source_assess_treatment_efficacy.systematic_analysis_of_biases package¶
Submodules¶
source_assess_treatment_efficacy.systematic_analysis_of_biases.import_csv_for_factors module¶
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.import_csv_for_factors.
import_csv
(csv_file)¶ Imports data from a csv file containing parents and sometimes teachers severity assessments of a disease and factor values. This csv file contains all the data required to perform the SAOB.
Parameters: csv_file: str
Name or localisation of the csv file that contains all the values of clinical trials required to perform the SAOB. The csv file must have a specific form:
- eight first columns: Author, Year, Score Name, Number of patients, Raters (Parents or Teachers), Time (pre and post), Mean, Std;
- other columns correspond to factors to analyze;
- each study has at least 2 lines: Author name, Year, Score Name, Number of patients, Raters (Parents or Teachers) repeated twice, Time (pre and post), Mean (at pre-test and post-test), Std (at pre-test and post-test). If Teachers assessments are available, two lines must be added;
- sometimes, for a study, several clinical scales are available, they are all entered in the csv file;
- for each author, the 2 lines of the Raters column have to be filled as follows: Parents, Parents, if teachers’ assessment is available 2 more lines are added (Teachers, Teachers);
- for each author, the 2 lines of the Time column have to be filled as follows: pre, post (pattern repeated one more time if teacher assessments is available);
- Mean and Std correspond to the clinical score extracted from studies at pre-test and post-test.
- Every additionnal column corresponds to a factor.
Returns: df_values_parents: pandas.DataFrame
Parents’ ratings required to perform the SAOB. Each row corresponds to a study and a specific clinical scale, disease symptoms are assessed by parents. Columns are: mean_post_test_treatment, mean_post_test_control, mean_pre_test_treatment, mean_pre_test_control, n_treatment, n_control, std_post_test_treatment, std_post_test_control, std_pre_test_treatment, std_pre_test_control, raters and factors.
df_values_teachers: pandas.DataFrame
Teachers’ ratings required to perform the SAOB. Each row corresponds to a study and a specific clinical scale, disease symptoms are assessed by teachers. Columns are: mean_post_test_treatment, mean_post_test_control, mean_pre_test_treatment, mean_pre_test_control, n_treatment, n_control, std_post_test_treatment, std_post_test_control, std_pre_test_treatment, std_pre_test_control, raters and factors.
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob module¶
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
decision_tree
(X_non_standardized, y)¶ Computes a Decision tree.
Non linear and hierarchical method.
Parameters: X: pandas.DataFrame
Preprocessed dataframe containing all observations in rows and factors in columns (the independent variables). Factors with too many missing values and with too many identical observations have been removed. Besides, values have been standardized. Categorical variables are coded in dummies. This dataframe is obtained thanks to the
preprocess_factors
function.y: pandas.Series
Effect size within subjects computed for each observation (the dependent variable) obtained after the outlier rejection.
Returns: decision_tree: pdf
Decision tree obtained.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
detect_and_reject_outliers
(df, y)¶ Detects and rejects outliers in the distribution of within effect sizes.
Studies with a within effect size out of the bounds are excluded.
Parameters: df: pandas.DataFrame
Dataframe containing all observations in rows, factors and also values to compute the effect size within subjects in columns. It is obtained after the import of the csv file containing all data by
import_csv_for_factors
.y: pandas.Series
Effect size within subjects computed for each observation.
Returns: df: pandas.DataFrame
Dataframe containing all observations with outliers excluded.
y: pandas.Series
Effect size within subjects with outliers excluded.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
effect_size_within_subjects
(mean_post_test_treatment, mean_pre_test_treatment, std_post_test_treatment, std_pre_test_treatment)¶ Computes effects sizes inside a treatment group, this effect size reflects the evolution inside a group between pre and post test. The fomula used comes from Cohen J. (1988), Statistical Power Analysis for the Behavioral Sciences.
Parameters: n_treatment: int
Number of patients included in the treatment group.
mean_post_test_treatment: float
Mean score after the treatment.
mean_pre_test_treatment: float
Mean score before the treatment.
std_pre_test_treatment: float
Standard deviation of the mean score before the treatment.
std_post_test_treatment: float
Standard deviation of the mean score before the treatment.
Returns: effect_size: float
Value estimating the efficacy of the treatment. If it’s negative, the result is in favor of the treatment.
Notes
Effect sizes computed for each study correspond to the effect sizes within subjects. Thus, the effect size is computed from the pre and post test values of the treatment group. So here a control group is not neccessary.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
normalize_severity_at_baseline
(mean_pre_test_treatment, maximum_on_clinical_scale)¶ Normalizes the pre-test scores in order to include them in the SAOB analysis.
Parameters: mean_post_test_treatment: float
Mean score after the treatment.
maximum_on_clinical_scale: int
Maximum score possible to be obtained on the clinical scale.
Returns: severity_at_baseline: float
Normalized pre-test score.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
ordinary_linear_regression
(X, y)¶ Performs Ordinary Least Squares.
Dependent variable = effect size within subjects; independent variable = factors. P independent variables and n observations. model: XB = y; y (nx1) column vector of dependent variables, X (nxP) matrix of independent variables, B (Px1) column vector of coefficients.
Parameters: X: pandas.DataFrame
Preprocessed dataframe containing all observations in rows and factors in columns (the independent variables). Factors with too many missing values and with too many identical observations have been removed. Besides, values have been standardized. Categorical variables are coded in dummies. This dataframe is obtained thanks to the
preprocess_factors
function.y: pandas.Series
Effect size within subjects computed for each observation (the dependent variable) obtained after the outlier rejection.
Returns: summary_ols: statsmodels.iolib.summary.Summary
Summary of the OLS regression. In particular values of coefficients, associated pvalues, F-statistics, Prob(Omnibus), skew and kurtosis.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
preprocess_factors
(df)¶ Preprocesses factors before running the SAOB.
Factors with too many missing values and with too many identical observations will be removed. Besides, values can be standardized. The categorical variables will be coded as dummies.
Parameters: df: pandas.DataFrame
Dataframe containing all observations in rows, factors and also values to compute the effect size within subjects in columns. It is obtained after the import of the csv file containing all data by
import_csv_for_factors
and the outlier rejection.Returns: X: pandas.DataFrame
Preprocessed dataframe containing all observations in rows and factors in columns. Factors with too many missing values and with too many identical observations have been removed. Categorical variables are coded in dummies. Values here are standardized.
X_non_standardized: pandas.DataFrame
Preprocessed dataframe containing all observations in rows and factors in columns. Factors with too many missing values and with too many identical observations have been removed. Categorical variables are coded in dummies. Values here are not standardized.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
regularization_lassoAIC
(X, y)¶ Performs Lasso model fit with Lars using AIC for model selection.
Dependent variable = effect size within subjects; independent variable = factors. P independent variables and n observations. model: XB = y; y (nx1) column vector of dependent variables, X (nxP) matrix of independent variables, B (Px1) column vector of coefficients.
Parameters: X: pandas.DataFrame
Preprocessed dataframe containing all observations in rows and factors in columns (the independent variables). Factors with too many missing values and with too many identical observations have been removed. Besides, values have been standardized. Categorical variables are coded in dummies. This dataframe is obtained thanks to the
preprocess_factors
function.y: pandas.Series
Effect size within subjects computed for each observation (the dependent variable) obtained after the outlier rejection.
Returns: coeff_aic: pandas.DataFrame
Results of the Lasso. Column with coefficients obtained after regularization and the names of the associated factors.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
regularization_lassocv
(X, y)¶ Performs Lasso linear model with iterative fitting along a regularization path. The best model is selected by cross-validation.
Dependent variable = effect size within subjects; independent variable = factors. P independent variables and n observations.
Parameters: X: pandas.DataFrame
Preprocessed dataframe containing all observations in rows and factors in columns (the independent variables). Factors with too many missing values and with too many identical observations have been removed. Besides, values have been standardized. Categorical variables are coded in dummies. This dataframe is obtained thanks to the
preprocess_factors
function.y: pandas.Series
Effect size within subjects computed for each observation (the dependent variable) obtained after the outlier rejection.
Returns: coeff: pandas.DataFrame
Results of the Lasso. Column with coefficients obtained after regularization and the names of the associated factors.
mse_test: numpy.ndarray
Mean square error for the test set on each fold, varying alpha. Shape (n_alphas, n_folds).
alphas: numpy.ndarray
The grid of alphas used for fitting. Shape (n_alphas).
alpha: float
The amount of penalization chosen by cross validation.
-
source_assess_treatment_efficacy.systematic_analysis_of_biases.perform_saob.
weighted_linear_regression
(df, X, y)¶ Performs Weighted Least Squares.
Dependent variable = effect size within subjects; independent variable = factors. P independent variables and n observations. model: WXB = Wy; W (nxn) diagonal matrix of weights, y (nx1) column vector of dependent variables, X (nxP) matrix of independent variables, B (Px1) column vector of coefficients.
Parameters: df: pandas.DataFrame
Dataframe containing all observations in rows, factors in columns and also values to compute the effect size within subjects. It is obtained after the import of the csv file containing all data by
import_csv_for_factors
and the outlier rejection.X: pandas.DataFrame
Preprocessed dataframe containing all observations in rows and factors in columns (the independent variables). Factors with too many missing values and with too many identical observations have been removed. Besides, values have been standardized. Categorical variables are coded in dummies. This dataframe is obtained thanks to the
preprocess_factors function
.y: pandas.Series
Effect size within subjects computed for each observation (the dependent variable) obtained after the outlier rejection.
Returns: summary: statsmodels.iolib.summary.Summary
Summary of the WLS regression. In particular values of coefficients, associated pvalues, F-statistics, Prob(Omnibus), skew and kurtosis.
Note
An example of the use of this package is proposed in example\systematic-analysis-of-biases
. Data is available to review and update the work presented in Bussalb et al., 2019.


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{{responsive_styles.render_responsive_styles()}}
{% endfor %}


H.B. Woodrose
The first dosage I took was 5 seeds scraped then singed to clean the fuzz, then chewed and swallowed. This yielded an interesting New Years, where I was unquestionably high but quite able to enjoy conversations with a little confusion. Eating was quite the ordeal, and I had trouble swallowing. It's like I had to force my body to perform the act of swallowing, but everything tasted really interesting.
Two days later, I made the same preparation but this time crushed the 9 seeds left and soaked them in lime juice for 5 hours to bring out the properties. I drank the concoction at 7pm and went to a friend's to wait for the effects. I noticed soon that my mind was tuning up as often happens on psychedelics. I would get waves of ecstacy and with each wave became higher. It was much as I remember strong weed highs beginning (as I've given up illegal subtances for some years).
As my buddy played music on his computer, it sounded profound, yet couldn't really keep my attention and I was buzzing pretty hard. So I headed back to my place. As I arrived home at about 8pm, I was very high and noticed everything was really bright. Suddenly, the apartment felt like the carribbean, wet and pleasant, even though it's the middle of winter in the mountains, and the windows were open to let the cold dry air in. I mean, I was IN the Carribbean at that moment. I found myself drifting back to beloved memories of the islands, really feeling the feelings from those times for the first time in years. I lay on my bed and looked out the window at the clouds in the night sky. Though it was dark, there was a beautiful purple sunset shining on them. It was a Carribbean sunset. Everything felt wonderful. This lasted for a little while and I started a movie on the tv.
At about 9:30, things turned a bit nasty. I found my breath getting short. No matter how I tried, I couldn't fill my lungs while laying down. Like an asthma attack. I started to toss and turn in the bed as the high wore off and all that was left was an over-stimulated anxiety. I started to moan and groan and was worried my roommates would hear me and come check on me. But groaning was the only thing that felt good. I got up and started out to see some girls I knew, but only made it downstairs to watch the neighbors play video games. I didn't get to sleep until 1:30am but slept like a rock for 10 hours when I did.
Overall, I don't feel this was a bad trip, but did worry a lot about dying when I was having trouble breathing. I realize now it was silly, as when I got up, and moved, I felt better. I probably won't try these again, but the initial couple of hours were the best legal high I've had and one of the more pleasant trips I've had. I wouldn't recommend doing these right before bed as there seems to be a strong stimulant effect to them and it was really unpleasant to be so wired and confused at the same time. If the high had lasted into the jitters, it would have been more worth it.
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


UNSTRUNG HEROES A film review by Mark R. Leeper Copyright 1995 Mark R. Leeper
Capsule: Family tragedy gives a twelve-year- old the opportunity to choose between the rationality of his father and the weirdness of his two unbalanced uncles in a sentimental but muddled story. The first dramatic feature film directed by Diane Keaton will strike a responsive chord in some, but it actually is not a very good piece of story-telling. Rating: high 0 (-4 to +4)
It is a lesson we tend to see a lot in the media. Road Runner cartoons tell us that technology does not work. In STAR TREK we learn that being logical like Spock can be useful but, it is better to be emotional. Data teaches us that being human is the ultimate to whicha machine can aspire. LITTLE MAN TATE, directed by Jodie Foster, showed us that child prodigies turn into twisted monsters who concoct experiments involving "lasers, sulphuric acid, and butterflies." Now another actress-turned-director, Diane Keaton, tells us a story of how in the face of family tragedy, two uncles, even ones with obvious mental problems, who are emotional are more comforting than a genius father who insists on being strictly rational.
In 1962 Steven Lidz (played by Nathan Watt) is the twelve-year-old product of a loving but strange family. His father, Sid (John Turturro), is an inventor and an eccentric genius constantly involving the children in fanciful creations that never seem to work out. The kids at school claim that Steven's father is an alien from another planet, an idea that Selma Lidz (Andie MacDowell), Steven's mother, does not completely discount. But Sid and Selma are so much in love that Selma overlooks the outright weirdness of her husband. She is not quite so willing to overlook the eccentricities of Sid's two very strange brothers, Danny (Michael Richards) and Arthur (Maury Chaykin). One is a super-paranoid; the other is just an adult with the mind of a child. In day-to-day family life Sid's cold, atheistic rationality is made bearable for the children by Selma's warm, loving care and attention. But when Selma becomes sick and cannot provide that warmth, the stress of the household becomes too much for young Steven and he runs away to live with uncles Danny and Arthur. There he discovers his uncles were stranger than he ever realized, but also finds them lovable.
Just why the craziness of the uncles is so wonderful or why it transforms Steven is never explained. And that is an important weakness of the film. The anti-rationality of the film would be onlya minor irritation, but for the film failing to make a case for its side yet still smugly declaring victory.
The acting is really not bad, particularly in the performances of Turturro and Richards as brothers. And while both performances seem a little exaggerated, Keaton does manage to suggest common threads in the two brothers' manias. Curiously, the male roles are better drawn and acted than the one major female role. MacDowell's character is just a bit too wonderful in a mistaken attempt to make her sickness a little more tragic.
But the big mistake of the film is to make so clear that contact with the crazy uncles was terrific for young Steven without giving the viewer much reason to understand why it was so good. Without filling in that blank the film has no chance to resonate. The only conclusion the viewer can draw is that rationality is a cold dead end. And that is a theme we see all too often already. I give this one a high 0 on the -4 to +4 scale.
Mark R. Leeper<EMAIL_ADDRESS>The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


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Initial Release.


The time has a format: hours:minutes
. Both hours and minutes has two digits, like 09:00
.
Make a regexp to find time in the string: subject:Breakfast at 09:00 in the room 123:456.
P.S. In this task there’s no need to check time correctness yet, so 25:99
can also be a valid result.
P.P.S. The regexp shouldn’t match 123:456
.


KRISTALOSE- lactulose powder, for solution
Cumberland Pharmaceuticals Inc.
KRISTALOSE® (LACTULOSE) is a synthetic disaccharide in the form of crystals for reconstitution prior to use for oral administration. Each 10 g of lactulose contains less than 0.3 g galactose and lactose as a total sum. The pH range is 3.0 to 7.0.
Lactulose is a colonic acidifier which promotes laxation.
The chemical name for lactulose is 4-O-β-D-Galactopyranosyl-D-fructofuranose. It has the following structural formula:
The molecular formula is C12H22O11. The molecular weight is 342.30. It is freely soluble in water.
KRISTALOSE® (LACTULOSE) is poorly absorbed from the gastrointestinal tract and no enzyme capable of hydrolysis of this disaccharide is present in human gastrointestinal tissue. As a result, oral doses of lactulose reach the colon virtually unchanged. In the colon, lactulose is broken down primarily to lactic acid, and also to small amounts of formic and acetic acids, by the action of colonic bacteria, which results in an increase in osmotic pressure and slight acidification of the colonic contents. This in turn causes an increase in stool water content and softens the stool.
Since lactulose does not exert its effect until it reaches the colon, and since transit time through the colon may be slow, 24 to 48 hours may be required to produce desired bowel movement.
Lactulose given orally to man and experimental animals resulted in only small amounts reaching the blood. Urinary excretion has been determined to be 3% or less and is essentially complete within 24 hours.
KRISTALOSE® (LACTULOSE) For Oral Solution is indicated for the treatment of constipation. In patients with a history of chronic constipation, lactulose therapy increases the number of bowel movements per day and the number of days on which bowel movements occur.
Since KRISTALOSE® (LACTULOSE) For Oral Solution contains galactose (less than 0.3 g/10 g as a total sum with lactose), it is contraindicated in patients who require a low galactose diet.
A theoretical hazard may exist for patients being treated with lactulose who may be required to undergo electrocautery procedures during proctoscopy or colonoscopy. Accumulation of H2 gas in significant concentration in the presence of an electrical spark may result in an explosive reaction. Although this complication has not been reported with lactulose, patients on lactulose therapy undergoing such procedures should have a thorough bowel cleansing with a non-fermentable solution. Insufflation of CO2 as an additional safeguard may be pursued but is considered to be a redundant measure.
Since KRISTALOSE® (LACTULOSE) For Oral Solution contains galactose and lactose (less than 0.3 g/10 g as a total sum), it should be used with caution in diabetics.
In the event that an unusual diarrheal condition occurs, contact your physician.
Elderly, debilitated patients who receive lactulose for more than six months should have serum electrolytes (potassium, chloride, carbon dioxide) measured periodically.
Results of preliminary studies in humans and rats suggest that nonabsorbable antacids given concurrently with lactulose may inhibit the desired lactulose-induced drop in colonic pH. Therefore, a possible lack of desired effect of treatment should be taken into consideration before such drugs are given concomitantly with lactulose.
There are no known human data on long-term potential for carcinogenicity, mutagenicity, or impairment of fertility.
There are no known animal data on long-term potential for mutagenicity.
Administration of lactulose syrup in the diet of mice for 18 months in concentrations of 3 and 10 percent (v/w) did not produce any evidence of carcinogenicity.
In studies in mice, rats, and rabbits, doses of lactulose syrup up to 6 or 12 mL/kg/day produced no deleterious effects in breeding, conception, or parturition.
Reproduction studies have been performed in mice, rats, and rabbits at doses up to 3 or 6 times the usual human oral dose and have revealed no evidence of impaired fertility or harm to the fetus due to lactulose. There are, however, no adequate and well-controlled studies in pregnant women. Because animal reproduction studies are not always predictive of human response, this drug should be used during pregnancy only if clearly needed.
Precise frequency data are not available.
Initial dosing may produce flatulence and intestinal cramps, which are usually transient. Excessive dosage can lead to diarrhea with potential complications such as loss of fluids, hypokalemia, and hypernatremia.
Nausea and vomiting have been reported.
The usual adult dosage is 10 g to 20 g of lactulose daily. The dose may be increased to 40 g daily if necessary. Twenty-four to 48 hours may be required to produce a normal bowel movement.
Dissolve contents of packet in half a glass (4 ounces) of water.
When Lactulose For Oral Solution is dissolved in water, the resulting solution may be colorless to a slightly pale yellow color.
KRISTALOSE® (LACTULOSE) For Oral Solution is available in single dose packets of 10 g (NDC 66220-719-01) and single dose packets of 20 g (NDC 66220-729-01). The packets are supplied as follows:
STORE AT ROOM TEMPERATURE, 15°-30°C (59°-86°F).
To report adverse events associated with this product, please call 1-877-484-2700.
www.kristalose.com
Manufactured for:
CUMBERLAND
PHARMACEUTICALS INC.
Nashville, TN 37203
KPI 021201
Principal Display panel – 10 Grams Carton Label
NDC 66220-719-30
Kristalose® ( lactulose )
For Oral Solution
10 Grams
30 Single Dose Packets
CUMBERLAND®
PHARMACEUTICALS
Rx only
Principal Display Panel – 10 Grams Pouch Label
NDC 66220-719-01
Kristalose® ( lactulose )
For Oral Solution
CUMBERLAND®
PHARMACEUTICALS
10 Grams
Single Dose Packet
Rx only
CONTENTS: Each packet contains 10 grams lactulose (and less than 0.3 g galactose and lactose as a total sum).
This unit dose packet is not child resistant.
INDICATIONS: For the treatment of constipation. See accompanying package insert.
USUAL ADULT DOSAGE: 10 to 20 grams daily. See accompanying package insert.
Since lactulose does not exert its effect until it reaches the colon, and since transit time through the colon may be slow, 24-48 hours may be required to produce a normal bowl movement.
DIRECTIONS FOR PREPARATION: Dissolve contents of packet in half a glass (4 ounces) of water.
Store at room temperature, 15°-30°C (59°-86°F).
Manufactured for:
Cumberland Pharmaceuticals Inc.
Nashville, TN, USA, 37203
Principal Display panel – 20 Grams Carton Label
NDC 66220-729-30
Kristalose® ( lactulose )
For Oral Solution
20 Grams
30 Single Dose Packets
CUMBERLAND®
PHARMACEUTICALS
Rx only
Principal Display Panel – 20 Grams Pouch Label
NDC 66220-729-01
Kristalose® ( lactulose )
For Oral Solution
CUMBERLAND®
PHARMACEUTICALS
20 Grams
Single Dose Packet
Rx only
CONTENTS: Each packet contains 20 grams lactulose (and less than 0.6 g galactose and lactose as a total sum).
This unit dose packet is not child resistant.
INDICATIONS: For the treatment of constipation. See accompanying package insert.
USUAL ADULT DOSAGE: 10 to 20 grams daily. See accompanying package insert.
Since lactulose does not exert its effect until it reaches the colon, and since transit time through the colon may be slow, 24-48 hours may be required to produce a normal bowl movement.
DIRECTIONS FOR PREPARATION: Dissolve contents of packet in half a glass (4 ounces) of water.
Store at room temperature, 15°-30°C (59°-86°F).
Manufactured for:
Cumberland Pharmaceuticals Inc.
Nashville, TN, USA, 37203
|
KRISTALOSE
lactulose powder, for solution | ||||||||||||||||||||
| ||||||||||||||||||||
| ||||||||||||||||||||
| ||||||||||||||||||||
|
|
KRISTALOSE
lactulose powder, for solution | ||||||||||||||||||||
| ||||||||||||||||||||
| ||||||||||||||||||||
| ||||||||||||||||||||
|
| Labeler - Cumberland Pharmaceuticals Inc. (069532880) |


Thank you for getting in touch!
We appreciate you contacting us about rock climbing. One of our members will be getting back to you within a few hours.
In the meantime, you can check out the following resources in the Navigation Bar:
News → Gallery
Professionals → Chris Sharma / Adam Ondra / Sasha DiGiulian
Have a great day ahead!


Here's the list of hardware we'll have at BostonHacks. Find the MLH or sponsor tables to rent hardware.


pd(1) pd(1) NAME pd - Pure Data SYNOPSIS pd [OPTIONS] puredata [OPTIONS] DESCRIPTION Pd is a graphical programming environment for real-time audio synthesis and related applications. It sports a rich set of real-time control and I/O features. To get a list of allowable arguments to pd, type pd -help and for more documentation either start pd and get help, or consult http://www.crca.ucsd.edu/~msp/Pd_documentation/index.htm or seek a copy on your own machine. On Debian, you should be able to find it in file:/usr/share/doc/puredata-core/1.manual/index.htm SEE ALSO pdsend(1), pdreceive(1), pdgui(1) GNU 1996 Mar 20 pd(1)


Welcome to a Currency Converter from USD to other currencies
Exchange Rates are updated every 24 hours.
Please Enter a monetary amount in USD $:
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Videos
German Sacristan on Direct Marketing Fundamentals
Digital Marketing with Kodak & X1
The power of words in marketing
Never trick your customers or they will trick you
Touch your customers' hearts and they will never forget you
Where do good ideas come from?
Personalization is not just about changing the message


Add a search bar to your app
A quick and easy way to add dynamic search functionality to your app is by using a SearchBar view.
Add a search bar
The search bar is a standard view that includes a text input for entering search queries and (optionally) a time range input that allows the user to change the search timeline. The ID of the search manager to bind to is set in the SearchBar properties. When a new search query or timeline is submitted, the search manager is updated and any other views that are bound to the search manager are notified.
Here is a basic search bar (although this won't do anything yet):
{% searchbar id="example search bar" managerid="example-search" %} {% searchmanager id="example-search" %}Create the view by adding the searchbar
tag to your HTML template, including the ID of the search manager in the managerid
property.
{% searchbar id="example search bar" managerid="example-search" %} {% searchmanager id="example-search" %}
Search bars can also be bound to and modify an existing hard-coded search.


Tutorial
Prerequisites
- A running RockScript server. See Getting started
- NodeJS 7.7.1+
Your first script
This is the script we’re going to execute.
var http = system.import('rockscript.io/http');
var response = http.get({url:'http://api.icndb.com/jokes/random'});
var joke = response.body.value.joke;
The script is available at docs/examples/chuck/get-joke.rs
The joke service
http.get(...);
in line 4 will perform a HTTP request and makes
a HTTP response object available in the script. For this particular URL,
the response object looks like this:
{ "status": 200,
"headers": {
"Transfer-Encoding": ["chunked"],
"other": "irrelevant properties"
},
"body": {
"type": "success",
"value": {
"joke":"...a Chuck Norris joke...",
"other": "irrelevant properties"
}
}
}
Deploy the script
When we deploy the script to the server, we
- Create a script named
get-joke.rs
, if no script with that name exists yet - Create a new script version with the given text
- Mark the new script version as the active script version. The active script version is the version that is started when a new execution is started.
For more about deployment and versioning, see Script versioning
Deploy using the rock command
To deploy this script to your local running RockScript engine, Type
rock deploy docs/examples/chuck/
You should get output like
$ rock deploy docs/examples/chuck/
Scanning directory /Code/rockscript/docs/examples/chuck (not recursive) for files matching .*\.rs(t)?
Deploying docs/examples/chuck/get-joke.rs to http://localhost:3652 ...
> POST http://localhost:3652/command
Content-Type: application/json
{
"deployScript": {
"scriptName": "docs/examples/chuck/get-joke.rs",
"scriptText": "var http \u003d system.import(\u0027rockscript.io/http\u0027);\n\nvar response \u003d http.get({url:\...
}
}
< HTTP/1.1 200 OK
Content-Type: application/json
{
"id": "sv1",
"scriptId": "s1",
"name": "docs/examples/chuck/get-joke.rs",
"version": 1,
"text": "var http \u003d system.import(\u0027rockscript.io/http\u0027);\n\nvar response \u003d http.get({url:\u0027htt...
"active": true
}
1 scripts successful deployed
If you want to see all the options for the deploy
command, type
rock help deploy
Deploy using only bash
Paste this into the command line to save your first script version
$ curl -v -H "Content-Type: application/json" \
-d "{\"deployScript\":{ \
\"scriptName\": \"get-joke.rs\", \
\"scriptText\": \"var http = system.import('rockscript.io\/http');\r\n\r\nvar response = http.get({url:'http:\/\/api.icndb.com\/jokes\/random'});\r\n\r\nvar joke = response.body.value.joke;\" \
}}" \
http://localhost:3652/command
You should see a response like this:
{
"id": "sv1",
"scriptId": "s1",
"name": "get-joke.rs",
"version": 1,
"text": "var http \u003d system.import(\u0027rockscript.io/http\u0027);\r\n\r\nvar response \u003d http.get({url:\u0027http://api.icndb.com/jokes/random\u0027});\r\n\r\nvar joke \u003d response.body.value.joke;",
"active": true
}
Starting the script
When starting an execution of the script, we’ll identify the script by name. In
this case, that’s get-joke.rs
Start script using rock
rock start -n get-joke.rs
If you want to see more options for the start
command, type
rock help start
Start script using only bash
curl -v -H "Content-Type:application/json" \
-d "{\"startScript\":{\"scriptName\":\"get-joke.rs\"}}" \
localhost:3652/command
Then congrats! You started your first RockScript.
Querying your script execution
Of course, now you want to see what the server has done. Let’s query the script execution details, including all the events that the server has stored.
curl http://localhost:3652/query?q=execution\&id=se1
Next, check out the language details and become a RockScript wizard.


--- layout: post title: OS X's Secret Double Life - Joy of Tech. categories: [] tags: [] status: publish type: post published: true meta: _original_post_id: '' _original_import_author: John Duprey author: ---
jduprey
amused
LOL!


<
SWstudio Universal
About SWU
Intruduction
The Technology
Contact us
Help
Tis studio Came from the man himself.


Doing What Now?
I'm in over my head, and I couldn't be happier
06/11/2015
Hello and welcome to my way less technical blog! Here you'll find me happily stumbling my way through Dev Bootcamp and it's culture. So let's get started shall we?
I am beyond ecstatic to be a part of this program.  What initially attracted me to the program, and what is even more apparent as I finish my first week, is this is an experience. I'm finally learning in a holistic way and I couldn't be happier. I've never been in a more supportive and awesome group of people, and it's only been a week! I can't wait to actually get on-site and really get to the nitty gritty with these amazing individuals in my cohort.
That said, I can't deny getting to on-site is kind of terrifying. Making mistakes in the safety of my own home is easy. I can take a minute, check my email (or twitter), and then come back to the issue whenever I have a problem. But on site it's hours upon hours of working through issues, something I'm not used to. But I think I'll be ready for it. If this first week has taught me anything it's that whenever I fall down I'll get picked back up by my peers. Over the years asking for help has been very hard for me. I think, through DBC, that less than positive trait of mine will go by the wayside. As Shareef said, DBC is what we make it, and I plan on making this the most transformative experience of my life.
I think that's all the rambling I have in me for today! Keep checking this space for my mostly coherent thoughts on my DBC experience.


Chinese woman who trespassed at Mar-a-Lago facing prison time
by Bradford BetzA Chinese businesswoman is facing prison time for trespassing at President Trump’s Mar-a-Lago resort and lying to federal agents.
Yujing Zhang, a 33-year-old Shanghai consultant, was convicted in September of trespassing at the Florida resort in March and lying to Secret Service agents who confronted her.
Prosecutors have suggested Judge Roy Altman give Zhang 18 months in prison.
Zhang had fraudulently gained entry onto the restricted Florida resort by telling a receptionist at the club and Secret Service agents that she was a member, taking photos ahead of a United Nations Chinese Friendship Association event – despite being repeatedly told that no such event was scheduled.
When Zhang was arrested, she was carrying four cellphones, a computer and an external hard drive. Authorities later found nine flash drives, five cellphone SIM cards, a signal detector that could spot hidden cameras, and around $8,000 in cash in her Palm Beach hotel room.
TRUMP MAKES FLORIDA HIS PRIMARY RESIDENCE, BUT SAYS NEW YORK WILL ‘HAVE A SPECIAL PLACE IN MY HEART’
Her bizarre behavior and backstory led to suspicions that she was a spy for Beijing, but she was never charged with espionage or related crimes. Zhang’s text messages presented at trial suggested she was obsessed with the president.
CLICK HERE TO GET THE FOX NEWS APP
Zhang had acted as her own attorney during her September trial and has not filed any documents regarding sentencing. She has no prior criminal record.
Fox News’ Vandana Rambaran and The Associated Press contributed to this report.


{% extends "openid_provider/base.html" %} {% load i18n %} {% block content %}
Client {{ client.name }} would like to access this information of you ...


正常的带箭头的下拉框
右下角手动拖动大小
| Button | class="" | Description |
|---|---|---|
btn |
Standard gray button with gradient | |
btn btn-primary |
Provides extra visual weight and identifies the primary action in a set of buttons | |
btn btn-info |
Used as an alternative to the default styles | |
btn btn-success |
Indicates a successful or positive action | |
btn btn-warning |
Indicates caution should be taken with this action | |
btn btn-danger |
Indicates a dangerous or potentially negative action | |
btn btn-inverse |
Alternate dark gray button, not tied to a semantic action or use |


John (JT) Shepple is an undergraduate student at University of Massachusetts, Lowell, studying Computer Science with a minor in Business Administration. You may contact him at:<PHONE_NUMBER> or<EMAIL_ADDRESS>Jason Downing is an undergraduate Computer Science student at University of Massachusetts, Lowell. You may contact him at<EMAIL_ADDRESS>Emily Seto is an undergraduate Computer Science student at University of Massachusetts, Lowell. You may contact her at<EMAIL_ADDRESS>or svnaptic@gmail.com.


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[command + b] (for MAC) or [ctrl + shift + b] (OTHERS) on arXiv abstract or pdf pages to save pdf files.


Young Scots family with newborn baby 'lose everything' in devastating house fire
Sophie Duffy and Daniel Taylor and their baby daughter, Ruby are left with nothing following the blaze at their home in last night.
by Kathleen SpeirsA young family with a newborn baby have lost everything weeks before Christmas after a fire ripped through their home.
Sophie Duffy and Daniel Taylor and their baby daughter , Ruby, have been left with nothing following the blaze at their home in Whitburn, West Lothian, last night.
In a desperate bid for help, Sophie took to social media to share their heartbreaking story.
On Facebook she wrote: "Due to Daniel Taylor and I's house going on fire we have totally lost everything.
"All our clothes and all our baby daughter's belongings.
"If anyone known anyone who has anything that could help us out, we would be forever grateful."
Daniel's sister-in-law, Kelly Taylor set up a Go Fund Me page to raise money for the young family.
In a statement on the page Kelly wrote: "My brother-in-law, Daniel, his partner, Sophie and my baby niece, Ruby lost their home and all their belongings after their home went on fire on Saturday, November 23.
"They have literally lost everything.
"They have no clothes, no baby stuff or anything left at all.
"I am fundraising to support them to rebuild and replace all their belongings.
"We would appreciate any donations that you can spare to help.
"Thankyou."
In just one day over £1,800 has been raised.
One fundraiser commented on the page: "What an awful tragic thing to happen, I am so sorry."
A second posted: "Terrible thing to happen, especially at this time of the year.
"Glad you’re all safe, hope you're back on your feet soon."
A third added: "So sad that this family lost their home.
"As we have a baby girl ourselves I know how expensive things can be.
"So close to Christmas too.
"I wish this family all the best and hope they can still enjoy Christmas with their beautiful baby."
Visit the Go Fund Me page to donate.


yield()
is non-deterministic and platform dependent, and it is rarely appropriate to use this method.
Its use should be combined with detailed profiling and benchmarking to ensure that it actually has the desired effect.
Example:
public static void main(String[] args) {
Runnable r = () -> {
for (int i = 0; i < 10; i++) {
System.out.println(i);
Thread.yield();
}
};
new Thread(r).start();
new Thread(r).start();
}


All deadlines are midnight AoE (Anywhere on Earth)
K-CAP encourages authors to embrace Open Science best practices by providing access to the data and code used in their publication. Accepted papers with available resources will be highlighted.
Coming soon


Paws And Claws Society
Paws And Claws Society
Partners in Prevention Not Destruction since 1993
LITLE JOHNNY CAME IN FROM THE COLD
|
Howdy! ,
I'm Lame Little Johnny, a ten week old precious male kitten, who desperately needs a helping paw! When I was younger, my front left leg was badly injured. I was shunned by my mom and siblings and was left to fend for myself.  Finally, a nice gentleman found me and called Delaware Valley Veterinary Hospital, who told him to call Shirl of Stubbs Animal Rescue, also a client of Del Val. I was examined by Dr. John Vinciguerra. He told my rescue mom that my leg had to be amputated! However, before I can be operated on, I must put on some weight and get stronger. Dr. Steve Milden and Dr. John Vinciguerra of Delaware Valley Veterinary Hospital will be doing my surgery. My rescue mom says they are the BEST and that they will take great care of me!
After I heal, I will need a very special loving home.
Thank you and please say a prayer for me.
Love,
Little Johnny
PS
UPDATE!!!!!!!  HE IS RUNNING AND PLAYING ON HIS THREE GOOD LEGS. LITTLE JOHNNY SENDS HIS LOVE TO ALL THE CARING PEOPLE WHO HELPED HIM THROUGH HIS ORDEAL.
UPDATE!!!!!!! LITTLE JOHNNY HAS BEEN ADOPTED BY HIS FOSTER PARENTS WHO COULD NOT BEAR TO PART WITH HIM. HE IS NOW ENJOYING LIFE IN HIS PERMANENT FOREVER HOME.
Animals for adoption will be posted shortly, including many, many sweet healthy kittens. In the meantime, should you wish to adopt a furry angel, please e-mail<EMAIL_ADDRESS>to reach an experienced adoption counselor.
PAWS AND CLAWS SOCIETY (PACS) LARGE PROJECT NEWS CENTER
"I ask for the privilege of not being born ... not to be born until you can assure me of a home and a master to protect me, and a right to live as long as I am physically able to enjoy life ... not to be born until my body is precious and men have ceased to exploit it because it is cheap and plentiful." Need we say more? Pet overpopulation is a monumental problem. Spay/Neuter is the solution.
CALENDAR YEAR 2006
FEBRUARY 1-28, 2006: PACS SPONSORS !!! PACS partners with Animal Welfare Society of Cape May County to help residents show their love for their pets. Pet Guardians gave their pets the gift of a healthier life that results when they are spayed/neutered.
FEBRUARY 28, 2006: CAT SPAY DAY INITIATIVE A BIG SUCCESS !!! PACS takes their Cat Spay Day initiative to Cape May County. PACS partners with Cape May County Animal Shelter Alliance, Beacon Animal Rescue, Animal Outreach of CMC and Animal Welfare Society of CMC to provide residents with 250 FREE spay/neuter coupons redeemable at nine (9) participating veterinarian offices and three (3) spay/neuter clinics. Our sincere thanks to Madelyn Filipski for making this event a complete success.
MARCH 1, 2006: Nine (9) billboards and their Spay/Neuter and Adoption message can now be seen throughout Cape May County. Partners in Prevention Not Destruction, Paws and Claws Society and Cape May County Animal Shelter Alliance send their sincerest thanks to Cape May County local artist, Joan Veneziano-D'avanzo for the engaging art design.
MARCH 16, 2006: SPAY YOUR BEST FRIEND CONTEST BEGINS: Paws and Claws Society developed Spay Your Best Friend Contest to help Cape May County Partners in Prevention Not Destruction to encourage residents to get their pets spayed/neutered.
MARCH 31, 2006: CAMDEN DOGS GET HOUSES: It takes a village to warm a Camden dog. Thanks to the efforts of Kathy Maguire and several Animal Control Officers, 98 dogs in Camden can come in out of the cold. With financial support from Compassion for Camden, Hearts and Paws, Kitty Bodeep, and Paws and Claws Society Founder, Jean Smith, several ACO's and Kathy Maguire were able to deliver 98 specially built dog houses which provide much needed shelter for dogs in Camden.
MARCH 31, 2006: CAMDEN SPAY/NEUTER PROJECT MARCHES ON: Partners in Prevention Not Destruction team up to spay/neuter Camden animals. Hearts and Paws, Kitty Bodeep, and Paws and Claws Society team up again with Kathy Maguire to get Camden animals spayed/neutered. Animals are picked up and transported to Dr. Haber at Cedarbrook Animal Hospital where they are spayed/neutered and vetted. After the necessary recovery period, the pets are returned to their grateful owners in Camden.
In addition to helping spay/neuter Camden animals, this same team worked together on TNR and hoarder projects. To date, 57 companion animals have been spayed/neutered and vetted. Animals that had to be removed from bad situations were made available for adoption.
APRIL 1, 2006: PACS SPONSORS LOWER TOWNSHIP SPAY/NEUTER BLITZ: Paws and Claws Society and Partner in Prevention Not Destruction, Cape May County Animal Shelter Alliance selected Lower Township as the 2006 “Neuter is Cuter” Community in Cape May County. As a result of this honor, Lower Township residents will be eligible to have their pets spayed/neutered at little or no cost while funds last.
In addition to the spay and neuter programs available to qualified Lower Township residents for their household pets, Paws and Claws also provides free spay/neuter vouchers for anyone wishing to spay/neuter stray or feral cats.
APRIL 1, 2006: DAIRY FARM CATS SPAYED/NEUTERED: Paws and Claws Society with Partners in Prevention Not Destruction, AWS and CMCASA join forces to spay/neuter cats on prison dairy farm. Thus far 34 cats have been trapped, transported, vetted and returned to their dairy farm home to live out their lives under the watchful eye of their caretakers on the farm.
APRIL 1, 2006: PITTSGROVE FARM CATS SPAYED/NEUTERED: Paws and Claws Society with Partners in Prevention Not Destruction, Stubbs Animal Rescue join forces to spay/neuter and relocate cats. After the dealth of an elderly caretaker, many cats needed to be spayed/neutered and relocated to a new location where they would be safe and have a caretaker look out for their well being. Thus far 20 cats have been trapped, transported, vetted and relocated to their new, safe home where they will have a warm bed and plenty of good food.
MAY 1, 2006: SUSSEX COUNTY STRAY AND FERAL CATS SPAYED/NEUTERED: Paws and Claws Society with Partners in Prevention Not Destruction, CLAWS Cat Rescue in Sussex County continue efforts to spay/neuter, socialize and place for adoption many homeless stray and feral cats. Thus far 50 cats have been trapped, transported, vetted, socialized and placed for adoption.
JUNE 1, 2006: SAFER (STRAY AND FERAL EMINENT RESCUE) EXPANDED TO CUMBERLAND COUNTY!!! Paws and Claws Society teams up with Partners in Prevention Not Destruction, Animal Friends Foundation to spay/neuter several colonies of stray and feral cats.
JUNE, 2006: ATLANTIC COUNTY FERAL COLONY SPAYED/NEUTERED!!! Paws and Claws Society with Partner in Prevention Not Destruction, Humane Society of Ocean City team up for TNR project in Estelle Manor. Thus far, 33 feral cats spay/neutered.
CALENDAR YEAR 2005
During calendar year 2005, Paws and Claws Society provided for 1066 FREE spay/neuter surgeries in an all out effort to end the cycle of cruelty caused by unchecked pet reproduction. PACS also provided for vaccinations, testings, internal and external parasite treatments. PACS spay/neuter programs and services certainly epitomizes our philosophy of Prevention Not Destruction. In addition to providing sheltering assistance for hundreds of homeless companion animals, Paws and Claws Society funded medical treatment to more than a hundred sick or injured cats and dogs, which included 6 life-saving surgeries.
MARCH 10, 2005: PACS COMPLETED HOARDER HOUSE PROJECT!!! The final 10 cats were spay/neutered. In total, 39 breeding cats were spay/neutered.
MAY 21, 2005: PACS CAT SPAY DAY IN PITTSGROVE COMPLETE SUCCESS!!! PACS provided residents with 100 FREE spay/neuter coupons redeemable at participating vets.
MAY 31, 2005: PACS PROJECT TO SPAY/NEUTER CATS AT TWO PRISONS A SUCCESS!!! PACS joined with 3 Partners in Prevention Not Destruction to spay/neuter all the cats at two correctional facilities. As a result, there will be no more births and no more destruction of unwanted, surplus cats at these locations. It was very heartwarming to see the love and devotion shown by employees and temporary residents of these two facilities.
Many litters of kittens were pulled, vetted, socialized, fostered, and will be placed for adoption when ready.
On behalf of the animals, many thanks to Animal Alliance of Cape May, Animal Welfare Assoc, representatives from the two government facilities, Stubbs Animal Rescue and, of course, Paws and Claws Society.
JUNE 15, 2005: PACS FUNDS THE BUILDING OF A 16 x 32 SHELTERING FACILITY. Just in time for all the kittens needing rescue, PACS teams with Partner in Prevention Not Destruction, Stubbs Animal Rescue, to build a sheltering facility. Additional space was needed so more furry angels could be rescued.
AUGUST, 2005: PACS EXPANDS SAFER PROGRAM (STRAY AND FERAL EMINENT RESCUE) INTO CAPE MAY COUNTY!!! Partners in Prevention NOT Destruction, Paw and Claws Society (PACS) and Cape May County Animal Shelter Alliance, implement spay/neuter voucher program.
This program is proving to be extremely successful in Cape May County. Almost 700 certificates for free spay/neuter surgeries and vaccinations were distributed in the first four months of operation. Certificates are currently redeemable at ten private veterinary offices and two spay/neuter clinics.
On behalf of our feline friends, we sincerely thank the veterinary community and local volunteers in Cape May County for joining PACS and CMCASA in this important endeavor. We especially thank Madelyn Filipski of Cape May County Animal Shelter Alliance who worked from morning to night to make this program a great success.
DECEMBER 10, 2005: PACS RECEIVES A WARM THANK YOU.
I wanted to thank you for helping us last week in a mass trapping event that was magnificent. It involved a colony located right in the midst of the Wharton State Forest, managed by a fellow living in one of those grandfathered houses and surrounded by state forest. This was as colony that was cause for consternation... Thanks for your help in this most remarkable day..... Thanks again for your very great help in this very good story with a most happy ending.
Preparation for the next project to spay/neuter 90+ cats is underway. Will keep you posted.
Who We Are
MISSION STATEMENT:
The mission of Paws And Claws Society, Inc is:
To promote the general welfare and natural conservation, protection and preservation of all species of animals,
To promote the development of programs and services that advance a philosophy of prevention not destruction,
To raise funds for the benefit of all species of animals;
To provide funding for the initiation and implementation of an animal adoption program;
To provide financial assistance for a spay/neuter program for animals;
To provide funding to initiate and carry out education programs in matters involving care and treatment of pets and other animals;
To provide funding to initiate and carry out a volunteer program to disseminate general information regarding animals by means of training courses, newsletters, books, bulletins and other media activities;
To work to prevent cruelty to all animals;
To work in cooperation with governmental and non-governmental agencies for the humane treatment of animals;
To devise methods to curb animal pet thefts and;
To provide such other services related to fostering the humane treatment of all animals as are, in the opinion of the corporation, needed from time to time.
Paws and Claws Society (PACS) is a 501(c)(3) non-profit corporation legally registered with the State and Federal governments
Paws and Claws Society financial records are audited every year by an independent Certified Public Accountant
Paws and Claws Society is legally registered, lawfully operated, and run entirely by volunteers
Paws and Claws Society
Partners in Prevention Not Destruction
Grove Avenue
Thorofare, NJ 08086
Email:
<EMAIL_ADDRESS>Click here! WE NEED A HOME TODAY...
[Home] [Information] [Shelters] [Search]


Installed product versions
- Visual Studio: [example 2015 Professional]
- This extension: [example 1.1.21]
Description
Replace this text with a short description
Steps to recreate
- Replace this
- text with
- the steps
- to recreate
Current behavior
Explain what it's doing and why it's wrong
Expected behavior
Explain what it should be doing after it's fixed.


{% extends "admin/base.html" %} {% block title %}Tasks{% endblock %} {% block content %}
The Blue Alliance has many tasks that are usually executed by cron jobs, but you can manually launch them from here.
Only works for Events that are already in the DB.
Only works for Events that are already in the DB.
Only works for Teams that are already in the DB.
Generate Insights by year or overall
Generate TypeaheadEntries


@* * Copyright 2016 HM Revenue & Customs * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. *@ @import iht.utils.CommonHelper._ @(form: Form[_], overrideKeys: Option[Map[String, String]] = None, endLineMessageKey: Option[String] = None)(implicit messages: Messages) @* * In general this template will be called with a single parameter, the form - which in turn contains the keys of the * error messages that must be shown to the customers. In general there are actually two error messages associated with * each problem, the error message itself, and a helpful summary message. So if the form contains an error message key * error.this.that then we also expect the messages file to contain error.this.that.summary. * * Occasionally we need to be more flexible about generating summary keys - the optional override map allows an entirely * different summary key to be associated with a standard error key. *@ @if(form.hasErrors) {
@Messages("error.checkCorrect")
@messages(messageKey)
}


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The Mathematics Department at the University of Houston expects to hire a tenure-track Assistant Professor as early as Fall 2020. Preference will be given to a candidate who works in Statistics, Applied Probability or Data Analytics. We are particularly interested in someone who can foster collaborative efforts with existing research teams in our department and the university at large, and whose research interests will allow collaborative interactions with local universities, local industry, as well as the Texas Medical Center.
The department is seeking outstanding candidates with the potential for exceptional research, excellence in teaching, and clear commitment to enhancing the diversity of the faculty, graduate and undergraduate student population.
Submit the following items online at http://jobs.uh.edu to complete your application:
Candidates should request four letters of recommendations of which one addresses teaching.
The department is seeking outstanding candidates with the potential for exceptional research, excellence in teaching, and clear commitment to enhancing the diversity of the faculty, graduate and undergraduate student population.
The University of Houston is responsive to the needs of dual career couples.
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Qualifications: A minimum requirement for this position is a PhD in Mathematics or Statistics or a related field.
Notes to Applicant: Official transcripts are required for a faculty appointment and will be requested upon selection of final candidate. All positions at the University of Houston are security sensitive and will require a criminal history check.
Required Attachments by Candidate: Curriculum Vitae, Cover Letter/Letter of Application, Teaching Philosophy or Statement, Research Statement


Learning plan
A plan to learn
19 November 2020
What is your long term goal and or career pathway?
My long term goal is to build creative websites or software that help people. Whether I am involved directly in coding, or perhaps project management, this path will be kickstarted after EDA with a Junior Dev role, where I will be able to glean from the experiences of better experienced Devs.
What skills (non-technical - human skills) would you like to see developed in yourself while at EDA?
Communication is key. I have experienced on many occasions how miscommunication in a team environment has negatively affected productivity, and I am certainly no exception to causing this. While at EDA I would like to focus on communicating problems clearly with team mates, and working together to create solutions.
A description of your own strengths and limitations
I believe that I am a fairly open and approachable person, however sometimes I think that this may not be how other people view me. As such, what could be a great strength in a team environment becomes a limitation. This is something else that I would like to focus on while at EDA: projecting myself as friendly and approachable.
Based on the above description, a commitment to how you will manage your workload in this programme. This should include - an explanation of how you will manage yourself to work productively and sustainably with other learners, facilitators and industry/community representatives.
Being an empathetic listener and communicator will be key to success here. I can often get caught up in my own interest. I will need to concentrate more on what others in my cohort are going through, as well as facilitators and others in the industry. A commitment as to how and where you will seek help in a timely way. When I need help I think it would be wise to first ask members of my cohort either on slack or in person, as they may be, or may have, also been struggling with the same thing.
A description of what you expect from the facilitation team
It would be great to have the facilitation team on hand to help if myself and my peers are stuck. I do not expect a facilitator to hand me a magical piece of perfect code when I need it, but rather to offer support and point me in the right direction to find the answer myself.


ConsoleDoc
Description: Console self-documentation functions. These output psuedo C++ suitable for feeeding through Doxygen or another auto documentation tool.
Methods:
dumpConsoleClasses(bool dumpScript=true, bool dumpEngine=true)
Description: dumps all declared console classes to the console.
Params:
dumpScript: Specifies whether or not classes defined in script should be dumped.
dumpEngine: Specifies whether or not classes defined in the engine should be dumped.
dumpConsoleFunctions(bool dumpScript=true, bool dumpEngine=true)
Description: Dumps all declared console functions to the console.
Params:
dumpScript: Specifies whether or not functions defined in script should be dumped.
dumpEngine: Specifies whether or not functions defined in the engine should be dumped.


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Differentially Private PAC Learning
The study of differentially private PAC learning runs all the way from its introduction in 2008 [KLNRS08] to a best paper award at the Symposium on Foundations of Computer Science (FOCS) this year [BLM20]. In this post, we’ll recap the history of this line of work, aiming for enough detail for a rough understanding of the results and methods.
Before we get to the “what” and “how” of private PAC learning, it’s worth thinking about the “why”. One motivation for this line of work is that it neatly captures a fundamental question: does privacy in machine learning come at a price? Machine learning is now sufficiently successful and widespread for this question to have real import. But to even start to address this question, we need a formalization of machine learning that allows us to reason about possible trade-offs in a rigorous way. Statistical learning theory, and its computational formalization as PAC learning, provide one such clean and well-studied model. We can therefore use PAC learning as a testbed whose insights we might carry to other less idealized forms of learning.
With this motivation in mind, the rest of this post is structured as follows. The first section covers the basics of the PAC model, and subsequent sections gradually build up a chronology of results. When possible, we give short sketches of the accompanying techniques.
PAC Learning
We’ll start with a brief overview of PAC learning absent any privacy restrictions. Readers familiar with PAC learning can probably skip this section while noting that
-
(the cardinality version of) Occam’s razor is a baseline learner using \(O(\log|\mathcal{H}|)\) samples,
-
VC dimension characterizes non-private PAC learning,
-
we’ll focus on the sample complexity of realizable PAC learning,
-
we’ll usually omit dependencies on accuracy and success probability parameters, and
-
we’ll usually ignore computational efficiency.
For readers needing a refresher on PAC learning, the basic element of the “probably approximately correct” (PAC) framework [Val84] is a hypothesis. Each hypothesis is a function \(h \colon \mathcal{X}\to \{-1,1\}\) mapping examples from some space \(\mathcal{X}\) to binary labels. A collection of hypotheses is a hypothesis class \(\mathcal{H}\), e.g., thresholds (a.k.a. perceptrons), rectangles, conjunctions, and so on. In the realizable setting, a learner receives examples drawn from some unknown distribution and labeled by an unknown \(h^\ast \in \mathcal{H}\). The learner’s goal is to with high probability (“probably”) output a hypothesis that mostly matches the labels of \(h^\ast\) on future examples from the unknown example distribution (“approximately correct”). In the agnostic setting, examples are not necessarily labeled by any \(h \in \mathcal{H}\), and the goal is only to output a hypothesis that approximates the best error of any hypothesis from \(\mathcal{H}\). As mentioned above, we focus on the realizable setting unless otherwise specified. In the proper setting, the learner must output a hypothesis from \(\mathcal{H}\) itself. In the improper setting, this requirement is removed.
In general, we say an algorithm \((\alpha,\beta)\)-PAC learns \(\mathcal{H}\) with sample complexity \(n\) if \(n\) samples are sufficient to with probability at least \(1-\beta\) obtain error at most \(\alpha\) over new examples from the distribution. For the purposes of this post, we generally omit these dependencies on \(\alpha\) and \(\beta\), as they typically vary little or not at all when switching between non-private and private PAC learning.
Fortunately, we always have a simple baseline learner based on empirical risk minimization: given a set of labeled examples, iterate over all hypotheses \(h \in \mathcal{H}\), check how many of the labeled examples each \(h\) mislabels, and output a hypothesis that mislabels the fewest examples. Using this learner, which is sometimes called “Occam’s razor,” \(O(\log|\mathcal{H}|)\) samples suffice to PAC learn \(\mathcal{H}\).
At the same time, \(|\mathcal{H}|\) is a pretty coarse measure of hypothesis class complexity, as it would immediately rule out learning any infinite hypothesis class (of which there are many). Thus, as you might expect, we can do better. We do so using VC dimension. \(\mathsf{VCD}\left(\mathcal{H}\right)\) is the size of the largest possible collection of examples such that, for every labeling of the examples, \(\mathcal{H}\) contains a hypothesis with that labeling. With VC dimension, we can essentially swap \(\log|\mathcal{H}|\) with \(\mathsf{VCD}\left(\mathcal{H}\right)\) in the Occam’s razor bound and PAC learn with \(O(\mathsf{VCD}\left(\mathcal{H}\right))\) samples. In fact, the “Fundamental Theorem of Statistical Learning” says that PAC learnability (realizable or agnostic) is equivalent to finite VC dimension. In this sense, \(\mathsf{VCD}\left(\mathcal{H}\right)\) is a good measure of how hard it is to PAC learn \(\mathcal{H}\). As a motivating example that will re-appear later, note that for the hypothesis class of 1-dimensional thresholds over \(T\) points, \(\log |\mathcal{H}| = \log T\), while \(\mathsf{VCD}\left(\mathcal{H}\right)\) is only 1.
An illustration of 1-dimensional thresholds. A given threshold is determined by some point \(x^\ast \in [T]\): any example \(x \leq x^\ast\) receives label \(-1\), and any example \(x > x^\ast\) receives label 1.
A Simple Private PAC Learner
It is straightforward to add a differential privacy constraint to the PAC framework: the hypothesis output by the learner must be a differentially private function of the labeled examples \((x_1, y_1), \ldots, (x_n, y_n)\). That is, changing any one of the examples — even to one with an inconsistent label — must not affect the distribution over hypotheses output by the learner by too much.
Since we haven’t talked about any other PAC learner, we may as well start with the empirical risk minimization-style Occam’s razor discussed in the previous section, which simply selects a hypothesis that minimizes empirical error. A private version becomes easy if we view this algorithm in the right light. All it is doing is assigning a score to each possible output (the hypothesis’ empirical error) and outputting one with the best (lowest) score. This makes it a good candidate for privatization by the exponential mechanism [MT07].
Recall that the exponential mechanism uses a scoring function over outputs to release better outputs with higher probability, subject to the privacy constraint. More formally, the exponential mechanism requires a scoring function \(u(X,h)\) mapping (database, output) pairs to real-valued scores and then selects a given output \(h\) with probability proportional to \(\exp\left(\tfrac{\varepsilon u(X,h)}{2\Delta(u)}\right)\). Thus a lower \(\varepsilon\) (stricter privacy requirement) and larger \(\Delta(u) := \sup_h \sup_{X \sim X’} u(X,h) - u(X’,h) \) (scoring function more sensitive to changing one element in the database \(X\) to make \(X’\)) both lead to a more uniform (more private) output distribution.
Fortunately for our PAC learning setting, empirical error is not a very sensitive scoring function: changing one sample only changes empirical error by 1. We can therefore use (negative) empirical error as our scoring function \(u(X,h)\), apply the exponential mechanism, and get a “private Occam’s razor.” This was exactly what Kasiviswanathan, Lee, Nissim, Raskhodnikova, and Smith [KLNRS08] did when they introduced differentially private PAC learning in 2008. The resulting sample complexity bounds differ from the generic Occam’s razor only by an \(\varepsilon\) factor in the denominator, and \(O(\log|\mathcal{H}|/\varepsilon)\) samples suffice to privately PAC learn \(\mathcal{H}\).
Of course, our experience with non-private PAC learning suggests that we shouldn’t be satisfied with this \(\log |\mathcal{H}|\) dependence. Maybe VC dimension characterizes private PAC learning, too?
Characterizing Pure Private PAC Learning
As it turns out, answering this question will take some time. We start with a partial negative answer. Specifically, we’ll see a class with VC dimension 1 and (a restricted form of) private sample complexity arbitrarily larger than 1. We’ll also cover the first in a line of characterization results for private PAC learning.
We first consider learners that satisfy pure privacy. Recall that pure \((\varepsilon,0)\)-differential privacy forces output distributions that may only differ by a certain \(e^\varepsilon\) multiplicative factor (like the exponential mechanism above). The strictly weaker notion of approximate \((\varepsilon,\delta)\)-differential privacy also allows a small additive \(\delta\) factor. Second, we restrict ourselves to proper learners, which may only output hypotheses from the learned class \(\mathcal{H}\).
With these assumptions in place, in 2010, Beimel, Kasiviswanathan, and Nissim [BKN10] studied a hypothesis class called \(\mathsf{Point}_d\). \(\mathsf{Point}_d\) consists of \(2^d\) hypotheses, one for each vector in \(\{0,1\}^d\). Taking the set of examples \(\mathcal{X}\) to be \(\{0,1\}^d\) as well, we define each hypothesis in \(\mathsf{Point}_d\) to label only its associated vector as 1, and the remaining \(2^d-1\) examples as -1. [BKN10] showed that the hypothesis class \(\mathsf{Point}_d\) requires \(\Omega(d)\) samples for proper pure private PAC learning. In contrast, \(\mathsf{VCD}\left(\mathsf{Point}_d\right) = 1\), so this \(\Omega(d)\) lower bound shows us that VC dimension does not characterize proper pure private PAC learning.
This result uses the classic “packing” lower bound method, which powers many lower bounds for pure differential privacy. The general packing method is to first construct a large collection of databases which are all “close enough” to each other but nonetheless all have different “good” outputs. Once we have such a collection, we use group privacy. Group privacy is a corollary of differential privacy that requires databases differing in \(k\) elements to have \(k\varepsilon\)-close output distributions. Because of group privacy, if we start with a collection of databases that are close together, then the output distributions for any two databases in the collection cannot be too different. This creates a tension: utility forces the algorithm to produce different output distributions for different databases, but privacy forces similarity. The packing argument comes down to arguing that, unless the databases are large, privacy wins out, and when privacy wins out then there is some database where the algorithm probably produces a bad output.
For \(\mathsf{Point}_d\), we sketch the resulting argument as follows. Suppose we have an \(\varepsilon\)-private PAC learner that uses \(m\) samples. Then we can define a collection of different databases of size \(m\), one for each hypothesis in \(\mathsf{Point}_d\). By group privacy, the output distribution for our private PAC learner changes by at most \(e^{m\varepsilon}\) between any two of the databases in this collection. Thus we can pick any \(h \in \mathsf{Point}_d\) and know that the probability of outputting the wrong hypothesis is at least roughly \(2^d \cdot e^{-m\varepsilon}\). Since we need this probability to be small, rearranging implies \(m = \Omega(d/\varepsilon)\).
[BKN10] then contrasted this result with an improper pure private PAC learner. This learner applies the exponential mechanism to a class \(\mathsf{Point}_d’\) of hypotheses derived from \(\mathsf{Point}_d\) — but not necessarily a subset of \(\mathsf{Point}_d\) — gives an improper pure private PAC learner with sample complexity \(O(\log d)\). Since this learner is improper, it circumvents the “one database per hypothesis” step of the packing lower bound. Moreover, [BKN10] gave a still more involved improper pure private PAC learner requiring only \(O(1)\) samples. This separates proper pure private PAC learning from improper pure private PAC learning. In contrast, the sample complexities of proper and improper PAC learning absent privacy are the same up to logarithmic factors in \(\alpha\) and \(\beta\).
In 2013, Beimel, Nissim, and Stemmer [BNS13] proved a more general result. They gave the first characterization of pure (improper) private PAC learning by defining a new hypothesis class measure called the representation dimension, \(\mathsf{REPD}\left(\mathcal{H}\right)\). Roughly, the representation dimension considers the collection of all distributions \(\mathcal{D}\) over sets of hypotheses, not necessarily from \(\mathcal{H}\), that “cover” \(\mathcal{H}\). By “cover,” we mean that for any \(h \in \mathcal{H}\), with high probability a set drawn from covering distribution \(\mathcal{D}\) includes a hypothesis that mostly produces labels that agree with \(h\). With this collection of distributions defined, \(\mathsf{REPD}\left(\mathcal{H}\right)\) is the minimum over all such covering distributions of the logarithm of the size of the largest set in its support. Thus a hypothesis class that can be covered by a distribution over small sets of hypotheses will have a small representation dimension. With the notion of representation dimension in hand, [BNS13] gave the following result:
Theorem 1 ([BNS13]). The sample complexity to pure private PAC learn \(\mathcal{H}\) is \(\Theta(\mathsf{REPD}\left(\mathcal{H}\right))\).
Representation dimension may seem like a strange definition, but a sketch of the proof of this result helps illustrate the connection to private learning. Recall from our private Occam’s razor, and the improper pure private PAC learner above, that if we can find a good and relatively small set of hypotheses to choose from, then we can apply the exponential mechanism and call it a day. It is exactly this kind of “good set of hypotheses” that representation dimension aims to capture. A little more formally, given an upper bound on \(\mathsf{REPD}\left(\mathcal{H}\right)\), we know there is some covering distribution whose largest hypothesis set is not too big. That means we can construct a learner that draws a hypothesis set from this covering distribution and applies the exponential mechanism to it. Just as we picked up a \(\log|\mathcal{H}|\) sample complexity dependence using private Occam’s razor, since \(\mathsf{REPD}\left(\mathcal{H}\right)\) measures the logarithm of the size of the largest hypothesis set in the support, this pure private learner picks up a \(\mathsf{REPD}\left(\mathcal{H}\right)\) sample complexity dependence here. This gives us one direction of Theorem 1.
This logic works in the other direction as well. To go from a pure private PAC learner with sample complexity \(m\) to an upper bound on \(\mathsf{REPD}\left(\mathcal{H}\right)\), we return to the group privacy trick used by [BKN10]. Suppose we fix a database of size \(m\) and pass it to the learner. By group privacy and the learner’s accuracy guarantee, if we fix some concept \(c\), the learner has probability at least roughly \(e^{-m}\) of outputting a hypothesis that mostly agrees with \(c\). Thus if we repeat this process roughly \(e^{m}\) times, we probably get at least one hypothesis that mostly agrees with \(c\). In other words, this repeated calling of the learner on the arbitrary database yields a covering distribution for \(\mathcal{H}\). Since we called the learner approximately \(e^m\) times, the logarithm of this is \(m\), and we get our upper bound on \(\mathsf{REPD}\left(\mathcal{H}\right)\).
To recap, we now know that proper pure private PAC learning is strictly harder than improper pure private PAC learning, which is characterized by representation dimension. A picture sums it up. Note the dotted line, since we don’t yet have any evidence separating finite representation dimension and finite VC dimension.
Separating Pure and Approximate Private PAC Learning
So far, we’ve focused only on pure privacy. In this section, we move on to the first separations between pure and approximate private PAC learning, as well as the first connection between private learning and online learning.
Our source is a pair of interconnected papers from around 2014. Among other things, Feldman and Xiao [FX14] introduced Littlestone dimension to private PAC learning. By connecting representation dimension to results from communication complexity to Littlestone dimension, they proved the following:
Theorem 2 ([FX14]). The sample complexity to pure private PAC learn \(\mathcal{H}\) is \(\Omega(\mathsf{LD}\left(\mathcal{H}\right))\).
Littlestone dimension \(\mathsf{LD}\left(\mathcal{H}\right)\) is, roughly, the maximum number of mistakes an adversary can force an online PAC-learning algorithm to make [Lit88]. We always have \(\mathsf{VCD}\left(\mathcal{H}\right) \leq \mathsf{LD}\left(\mathcal{H}\right) \leq \log|\mathcal{H}|\), but these inequalities can be strict. For example, denoting by \(\mathsf{Thresh_T}\) the class of thresholds over \(\{1, 2, \ldots, T\}\), since an adversary can force \(\Theta(\log T)\) wrong answers from an online learner binary searching over \(\{1,2, \ldots, T\}\), \(\mathsf{LD}\left(\mathsf{Thresh_T}\right) = \Omega(\log T)\). In contrast, \(\mathsf{VCD}\left(\mathsf{Thresh_T}\right) = 1\).
At first glance it’s not obvious what Theorem 2 adds over Theorem 1. After all, Theorem 1 gives an equivalence, not just a lower bound. One advantage of Theorem 2 is that Littlestone dimension is a known quantity that has already been studied in its own right. We can now import results like the lower bound on \(\mathsf{LD}\left(\mathsf{Thresh_T}\right)\), whereas bounds on \(\mathsf{REPD}\left(\cdot\right)\) are not common. A second advantage is that Littlestone dimension conceptually connects private learning and online learning: we now know that pure private PAC learning is no easier than online PAC learning.
A second paper by Beimel, Nissim, and Stemmer [BNS13b] contrasted this \(\Omega(\log T)\) lower bound for pure private learning of thresholds with a \(2^{O(\log^\ast T)}\) upper bound for approximate private PAC learning \(\mathsf{Thresh_T}\). Here \(\log^\ast\) denotes the very slow-growing iterated logarithm, the number of times we must take the logarithm of the argument to bring it \(\leq 1\). (We’re not kidding about “very slow-growing” either: \(\log^\ast(\text{number of atoms in universe}) \approx 4\).) With Feldman and Xiao’s result, this separates pure private PAC learning from approximate private PAC learning. It also shows that representation dimension does not characterize approximate private PAC learning.
At the same time, Feldman and Xiao observed that the connection between pure private PAC learning and Littlestone dimension is imperfect. Again borrowing results from communication complexity, they observed that the hypothesis class \(\mathsf{Line_p}\) (which we won’t define here) has \(\mathsf{LD}\left(\mathsf{Line_p}\right) = 2\) but \(\mathsf{REPD}\left(\mathsf{Line_p}\right) = \Theta(\log(p))\). In contrast, they showed that an approximate private PAC learner can learn \(\mathsf{Line_p}\) using \(O\left(\tfrac{\log(1/\beta)}{\alpha}\right)\) samples. Since this entails no dependence on \(p\) at all, it improves the separation between pure and approximate private PAC learning given by [BNS13b].
Let’s pause to recap what’s happened so far. We learned in the last section that representation dimension characterizes pure private PAC learning [BNS13]. We learned in this section that Littlestone dimension gives lower bounds for pure private PAC learning but, as shown by \(\mathsf{Line_p}\), these bounds are sometimes quite loose [FX14]. \(\mathsf{Thresh_T}\) shows that representation dimension does not characterize approximate private PAC learning [FX14 ; BNS13b], and we still have no privacy-specific lower bounds for approximate private learners. So the picture now looks like this:
In particular, we might still find that VC dimension characterizes approximate private PAC learning!
Lower Bounds for Approximate Private PAC Learning
We now dash this hope. In 2015, Bun, Nissim, Stemmer, and Vadhan [BNSV15] gave the first nontrivial lower bound for approximate private PAC learning. They showed that learning \(\mathsf{Thresh_T}\) has proper approximate private sample complexity \(\Omega(\log^\ast(T))\) and \(O(2^{\log^\ast(T)})\).
We’ll at least try to give some intuition for the presence of \(\log^\ast\) in the lower bound. Informally, the lower bound relies on an inductive construction of a sequence of hard problems for databases of size \(n=1, 2, \ldots\). The \(k^{th}\) hard problem relies on a distribution over databases of size \(k\) whose data universe is of of size exponential in the size of the data universe for the \((k-1)^{th}\) distribution. The base case is the uniform distribution over the two singleton databases \(\{0\}\) and \(\{1\}\), and they show how to inductively construct successive problems such that a solution for the \(k^{th}\) problem implies a solution for the \((k-1)^{th}\) problem. Unraveling the recursive relationship between the problem domain sizes implies a general lower bound of roughly \(\log^\ast|X|\) for domain \(X\).
The inclusion of \(\log^\ast\) makes this is an extremely mild lower bound. However, \(\log^\ast(T)\) can still be arbitrarily larger than 1, so this is the first definitive evidence that proper approximate privacy introduces a cost over non-private PAC learning.
In 2018, Alon, Livni, Malliaris, and Moran [ALMM19] extended this \(\Omega(\log^\ast T)\) lower bound for \(\mathsf{Thresh_T}\) to improper approximate privacy. More generally, they gave concrete evidence for the importance of thresholds, which have played a seemingly outsize role in the work so far. They did so by relating a class’ Littlestone dimension to its ability to “contain” thresholds. Here, we say \(\mathcal{H}\) “contains” \(m\) thresholds if there exist \(m\) (unlabeled) examples \(x_1,\ldots,x_m\) and hypotheses \(h_1, \ldots, h_m \in \mathcal{H}\) such that the hypotheses “behave like” thresholds on the \(m\) examples, i.e., \(h_i(x_j) = 1 \Leftrightarrow j \geq i\). With this language, they imported a result from model theory to show that any hypothesis class \(\mathcal{H}\) contains \(\log(\mathsf{LD}\left(\mathcal{H}\right))\) thresholds. This implies that learning \(\mathcal{H}\) is at least as hard as learning \(\mathsf{Thresh_T}\) with \(T = \log(\mathsf{LD}\left(\mathcal{H}\right))\). Since \(\log^\ast(\log(\mathsf{LD}\left(\mathcal{H}\right))) = \Omega(\log^\ast(\mathsf{LD}\left(\mathcal{H}\right)))\), combining these two results puts the following limit on private PAC learning:
Theorem 3 ([ALMM19]). The sample complexity to approximate private PAC learn \(\mathcal{H}\) is \(\Omega(\log^\ast(\mathsf{LD}\left(\mathcal{H}\right)))\).
Littlestone dimension characterizes online PAC learning, so we now know that online PAC learnability is necessary for private PAC learnability. Sufficiency, however, remains an open question. This produces the following picture, where the dotted line captures the question of sufficiency.
Characterizing Approximate Private PAC Learning
Spurred by this question, several advances in private PAC learning have appeared in the last year. First, Gonen, Hazan, and Moran strengthened Theorem 3 by giving a constructive method for converting pure private learners to online learners [GHM19]. Their result reaches back to the 2013 characterization of pure private learning in terms of representation dimension by using the covering distribution to generate a collection of “experts” for online learning. Again revisiting \(\mathsf{Thresh_T}\), Kaplan, Ligett, Mansour, Naor, and Stemmer [KLMNS20] significantly reduced the \(O(2^{\log^\ast(T)})\) upper bound of [BNSV15] to just \(O((\log^\ast(T))^{1.5})\). And Alon, Beimel, Moran, and Stemmer [ABMS20] justified this post’s focus on realizable private PAC learning by giving a transformation from a realizable approximate private PAC learner to an agnostic one at the cost of slightly worse privacy and sample complexity. This built on an earlier transformation that only applied to proper learners [BNS15].
Finally, Bun, Livni, and Moran [BLM20] answered the open question posed by [ALMM19]:
Theorem 4 ([BLM20]). The sample complexity to approximate private PAC learn \(\mathcal{H}\) is \(2^{O({\mathsf{LD}\left(\mathcal{H}\right)})}\).
To prove this, [BLM20] introduced the notion of a globally stable learner and showed how to convert an online learner to a globally stable learner to a private learner. Thus, combined with the result of [ALMM19], we now know that the sample complexity of private PAC learning any \(\mathcal{H}\) is at least \(\Omega(\log^\ast(\mathsf{LD}\left(\mathcal{H}\right)))\) and at most \(2^{O({\mathsf{LD}\left(\mathcal{H}\right)})}\). In this sense, online learnability characterizes private learnability.
Narrowing the gap between the lower and upper bounds above is an open question. Note that we cannot hope to close the gap completely. For the lower bound, the current \(\mathsf{Thresh_T}\) upper bound implies that no general lower bound can be stronger than \(\Omega((\log^\ast(\mathsf{LD}\left(\mathcal{H}\right)))^{1.5})\). For the upper bound, there exist hypotheses classes \(\mathcal{H}\) with \(\mathsf{VCD}\left(\mathcal{H}\right) = \mathsf{LD}\left(\mathcal{H}\right)\) (e.g., \(\mathsf{VCD}\left(\mathsf{Point}_d\right) = \mathsf{LD}\left(\mathsf{Point}_d\right)= 1\)), so since non-private PAC learning requires \(\Omega(\mathsf{VCD}\left(\mathcal{H}\right))\) samples, the best possible private PAC learning upper bound is \(O(\mathsf{LD}\left(\mathcal{H}\right))\). Nevertheless, proving either bound remains open.
Conclusion
This concludes our post, and with it our discussion of this fundamental question: the price of privacy in machine learning. We now know that in the PAC model, proper pure private learning, improper pure private learning, approximate private learning, and non-private learning are all strongly separated. By the connection to Littlestone dimension, we also know that approximate private learnability is equivalent to online learnability. However, many questions about computational efficiency and tight sample complexity bounds remain open.
As mentioned in the introduction, we focused on the clean yet widely studied and influential model of PAC learning. Having characterized how privacy enters the picture in PAC learning, we can hopefully convey this understanding to other models of learning, and now approach these questions from a rigorous and grounded point of view.
Congratulations to Mark Bun, Roi Livni, and Shay Moran on their best paper award — and to the many individuals who paved the way before them!
Acknowledgments
Thanks to Kareem Amin and Clément Canonne for helpful feedback while writing this post.
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API
Get Phone Info Phone.getPhoneInternational(number)
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{{ getInfo.result }}
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{{ format.value | phone:'national' }}
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Validate Phone.validate(number)
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AngularJS Support
{{ '552189898989' | phone:'international' }}
{{ '552189898989' | phone:'national' }}
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{{ '2189898989' | phone:'international':55 }}
{{ '2189898989' | phone:'national':55 }}
{{ '2189898989' | phone:'local':55 }}


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{{ search_term }}
{{ amount }} results are were found
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{% for entry in entries %}
{{ entry[0] }}
{{ entry[1] }}
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{% endfor %}


{% extends 'layout-lab-3-pregnant.html' %} {% block pageTitle %} Pregnancy - Labour and birth - Signs that labour has begun - NHS.UK {% endblock %} {% block beforeContent %} {% from 'details/macro.njk' import details %} {{ details({ "classes": "alpha-lab-breadcrumbs", "text": "The start of labour", "HTML": "
The start of labour is called the latent phase. This is when your cervix becomes soft and thin, and starts opening for your baby to be born. This can take hours or, for some women, days.