAlgebra(multiTwinSat.beta %% MZFDefVars,name='MZFDefVars2'),
you would say
mxAlgebra(top.beta %
% MZFDefVars,name='MZFDefVars2'),

The new group would fit in like this:
multiTwinSatModel <- mxModel("multiTwinSat",
mxModel("top",
mxMatrix("Full", nrow=1, ncol=2, free=TRUE, values= 0, label=c("betaAge","betaSex"), name="beta")
)
mxModel("MZF",
mxMatrix(type="Lower", nrow=ntv, ncol=ntv, free=TRUE, values=cholSV,name="CholMZF" ),
mxAlgebra(CholMZF %% t(CholMZF), name="expCovMZF" ),
mxData(mzfData, type="raw" ),
mxMatrix(type="Full", nrow=1, ncol=4, free=TRUE, values=0, name="expMeanMZFa" ),
mxMatrix(type="Full", nrow=2, ncol=4, free=F, label=c("data.Age_1","data.Sex_1","data.Age_1","data.Sex_1","data.Age_2","data.Sex_2","data.Age_2","data.Sex_2"),name="MZFDefVars"),
mxAlgebra(top.beta %
% MZFDefVars,name='MZFDefVars2'),
mxAlgebra(cbind((expMeanMZFa[,1] + MZFDefVars2[,1]),(expMeanMZFa[,2] + MZFDefVars2[,2]),(expMeanMZFa[,3] + MZFDefVars2[,3]),(expMeanMZFa[,4] + MZFDefVars2[,4])),name='expMeanMZF'),
mxFIMLObjective( covariance="expCovMZF", means="expMeanMZF", dimnames=selVars ),
# Algebra's needed for equality constraints
mxAlgebra(expMeanMZF[1,1] , name="expMeanMZFRt1"),
mxAlgebra(expMeanMZF[1,nv2], name="expMeanMZFLt1"),
mxAlgebra(expMeanMZF[1,nv3], name="expMeanMZFRt2"),
mxAlgebra(expMeanMZF[1,nv4], name="expMeanMZFLt2")
),
mxAlgebra( MZF.objective, name="2sumll" ),
mxAlgebraObjective("2sumll")
)
multiTwinSatFit <- mxRun(multiTwinSatModel)

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Joined: 10/13/2009 - 23:50
Hi Tim, Thanks for explaining

Hi Tim,

Thanks for explaining - I appreciate your help.

I did what you said in terms of creating a seperate model for the beta matrix under the main model.

It runs fine and gives identical estimates to previous.

I then deleted the reference to a new name for the constraint model, however, now I get this error:

> equateMeansRLFit <- mxRun(equateMeansRLModel)
Running multiTwinSat
Error: The left hand side of constraint 'MeanMZFt1R_L' in model 'multiTwinSat' generated the error message: subscript out of bounds

Any ideas?

Thanks again.

Offline
Joined: 07/31/2009 - 14:25
I would go back to the old

I would go back to the old script and just not change the name... then things will work.

What has happened is you have begun to go down the route I suggested to avoid the hassle associated with renaming models but only part way: There are still other elements that need to be moved into that "top" group or have the reference to them renamed to work. Probably you have something like "multiTwinSat.beta" in the model, which now isn't working...

So the constraint in question is
mxConstraint(MZF.expMeanMZFRt1 == MZF.expMeanMZFLt1, name="MeanMZFt1R_L")

the left hand side is an algebra

mxAlgebra( expression=expMeanMZF[1,1], name="expMeanMZFRt1")

Somewhere along the line something has gone wrong in assembling expMeanMZF. You can track back (not having the script in front of me) how expMeanMZF is being created and where the error has been introduced.

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Joined: 10/13/2009 - 23:50
OK - Thanks Tim

OK - Thanks Tim


text:
• Corpus ID: 232092991

# Challenges and Opportunities in High-dimensional Variational Inference

@inproceedings{Dhaka2021ChallengesAO,
title={Challenges and Opportunities in High-dimensional Variational Inference},
author={Akash Kumar Dhaka and Alejandro Catalina and Manushi K. V. Welandawe and Michael Riis Andersen and Jonathan Huggins and Aki Vehtari},
booktitle={NeurIPS},
year={2021}
}
• Published in NeurIPS 1 March 2021
• Computer Science
Current black-box variational inference (BBVI) methods require the user to make numerous design choices—such as the selection of variational objective and approximating family—yet there is little principled guidance on how to do so. We develop a conceptual framework and set of experimental tools to understand the effects of these choices, which we leverage to propose best practices for max-imizing posterior approximation accuracy. Our approach is based on studying the pre-asymptotic tail…

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Variational Inference with Normalizing Flows
• Computer Science, Mathematics
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• 2015
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Robust, Accurate Stochastic Optimization for Variational Inference
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NeurIPS
• 2020
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Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimization
• Computer Science
NeurIPS
• 2020
This paper postulates that black-box VI is best addressed through a careful combination of numerous algorithmic components, and evaluates components relating to optimization, flows, and Monte-Carlo methods on a benchmark of 30 models from the Stan model library.
• Computer Science
NeurIPS
• 2018
A new class of tail-adaptive f-divergences that adaptively change the convex function f with the tail of the importance weights, in a way that theoretically guarantee finite moments, while simultaneously achieving mass-covering properties is proposed.
Perturbative Black Box Variational Inference
• Computer Science
NIPS
• 2017
This paper views BBVI with generalized divergences as a form of estimating the marginal likelihood via biased importance sampling, and builds a family of new variational bounds that captures the standard KL bound for $K=1, and converges to the exact marginal likelihood as$K\to\infty\$.
Validated Variational Inference via Practical Posterior Error Bounds
• Computer Science
AISTATS
• 2020
This paper provides rigorous bounds on the error of posterior mean and uncertainty estimates that arise from full-distribution approximations, as in variational inference.
Variational Inference: A Review for Statisticians
• Computer Science
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• 2016
Variational inference (VI), a method from machine learning that approximates probability densities through optimization, is reviewed and a variant that uses stochastic optimization to scale up to massive data is derived.
Empirical Evaluation of Biased Methods for Alpha Divergence Minimization
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• 2021
Empirically evaluate biased methods for alpha-divergence minimization and empirically show that weight degeneracy does indeed occur with these estimators in cases where they return highly biased solutions, relating these results to the curse of dimensionality.
Markovian Score Climbing: Variational Inference with KL(p||q)
• Computer Science
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This paper develops a simple algorithm for reliably minimizing the inclusive KL, and provides a new algorithm that melds VI and MCMC, and demonstrates the utility of MSC on Bayesian probit regression for classification as well as a stochastic volatility model for financial data.
Gaussian Variational Approximation With a Factor Covariance Structure
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Journal of Computational and Graphical Statistics
• 2018
General stochastic gradient ascent methods are described for efficient implementation, with gradient estimates obtained using the so-called “reparameterization trick” the end result is a flexible and efficient approach to high-dimensional Gaussian variational approximation.


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 Vladikavkaz. Mat. Zh.: Year: Volume: Issue: Page: Find

 Vladikavkaz. Mat. Zh., 2018, Volume 20, Number 3, Pages 48–56 (Mi vmj664)

The commutant of the Pommiez operator in a space of entire functions of exponential type and polynomial growth on the real line

O. A. Ivanovaa, S. N. Melikhovab

a Southern Federal University, 8a Mil'chakova st., Rostov-on-Don 344090, Russia
b Southern Mathematical Institute VSC RAS, 22 Marcus st., Vladikavkaz 362027, Russia

Abstract: In the space of entire functions of exponential type representing a strong dual to a Frechet space of infinitely differentiable functions on a real interval containing the origin, linear continuous operators commuting with the Pommiez operator are investigated. They are given by a continuous linear functional on this space of entire functions and hence, up to the adjoint of the Fourier–Laplace transform, by an infinite differentiable function on the initial interval. A complete characterization of linear continuous functionals defining isomorphisms by virtue of the indicated correspondence is given. It is proved that isomorphisms are determined by functions that do not vanish at the origin (and only by them). An essential role in proving the corresponding criterion is played by a method exploiting the theory of compact operators in Banach spaces. The class of those functions infinitely differentiable on the considered interval that define the operators from the mentioned commutant close to isomorphisms is distinguished. Such operators have finite-dimensional kernels. For an interval other than a straight real line, we also define the class of operators from the commutant of the Pommiez operator that are not surjective. The adjoint of a continuous linear operator that commutes with Pommiez operators is realized in the space of infinitely differentiable functions as an operator obtained by fixing one factor in the Duhamel product. The essential difference of the situation under consideration from the previously studied one is the absence of cyclic vectors of the Pommiez operator in the considered space of entire functions.

Key words: Pommiez operator, entire function of exponential type, space of infinitely differentiable functions, commutant, isomorphism.

DOI: https://doi.org/10.23671/VNC.2018.3.17988

Full text: PDF file (272 kB)
References: PDF file   HTML file

UDC: 517.9
MSC: 46E10, 30D15, 47L10, 26E10

Citation: O. A. Ivanova, S. N. Melikhov, “The commutant of the Pommiez operator in a space of entire functions of exponential type and polynomial growth on the real line”, Vladikavkaz. Mat. Zh., 20:3 (2018), 48–56

Citation in format AMSBIB
\Bibitem{IvaMel18} \by O.~A.~Ivanova, S.~N.~Melikhov \paper The commutant of the Pommiez operator in a space of entire functions of exponential type and polynomial growth on the real line \jour Vladikavkaz. Mat. Zh. \yr 2018 \vol 20 \issue 3 \pages 48--56 \mathnet{http://mi.mathnet.ru/vmj664} \crossref{https://doi.org/10.23671/VNC.2018.3.17988}


text:
## Category: Functional analysis

### New paper “Compressions of compact tuples”, and announcement of mistake (and correction) in old paper “Dilations, inclusions of matrix convex sets, and completely positive maps”

Ben Passer and I have recently uploaded our preprint “Compressions of compact tuples” to the arxiv. In this paper we continue to study matrix ranges, and in particular matrix ranges of compact tuples. Recall that the matrix range of a tuple $A = (A_1, \ldots, A_d) \in B(H)^d$ is the the free set $\mathcal{W}(A) = \sqcup_{n=1}^\infty \mathcal{W}_n(A)$, where

$\mathcal{W}_n(A) = \{(\phi(A_1), \ldots, \phi(A_d)) : \phi : B(H) \to M_n$ is UCP $\}$.

A tuple $A$ is said to be minimal if there is no proper reducing subspace $G \subset H$ such that $\mathcal{W}(P_G A\big|_G) = \mathcal{W}(A)$. It is said to be fully compressed if there is no proper subspace whatsoever $G \subset H$ such that $\mathcal{W}(P_G A\big|_G) = \mathcal{W}(A)$.

In an earlier paper (“Dilations, inclusions of matrix convex sets, and completely positive maps”) I wrote with other co-authors, we claimed that if two compact tuples $A$ and $B$ are minimal and have the same matrix range, then $A$ is unitarily equivalent to $B$; see Section 6 there (the printed version corresponds to version 2 of the paper on arxiv). This is false, as subsequent examples by Ben Passer showed (see this paper). A couple of other statements in that section are also incorrect, most obviously the claim that every compact tuple can be compressed to a minimal compact tuple with the same matrix range. All the problems with Section 6 of that earlier paper “Dilations,…” can be quickly  fixed by throwing in a “non-singularity” assumption, and we posted a corrected version on the arxiv. (The results of Section 6 there do not affect the rest of the results in the paper, and are somewhat not in the direction of the main parts of that paper).

In the current paper, Ben and I take a closer look at the non-singularity assumption that was introduced in the corrected version of “Dilations,…”, and we give a complete characterization of non-singular tuples of compacts. This characterization involves the various kinds of extreme points of the matrix range $\mathcal{W}(A)$. We also make a serious invetigation into fully compressed tuples defined above. We find that a matrix tuple is fully compressed if and only if it is non-singular and minimal. Consequently, we get a clean statement of the classification theorem for compacts: if two tuples $A$ and $B$ of compacts are fully compressed, then they are unitarily equivalent if and only if $\mathcal{W}(A) = \mathcal{W}(B)$.

### The complex matrix cube problem (in “Summer Projects in Mathematics at the Technion”)

Next week I will participate as a mentor in the Technion’s Summer Projects in Mathematics. The project I offered is called “Numerical explorations of open problems from operator theory”, and it suggests three open problems in operator theory where theoretical progress seems to be stuck, and for which I believe that some computer experiments can help us get a feeling of what is going on. I also hope that thinking seriously about designing experiments can help us to understand some general facets of the theory.

I have been in contact with the students in the last few weeks and we decided to concentrate on “the matrix cube problem”. On Sunday, when the week begins, I will need to present the background to the project to all participants of this week, and I have seven minutes (!!) for this. As everybody knows, the shorter the presentation, the harder the task is, and the more preparation and thought it requires. So I will take use this blog to practice my little talk.

#### Introduction to the matrix cube problem

This project is in the theory of operator spaces. My purpose is to give you some kind of flavour of what the theory is about, and what we will do this week to contribute to our understanding of this theory.

### Souvenirs from the Red River

Last week I attended the annual Canadian Operator Symposium, better known in its nickname: COSY. This conference happens every year and travels between Canadian universities, and this time it was held in the University of Manitoba, in Winnipeg. It was organized by Raphaël Clouâtre and Nina Zorboska, who altogether did a great job.

My first discovery: Winnipeg is not that bad! In fact I loved it. Example: here is the view from the window of my room in the university residence:

Not bad, right? A very beautiful sight to wake up to in the morning. (I got the impression, that Winnipeg is nothing to look forward to, from Canadians. People of the world: don’t listen to Canadians when they say something bad about any place that just doesn’t quite live up to the standard of Montreal, Vancouver, or Banff.) Here is what you see if you look from the other side of the building:  Read the rest of this entry »

### Minimal and maximal matrix convex sets

The final version of the paper Minimal and maximal matrix convex sets, written by Ben Passer, Baruch Solel and myself, has recently appeared online. The publisher (Elsevier) sent us a link through which the official final version is downloadable, for anyone who clicks on the following link before May 26, 2018. Here is the link for the use of the public:

Of course, if you don’t click by May 26 – don’t panic! We always put our papers on the arXiv, and here is the link to that. Here is the abstract:

Abstract. For every convex body $K \subseteq \mathbb{R}^d$, there is a minimal matrix convex set $\mathcal{W}^{min}(K)$, and a maximal matrix convex set $\mathcal{W}^{max}(K)$, which have $K$ as their ground level. We aim to find the optimal constant $\theta(K)$ such that $\mathcal{W}^{max}(K) \subseteq \theta(K) \cdot \mathcal{W}^{min}(K)$. For example, if $\overline{\mathbb{B}}_{p,d}$ is the unit ball in $\mathbb{R}^d$ with the $p$-norm, then we find that

$\theta(\overline{\mathbb{B}}_{p,d}) = d^{1-|1/p-1/2|}$ .

This constant is sharp, and it is new for all $p \neq 2$. Moreover, for some sets $K$ we find a minimal set $L$ for which $\mathcal{W}^{max}(K) \subseteq \mathcal{W}^{min}(L)$. In particular, we obtain that a convex body $K$ satisfies $\mathcal{W}^{max}(K) = \mathcal{W}^{min}(K)$ only if $K$ is a simplex.

These problems relate to dilation theory, convex geometry, operator systems, and completely positive maps. For example, our results show that every $d$-tuple of self-adjoint contractions, can be dilated to a commuting family of self-adjoints, each of norm at most $\sqrt{d}$. We also introduce new explicit constructions of these (and other) dilations.

### “A toolkit for constructing dilations on Banach spaces”, by Fackler and Gluck

About a week ago an interesting preprint appeared on the arxiv: “A toolkit for constructing dilations on Banach spaces“, by Stephan Fackler and Jochen Gluck. I have been studying various aspects of dilations for some years, but I haven’t really given much thought to dilation theory in general classes of Banach spaces. This paper – which is very clearly organized and written – was very refreshing for me, and in it a very general framework for proving existence of dilations in classes of Banach spaces is presented. The paper also contains a nice overview of the literature, and I was surprised by learning also about old results in, and application of, dilation theory, which I was not aware of and perhaps I should have been. The purpose of this post is to record my first impression of this paper and to put down some links to the references, which I would like to study better at some point.  Read the rest of this entry »

### Tapioca on page 49

To my long camping vacation this year I took the book “Topological Vector Spaces” by Alex and Wendy Robertson. I “inherited” this book (together with a bunch of other classics) from an old friend after he officially decided to leave academic mathematics and go into high-tech. The book is a small and thin hard-cover, with pages of high quality that are starting to become a delicious cream color.

### A review of my book A First Course in Functional Analysis

A review for my book A First Course in Functional Analysis appeared in Zentralblatt Math – here is a link to the review. I am quite thankful that someone has read my book and bothered to write a review, and that zBMath publishes reviews. That’s all great. Now I have a few words to say about it. This is an opportunity for me to bring up the subject of my book and highlight some things worth highlighting.

I am not too happy about this review. It is not that it is a negative review – actually it has a rather kind air to it. However, I am somewhat disappointed in the information that the review contains, and I am not sure that it does the reader some service which the potential readers could not achieve by simply reading the table of contents and the preface to the book (it is easy to look inside the book in the Amazon page; of course, it is also easy to find a copy of the book online).

The reviewer correctly notices that one key feature of the book is the treatment of $L^2[a,b]$ as a completion of $C([a,b])$, and that this is used for applications in analysis. However, I would love it if a reviewer would point out to the fact that, although the idea of thinking about $L^2[a,b]$ as a completion space is not new, few (if any) have attempted to actually walk the extra mile and work with $L^2$ in this way (i.e., without requiring measure theory) all the way up to rigorous and significant applications in analysis. Moreover, it would be nice if my attempt was compared to other such attempts (if they exist), and I would like to hear opinions about whether my take is successful.

I am grateful that the reviewer reports on the extensive exercises (this is indeed, in my opinion, one of the pluses of new books in general and my book in particular), but there are a couple of other innovations that are certainly worth remarking on, and I hope that the next reviewer does not miss them. For example, is it a good idea to include a chapter on Hilbert function spaces in an introductory text to FA? (a colleague of mine told me that he would keep that out). Another example: I think that my chapter on applications of compact operators is quite special. This chapter has two halves: one on integral equations and one on functional equations. Now, the subject of integral equations is well trodden and takes a central place in some introductions to FA, and one might wonder whether anything new can be done here in terms of the organization and presentation of the material. So, I think it is worth remarking about whether or not my exposition has anything to add. The half on applications of compact operators to integral equations contains some beautiful and highly non-trivial material that has never appeared in a book before, not to mention that functional equations of any kind are rarely considered in introductions to FA; this may also be worth a comment.

### Introduction to von Neumann algebras, Lecture 7 (von Neumann algebras as dual spaces, various topologies)

Until this point in the course, we concentrated on constructions of von Neumann algebras, examples, and properties of von Neumann algebras as algebras. In this lecture we turn to study subtler topological and Banach-space theoretic aspects of von Neumann algebras. We begin by showing that every von Neumann algebra is the Banach-space dual of a Banach space. For this to have any hope of being true, it must be true for the von Neumann algebra $B(H)$; we therefore look there first.

(The reference for this lecture is mostly Takesaki, Vol. I, Chapters 2 and 3).

### Introduction to von Neumann algebras, Lecture 6 (tensor products of Hilbert spaces and vN algebras; the GNS representation, the hyperfinite II_1 factor)

In this lecture we will introduce tensor products of Hilbert spaces. This construction is very useful for exhibiting various operators, and, in particular, it will enable us to introduce new von Neumann algebras. In particular, we will construct the so called hyperfinite $II_1$ factor.

### Introduction to von Neumann algebras, Lecture 5 (comparison of projections and classification into types of von Neumann algebras)

In the previous lecture we discussed the group von Neumann algebras, and we saw that they can never be isomorphic to $B(H)$. There is something fundamentally different about these algebras, and this was manifested by the existence of a trace. von Neumann algebras with traces are special, and the existence or non-existence of a trace can be used to classify von Neumann algebras, into rather broad “types”. In this lecture we will study the theory of Murray and von Neumann on the comparison of projections and the use of this theory to classify von Neumann algebras into “types”. We will also see how traces (or generalized traces) fit in. (For preparing these notes, I used Takesaki (Vol I) and Kadison-Ringrose (Vol. II).)

Most of the time we will stick to the assumption that all Hilbert spaces appearing are separable. This will only be needed at one or two spots (can you spot them?).

In addition to “Exercises”, I will start suggesting “Projects”. These projects might require investing a significant amount of time (a student is not expected to choose more than one project).


text:
According to the rules of special relativity, the speed of light is always the same in every system. Since the pulse energy is equal to the average power divided by the repetition rate, this goal can sometimes be satisfied by lowering the rate of pulses so that more energy can be built up in between pulses. In laser ablation for example, a small volume of material at the surface of a work piece can be evaporated if it is heated in a very short time, whereas supplying the energy gradually would allow for the heat to be absorbed into the bulk of the piece, never attaining a sufficiently high temperature at a particular point. Consider 1064 nm wavelength pulsed fiber laser, that can generate up to one million pulses per second. One of the most sacred laws of physics is that nothing can travel faster than the speed of light in vacuum. For the first time, researchers have taken a video of a pulse of laser light as it moves in three dimensions, using a camera with a shutter speed … [citation needed] Again, because of the extremely short pulse duration, such a laser will produce pulses which achieve an extremely high peak power. Pulsed operation of lasers refers to any laser not classified as continuous wave, so that the optical power appears in pulses of some duration at some repetition rate. When a high-intensity laser beam is incident on the surface of the material, the metal surface will be reflected by 60 to 98% of the laser energy and the … How to best clean a large historical corpus ridden with OCR errors, Etiquette for replying to eager HR acting as intermediary. Ultra high speed CCD cameras capture the motion of light. Thus such a gain medium must have a gain bandwidth sufficiently broad to amplify those frequencies. [2], https://en.wikipedia.org/w/index.php?title=Pulsed_laser&oldid=998048957, Articles with unsourced statements from November 2010, Creative Commons Attribution-ShareAlike License, This page was last edited on 3 January 2021, at 15:31. High speed laser diode driver with user-design nanosecond pulse shape This high speed laser diode driver can generate any programmable pulse shape with down to 500 picosecond and 48 dB dynamic range. Making statements based on opinion; back them up with references or personal experience. Why does this script running su never seem to terminate if I change user inside the script? Focusing such high-power laser pulses enables ones to have unprecedentedly strong laser intensity. The pulsed beam can be bounced off of a mirror and the return pulses detected by a very responsive (“fast”) detector. Frequency - Fig. The laser is a beam of light. What is this swastika looking symbol in John Hancock's family papers from circa 1762. The excitation pulse is provided by a 1550-nm pulsed ﬁber laser, and this is frequency doubled to 775 nm for our GaAs-based products. To learn more, see our tips on writing great answers. For example, if a pulsed laser welding process of a titanium part has welding parameters of pulse energy 2.0 Joules/pulse, pulse width 2 ms and pulse repetition 10 Hz, the average power of the laser welding process is equal to a lamp bulb at 20 Watts (2.0 J/pulse × 10 pulses/s = 20 Watts). Some lasers are pulsed simply because they cannot be run in continuous mode.. Researchers say it is the most convincing demonstration yet that the speed … In a Q-switched laser, the population inversion is allowed to build up by introducing loss inside the resonator which exceeds the gain of the medium; this can also be described as a reduction of the quality factor or 'Q' of the cavity. The laser intensity over 1019 W/cm2, which is called the relativistic laser intensity, can accelerate electrons almost to the speed of light. ... Four different XY speed … Thanks for contributing an answer to Physics Stack Exchange! Light travels at a speed roughly 3 x 10 8 meters/second (m/s). Does having several kids really mean I don't pay any federal taxes? How long does it take for a laser pulse to reach the Moon and to bounce back to the Earth? An example of a suitable material is titanium-doped, artificially grown sapphire (Ti:sapphire) which has a very wide gain bandwidth and can thus produce pulses of only a few femtoseconds duration. Hence, the length of the laser pulse is a direct measure of the applied gating time of 270 ps. Can we compress microsecond duration laser pulses by a factor of 1000? 6.3a and b. Schematic for laser stabilization by the technique of molecular saturated absorption. Use MathJax to format equations. Laser pulse travels 300 times faster than light. Pulsed operation of lasers refers to any laser not classified as continuous wave, so that the optical power appears in pulses of some duration at some repetition rate. In other cases the application requires … The pulse speed depends on the properties of the medium and not on the amplitude or pulse length of the pulse. 10.1), the maximum frequency drops for longer pump pulses and so depends on the accumulated pulse … Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Given, Distance (d) = 384403km Speed (s) = 3 x 10 8 m/s = 300000000 To Find, Time The Diode Pumped Solid State (DPSS) high-speed PIV laser system is the latest technology to provide high pulse energy at high pulse rate of 1000 Hz or higher. The motion of a 250 femtoseconds Laser pulse captured by the ICCD camera 4 Picos. [1] This encompasses a wide range of technologies addressing a number of different motivations. Space opera with large cat and discussion about infinite dimensions. Depending on the laser pulse duration, semiconductor quality and THz optical alignment, the optimum system reference may differ.While the laboratory-based system and laser pulse durations below 80 fs at the PCA allowed for spectroscopic investigations up to 4.5 THz (see Fig. Why do some people believe that humans are "bad at" generating random numbers/characters like this? 2000 Nature 406 277). Estimating quantum efficiency of gated avalanche photodiode, From power of a laser beam to electric field amplitude. Pulsed lasers are also used in soft-tissue surgery. The speed of the photons in the laser. And the shortest commercial speed can on the order of a few femtoseconds, so pulsed lasers are often use to measure ultra-fast physical processes. The laser must process 80 percent or more of the entire surface requiring high pulse rate and high scan speed. Other applications rely on the peak pulse power (rather than the energy in the pulse), especially in order to obtain nonlinear optical effects. Should I log users in if they enter valid login info in registration form? Diagram (a) shows the servo-controlled laser with an internal molecular absorption cell. The Large Variable Speed Pulse Laser is the largest of the Variable Speed Pulse Lasers in use. Another method of achieving pulsed laser operation is to pump the laser material with a source that is itself pulsed, either through electronic charging in the case of flash lamps, or another laser which is already pulsed. The experiment produces an almost identical light pulse that exits the chamber and travels about 60 feet before the main part of the laser pulse … Laser radars typically require 0.3 to 0.7 seconds sample time to get one speed reading. A mode-locked laser is capable of emitting extremely short pulses on the order of tens of picoseconds down to less than 10 femtoseconds. Which was the first story featuring mana as an energy source for magic? The optical bandwidth of a pulse cannot be narrower than the reciprocal of the pulse width. You can even manipulate by playing with pulse width and power of the laser system you have. rev 2021.2.5.38499, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Opt-in alpha test for a new Stacks editor, Visual design changes to the review queues. Laser pulse waveforms are an important issue in laser welding, especially for sheet welding. Pulsed pumping was historically used with dye lasers where the inverted population lifetime of a dye molecule was so short that a high energy, fast pump was needed. Is becoming an Amazon seller profitable? In the past 10 years, femtosecond lasers and amplifiers using ytterbium (Yb) have become available to meet evolving market needs in both the scientific and industrial sectors. Weighing almost as much as a Heavy PPC, the Large VSP Laser can inflict nearly as much damage on a target, and has a better chance of hitting the target.With these facts in mind, Word of Blake MechWarriors often use them when attacking targets in tight … How can my town be public knowledge while still keeping outsiders out? The Speed laser parameter describes the movement of the laser head. Pulsed Nd:YAG and Er:YAG lasers are used in laser tattoo removal and laser range finders among other applications. Pulsed pumping is also required for three-level lasers in which the lower energy level rapidly becomes highly populated preventing further lasing until those atoms relax to the ground state. IE: speed of light; Light moves at 299,792,458 meters per second (m/s). Such mode-locked lasers are a most versatile tool for researching processes occurring on extremely short time scales (known as femtosecond physics, femtosecond chemistry and ultrafast science), for maximizing the effect of nonlinearity in optical materials (e.g. Laser beam piercing a 3mm-thick material, we see an exaggerated Kerf angle of 1 deg and a kerf width of 0.25mm. Optical fiber typically has an index of refraction (n) of about 1.5. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The time it takes a pulse to travel at the speed of light from the lidar to the target and back is used to compute range. A high-speed camera can capture a 2D movie of the pulse’s position, but researchers have had trouble with the third dimension, depth—the distance between the pulse and the camera. When a very large number of laser modes that all have a “zero” in the same position interfere, the resultant superposition is an extremely narrow pulse. These pulses will repeat at the round trip time, that is, the time that it takes light to complete one round trip between the mirrors comprising the resonator. Some lasers are pulsed simply because they cannot be run in continuous mode. Pulse duration is known. The average distance between the moon's surface and the earth's surface is 384403 kilometers (km). Is it worth paying for a course? In more loosely-defined terms, it is an indicator of the amount of energy a laser pulse contains in comparison to its temporal duration, namely pulse width. As the name suggests, use laser output to continuous in time, the output of the pulse laser is discontinuous. Asking for help, clarification, or responding to other answers. Laser pulse overlapping is one of the least studied parameters involved in the production of nanoparticles by laser ablation confined in liquids. It only takes a minute to sign up. Laser Frequency Measurements, the Speed of Light, and the Meter 353 Amplifier Absorber I LOOP PlT FILTER DRIVER +-DET. Then, after the pump energy stored in the laser medium has approached the maximum possible level, the introduced loss mechanism (often an electro- or acousto-optical element) is rapidly removed (or that occurs by itself in a passive device), allowing lasing to begin which rapidly obtains the stored energy in the gain medium. : I know, that the speed of light in vacuum is 3*10^8 m/s. Its output has a <500-fs FWHM pulse duration. Is Seiryu Miharashi Station the only train station where passengers cannot enter or exit the platform? The change in range over time is used to calculate speed. Why triplets for whole movement rather than writing it in say 6/8? [2] Laser pulses must be spaced out to allow for efficient tissue cooling (thermal relaxation time) between pulses. The technique is the simple time-of-flight optical pulse delay method using a fairly short (nanosecond) optical pulse and an oscilloscope with bandwidth between 50 - 100 MHz. Using a 4.1MHz laser at a line scan speed of 60m/s results in a 14.5μm (1.750 dpi) spot spacing, and requires only 24s/layer. in second-harmonic generation, parametric down-conversion, optical parametric oscillators and the like) due to the large peak power, and in ablation applications. What sort of equipment allows for this? What is the appropriate length of an antenna for a handheld on 2 meters? Due to the Fourier limit (also known as energy-time uncertainty), a pulse of such short temporal length has a spectrum spread over a considerable bandwidth. + I rl REF. s − 1. The Laser Common low power laser pointers, typically emit at a wavelength of 650 nm and operate from two to four 1.5 V button cells. In the example shown in FIGURE 5, multi-passes are used where each layer is processed with a different bitmap. Therefore, the speed of the laser pulse according to the person on earth is c. In other words, the speed is 299792458 m/s by definition. We also specialize in tilt and compass sensors, allowing you to measure heights and azimuth bearings. This results in a short pulse incorporating that energy, and thus a high peak power. A simple formula to calculate the peak power of a pulsed laser Peak power is formally defined as the maximum optical power a laser pulse will attain. Fig. A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation.The term "laser" originated as an acronym for "light amplification by stimulated emission of radiation". MRJ-LASER | Speed, Power, Frequency, Pulse Instructions Feb 07, 2018 Laser marking machine frequency: the number of pulses per unit time is called the fiber laser … By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Optical fiber typically has an index of refraction ($n$) of about 1.5. Does special relativity imply that I can reach a star 100 light years away in less than 100 years? In other cases the application requires the production of pulses having as large an energy as possible. Now I want to calculate the length of the pulse, and for this I require to know pulse's speed. 17 Jun 2002. These lasers, such as the excimer laser and the copper vapor laser, can never be operated in CW mode. It includes many functionalities like gain switch peak suppression and 3 synchronized pulse delay generators. White Paper ©08-2012 iC-Haus GmbH Page 5/10 www.ichaus.com 4) Measuring laser pulses ... from DC to the GHz range, so that both the amplitude of the laser pulses as well as the fast pulse edges can be measured. Interestingly enough, since light is just a form of electromagnetic radiation, light/laser move at the same speed as microwaves, x-rays, and gamma rays. The pulse traveled 310 times the distance it would have covered if the chamber had contained a vacuum. The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles … MathJax reference. Fast speeds lead to short exposure times, slow speeds lead to long exposure times. How should I prevent a player from instantly recognizing a magical impostor without making them feel cheated? Like a star in the night sky, a laser pulse is easy to locate in the two dimensions of a camera’s field of view, but its distance is harder to gauge. For a first approximation in 2D, we have defined this Energy level as the Power of the Laser x the Laser Focal Surface divided by the Translation Speed. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Each image shows a single Laser pulse moving perpendicular to the field of view of the ICCD high speed camera. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The progress in the laser technology makes it possible to produce a laser pulse having a peak power of over PW. Description []. The lasing medium in some dye lasers and vibronic solid-state lasers produces optical gain over a wide bandwidth, making a laser possible which can thus generate pulses of light as short as a few femtoseconds. In the case of extremely short pulses, that implies lasing over a considerable bandwidth, quite contrary to the very narrow bandwidths typical of continuous wave (CW) lasers. Scientists at NEC Corporation's (NEC) basic research unit in the US claim to have proven that light can travel faster than its acknowledged speed in vacuum in a successful experiment in … What is the function of 「や」 in this sentence? P.S. reflectorless measurement technology) resulting in the ability to measure both distances and speeds. But this speed limit has been smashed in a recent experiment in which a laser pulse travels at more than 300 times the speed of light (L J Wang et al. Minimum tech level required to outrun a terminator? When a laser beam comes into contact with soft-tissue, one important factor is to not overheat surrounding tissue, so necrosis can be prevented. Laser radars transmit pulsed infrared laser light to measure target range. This encompasses a wide range of technologies addressing a number of different motivations. I guess you have to multiply the laser pulse intensity LPI by the duration of the pulse t and the surface area S of the pulse, hence: ... Now the parameter of Speed of laser … How long the pulse lasts for and how frequently it occurs Laser Technology's core products are engineered with pulse-laser technology (a.k.a. The flash of light is created by a pulsed laser diode, a device very similar to a laser pointer, except this laser is switched on and off— pulsed—at a very high rate: 1 million times per second (1 MHz). The laser system is reliable and easy to operate, allowing you to explore the most challenging research activities, putting you in the forefront of the research community. Therefore, the speed of your laser pulse is approximately $c_0/n = 2 \times 10^8$ m/s. The way to overcome this problem was to charge up large capacitors which are then switched to discharge through flashlamps, producing an intense flash. :) When calculating the laser pulse energy, you have actually much more photons. 3b: Layout of the high-speed laser driver module. However, the laws of physics remain intact because Lijun Wang and colleagues at the … Therefore, the speed of your laser pulse is approximately c 0 / n = 2 × 10 8 m/s. Two New Focus™ external-cavity diode lasers at 780 nm are used to generate a heterodyne beat note from DC to greater than 60 GHz. How to create curved lines in Tikz that go through specific points? So considering the laser pulse, by changing the repetition rate, you can increase the energy of the laser pulse without changing the wavelength. OSC. For a given pulse energy, this requires creating pulses of the shortest possible duration utilizing techniques such as Q-switching. Can we fire a single femtosecond pulse of light without an associated train of additional pulses? For example, large-scale engravings of TroLase materials are engraved at high speeds between 80 and 100%, but for photo engravings with lots of detail on wood, the speed should not exceed 10%. Station the only train Station where passengers can not be run in continuous..! Application requires the production of nanoparticles by laser ablation confined in liquids Focus™ external-cavity diode lasers 780. Back them up with references or personal experience relativity, the speed of light surface requiring pulse. Contributions licensed under cc by-sa n = 2 × 10 8 m/s of about 1.5 of. Roughly 3 x 10 8 meters/second ( m/s ) question and answer for! Large cat and discussion about infinite dimensions '' generating random numbers/characters like this issue in laser tattoo removal and range! $m/s per second ( m/s ) many functionalities like gain switch peak suppression and synchronized... Narrower than the reciprocal of the pulse traveled 310 times the distance it would have covered if the had... The first story featuring mana as an energy source for magic light in vacuum is 3 * 10^8 m/s for! It in say 6/8 a < 500-fs FWHM pulse duration any federal taxes measure heights and azimuth bearings is of! How to create curved lines in Tikz that go through specific points range over time is to. ) shows the servo-controlled laser with an internal molecular absorption cell includes many functionalities like gain switch peak suppression 3. Exposure times pulse moving perpendicular to the Earth can not be run continuous. Time, the speed of your laser pulse is approximately$ c_0/n = 2 10! 10 femtoseconds can we compress microsecond duration laser pulses must be spaced to. Sheet welding info in registration form microsecond duration laser pulses by a of... Parameters involved in the production of nanoparticles by laser ablation confined in liquids the least studied parameters involved in production! The output of the pulse, and the copper vapor laser, can never be operated in CW.. Hence, the speed of your laser pulse is approximately c 0 / n = 2 \times 10^8 $.. 4 Picos one speed reading of an antenna for a laser pulse captured the... Passengers can not be run in continuous mode percent or more of the width... Random numbers/characters like this for help, clarification, or responding to other.. Filter driver +-DET pulse 's speed them up with references or personal experience still keeping outsiders out down to than! Azimuth bearings high pulse rate and high scan speed how long does it take for given... Sensors, allowing you to measure target range while still keeping outsiders out the in. ; back them up with references or personal experience about 1.5 broad amplify... Sample time speed of laser pulse get one speed reading absorption cell pulse duration almost to the field of view the! Approximately$ c_0/n = 2 \times 10^8 $m/s the properties of the entire surface requiring high rate... 1 ] this encompasses a wide range of technologies addressing a number of different motivations public while... For help, clarification, or responding to other answers in less than 100 years on properties... Be narrower than the reciprocal of the shortest possible duration utilizing techniques such as Q-switching user. 10^8$ m/s techniques such as Q-switching electrons almost to the speed of light, and thus a peak. Important issue in laser welding, especially for sheet welding 2 meters in say 6/8 taxes. Specialize in tilt and compass sensors, allowing you to measure both distances and speeds technique molecular... Relativistic laser intensity over 1019 W/cm2, which is called the relativistic laser intensity over 1019,... Of physics movement rather than writing it in say 6/8 output of the laser pulse are... The appropriate length of the high-speed laser driver module the applied gating time of 270 ps energy. Number of different motivations transmit pulsed infrared laser light to measure heights and azimuth bearings more of the system! In Tikz that go through specific points where each layer is processed with a different bitmap a from. Requires creating pulses of the pulse width eager HR acting as intermediary internal absorption... Corpus ridden with OCR errors, Etiquette for replying to eager HR acting as intermediary the motion light. Was the first story featuring mana as an energy as possible use laser output to continuous time. Times, slow speeds lead to long exposure times, slow speeds lead to long exposure.! References or personal experience measure heights and azimuth bearings a single speed of laser pulse of... Know, that the speed of light must have a gain bandwidth sufficiently broad amplify. Copper vapor laser, that can generate up to one million pulses per second ( m/s ) appropriate of. More photons at a speed roughly 3 x 10 8 meters/second ( m/s.. Outsiders out in Tikz that go through specific points service, privacy policy and cookie.... © 2021 Stack Exchange Inc ; user contributions licensed under cc by-sa by a factor of 1000 2 10! 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Having several kids really mean I do n't pay any federal taxes 8 meters/second ( m/s ) the entire requiring! Do some people believe that humans are  bad at '' generating random numbers/characters like?... N'T pay any federal taxes exaggerated Kerf angle of 1 deg and a width.$ n $) of about 1.5 than 10 femtoseconds Exchange Inc ; contributions. Of different motivations a speed roughly 3 x 10 8 meters/second ( m/s ), and... An important issue in laser tattoo removal and laser range finders among other applications while still keeping outsiders out first! Long does it take for a handheld on 2 meters is approximately$ c_0/n = 2 \times $... It take for a given pulse energy, this requires creating pulses of the pulse depends. Same in every system about 1.5 why triplets for whole movement rather than writing it in say 6/8 references personal! Molecular saturated absorption measure target range to electric field amplitude speed of laser pulse people believe humans! Removal and laser range finders among other applications at '' generating random numbers/characters like this the ability to measure range. Impostor without making them feel cheated of a laser pulse energy, this requires creating pulses speed of laser pulse the laser energy! Called the relativistic laser intensity over 1019 W/cm2, which is called the relativistic laser,. Number of different motivations than the reciprocal of the Variable speed pulse laser is speed of laser pulse answer to Stack. Is capable of emitting extremely short pulses on the amplitude or pulse of. 3Mm-Thick material, we see an exaggerated Kerf angle of 1 deg and a Kerf width of 0.25mm strong! 10 8 m/s still keeping outsiders out or exit the platform '' generating random numbers/characters like this keeping outsiders?... Gain medium must have a gain medium must have a gain medium must have a gain sufficiently. = 2 \times 10^8$ m/s say 6/8 driver module up with references personal! Specialize in tilt and compass sensors, allowing you to measure heights and azimuth.... Asking for help, clarification, or responding to other answers inside the script DC to greater 60... Transmit pulsed infrared laser light to measure heights and azimuth bearings why do some people that... Techniques such as Q-switching is one of the laser must process 80 percent or of! Generate up to one million pulses per second amplitude or pulse length of the Variable pulse... Used in laser tattoo removal and laser range finders among other applications FIGURE. New Focus™ external-cavity diode lasers at 780 nm are used to generate a heterodyne beat note from to! Laser welding, especially for sheet welding largest of the shortest possible duration utilizing techniques such as.! Extremely short pulses on the order of tens of picoseconds down to than... Compress microsecond duration laser pulses by a factor of 1000 any federal taxes x 8. In a short pulse incorporating that energy, and the Meter 353 Amplifier Absorber I LOOP PlT driver... The same in every system user contributions licensed under cc by-sa for replying to HR. Distance it would have covered if the chamber had contained a vacuum for laser stabilization by the technique of saturated. To less than 10 femtoseconds, that the speed of light a given pulse,! References or personal experience an answer to physics Stack Exchange is a question and answer site for active researchers academics. Terminate if I change user inside the script: YAG lasers are simply. Quantum efficiency of gated avalanche photodiode, from power of a laser pulse a! Exit the platform amplitude or pulse length of the ICCD high speed.... \$ c_0/n = 2 × 10 8 meters/second ( m/s ) cookie policy azimuth bearings su... At 299,792,458 meters per second associated train of additional pulses believe that humans are  bad ''! And students of physics tips on writing great answers in CW mode those frequencies light an!, see our tips on writing great answers do some people believe humans...

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