text:
Getting a Medical Marijuana ID Card in Broward County, FL
Regulated cannabis products are available to qualified patients that are approved by a certifying doctor.
Do you…
Have a medical condition that marijuana may help?
Take one or more drugs prescribed by doctors and want to explore holistic treatment options?
Want to learn more about the medicinal benefits of cannabis?
Already use marijuana in some form and want to go legal?
Want to take advantage of juicy discounts on cannabis products at the dispensaries?
What Does Having a Marijuana Card Do?
A Florida Marijuana ID Card is a Medical Marijuana Use Registry identification card issued by the state. These allow qualified patients access to buy cannabis products from licensed Medical Marijuana Treatment Centers, or MMTC.
If you have a medical condition that qualifies, which many do, you can get a marijuana card after visiting with a certified doctor. After getting your Florida medical card you are allowed to shop at any Florida dispensary to buy CBD and THC cannabis products…legally!
How to Get Your Florida Marijuana ID Card
Getting a Medical Marijuana ID Card in Broward County, FL has never been easier. To visit with a doctor and get certified for a marijuana card, you must be a full or part time Florida resident, are 18 or older, or have parental consent.
Schedule an appointment and visit with a medical marijuana doctor in Broward County. 1st time appointments must be done face to face with the doctor. If approved, the certifying doctor will login and register the patient with the Medical Marijuana Use Registry.
If you live in Broward County full or part time, and are interested in medical marijuana for treatment of a qualifying medical condition, you do not need a recommendation from your primary care provider to make an appointment.
To get started now, fill out the MMJ Patient Registration Form below, press submit and a clinic representative will contact you as available.
MMJ Patient Registration Form
Are there any other associated fees?
After receiving a cannabis recommendation from your doctor, login to the Office of Medical Marijuana Use website at mmuregistry.flhealth.gov to complete the electronic application. Many times, the helpful staff an the medical card clinic will assist with this. There is a processing fee of $75 charged by the state that will be paid at this time online or by mail. A $2.75 convenience fee is charged for each online payment.
The cost to change information, replace or surrender your marijuana ID card is $15. Physical application and payments can be mailed to:
Office of Medical Marijuana Use
PO Box 31313
Tampa, FL 33631-3313
Need help with your application or to check the status of a pending one? Please call: 800.808.9580.
What's next after that?
Shortly after paying the state, an email will be sent to the now certified patient. This email will suffice as your medical marijuana ID card prior to a physical one showing up in the mail.
Newly minted and freshly renewed MMJ patients can shop immediately once the email is received or their card is renewed. The different MMTC's, that is what the state calls dispensaries, all have online menus available or walk in is welcomed as well. There are several that offer delivery in Broward County.
It's renewal time, what do I do?
Every 210 days, or within, to keep an active medical marijuana card, patients have to visit with their MMJ doctor. This can now be done online using MedCard telemedicine or in person. It is one of the friendlier doctor visits in life.


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Whether unemployed or underemployed, searching for a new job can be frustrating and overwhelming. You need all the resources you can get – and you need them free, fast, and easy.
The Western Piedmont Workforce Development Board can help.
We provide jobseekers with a variety of no-cost resources including workshops, networking opportunities, job fairs, coaching, and (depending on eligibility) training support to help you find your next career.
NCWorks Online is a robust new website launched by the state of North Carolina to better connect you to employers and their thousands of job listings across the state. By registering on NCWorks Online you can:
Access jobs posted directly by employers as well as those collected from major career sites such as CareerBuilder, Monster, LinkedIn and more – all aggregated in one place online so you no longer have to search multiple sites.
Apply to those jobs directly from NCWorks Online, using a resume and cover letter you create with the site's easy-to-use tools (or upload your own).
Help employers find you faster by being present on NCWorks Online.
Create a "virtual recruiter" to search job postings and notify you when one matches your skills; Track your job-search activities.
Research real-time labor market information such as salaries.
Assess your job skills, research training providers, determine a training budget, and create a training plan.
Contact a member of our staff to learn about and determine if you're eligible to receive an On-the-Job Training grant through your new employer or participate in classroom-based or other training programs to enhance your skills.
The Western Piedmont Workforce Development Board requires all job-seekers to register on NCWorks Online to access our programs and services. Once you complete your profile there, you'll be able to search and apply for jobs, review our events calendar and register and take full advantage of the power and convenience of NCWorks Online.
If you have already registered with your local workforce center, you'll need to register again on NCWorks Online. All job-seekers are required to register on NCWorks Online to access workshops and other services. We apologize for the inconvenience and encourage you to explore and use all the tools on this new site!
NCWorks Online
How-to Guide onn Registering at NCWorks.org

subset: commoncrawl


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text:
May you recognize in your life the presence, power, and light of your soul.
May you realize that you are never alone, that your soul in its brightness and belonging connects you intimately with the rhythm of the universe.
May you have respect for your own individuality and difference.
May you realize that the shape of your soul is unique, that you have a special destiny here,
that behind the facade of your life there is something beautiful, good, and eternal happening.
May you learn to see yourself with the same delight, pride, and expectation with which God sees you in every moment.


text:
- Home
- Cardiac Science AED Products and Accessories
- $500 to $1000
You are looking at products by the Cardiac Science AED brand. Cardiac Science extends lives by providing the public and healthcare professionals with life-saving devices. They are committed to eliminating needless delays between sudden cardiac arrest (SCA) and life-saving defibrillation by ensuring automated external defibrillators (AEDs) are accessible and simple to use. Our innovative, patented Powerheart® AEDs provide assistance to SCA victims in all walks of life.


text:
My copy of this book is sixty years old. It was given to me as a leaving present by my teacher when I left my school in Lagos to go to Jesselton, North Borneo. I covered it back then in brown paper to preserve it and the paper has weathered the years very well.
The inscription inside the front cover reads: Adele weston June 1st 1951. Lagos.
I wasn't as fussy then as I am now about the accent on my first name and I'm not a hundred percent sure of my capital letters either.
Our Island Story is written by a woman, Henrietta Elizabeth Marshall. It was first published in 1905 and in 2005, after having been out of print for ages, it reappeared in a centenary edition. If any of you was a teacher at that time, you might remember your free copy of this book appearing in the post. It was distributed, apparently, to every school in the country as a kind of present and I have no idea of the way it was received when it arrived, nor what the children who read it in the 21st century thought of it. Marshall mixes legends in with 'proper history' and that might have made it seem a little more 'fictional' than your average history book.
I'm certain that the kind of history purveyed in its pages is full of dreadfully old-fashioned things: Colonial not to say Imperialist views and a storytelling style that was common in the kind of book read by children in the Enid Blyton days: bland and cosy to say the least. There are clear villains and heroes. The British are always the best, it goes without saying, but one thing can be said for Our Island Story: it had lots of great women in it: Elizabeth, Queen Victoria and Flora Macdonald, not to mention Florence Nightingale and the wonderful (no Boudicca nonsense here!) Boadicea.
Just get a load of that hair! This picture accounts for my passion for red-headed heroines. They feature in a great many of my books. Okay, Rita Hayworth and Anne of Green Gables can take their share of the blame, but Boadicea was the start of it. The caption under the picture reads: "Will you follow me, men?" - a feminist call to arms if ever there was one. I fell in love with the romance of history through pictures like these and the stories which accompanied them.
Look at this illustration showing the two Princes in the Tower. Was there ever a more heart-rending caption than the one under this picture? It reads: The days seemed very long and dreary to the two little boys.
And now see this. Look at the dresses accompanying the story of the Pipes at Lucknow. In the text, one of the women is described as being in a fever and crying out deliriously: "Dinna ye hear them? Dinna ye hear them?" and those are the words under this picture:
Well, if that was what one looked like while waiting in agonies of fever for the relief of Lucknow, it didn't seem to be such a terrible fate after all. The illustration led directly to years and years of very inadequate crinoline-drawing on my part. My rough book at school was covered in dresses just like these and these two outfits, the purple and the blue are what come into my mind when I think of someone in Victorian costume.
Here is Richard Coeur de Lion...oh, I loved his story! The caption reads. "Richard went away to Palestine."
Here, another favourite of mine to this day, is the tragic Mary, Queen of Scots. Her caption says: "For nineteen years, this poor queen was kept in prison." I found it heart-rending and cried whenever I read her story.
And here was a tale that bred in me a continuing love of romance. It's the story of Flora Macdonald and Bonnie Prince Charlie and the words under the picture say: "They took a sad farewell of each other." To me, when I was seven, it was total bliss, imagining that farewell. You can't see it very well in my photo, but that white blob at the lovers' feet is a pretty little sheep.
These photos were taken with my very low-tech camera and my non-existent photographic skills but I hope they've shown a little of the magic of this book. Almost every history book I've read since is 'better' in the sense of being more accurate or better-written or illluminating, but this will always be the enchanting one, the one that told me, loud and clear: There are brilliant stories in these pages of gallantry and tragedy and love. Come in, don't be scared you won't understand this thing called History. You will, and you'll love it.
PS Since I wrote the first draft of this post, it's emerged that fewer and fewer pupils are opting to study History for GCSE. Eve Edwards argued recently on this blog that historical novels should be used to enthuse children about history and she's right. She says, also, that History is being studied in all sorts of interesting ways today, when it IS studied. But I think there's also room for presenting it as a series of thrilling stories, just as H. E.Marshall did in her book.


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perl5162delta - what is new for perl v5.16.2
This document describes differences between the 5.16.1 release and the 5.16.2 release.
If you are upgrading from an earlier release such as 5.16.0, first read perl5161delta, which describes differences between 5.16.0 and 5.16.1.
There are no changes intentionally incompatible with 5.16.0 If any exist, they are bugs, and we request that you submit a report. See Reporting Bugs below.
Module::CoreList has been upgraded from version 2.70 to version 2.76.
Configure now always adds -qlanglvl=extc99 to the CC flags on AIX when using xlC. This will make it easier to compile a number of XS-based modules that assume C99 [perl #113778].
There are no new known problems.
Perl 5.16.2 represents approximately 2 months of development since Perl 5.16.1 and contains approximately 740 lines of changes across 20 files from 9 authors.
Perl continues to flourish into its third decade thanks to a vibrant community of users and developers. The following people are known to have contributed the improvements that became Perl 5.16.2:
Andy Dougherty, Craig A. Berry, Darin McBride, Dominic Hargreaves, Karen Etheridge, Karl Williamson, Peter Martini, Ricardo Signes, Tony Cook.
The list above is almost certainly incomplete as it is automatically generated from version control history. In particular, it does not include the names of the (very much appreciated) contributors who reported issues to the Perl bug tracker.
For a more complete list of all of Perl's historical contributors, please see the AUTHORS file in the Perl source distribution.
If you find what you think is a bug, you might check the articles recently posted to the comp.lang.perl.misc newsgroup and the perl bug database at http://rt.perl.org/perlbug/ . There may also be information at http://www.perl.org/ , the Perl Home Page.
If you believe you have an unreported bug, please run the perlbug
program included with your release. Be sure to trim your bug down
to a tiny but sufficient test case. Your bug report, along with the
output of perl -V
, will be sent off to firstname.lastname@example.com to be
analysed by the Perl porting team.
If the bug you are reporting has security implications, which make it inappropriate to send to a publicly archived mailing list, then please send it to email@example.com. This points to a closed subscription unarchived mailing list, which includes all the core committers, who will be able to help assess the impact of issues, figure out a resolution, and help co-ordinate the release of patches to mitigate or fix the problem across all platforms on which Perl is supported. Please only use this address for security issues in the Perl core, not for modules independently distributed on CPAN.
The Changes file for an explanation of how to view exhaustive details on what changed.
The INSTALL file for how to build Perl.
The README file for general stuff.
The Artistic and Copying files for copyright information.


text:
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Regularized Identification of Dynamic Systems
This example shows the benefits of regularization for identification of linear and nonlinear models.
What is Regularization
When a dynamic system is identified using measured data, the parameter estimates are determined as:
where the criterion typically is a weighted quadratic norm of the prediction errors . An regularized criterion is modified as:
A common special case of this is when . This is called ridge regression in statistics, e.g., see the ridge
command in Statistics and Machine Learning Toolbox™.
A useful way of thinking about regularization is that represents prior knowledge about the unknown parameter vector and that describes the confidence in this knowledge. (The larger , the higher confidence). A formal interpretation in a Bayesian setting is that has a prior distribution that is Gaussian with mean and covariance matrix , where is the variance of the innovations.
The use of regularization can therefore be linked to some prior information about the system. This could be quite soft, like that the system is stable. The regularization variables and can be seen as tools to find a good model complexity for best tradeoff between bias and variance. The regularization constants and are represented by options called Lambda
and R
respectively in System Identification Toolbox™. The choice of is controlled by the Nominal
regularization option.
Bias - Variance Tradeoff in FIR modeling
Consider the problem of estimating the impulse response of a linear system as an FIR model:
These are estimated by the command: m = arx(z,[0 nb 0])
. The choice of order nb
is a tradeoff between bias (large nb
is required to capture slowly decaying impulse responses without too much error) and variance (large nb
gives many parameters to estimate which gives large variance).
Let us illustrate it with a simulated example. We pick a simple second order butterworth filter as system:
Its impulse response is shown in Figure 1:
trueSys = idtf([0.02008 0.04017 0.02008],[1 -1.561 0.6414],1); [y0,t] = impulse(trueSys); plot(t,y0) xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response')
Figure 1: The true impulse response.
The impulse response has decayed to zero after less than 50 samples. Let us estimate it from data generated by the system. We simulate the system with low-pass filtered white noise as input and add a small white noise output disturbance with variance 0.0025 to the output. 1000 samples are collected. This data is saved in the regularizationExampleData.mat file and shown in Figure 2.
load regularizationExampleData.mat eData plot(eData)
Figure 2: The data used for estimation.
To determine a good value for nb
we basically have to try a few values and by some validation procedure evaluate which is best. That can be done in several ways, but since we know the true system in this case, we can determine the theoretically best possible value, by trying out all models with nb=1,...,50
and find which one has the best fit to the true impulse response. Such a test shows that nb = 13
gives the best error norm (mse = 0.2522) to the impulse response. This estimated impulse response is shown together with the true one in Figure 3.
nb = 13; m13 = arx(eData,[0 nb 0]);
[y13,~,~,y13sd] = impulse(m13,t); plot(t,y0,t,y13) xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True system','13:th order FIR model')
Figure 3: The true impulse response together with the estimate for order nb = 13
Despite the 1000 data points with very good signal to noise ratio the estimate is not impressive. The uncertainty in the response is also quite large as shown by the 1 standard deviation values of response. The reason is that the low pass input has poor excitation.
plot(t,y0,t,y13,t,y13+y13sd,'r:',t,y13-y13sd,'r:') xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True system','13:th order FIR model','Bounds')
Figure 4: Estimated response with confidence bounds corresponding to 1 s.d.
Let us therefore try to reach a good bias-variance trade-off by ridge regression for a FIR model of order 50. Use arxOptions
to configure the regularization constants. For this exercise we apply a simple penalty of .
aopt = arxOptions; aopt.Regularization.Lambda = 1; m50r = arx(eData, [0 50 0], aopt);
The resulting estimate has an error norm of 0.1171 to the true impulse response and is shown in Figure 5 along with the confidence bounds.
[y50r,~,~,y50rsd] = impulse(m50r,t); plot(t,y0,t,y50r,t,y50r+y50rsd,'r:',t,y50r-y50rsd,'r:') xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True system','50:th order regularized estimate')
Figure 5: The true impulse response together with the ridge-regularized estimate for order nb = 50
Clearly even this simple choice of regularization gives a much better bias-variance tradeoff, than selecting an optimal FIR order with no regularization.
Automatic Determination of Regularization Constants for FIR Models
We can do even better. By using the insight that the true impulse response decays to zero and is smooth, we can tailor the choice of to the data. This is achieved by the arxRegul
[L,R] = arxRegul(eData,[0 50 0],arxRegulOptions('RegularizationKernel','TC')); aopt.Regularization.Lambda = L; aopt.Regularization.R = R; mrtc = arx(eData, [0 50 0], aopt); [ytc,~,~,ytcsd] = impulse(mrtc,t);
uses fmincon
from Optimization Toolbox™ to compute the hyper-parameters associated with the regularization kernel ("TC" here). If Optimization Toolbox is not available, a simple Gauss-Newton search scheme is used instead; use the "Advanced.SearchMethod" option of arxRegulOptions
to choose the search method explicitly. The estimated hyper-parameters are then used to derive the values of and .
Using the estimated values of and in ARX leads to an error norm of 0.0461 and the response is shown in Figure 6. This kind of tuned regularization is what is achieved also by the impulseest
command. As the figure shows, the fit to the impulse response as well as the variance is greatly reduced as compared to the unregularized estimates. The price is a bias in the response estimate, which seems to be insignificant for this example.
plot(t,y0,t,ytc,t,ytc+ytcsd,'r:',t,ytc-ytcsd,'r:') xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True system','50:th order tuned regularized estimate')
Figure 6: The true impulse response together with the tuned regularized estimate for order nb = 50
Using Regularized ARX-models for Estimating State-Space Models
Consider a system m0
, which is a 30:th order linear system with colored measurement noise:
where G(q)
is the input-to-output transfer function and H(q)
is the disturbance transfer function. This system is stored in the regularizationExampleData.mat data file. The impulse responses of G(q)
and H(q)
are shown in Figure 7.
load regularizationExampleData.mat m0 m0H = noise2meas(m0); % the extracted noise component of the model [yG,t] = impulse(m0); yH = impulse(m0H,t); clf subplot(211) plot(t, yG) title('Impulse Response of G(q)'), ylabel('Amplitude') subplot(212) plot(t, yH) title('Impulse Response of H(q)'), ylabel('Amplitude') xlabel('Time (seconds)')
Figure 7: The impulse responses of G(q)
(top) and H(q)
We have collected 210 data points by simulating m0
with a white noise input u
with variance 1, and a noise level e
with variance 0.1. This data is saved in regularizationExampleData.mat and is plotted below.
load regularizationExampleData.mat m0simdata clf plot(m0simdata)
Figure 8: The data to be used for estimation.
To estimate the impulse responses of m0
from these data, we can naturally employ state-space models in the innovations form (or equivalently ARMAX models) and compute the impulse response using the impulse
command as before. For computing the state-space model, we can use a syntax such as:
mk = ssest(m0simdata, k, 'Ts', 1);
The catch is to determine a good order k
. There are two commonly used methods:
Cross validation CV: Estimate
fork = 1,...,maxo
using the first half of the dataze = m0simdata(1:150)
and evaluate the fit to the second half of the datazv = m0simdata(151:end)
using thecompare
command:[~,fitk] = compare(zv, mk, compareOptions('InitialCondition', 'z'))
. Determine the orderk
that maximizes the fit. Then reestimate the model using the whole data record.
Use the Akaike criterion AIC: Estimate models for orders
k = 1,...,maxo
using the whole data set, and then pick that model that minimizesaic(mk)
Applying these techniques to the data with a maximal order maxo = 30
shows that CV picks k = 15
and AIC picks k = 3
The "Oracle" test: In addition to the CV and AIC tests, one can also check for what order k
the fit between the true impulse response of G(q)
(or H(q)
) and the estimated model is maximized. This of course requires knowledge of the true system m0
which is impractical. However, if we do carry on this comparison for our example where m0
is known, we find that k = 12
gives the best fit of estimated model's impulse response to that of m0
(=|G(q)|). Similarly, we find that k = 3
gives the best fit of estimated model's noise component's impulse response to that of the noise component of m0
(=|H(q)|). The Oracle test sets a reference point for comparison of the quality of models generated by using various orders and regularization parameters.
Let us compare the impulse responses computed for various order selection criteria:
m3 = ssest(m0simdata, 3, 'Ts', 1); m12 = ssest(m0simdata, 12, 'Ts', 1); m15 = ssest(m0simdata, 15, 'Ts', 1); y3 = impulse(m3, t); y12 = impulse(m12, t); y15 = impulse(m15, t); plot(t,yG, t,y12, t,y15, t,y3) xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True G(q)',... sprintf('Oracle choice: %2.4g%%',100*(1-goodnessOfFit(y12,yG,'NRMSE'))),... sprintf('CV choice: %2.4g%%',100*(1-goodnessOfFit(y15,yG,'NRMSE'))),... sprintf('AIC choice: %2.4g%%',100*(1-goodnessOfFit(y3,yG,'NRMSE'))))
Figure 9: The true impulse response of G(q)
compared to estimated models of various orders.
yH3 = impulse(noise2meas(m3), t); yH15 = impulse(noise2meas(m15), t); plot(t,yH, t,yH3, t,yH15, t,yH3) xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True H(q)',... sprintf('Oracle choice: %2.4g%%',100*(1-goodnessOfFit(yH3,yH,'NRMSE'))),... sprintf('CV choice: %2.4g%%',100*(1-goodnessOfFit(yH15,yH,'NRMSE'))),... sprintf('AIC choice: %2.4g%%',100*(1-goodnessOfFit(yH3,yH,'NRMSE'))))
Figure 10: The true impulse response of H(q)
compared to estimated noise models of various orders.
We see that a fit as good as 83% is possible to achieve for G(q)
among the state-space models, but the order selection procedure may not find that best order.
We then turn to what can be obtained with regularization. We estimate a rather high order, regularized ARX-model by doing:
aopt = arxOptions; [Lambda, R] = arxRegul(m0simdata, [5 60 0], arxRegulOptions('RegularizationKernel','TC')); aopt.Regularization.R = R; aopt.Regularization.Lambda = Lambda; mr = arx(m0simdata, [5 60 0], aopt); nmr = noise2meas(mr); ymr = impulse(mr, t); yHmr = impulse(nmr, t); fprintf('Goodness of fit for ARX model is: %2.4g%%\n',100*(1-goodnessOfFit(ymr,yG,'NRMSE'))) fprintf('Goodness of fit for noise component of ARX model is: %2.4g%%\n',100*(1-goodnessOfFit(yHmr,yH,'NRMSE')))
Goodness of fit for ARX model is: 83.12% Goodness of fit for noise component of ARX model is: 78.71%
It turns out that this regularized ARX model shows a fit to the true G(q)
that is even better than the Oracle choice. The fit to H(q)
is more than 80% which also is better that the Oracle choice of order for best noise model. It could be argued that mr
is a high order (60 states) model, and it is unfair to compare it with lower order state space models. But this high order model can be reduced to, say, order 7 by using the balred
command (requires Control System Toolbox™):
mred7 = balred(idss(mr),7); nmred7 = noise2meas(mred7); y7mr = impulse(mred7, t); y7Hmr = impulse(nmred7, t);
Figures 11 and 12 show how the regularized and reduced order regularized models compare with the Oracle choice of state-space order for ssest
without any loss of accuracy.
plot(t,yG, t,y12, t,ymr, t,y7mr) xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True G(q)',... sprintf('Oracle choice: %2.4g%%',100*(1-goodnessOfFit(y12,yG,'NRMSE'))),... sprintf('High order regularized: %2.4g%%',100*(1-goodnessOfFit(ymr,yG,'NRMSE'))),... sprintf('Reduced order: %2.4g%%',100*(1-goodnessOfFit(y7mr,yG,'NRMSE'))))
Figure 11: The regularized models compared to the Oracle choice for G(q)
plot(t,yH, t,yH3, t,yHmr, t,y7Hmr) xlabel('Time (seconds)'), ylabel('Amplitude'), title('Impulse Response') legend('True H(q)',... sprintf('Oracle choice: %2.4g%%',100*(1-goodnessOfFit(yH3,yH,'NRMSE'))),... sprintf('High order regularized: %2.4g%%',100*(1-goodnessOfFit(yHmr,yH,'NRMSE'))),... sprintf('Reduced order: %2.4g%%',100*(1-goodnessOfFit(y7Hmr,yH,'NRMSE'))))
Figure 12: The regularized models compared to the Oracle choice for H(q)
A natural question to ask is whether the choice of orders in the ARX model is as sensitive a decision as the state space model order in ssest
. Simple test, using e.g. arx(z,[10 50 0], aopt)
, shows only minor changes in the fit of G(q)
State Space Model Estimation by Regularized Reduction Technique
The above steps of estimating a high-order ARX model, followed by a conversion to state-space and reduction to the desired order can be automated using the ssregest
command. ssregest
greatly simplifies this procedure while also facilitating other useful options such as search for optimal order and fine tuning of model structure by specification of feedthrough and delay values. Here we simply reestimate the reduced model similar to mred7
using ssregest
opt = ssregestOptions('ARXOrder',[5 60 0]); mred7_direct = ssregest(m0simdata, 7, 'Feedthrough', true, opt); compare(m0simdata, mred7, mred7_direct)
Figure 13: Comparing responses of state space models to estimation data.
h = impulseplot(mred7, mred7_direct, 40); showConfidence(h,1) % 1 s.d. "zero interval" hold on s = stem(t,yG,'r'); s.DisplayName = 'True G(q)'; legend('show')
Figure 14: Comparing impulse responses of state space models.
In Figure 14, the confidence bound is only shown for the model mred7_direct
since it was not calculated for the model mred7
. You can use the translatecov
command for generating confidence bounds for arbitrary transformations (here balred
) of identified models. Note also that the ssregest
command does not require you to provide the "ARXOrder" option value. It makes an automatic selection based on data length when no value is explicitly set.
Basic Bias - Variance Tradeoff in Grey Box Models
We shall discuss here grey box estimation which is a typical case where prior information meets information in observed data. It will be good to obtain a well balanced tradeoff between these information sources, and regularization is a prime tool for that.
Consider a DC motor (see e.g., iddemo7
) with static gain G
to angular velocity and time constant :
In state-space form we have:
where is the state vector composed of the angle and the velocity . We observe both states in noise as suggested by the output equation.
From prior knowledge and experience we think that is about 4 and is about 1. We collect in motorData
400 data points from the system, with a substantial amount of noise (standard deviation of e
is 50 in each component. We also save noise-free simulation data for the same model for comparison purposes. The data is shown in Figure 15.
load regularizationExampleData.mat motorData motorData_NoiseFree t = motorData.SamplingInstants; subplot(311) plot(t,[motorData_NoiseFree.y(:,1),motorData.y(:,1)]) ylabel('Output 1') subplot(312) plot(t,[motorData_NoiseFree.y(:,2),motorData.y(:,2)]) ylabel('Output 2') subplot(313) plot(t,motorData_NoiseFree.u) % input is the same for both datasets ylabel('Input') xlabel('Time (seconds)')
Figure 15: The noisy data to be used for grey box estimation superimposed over noise-free simulation data to be used for qualifications. From top to bottom: Angle, Angular Velocity, Input voltage.
The true parameter values in this simulation are G
= 2.2 and = 0.8. To estimate the model we create an idgrey
model file DCMotorODE.m
function [A,B,C,D] = DCMotorODE(G,Tau,Ts) %DCMOTORODE ODE file representing the dynamics of a DC motor parameterized %by gain G and time constant Tau. % % [A,B,C,D,K,X0] = DCMOTORODE(G,Tau,Ts) returns the state space matrices % of the DC-motor with time-constant Tau and static gain G. The sample % time is Ts. % % This file returns continuous-time representation if input argument Ts % is zero. If Ts>0, a discrete-time representation is returned. % % See also IDGREY, GREYEST. % Copyright 2013 The MathWorks, Inc. A = [0 1;0 -1/Tau]; B = [0; G/Tau]; C = eye(2); D = [0;0]; if Ts>0 % Sample the model with sample time Ts s = expm([[A B]*Ts; zeros(1,3)]); A = s(1:2,1:2); B = s(1:2,3); end
An idgrey
object is then created as:
mi = idgrey(@DCMotorODE,{'G', 4; 'Tau', 1},'cd',{}, 0);
where we have inserted the guessed parameter value as initial values. This model is adjusted to the information in observed data by using the greyest
m = greyest(motorData, mi)
m = Continuous-time linear grey box model defined by @DCMotorODE function: dx/dt = A x(t) + B u(t) + K e(t) y(t) = C x(t) + D u(t) + e(t) A = x1 x2 x1 0 1 x2 0 -1.741 B = u1 x1 0 x2 3.721 C = x1 x2 y1 1 0 y2 0 1 D = u1 y1 0 y2 0 K = y1 y2 x1 0 0 x2 0 0 Model parameters: G = 2.138 Tau = 0.5745 Parameterization: ODE Function: @DCMotorODE (parametrizes both continuous- and discrete-time equations) Disturbance component: none Initial state: 'auto' Number of free coefficients: 2 Use "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using GREYEST on time domain data "motorData". Fit to estimation data: [29.46;4.167]% FPE: 6.074e+06, MSE: 4908
The model m
has the parameters = 0.57 and G
= 2.14 and reproduces the data is shown in Figure 16.
copt = compareOptions('InitialCondition', 'z'); [ymi, fiti] = compare(motorData, mi, copt); [ym, fit] = compare(motorData, m, copt); t = motorData.SamplingInstants; subplot(211) plot(t, [motorData.y(:,1), ymi.y(:,1), ym.y(:,1)]) axis tight ylabel('Output 1') legend({'Measured output',... sprintf('Initial: %2.4g%%',fiti(1)),... sprintf('Estimated: %2.4g%%',fit(1))},... 'Location','BestOutside') subplot(212) plot(t, [motorData.y(:,2), ymi.y(:,2), ym.y(:,2)]) ylabel('Output 2') axis tight legend({'Measured output',... sprintf('Initial: %2.4g%%',fiti(2)),... sprintf('Estimated: %2.4g%%',fit(2))},... 'Location','BestOutside')
Figure 16: Measured output and model outputs for initial and estimated models.
In this simulated case we have also access to the noise-free data (motorData_NoiseFree
) and depict the fit to the noise-free data in Figure 17.
[ymi, fiti] = compare(motorData_NoiseFree, mi, copt); [ym, fit] = compare(motorData_NoiseFree, m, copt); subplot(211) plot(t, [motorData_NoiseFree.y(:,1), ymi.y(:,1), ym.y(:,1)]) axis tight ylabel('Output 1') legend({'Noise-free output',... sprintf('Initial: %2.4g%%',fiti(1)),... sprintf('Estimated: %2.4g%%',fit(1))},... 'Location','BestOutside') subplot(212) plot(t, [motorData_NoiseFree.y(:,2), ymi.y(:,2), ym.y(:,2)]) ylabel('Output 2') axis tight legend({'Noise-free output',... sprintf('Initial: %2.4g%%',fiti(2)),... sprintf('Estimated: %2.4g%%',fit(2))},... 'Location','BestOutside')
Figure 17: Noise-free output and model outputs for initial and estimated models.
We can look at the parameter estimates and see that the noisy data themselves give estimates that not quite agree with our prior physical information. To merge the data information with the prior information we use regularization:
opt = greyestOptions; opt.Regularization.Lambda = 100; opt.Regularization.R = [1, 1000]; % second parameter better known than first opt.Regularization.Nominal = 'model'; mr = greyest(motorData, mi, opt)
mr = Continuous-time linear grey box model defined by @DCMotorODE function: dx/dt = A x(t) + B u(t) + K e(t) y(t) = C x(t) + D u(t) + e(t) A = x1 x2 x1 0 1 x2 0 -1.119 B = u1 x1 0 x2 2.447 C = x1 x2 y1 1 0 y2 0 1 D = u1 y1 0 y2 0 K = y1 y2 x1 0 0 x2 0 0 Model parameters: G = 2.187 Tau = 0.8938 Parameterization: ODE Function: @DCMotorODE (parametrizes both continuous- and discrete-time equations) Disturbance component: none Initial state: 'auto' Number of free coefficients: 2 Use "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using GREYEST on time domain data "motorData". Fit to estimation data: [29.34;3.848]% FPE: 6.135e+06, MSE: 4933
We have here told the estimation process that we have some confidence in the initial parameter values, and believe more in our guess of than in our guess of G
. The resulting regularized estimate mr
considers this information together with the information in measured data. They are weighed together with the help of Lambda
and R
. In Figure 18 it is shown how the resulting model can reproduce the output. Clearly, the regularized model does a better job than both the initial model (to which the parameters are "attracted") and the unregularized model.
[ymr, fitr] = compare(motorData_NoiseFree, mr, copt); subplot(211) plot(t, [motorData_NoiseFree.y(:,1), ymi.y(:,1), ym.y(:,1), ymr.y(:,1)]) axis tight ylabel('Output 1') legend({'Noise-free output',... sprintf('Initial: %2.4g%%',fiti(1)),... sprintf('Estimated: %2.4g%%',fit(1)),... sprintf('Regularized: %2.4g%%',fitr(1))},... 'Location','BestOutside') subplot(212) plot(t, [motorData_NoiseFree.y(:,2), ymi.y(:,2), ym.y(:,2), ymr.y(:,2)]) ylabel('Output 2') axis tight legend({'Noise-free output',... sprintf('Initial: %2.4g%%',fiti(2)),... sprintf('Estimated: %2.4g%%',fit(2)),... sprintf('Regularized: %2.4g%%',fitr(2))},... 'Location','BestOutside')
Figure 18: Noise-Free measured output and model outputs for initial, estimated and regularized models.
The regularized estimation also has reduced parameter variance as compared to the unregularized estimates. This is shown by tighter confidence bounds on the Bode plot of mr
compare to that of m
clf showConfidence(bodeplot(m,mr,logspace(-1,1.4,100)),3) % 3 s.d. region legend('show')
Figure 19: Bode plot of m
and mr
with confidence bounds
This was an illustration of how the merging prior and measurement information works. In practice we need a procedure to tune the size of Lambda
to the existing information sources. A commonly used method is to use cross validation. That is:
Split the data into two parts - the estimation and the validation data
Compute the regularized model using the estimation data for various values of
Evaluate how well these models can reproduce the validation data: tabulate NRMSE fit values delivered by the
command or thegoodnessOfFit
command.Pick that
which gives the model with the best fit to the validation data.
Use of Regularization to Robustify Large Nonlinear Models
Another use of regularization is to numerically stabilize the estimation of large (often nonlinear) models. We have given a data record nldata
that has nonlinear dynamics. We try nonlinear ARX-model of neural network character, with more and more units:
load regularizationExampleData.mat nldata opt = nlarxOptions('SearchMethod','lm'); m10 = nlarx(nldata, [1 2 1], idSigmoidNetwork(10), opt); m20 = nlarx(nldata, [1 2 1], idSigmoidNetwork(20), opt); m30 = nlarx(nldata, [1 2 1], idSigmoidNetwork(30), opt);
compare(nldata, m10, m20) % compare responses of m10, m20 to measured response
Figure 20: Comparison plot for models m10
and m20
fprintf('Number of parameters (m10, m20, m30): %s\n',... mat2str([nparams(m10),nparams(m20),nparams(m30)])) compare(nldata, m30, m10, m20) % compare all three models axis([1 800 -57 45])
Number of parameters (m10, m20, m30): [54 104 154]
Figure 21: Comparison plot for models m10
, m20
and m30
The first two models show good and improving fits. But when estimating the 154 parameters of m30
, numerical problems seem to occur. We can then apply a small amount of regularization to get better conditioned matrices:
opt.Regularization.Lambda = 1e-8; m30r = nlarx(nldata, [1 2 1], idSigmoidNetwork(30), opt); compare(nldata, m30r, m10, m20)
Figure 22: Comparison plot for models m10
, m20
and regularized model m30r
The fit to estimation data has significantly improved for the model with 30 neurons. As discussed before, a systematic search for the Lambda
value to use would require cross validation tests.
We discussed the benefit of regularization for estimation of FIR models, linear grey-box models and Nonlinear ARX models. Regularization can have significant impact on the quality of the identified model provided the regularization constants Lambda
and R
are chosen appropriately. For ARX models, this can be done very easily using the arxRegul
function. These automatic choices also feed into the dedicated state-space estimation algorithm ssregest
For other types of estimations, you must rely on cross validation based search to determine Lambda
. For structured models such as grey box models, R
can be used to indicate the reliability of the corresponding initial value of the parameter. Then, using the Nominal
regularization option, you can merge the prior knowledge of the parameter values with the information in the data.
Regularization options are available for all linear and nonlinear models including transfer functions and process models, state-space and polynomial models, Nonlinear ARX, Hammerstein-Wiener and linear/nonlinear grey box models.


text:
Sathamangalam Ranga Iyengar Srinivasa Varadhan
Quick Info
Madras, (now Chennai) India
Srinivasa Varadhan is known as S R S Varadhan for short and Raghu to his friends and colleagues. His father, Ranga Iyengar, was a science teacher who became the Principal of the Board High School in Ponneri, a small town about 30 km from Madras (now called Chennai). Varadhan, in [12], thanked his parents for their support as he grew up:-Education always got high priority in our house and I received constant encouragement from both my parents.He explained in [10] how he first became interested in mathematics while at high school:-
At high school I had an excellent mathematics teacher who asked some of his better students to come to his house during weekends, Saturday or Sunday, and gave them extra problems to work on. We thought of these problems just as intellectual games that we played, it was not like an exam; it was more for enjoyment. That gave me the idea that mathematics is something that you can enjoy doing like playing chess or solving puzzles. That attitude made mathematics a much more friendly subject, not something to be afraid of, and that played a role in why I got interested in mathematics.After graduating from high school in 1955, Varadhan entered Presidency College of the University of Madras. There he chose to study for the degree in Statistics rather than in Mathematics. The reason for this was that the Mathematics degree consisted of Pure and Applied Mathematics while the Statistics degree replaced the applied mathematics with statistics but otherwise provided the same pure mathematics courses. At this stage in his career Varadhan thought he would enter industry after graduating and felt that his prospects were much better with the Statistics degree. He was awarded his B.A. with honours in Statistics in 1959 and continued for a fifth year to study for his Master's Degree which he received in 1960. He then went to the Indian Statistical Institute at Kolkata (Calcutta) although at this stage he still had the idea that he would find a job in industry [10]:-
I was told that I should work on statistical quality control, so I spent close to 6 or 8 months studying statistical quality control; in the end, that left me totally unsatisfied. Then I met Varadarajan, Parthasarathy, and Ranga Rao, who worked in probability from a totally mathematical point of view. They convinced me that I was not spending my time usefully, and that I better learn some mathematics if I wanted to do anything at all. I got interested, and I think in the second year I was there, we said to ourselves: Let us work on a problem. We picked a problem concerning probability distributions on groups. That got us started; we eventually solved the problem and in the process also learned the tools that were needed for it.At the Indian Statistical Institute Varadhan's advisor was Calyampudi Radhakrishna Rao but this was only a formal arrangement and Varadhan's thesis grew out of interactions with his colleagues. He was awarded his doctorate for his dissertation Convolution Properties of Distributions on Topological Groups in 1963. In fact Andrei Nikolaevich Kolmogorov had spent a month at the Indian Statistical Institute in 1962 and was appointed as one the examiners of Varadhan's thesis. He took the thesis back with him to Moscow and sent in his report which said [10]:-
This is not the work of a student, but of a mature master.After the award of his doctorate, Varadhan went as a post-doctoral visitor to the Courant Institute of Mathematical Sciences at New York University, a position he held for three years (1963-66). Daniel Stroock, who collaborated with him over many years, wrote about Varadhan's arrival [11]:-
Varadhan, whom everyone calls Raghu, came to these shores from his native India in the fall of 1963. He arrived by plane at Idlewild Airport and proceeded to Manhattan by bus .... His destination was that famous institution with the modest name, The Courant Institute of Mathematical Sciences, where, at the behest of Monroe Donsker, he had been given a postdoctoral fellowship.In 1964 he married Vasundra, who was born in 1947 in Chennai in India but had spent most of the first twelve years of her life in New York. Vasu, like Srinivasa Varadhan, became a professor at New York University. They had two children, Gopal (born in 1969) and his younger brother Ashok. Gopal joined Cantor Fitzgerald as the Managing Director of its interest rate derivatives business in the United States in August 2001 and died in the north tower of the World Trade Center on September 11, 2001. Returning to our summary of Varadhan's career, we note he was appointed as an assistant professor at New York University in 1966. This followed the recommendation which Louis Nirenberg made in a letter to Monroe Donsker in 1965 [12]:-
I think very highly indeed of Varadhan and predict a great future for him. He is very young, and I think in many ways he might be the best appointment as assistant professor in probability we could make.Varadhan was promoted to associate professor in 1968 and became a full professor at New York University in 1972.
Although Varadhan's research has ranged widely over different areas of probability theory we single out two main streams of this research. His work in these two areas has been recognised in the citations for the major prizes which Varadhan has been awarded and we give brief details of these areas by quoting from the citations for these awards. In 1996 Varadhan won the American Mathematical Society's Leroy P Steele Prize for fundamental contribution to research along with his collaborator Daniel Stroock. The citation reads [1]:-
To Daniel Stroock and Srinivasa Varadhan for their four papers 'Diffusion processes with continuous coefficients I and II' (1969), 'On the support of diffusion processes with applications to the strong maximum principle (1970), Multidimensional diffusion processes (1979), in which they introduced the new concept of a martingale solution to a stochastic differential equation, enabling them to prove existence, uniqueness, and other important properties of solutions to equations which could not be treated before by purely analytic methods; their formulation has been widely used to prove convergence of various processes to diffusions.On receiving the award Varadhan spoke about his colleagues and the environment at the Courant Institute in the 1960s [1]:-
I am very pleased that my colleagues have chosen to single out some of my work with Dan Stroock in the late sixties as important. The Courant Institute, where most of the work was done, provided us with an ideal intellectual environment. We had the active encouragement and support of our senior colleagues, particularly Louis Nirenberg and Monroe Donsker. With the presence of Henry McKean and Mark Kac at Rockefeller, New York was indeed a very exciting place to be for an aspiring probabilist. Dan and I worked closely during this period, and to me it was very exciting and fruitful. I thank him, not just because he was a great person to work with, but for the years of close friendship as well. I am particularly pleased to be sharing this prize with him.The second of the two areas of Varadhan's work which we single out is his remarkable contributions to the theory of large deviations. In 2007 he was awarded the highly prestigious Abel Prize and the citation for that award gives some details of his work in this area [12]:-
In his landmark paper 'Asymptotic probabilities and differential equations' in 1966 and his surprising solution of the polaron problem of Euclidean quantum field theory in 1969, Varadhan began to shape a general theory of large deviations that was much more than a quantitative improvement of convergence rates. It addresses a fundamental question: what is the qualitative behaviour of a stochastic system if it deviates from the ergodic behaviour predicted by some law of large numbers or if it arises as a small perturbation of a deterministic system? The key to the answer is a powerful variational principle that describes the unexpected behaviour in terms of a new probabilistic model minimizing a suitable entropy distance to the initial probability measure. In a series of joint papers with Monroe D Donsker exploring the hierarchy of large deviations in the context of Markov processes, Varadhan demonstrated the relevance and the power of this new approach. A striking application is their solution of a conjecture of Mark Kac concerning large time asymptotics of a tubular neighbourhood of the Brownian motion path, the so-called 'Wiener sausage'. Varadhan's theory of large deviations provides a unifying and efficient method for clarifying a rich variety of phenomena arising in complex stochastic systems, in fields as diverse as quantum field theory, statistical physics, population dynamics, econometrics and finance, and traffic engineering. It has also greatly expanded our ability to use computers to simulate and analyze the occurrence of rare events. Over the last four decades, the theory of large deviations has become a cornerstone of modern probability, both pure and applied.Varadhan has been honoured, in addition to the awards mentioned above, with his election to the American Academy of Arts and Sciences (1988), the Third World Academy of Sciences (1988), and the National Academy of Sciences (1995). He was elected a Fellow of the Institute of Mathematical Statistics (1991), and of the Royal Society of London (1998). In 1994 he received the George David Birkhoff Prize, jointly awarded by the American Mathematical Society and the Society for Industrial and Applied Mathematics:-
... for important contributions to the martingale characterization of diffusion processes, to the theory of large deviations for functionals of occupation times of Markov processes, and to the study of random media ...and he received the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University in 1995.
Varadhan is Frank J Gould Professor of Science and professor of mathematics at the Courant Institute of Mathematical Sciences at New York University. He had served for two terms as director of the Institute, namely 1980-84 and 1992-94. When Varadhan was awarded the Abel Prize in 2007, the President of New York University John Sexton said [9]:-
We are so happy and proud of Raghu. Not only is he an outstanding scholar, he is also a kind and wonderful colleague, a devoted teacher, and an exemplary 'University citizen,' serving with dedication and professionalism as director of the Courant Institute and on such bodies as the University Senate. This distinction is a well-deserved honour for a faculty member whose modesty and discretion are almost as great as his scholarly contributions. In the time that Raghu has been at NYU, our University has changed a great deal, but it is the persistent presence of scholars such as he that has enabled us to build NYU into what it is today and to continue to attract top scholars and researchers to our midst.In 2008 Varadhan received the Padma award, given by India on the day that the people celebrated their 59th Republic Day. He was one of nine winners in the field of Literature and Education.
Let us now say a little about some of the books written by Varadhan, many of which have been based on lecture notes of graduate courses he has given at the Courant Institute. He published Stochastic processes (1968) which was reviewed by J R Kinney whose begins his description as follows:-
These are lecture notes of a course on stochastic processes given at the Courant Institute during 1967-68. The author intends to give a survey rather than going into special details. ... This set of notes is a very readable survey of material available elsewhere only in very technical form.The book Mathematical statistics (1974), was based on lectures given during the academic year 1973-1974, but his monograph (written jointly with Daniel Stroock) Multidimensional diffusion processes (1979) was one of the works for which he received the Leroy P Steele Prize. A D Wentzell begins a review as follows:-
The book is about the martingale approach to the theory of Markov processes. The authors demonstrate this approach by treating carefully just one problem rather than showing the reader a great number of widely different examples. This one problem is the construction of diffusion processes for the widest possible class of coefficients along the lines initiated by the authors ...Varadhan's book Lectures on diffusion problems and partial differential equations (1980) starts from Brownian motion and leads the students to stochastic differential equations and diffusion theory. François Bronner, reviewing Varadhan's book Large deviations and applications (1984), explains that it:-
... covers a great deal of material not treated anywhere else outside of journal articles. So it is of prime interest to read this text, written in a pleasant and clear style, by a master of the theory of large deviations. In a few pages one can find the setting of the problem, a survey of the fundamental applications including, for example, the Wentzell and Freodlin theory, and a very clearly presented construction of the lower and upper bounds in the Markov case.The 2001 book Probability theory (2001) was based on a first year graduate course given from 1996 to 1999 at the Courant Institute. The material presented in this highly successful book was continued in Stochastic processes (2007), also based on courses at the Courant Institute.
Let us now look at Varadhan's interests outside mathematics [10]:-
I like to travel. I like the pleasure and experience of visiting new places, seeing new things and having new experiences. In our profession, you get the opportunity to travel, and I always take advantage of it. I like music, both classical Indian and a little bit of classical Western music. I like to go to concerts if I have time; I like the theatre, and New York is a wonderful place for theatre. I like to go to movies. I like reading Tamil literature, which I enjoy. Not many people in the world are familiar with Tamil as a language. It is a language which is 2,000 years old, almost as old as Sanskrit. It is perhaps the only language which today is not very different from the way it was 2,000 years ago. So, I can take a book of poetry written 2,000 years ago, and I will still be able to read it. To the extent I can, I do that.We end this biography by quoting from Daniel Stroock's 1997 article [11]:-
I am not going to claim that Varadhan does not enjoy his success; he does. Nor am I about to say that he is some sort of saint; we could never have become friends if he were. Nonetheless, what distinguishes Varadhan from nearly all the other gifted people whom I have met is the remarkable command he exercises over his own gift. In particular, he has learned how to prevent his unusual intellectual powers from poisoning his relations with lesser intellects. For example, Varadhan can tolerate being wrong, at least occasionally. In addition, he is not one of the many mathematical princes who espouse the notion that all their obligations to humanity can be met through their contributions to mathematical research.
References (show)
- 1996 Steele Prizes, Notices Amer. Math. Soc. 43 (11), 1340-1347.
- K B Athreya, Professor Srinivasa R S Varadhan, Current Sci. 78 (9) (2000), 1151-1152.
- R Bhatia, A conversation with S R S Varadhan, Math. Intelligencer 30 (2) (2008), 24-42.
- E Bolthausen and A-S Sznitman, Zur Verleihung des Abel-Preises 2007 an S R Srinisava Varadhan, Mitt. Dtsch. Math.-Ver. 15 (3) (2007), 173-175.
- M Freiberger, The Abel Prize 2007, Plus magazine (2 April 2007).
- F den Hollander, Srinivasa Varadhan (Dutch), Nieuw Arch. Wiskd. (5) 9 (3) (2008), 192-196.
- T L Lindstrom, S R S Varadhan.
- R Ramachandran, Mathematician S R S Varadhan joins an illustrious line of scientists who have been awarded the Abel Prize, Frontline 24 (7) (2007).
- NYU Mathematician Srinivasa Varadhan Named Winner of Abel Prize : Second NYU Winner of 'Nobel Prize' of Mathematics In Three Years, New York University Press Release (Thursday, March 22, 2007).
- M Raussen and C Skau, Interview with Srinivasa Varadhan, Notices Amer. Math. Soc. 55 (2) (2008), 238-246.
- D Stroock, Nomination for Srinivasa S R Varadhan, Notices Amer. Math. Soc. 44 (8) (1997), 955-957.
- The Abel Prize 2007.
- Varadhan receives 2007 Abel Prize, Notices Amer. Math. Soc. 54 (6) (2007), 738-739.
Additional Resources (show)
Other websites about Srinivasa Varadhan:
Honours (show)
Written by J J O'Connor and E F Robertson
Last Update February 2010
Last Update February 2010


text:
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Pedro Sandoval-Segura received a National Defense Science and Engineering Graduate Fellowship, which aims to increase U.S. citizens pursuing doctoral degrees in science and engineering
Pedro Sandoval-Segura, UMD alum (M.S. '21, computer science ) and current doctoral student in the Department of Computer Science at UMD, received a 2023 National Defense Science and Engineering Graduate (NDSEG) Fellowship. The fellowship, established by Congress in 1989, aims to bolster the number of U.S. citizens pursuing doctoral degrees in science and engineering disciplines relevant to the Department of Defense. Sandoval-Segura received the three-year fellowship, which provides funding for all tuition, mandatory fees, and health insurance; a monthly stipend; and a travel budget for... read more
According to researchers at UMD existing AI text-detectors are susceptible to errors that comprise their efficiency at the most crucial of moments
The explosion of open-sourced artificial intelligence (AI) tools that use deep learning techniques to generate text, also known as large language models, has raised alarms with government officials, content creators and educators in light of how easy the technology can be abused for plagiarism, deception and misinformation. A number of AI detectors have been released in response to these concerns, but none of them are sufficiently reliable in practical scenarios, says Soheil Feizi, an associate professor of computer science with a joint appointment in the University of Maryland Institute for... read more


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Excellent overview of the current war: Israel and Hamas - The facts by Ashley Church
The signing of the Abraham Accords Peace Agreement has opened a new page in the history of the Arab-Israeli relations. Thus, this website has also opened a new page and directory entitled Arab-Israeli cooperation.
A must see movie on World War III - Global Jihad of Islam against the Civilized World
- Arab countries versus Israel - Table
- History
- Role of Religion in the Arab-Israeli Conflict
- Holy Places
- Education
- Is improving economic conditions for Palestinian Arabs conducive to Peace?
- Other resources about the Arab-Israeli Conflict
Arab countries versus Israel
The Arab nations are represented by 21 separate countries (see Table). There is only one Jewish nation with a tiny country, Israel. The combined territories of Arab countries is 650 fold greater than Israel (see map above comparing size of Israel versus those of Arab countries). Their population is 50 fold greater than Israel. The average per capita GDP in Arab countries is $3,700 versus $18,000 for Israel. This despite the fact that many Arab countries have world's richest oil resources.
Country | Government | Territory (sq km) | Population (2001 est.) | GDP (Billions) |
ARAB Total | Mostly monarchies | 13,486,861 | 292,400,267 | $1,195.49 |
Israel | Democracy | 20,770 | 5,938,093 | $110.20 |
Arabs > Israel | 649 fold | 49 fold | 11 fold | |
Algeria | Republic | 2,381,740 | 31,736,053 | $171.00 |
Bahrain | Monarchy | 620 | 645,361 | $10.10 |
Comoros | Republic | 2,170 | 596,202 | $0.42 |
Djibouti | Republic | 22,000 | 460,700 | $0.57 |
Egypt | Republic | 1,001,450 | 69,536,644 | $247.00 |
Iraq | In transition | 437,072 | 23,331,985 | $57.00 |
Jordan | Monarchy | 89,213 | 5,153,378 | $17.30 |
Kuwait | Monarchy | 17,820 | 2,041,961 | $29.30 |
Lebanon | Republic | 10,400 | 3,627,774 | $18.20 |
Libya | Dictatorship | 1,759,540 | 5,240,599 | $45.40 |
Mauritania | Republic | 1,030,700 | 2,747,312 | $5.40 |
Morocco | Monarchy | 446,550 | 30,645,305 | $105.00 |
Oman | Monarchy | 212,460 | 2,622,198 | $19.60 |
Qatar | Monarchy | 11,437 | 769,152 | $15.10 |
Saudi Arabia | Monarchy | 1,960,582 | 22,757,092 | $232.00 |
Somalia | None | 637,657 | 7,488,773 | $4.30 |
Sudan | Military regime | 2,505,810 | 36,080,373 | $35.70 |
Syria | Military regime | 185,180 | 16,728,808 | $50.90 |
Tunisia | Republic | 163,610 | 9,705,102 | $62.80 |
UAE | Emirates | 82,880 | 2,407,460 | $54.00 |
Yemen | Republic | 527,970 | 18,078,035 | $14.40 |
ARAB Total | Mostly monarchies | 13,486,861 | 292,400,267 | $1,195.49 |
Israel Total | Democracy | 20,770 | 5,938,093 | $110.20 |
Arabs > Israel | 649 fold | 49 fold | 11 fold |
Figures in the table were compiled from The World Fact Book.
Arab-Israeli wars
The Arab nations initiated four wars against Israel:
- 1948 War of Independence https://www.linkedin.com/posts/ttsufi_and-now-a-trivia-game-we-will-ask-the-question-activity-6981135256959512576-5eMd/ In 1948 when the State of Israel declared its independence 5 Arab armies attacked Israel on the next day. They were: The Egyptian army The Syrian army The Iraqi army The Lebanese army and The Jordenean army. The question is: why didn't the "palestinian" army attack Israel also?
- 1956 Sinai War
- 1967 Six Day War
- 1973 Yom Kippur War
Israel defended itself each time and won. After each war Israeli army withdrew from most of the areas it captured (see maps). (see Camp-David Accords). This is unprecedented in World history and shows Israel's willingness to reach peace even at the risk of fighting for its very existence each time anew.
Anonymous quote:
If the Arabs (Moslems) put down their weapons today there would be no more violence. If the Israelis put down their weapons today there would be no more Israel.
Think about it...
Quote from Charles Krauthammer - The Weekly Standard, May 11, 1998
"Israel is the very embodiment of Jewish continuity: It is the only nation on earth that inhabits the same land, bears the same name, speaks the same language, and worships the same God that it did 3,000 years ago. You dig the soil and you find pottery from Davidic times, coins from Bar Kokhba, and 2,000-year-old scrolls written in a script remarkably like the one that today advertises ice cream at the corner candy store."
Israel became a nation about 1300 BCE, two thousand years before the rise of Islam. The people of modern day Israel share the same language and culture shaped by the Jewish heritage and religion passed through generations starting with the founding father Abraham. Since the Jewish conquest in 1272 BCE, the Jews have had dominion over the land for one thousand years with a continuous presence in the land for the past 3,300 years.
After the Romans conquered Jerusalem about 2,000 years ago, Jewish people were expelled and dispersed to the Diaspora, and the Land of Israel was ruled by Rome, by Islamic and Christian crusaders, by the Ottoman Empire, and by the British Empire.
Throughout centuries Jews prayed to return from the Diaspora to Israel. During the first half of the 20th century there were major waves of immigration of Jews back to Israel from the Arab countries and from Europe. In 1948 Jews reestablished their sovereignty over their ancient homeland with the establishment of the modern State of Israel.
It was only after the Jews re-inhabited their historic homeland of Judea and Samaria, that the myth of a Palestinian nation was created and marketed worldwide. Jews come from Judea, not Palestinians. There is no language known as Palestinian, or any Palestinian culture distinct from that of all the Arabs in the area. There has never been a land known as Palestine governed by Palestinians. Palestinians are Arabs indistinguishable from Arabs throughout the Middle East. The Palestinian National Charter adopted by the PLO states this fact in the first article (See the covenant)
The area called Palestine included the territories of present day Israel and Jordan. Under Lausanne agreement of 1923 Turkey transferred all claims to Palestine to mandatory power Britain. In 1922 Britain allocated nearly 80% of Palestine to Transjordan. In 1947 UN partitioned this remaining land into two states, a second Arab state, Palestine, and Israel. The great majority of Arabs in greater Palestine and Israel share the same culture, language and religion. The Arabs in the area began identifying themselves as part of a Palestinian people in 1967, two decades after the establishment of the modern State of Israel. Virtually all the Arabs in Judea, Samaria and Gaza in the West Bank of Jordan River have complete autonomy under the rule of the Palestinian Authority.
See: The History and Meaning of "Palestine" and "Palestinians"
For over 3,300 years, Jerusalem has been the Jewish capital. Jerusalem has never been the capital of any Arab or Muslim entity. Even when the Jordanians occupied Jerusalem (1948-1967), they never sought to make it their capital, and Arab leaders did not come to visit.
In the Jewish Bible, Jerusalem is mentioned over 669 times and Zion (which usually means Jerusalem, sometimes the Land of Israel) 154 times, or 823 times. The Christian Bible mentions Jerusalem 154 times and Zion 7 times. Jerusalem is not mentioned once in the Koran. Jerusalem is also not mentioned in the Palestinian Covenant.
King David established the city of Jerusalem as the capital of the whole Land of Israel. Mohammed never came to Jerusalem. Jerusalem remained under Turkish Ottoman Empire rule from 1517 to 1917, and under British rule from 1917 to 1948.
Arab and Jewish Refugees
The UN partition plan of 1947 was rejected by all the Arab countries. Arab leadership in Israel and in the countries surrounding Israel, planned a Jihad, holy war, against Israel and encouraged the Arabs to leave Israel promising their return after they purge the land of Jews. The great majority of Arabs left without ever seeing an Israeli soldier (see article and Arab sources that describe what happened during the war of 1948 that caused the Palestinian refugee problem).
During 1940's through 1950's nearly ALL the Jews had to flee from Arab countries to avoid persecution and pogroms. The number of Jewish refugees from Arab countries is estimated to be a million. This number is greater than the number of Arab refugees who left Israel in 1948, estimated as 343,000 (see Peters' book cited below).
• See video entitled "Arab countries: Where are your Jews?"
Most of the Jewish refugees from Arab countries rapidly integrated into the modern society of Israel. This, despite the fact that Israel is a tiny country (about size of New Jersey) without any of the world's richest resources of petroleum in Arab countries. Today, the majority of the people in Israel are the descendants of Jews from Arab countries. (European Jews and their descendants constitute less than half the population of Israel).
The development of the Jewish community under British mandate led to economic growth in the region providing job opportunities for Arab workers. Consequently, the Arab population of Palestine swelled by the influx of Arab immigrants from Egypt, Syria, Lebanon, and other Arab countries until 1947 (The trend of Arab migration into Israel to find a job continues to the present day). While the British forces limited Jewish immigration, they allowed free entry of Arab migrants. The UN agency UNRWA defined a "Palestinian refugee", as any Arab who stayed in the country for two years prior to 1948. Thus, UNRWA included in their statistics migrant workers greatly swelling the ranks of so called "Palestinian refugees" (for best reference on the subject see: From Time Immemorial: The Origins of the Arab-Jewish Conflict over Palestine by Joan Peters).
Also see a review of From Time Immemorial: The Origins of the Arab-Jewish Conflict over Palestine by Daniel Pipes.
Arab refugee problem was created by the seven Arab countries that attacked Israel in 1948. Arab refugees were intentionally not integrated into the Arab lands to which they fled, despite the fact total territory of Arab countries is about 700 times greater than that of Israel. Out of about 100,000,000 refugees since World War II, theirs is the only refugee group in the world that has not been absorbed into their own peoples' lands. Arab nations still maintain generations of the descendants of the refugees in so called "refugee camps" under squalid conditions with the hope that someday they will dislodge the Jews in Israel. The money spent by the Arab countries on armaments would be sufficient to build houses for all so called "refugees". Arab countries should be encouraged to care for their poor population instead of spending their richest resources in the world on armaments and development of terrorist groups such as Osama Bin Laden from Saudi Arabia.
Since 1948, after three generations the descendants of the Arab refugees are still called "refugees" and are supported by UN "refugee" funds! With the highest birth rate in Arab countries this population has now grown to about four million. In negotiations, Arab leadership requests the "right of return" of this mass of millions into the tiny land of Israel. The settlement of millions of Arabs in Israel would immediately eliminate Israel as a Jewish state. This is the real aim of the Arab countries, to achieve by supposedly "peaceful" means what they could not achieve by unceasing violence in whole scale wars and daily terrorism.
The responsibility for keeping the Arab population who are descendants of the Arab refugees, rests only on the shoulders of the Arab countries that created the problem by attacking Israel in 1948.
Quote from Ralph Galloway, a former head of the UN Relief and Works Agency for Palestine Refugees in the Near East (UNRWA), in Amman, capital of Jordan, in August 1958:
"The Arab states do not want to solve the refugee problem. They want to keep it as open sore, as an affront to the United Nations and as a weapon against Israel. Arab leaders don't give a damn whether the refugees live or die."
Related resources:
- Who cares about Palestinians?
- Jewish Communities of the Middle East and the Maghreb
- Jimena - Jews indigenous to the Middle East and North Africa
- Jews, almost extinct in Egyptian city Alexandria
Holy Places
The Temple Mount in Jerusalem is the holiest site for Jews. It was the site of the Beit HaMikdash ("Temple") built by King Solomon (950 BCE), which was destroyed by Nebuchadnezzar (587 BCE), rebuilt in 541 BCE, and then destroyed again by the Roman army in 70 CE leading to the exile of Jews from Israel. Al Aqsa Mosque and Shrine Of Omar were built at the site of the ancient Jewish temples. The Arabic name for Jerusalem "el-KuDS" is derived from the Arabic name "BeT el-MaKDeS", a translation of the Hebrew "BeiT ha-MiKDaSH", the name of the Jewish Temple (see articles).
Under Jordanian rule, Jewish holy sites were desecrated and the Jews were denied access to places of worship. Under Israeli rule, all Muslim and Christian sites have been preserved and made accessible to people of all faiths. Arabs recently burnt the Tomb of Joseph and the ancient synagogue in Jericho (see pictures). To this days Arab Waqf in control of the Temple Mount does not allow Jews to pray in the Temple Mount. Jews pray facing Jerusalem as the location of the Beit Hamikdash. Muslims pray facing their holy city Mecca with their backs toward Jerusalem. Throughout the ages the Arabs have ignored The Temple Mount and renewed interest only recently because of their political exigencies and not religious history (see pictures and articles).
U.N. Record on Israel and the Arabs
Of the 175 United Nations Security Council resolutions passed before 1990, 97 were directed against Israel. Of the 690 General Assembly resolutions voted on before 1990, 429 were directed against Israel. The U.N. was silent while 58 Jerusalem synagogues were destroyed by the Jordanians. The U.N. was silent while the Jordanians destroyed 58 Jerusalem Synagogues and systematically desecrated the ancient Jewish cemetery on the Mount of Olives. The U.N. was silent while the Jordanians prevented Jews from visiting the Temple Mount and the Western Wall.
This anti-Israel stance of the UN is a natural consequence of its membership structure. 21 members of the UN are Arab countries, and 52 members represent Islamic countries. Since the Arab Israeli conflict is represented as a religious conflict (see article) Israel as the only Jewish state has no chance for a fair hearing in the UN.
Related articles
- Articles from the press about the United Nations' bias against Israel
- What is the evidence that the United Nations is biased against Israel?
- Articles on the role of the UN in the Arab-Israeli conflict
- UN versus Israel
Oslo accords and "Peace Process"
The Oslo "Peace" accords have not brought peace. The number of terror attacks against Israel and the number of Israelis killed by Arab terror bombings greatly escalated after Oslo to a level that has not been seen since 1948 (see statistics). The Palestinian Authority has repeatedly violated all aspects of the agreement (see full report of violations).
Recent armed violence by the army of Arafat confirm the predictions that this agreement would escalate the conflict rather than subdue it (see article). In the history there are many examples of international "peace agreements" that were rapidly followed by major wars. A well known relevant case is the Munich agreement signed by Chamberlain from Great Britain and Hitler from Germany in 1938, which was rapidly revoked by Hitler as German armies invaded Czechoslovakia in 1939.
The P.L.O.'s Charter still calls for the destruction of the State of Israel. Fatah Constitution that is adopted as the unofficial constitution of the Palestinian Authority also calls for the destruction of the Jewish State in most of its clauses.
One of primary means to promote peace between nations is the educational system. In Israeli high schools Arabic is taught as one of required languages. Special educational programs greatly emphasize the need for peaceful coexistence with Israel's Arab neighbors. In contrast, textbooks used in Palestinian Authority schools portray Jews and Israelis in most derogatory and hateful terms (see reports). In summer camps and kindergartens, Palestinian Arab children undergo paramilitary training against Israel. Some Arab Institutions and parents train children at an early age as suicide bombers. This educational atmosphere makes peace impossible in this generation, and plants the seeds of hatred among the coming generations of Arab children as well.
The link to the video below is a compilation of kindergarten graduation ceremonies in the city of Tulkarm. The common theme at these ceremonies is the gun-waving children, the songs calling for terror, and the imitations of terror groups. These children don't stand a chance at a peaceful future when they are taught that terror is to be celebrated.
Related sources:
- Arab child illustrating how to cut the throat of a baby
- Video: Kindergarten graduation ceremonies: Children with toy guns, Fatah headbands
- The Portrayal of Israel and of the Jew in the Palestinian Authority School Textbooks
- PowerPoint slide show with vivid pictures: Education of Arab Palestinian children.
- Personal narrative of the growing up of a child in Gaza.
Is improving economic conditions for Palestinian Arabs conducive to peace?
No, the opposite is true! A landmark study on the subject indicates that the prerequisite for Peace-seeking is not better economic conditions but rather democratic forms of government. Since most Arab countries are far removed from multi-party democracy (see table above), the conditions are not ripe for overall peace in the Middle East. The study concludes that "making inherently aggressive dictatorships of the region more prosperous will not make them more pacific only more powerful" and more willing to pursue armed violence (see article). This is true not only for conflict with Israel but for Intra-Arab conflicts as well (see most recent examples of Iran-Iraq war, Gulf War, etc.).
One of the assumptions of the "Oslo Peace Process" was that it would increase stability by improving the economic conditions for the Arabs of the region. Ironically, since the establishment of the Palestinian Authority (P.A.) the per capita GDP among the P.A. Arabs dropped from $3,500 in 1987 to around $1,000 in 1999. There are many factors responsible for this drop, prominent among them is the corruption of the P.A.
Other resources about the Arab-Israeli Conflict
- Boomerang's Annual 2019 Terror Report
- Radical Islam: Information about the threat posed by Radical Islam to freedom, democracy and other Western values
- Arab Anti-Semitism
- The Middle East Problem
- Myths & Facts about the Arab-Israeli Conflict
- Pictures of Hamas and Islamic Jihad Mass Killing Terrorist Attacks
- Victims of Palestinian Violence and Terrorism since September 2000
- Middle East Media and Research Institute (MEMRI) - Publications on Radical Islam and Islamists engaged in terrorist activities
- What is a Palestinian Arab?
- Palestinian Media Watch
- Palestine Facts
- The Involvement of Arafat, PA Senior Officials and Apparatuses in Terrorism against Israel, Corruption and Crime
- Foreign Military Aid To The Palestinian Authority
- Scholars for Peace in the Middle East
- Palestinian Corruption and Humanitarian Aid


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(Daniel Chang, KHN) In hindsight, Nikki Ruston said, she should have recognized the red flags.
The office in Miami where she scheduled what's known as a Brazilian butt lift had closed and transferred her records to a different facility, she said. The price she was quoted — and paid upfront — increased the day of the procedure, and she said she did not meet her surgeon until she was about to be placed under general anesthesia.
"I was ready to walk out," said Ruston, 44, of Lake Alfred in Central Florida. "But I had paid everything."
A few days after the July procedure, Ruston was hospitalized due to infection, blood loss, and nausea, her medical records show.
"I went cheap. That's what I did," Ruston recalled recently. "I looked for the lowest price, and I found him on Instagram."
People like Ruston are commonly lured to office-based surgery centers in South Florida through social media marketing that makes Brazilian butt lifts and other cosmetic surgery look deceptively painless, safe, and affordable, say researchers, patient advocates, and surgeon groups.
Unlike ambulatory surgery centers and hospitals, where a patient might stay overnight for observation after treatment, office-based surgery centers offer procedures that don't typically require an inpatient stay and are regulated as an extension of a doctor's private practice.
But such surgical offices are often owned by corporations that can offer discount prices by contracting with surgeons who are incentivized to work on as many patients per day as possible, in as little time as possible, according to state regulators and physicians critical of the facilities.
Ruston said she now lives with constant pain, but for other patients a Brazilian butt lift cost them their lives. After a rash of deaths, and in the absence of national standards, Florida regulators were the first in the nation to enact rules in 2019 meant to make the procedures safer. More than three years later, data shows deaths still occur.
Patient advocates and some surgeons — including those who perform the procedure themselves — anticipate the problem will only get worse. Emergency restrictions imposed by the state's medical board in June expired in September, and the corporate business model popularized in Miami is spreading to other cities.
"We're seeing entities that have a strong footprint in low-cost, high-volume cosmetic surgery, based in South Florida, manifesting in other parts of the country," said Dr. Bob Basu, a vice president of the American Society of Plastic Surgeons and a practicing physician in Houston.
During a Brazilian butt lift, fat is taken via liposuction from other areas of the body — such as the torso, back, or thighs — and injected into the buttocks. More than 61,000 buttock augmentation procedures, both butt lifts and implants, were performed nationwide in 2021, a 37% increase from the previous year, according to data from the Aesthetic Society, a trade group of plastic surgeons.
As with all surgery, complications can occur. Miami-Dade County's medical examiner has documented nearly three dozen cosmetic surgery patient deaths since 2009, of which 26 resulted from a Brazilian butt lift. In each case, the person died from a pulmonary fat embolism, when fat entered the bloodstream through veins in the gluteal muscles and stopped blood from flowing to the lungs.
No national reporting system nor insurance code tracks outcomes and patient demographics for a Brazilian butt lift. About 3% of surgeons worldwide had a patient die as a result of the procedure, according to a 2017 report from an Aesthetic Surgery Education and Research Foundation task force.
Medical experts said the problem is driven, in part, by having medical professionals like physician assistants and nurse practitioners perform key parts of the butt lift instead of doctors. It's also driven by a business model that is motivated by profit, not safety, and incentivizes surgeons to exceed the number of surgeries outlined in their contracts.
In May, after a fifth patient in as many months died of complications in Miami-Dade County, Dr. Kevin Cairns proposed the state's emergency rule to limit the number of butt lifts a surgeon could perform each day.
"I was getting sick of reading about women dying and seeing cases come before the board," said Cairns, a physician and former member of the Florida Board of Medicine.
Some doctors performed as many as seven, according to disciplinary cases against surgeons prosecuted by the Florida Department of Health. The emergency rule limited them to no more than three, and required the use of an ultrasound to help surgeons lower the risk of a pulmonary fat clot.
But a group of physicians who perform Brazilian butt lifts in South Florida clapped back and formed Surgeons for Safety. They argued the new requirements would make the situation worse. Qualified doctors would have to do fewer procedures, they said, thus driving patients to dangerous medical professionals who don't follow rules.
The group has since donated more than $350,000 to the state's Republican Party, Republican candidates, and Republican political action committees, according to campaign contribution data from the Florida Department of State.
Surgeons for Safety declined KHN's repeated interview requests. Although the group's president, Dr. Constantino Mendieta, wrote in an August editorial that he agreed not all surgeons have followed the standard of care, he called the limits put on surgeons "arbitrary." The rule sets "a historic precedent of controlling surgeons," he said during a meeting with Florida's medical board.
In January, Florida state Sen. Ileana Garcia, a Republican, filed a draft bill with the state legislature that proposes no limit on the number of Brazilian butt lifts a surgeon can perform in a day. Instead, it requires office surgery centers where the procedures are performed to staff one physician per patient and prohibits surgeons from working on more than one person at a time.
The bill would also allow surgeons to delegate some parts of the procedure to other clinicians under their direct supervision, and the surgeon must use an ultrasound.
Florida's legislature convenes on March 7.
Consumers considering cosmetic procedures are urged to be cautious. Like Ruston, many people base their expectations on before-and-after photos and marketing videos posted on social media platforms such as Facebook, Snapchat, and Instagram.
"That's very dangerous," said Basu, of the American Society of Plastic Surgeons. "They're excited about a low price and they forget about doing their homework," he said.
The average price of a buttocks augmentation in 2021 was $4,000, according to data from the Aesthetic Society. But that's only for the physician's fee and does not cover anesthesia, operating room fees, prescriptions, or other expenses. A "safe" Brazilian butt lift, performed in an accredited facility and with proper aftercare, costs between $12,000 and $18,000, according to a recent article on the American Society of Plastic Surgeons' website.
Although Florida requires a physician's license to perform liposuction on patients who are under general anesthesia, it's common in the medical field for midlevel medical practitioners, such as physician assistants and nurse practitioners, to do the procedure in office settings, according to Dr. Mark Mofid, who co-authored the 2017 Aesthetic Surgery Education and Research Foundation task force study.
By relying on staffers who don't have the same specialty training and get paid less, office-based surgeons can complete more butt lifts per day and charge a lower price.
"They're doing all of them simultaneously in three or four different rooms, and it's being staffed by one surgeon," said Mofid, a plastic surgeon in San Diego, who added that he does not perform more than one Brazilian butt lift in a day. "The surgeon isn't doing the actual case. It's assistants."
Basu said patients should ask whether their doctor holds privileges to perform the same procedure at a hospital or ambulatory surgery center, which have stricter rules than office surgery centers in terms of who can perform butt lifts and how they should be done.
People in search of bargains are reminded that cosmetic surgery can have other serious risks beyond the deadly fat clots, such as infection and organ puncture, plus problems with the kidneys, heart, and lungs.
Ruston's surgery was performed by a board-certified plastic surgeon she said she found on Instagram. She was originally quoted $4,995, which she said she paid in full before surgery. But when she arrived in Miami, she said, the clinic tacked on fees for liposuction and for post-surgical garments and devices.
"I ended up having to pay, like, $8,000," Ruston said. A few days after Ruston returned home to Lake Alfred, she said, she started to feel dizzy and weak and called 911.
Paramedics took her to an emergency room, where doctors diagnosed her with anemia due to blood loss, and blood and abdominal infections, her medical records show.
"If I could go back in time," she said, "I wouldn't have had it done."
KHN's Chaseedaw Giles contributed to this report.


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Lady Gaga, Britney Spears + More Sign Letter Condemning Texas Bathroom Bill
Lady Gaga and Britney Spears are just two of a whopping 140 celebrities who recently signed a letter condemning Texas's proposed bathroom bill, which would prevent public school transgender students from using the bathroom that coincides with their gender identity.
Laverne Cox, Alicia Keys, Jennifer Lawrence, Zoe Kravitz, Whoopi Goldberg, Sia, Panic! at the Disco, Emma Stone and many other stars added their names to the letter in protest of the Senate Bill 6 (SB6) and House Bill 1362 (HB1362), which they refer to as "a violation of the trust built between kids and educators."
"Transgender and gender-nonconforming young people are already subjected to bullying and harassment," the letter reads, in part. "Can you imagine the message these bills send to children — the message of 'that child is unwelcome, that child is dangerous?'
"Transgender and gender non-conforming young people also already face higher rates of family rejection and homelessness, mental health issues and suicidality, and they already are more likely to be denied work and housing," it continues. "How much more can you punish them for living honestly and openly?"
The NFL similarly protested the bill in a statement released over the weekend, hinting they may pass over Texas for future events, should the discriminatory bill be passed.
"The NFL embraces inclusiveness. We want all fans to feel welcomed at our events and NFL policies prohibit discrimination based on age, gender, race, religion, sexual orientation, or any other improper standard," spokesman Brian McCarthy wrote in an email via The Washington Post. "If a proposal that is discriminatory or inconsistent with our values were to become law (in Texas), that would certainly be a factor considered when thinking about awarding future events."
Head over to TX Together to read their official letter against the Texas bathroom bill in full.
Stars Who Protest Trump's Immigration Ban


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This exercise stretches and strengthens your shoulders. Before starting, talk about the exercise with your healthcare provider and read through all the directions. During the exercise, breathe normally and use smooth movements. Stop if you feel any pain. If pain persists, call your healthcare provider.
Stand straight, holding a ____ pound weight in each hand, arms at sides, feet shoulder-width apart. Ask your physical therapist or healthcare provider how much weight to use.
Slowly extend your arms up and out until weights are at shoulder level. Slowly return to starting position.
Repeat ____ times. Do ____ sets ____ times a day.
Don't swing the weights or raise weights above shoulder level.