WHAT WOMEN WANT RATING: 5/10 --> Not a good movie
For more reviews and movie screensavers, visit http://www.joblo.com/
Can Mel Gibson ever do any wrong?  Unfortunately, a solid performance by Mel, charming as usual, and the great shots of him without his shirt, you can bounce quarters of that six-pack of his, still don't save this film from saying very little about anything. It's a very, very "surface" kind of movie...with lots of songs packed into its best-selling soundtrack-to-be. Great performance by Mel, enjoyable overused tunes and a few funny moments and you've got yourself a perfect example of a "video date movie".
PLOT: A macho, rich, jerk suddenly gets the power to read women's minds and decides to use it to help him make his life better. He wants to better his job, better the relationship he has with his daughter and better the way that he treats the women in his life. Will it work? Will it fall apart? Will we be suffocated by the many cute "Mel" moments before being treated to an actual story? Find out below.
CRITIQUE: See Mel Gibson dance around by himself to Sinatra tunes. Hear Mel do his best Sean Connery impression. See Mel walking around shirtless half the movie.  See Mel relate to his daughter over a loud montage featuring Christina Aguilera's "What A Girl Wants", as she tries on different prom dresses. Sigh. See women swoon as all of this takes place on the big screen. Hear men moan as they sit there next to their ladies. This one ain't for us, fellas. In fact, I wouldn't even recommend this to any women either, unless they were just looking for a fluffy ol' time. This movie has a great premise, and I mean a GREAT one! Here's a man who by some crazy fluke of an accident, can actually hear what women think. Wow. Isn't that a great way to start a movie? Yup, sure is. Unfortunately, the makers of this movie decided to concentrate more on the number of musical interludes that they would have in the film, rather than any actual story! Let's add another Sinatra number here, and another cool song from the soundtrack there, and wouldn't it be cool if we added a montage with another song playing as Mel moves from place to place here? Uuuuuhmm, I guess someone forget to tell the filmmakers that they were actually producing a movie...not a soundtrack!
Ugh, one of the most blatantly commercial movies to come down the pike in a long time. And by commercial, I mean a film so OBVIOUSLY created for a certain target audience. We've got the sad sack emotionally vulnerable character drifting in and out of the movie, for the sake of depth. Disposable secondary characters based on their obvious proclivity to the target audience (females 30-45). Remember who women chose as the most sensitive guy back in the old days? Alan Alda, that's right, he's in this movie! And what's any "chick flick" without Bette Midler. Oy vey, is right! I don't know, maybe I've seen too many of these types of movies in my day and the whole schtick is getting to be a little too see-through for me, but even without the obvious manipulative stuff going on behind the scenes, the story here is really quite underdeveloped. Mel gets this great power and does barely anything with it.
And despite several cute and funny moments, especially the whole scene in bed with Marisa Tomei (tough shoot, hey Marisa?), the film just never really does much with its initial great concept. In fact, the wrap-up of Mel's newfound "power" is handled in an extremely clumsy way. Things just never seem to go under any type of surface in this movie, but if that's the kind of film that you're looking, then you might just enjoy this fluff piece. And no offense to Helen Hunt, whom I consider to be a solid actress, but am I the only one that's a bit Helen-ed out? That's four movies with her in the past six weeks! Phew. At least she had a "tan" in this one, despite the lack of color in her character's persona. This film is a study into the art of Nora Ephron romance movies gone awry!
Review Date: December 13, 2000 Director: Nancy Meyers Writers: Josh Goldsmith and Cathy Yuspa Producers: Susan Cartsonis, Bruce Davey, Gina Matthews, Nancy Myers, Matt Williams Actors: Mel Gibson as Nick Marshall Helen Hunt as Darcy Maguire Marisa Tomei Genre: Romantic Comedy Year of Release: 2000 ------------------------------------ JoBlo's Movie Emporium http://www.joblo.com/ ------------------------------------ (c) 2000 Berge Garabedian
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
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Related links: index of all rec.arts.movies.reviews reviews


[§435C-10] Examinations. The insurance commissioner shall make an examination into the affairs of the plan at least annually. Such examination shall be conducted and the report thereon filed in the manner prescribed in section 431:2-302. The expenses of every such examination shall be borne and paid by the plan in the manner prescribed by section 431:2-306. [L 1975, c 161, pt of §1]
Revision Note
Sections 431:2-302 and 431:2-306 substituted for sections 431-54 and 431-59, respectively.


This sample demonstrates how an application can communicate with a cloud-based service and synchronize its data with data stored locally in a content provider. The sample uses two related parts of the Android framework — the account manager and the synchronization manager (through a sync adapter). It also demonstrates how to provide users the ability to create and edit synchronized contacts using a custom editor.
The account
manager allows sharing of credentials across multiple applications and
services. Users enter the credentials for each account only once —
applications with the USE_CREDENTIALS
permission can then query the
account manager to obtain an auth token for the account. An authenticator (a
pluggable component of account manager) requests credentials from the user,
validates them with an authentication server running in the cloud, and then
stores them to the account manager. This sample demonstrates how to write an
authenticator for your service by extending the new
AbstractAccountAuthenticator
abstract class.
The sync adapter (essential to the synchronization service) declares the
account type and ContentProvider authority to the sync manager. This sample
demosntrates how to write your own sync adapters by extending the
AbstractThreadedSyncAdapter
abstract class and implementing the
onPerformSync()
method, which gets called whenever the sync manager
issues a sync operation for that sync adapter.
Update: This sample has been updated for Android 4.0 to demonstrate new features, including: syncing and viewing contact groups, handling the "invite" intent, and a few other improvements.
The cloud-based service for this sample application is running at:
http://samplesyncadapter2.appspot.com/
When you install this sample application, a new syncable "SampleSyncAdapter" account will be added to your phone's account manager. You can go to "Settings | Accounts & Sync" to view the account and change its sync settings.


Results From The 2003 Marcus Daly Criterium
Hamilton Montana, August 3
Thanks
to our Sponsors: Pioneer Log Homes, Todd Lindsey, Bitteroot Brewing, Valley
Bike and Ski, Citizens State Bank, Chapter One Books, Pizza Hut, Subway, Darby
Distribution, Grocery Emporium, and Montana Shirts
Masters Men 35+
30 laps
1 Mike
Longmire Northern Rockies 63
2 Rich
Graves Flathead
Cycling 130
3 John
Hartpence Yellow Breeches 83
4 Eric
Greenberg Flathead Cycling 87
5 Mark
Bates Logan
Racing 75
6 Craig
Pozega 76
7 Jeremy
Oury Five
Valley Velo 82
8 Richard
Allen Five
Valley Velo 90
9 Bruce
Hunner 65
DNF Eric
Grove Great
Divide (wreck)
Prime Winners- Mike Longmire, Rich Graves
Men 4-5 36
laps
1 Patrick
Hutchins Five Valley Velo 95
2 John
Hartpence Yellow Breeches 83
3 Jeremy
Oury Five
Valley Velo 82
4 Bob
Presta 77
5 Shaun
Fulmer Five
Valley Velo 79
6 Bob
Foley Flathead
Cycling 86
7 Miles
Key Five
Valley Velo 88
8 Joe
Scott Five
Valley Velo 85
9 Elliot
Bassett Five
Valley Velo 81
10 Steve
Helstrom 129
11 Dan
Gager Five
Valley Velo 98
12 Howard
Williams 96
13 Graham
Baskett Five Valley Velo 80
14 Steve
Visser 78
DNF Mark
Nitz Yellowstone
Valley 92
Prime Winners-Patrick Hutchins, John Hartpence, Shaun
Fulmer
Junior Men 27 laps
1 Nigel
Neaves Valley
Bike and Ski 15
Women 27
laps
1 Jen
Nerison Five Valley Velo 293
2 Sheryl
Burright 291
Men 1,2,3 44
laps
1 Evan
Lawrence Hammer Gel 64
2 Will
Schneider USI 89
3 Robert Amrine 99
4 Chad
Devall 94
DNF Todd
Jankewitz Five Valley Velo
(wreck)
DNF Matt
Seeley Five
Valley Velo (mechanical)
Prime Winners- Evan Lawrence, Chad Devall, Robert
Amrine


Pulling Up Your Legacy App by Its Bootstraps
by Emily Stamey
by Emily Stamey
Talk to users of the application
Study the codebase
Examine the new feature requests
Talk to users of the application
Study the codebase
Examine the new feature requests
// Useless comment.
alert('hi');
This focuses on the comment.
Another fragment.
function linkify( selector ) {
if( supports3DTransforms ) {
var nodes = document.querySelectorAll( selector );
for( var i = 0, len = nodes.length; i < len; i++ ) {
var node = nodes[i];
if( !node.className ) {
node.className += ' roll';
}
}
}
}
This focuses on the comment.
Another fragment.


Page Views By Month Report
The Page Views By Month report displays the total number of visitors and users who viewed the site each month for the selected range of months.
Report Fields:
- Month: The number of the current calendar month. E.g. 1 = January
- Views: Number of views for the month
- Visitors: Total number of all visitors for the month
- Users: Number of visits by registered user for the month
The Page Views By Month Site Log Report


transform
I've seen things you people wouldn't believe. Attack ships on fire off the
shoulder of Orion. I watched C-beams glitter in the dark near the Tannhauser
gate. All those moments will be lost in time... like tears in rain...  Attack ships on fire off the
shoulder of Orion. I watched C-beams glitter in the dark near the Tannhauser
gate. All those moments will be lost in time... like tears in rain...  Attack ships on fire off the
shoulder of Orion. I watched C-beams glitter in the dark near the Tannhauser
gate. All those moments will be lost in time... like tears in rain...


Create and design modern responsive websites using HTML5, CSS, Bootstrap, Javascript and React.
Develop web applications on the server side using Node.js, Express, MongoDB, SQL and Firebase. Also, pulling data from various API's to make better and more interactive web applications.
Create android apps with Android Studio while using Java.
First and foremost I try to be the best version of myself. Whatever I do, I give it my best. Whether it be programming, baking or playing sports. I will always give it 100 per cent! Ever since I was introduced to coding, I found something I love doing. I like to use a creative approach for problem solving, try to find the most efficient way to get a job done. I am energetic and like to learn new skills. I like working within a team organising events and working on innovative ideas.
In my leisure time, I like to read, play sports, watch documentaries and go to the gym.
Frontend projects
Backend projects
Group projects


Share/Unshare Snova(GAE) AppID
Note:
- You can share your snova appid to people who do NOT known how to deploy snova(GAE) server.
- An email account needed as a verify id for sharing/unsharing appid.
- The shared appid can be used by anybody as 'anonymouse' user.
- You can use snova admin tool to control traffic and blacklist for 'anonymouse'.


We Want Your Feedback!
We love helping our community. Help us out by providing us details on what you want to see.
Your phone and email will only be used for security purposes and to notify you in case we use your example!
A example URL is required for us to know what you'd like to see.


Pig is a folk jeopardy dice game with simple rules: Two players race to reach 100 points. Each turn, a player repeatedly rolls a die until either a 1 ("pig") is rolled or the player holds and scores the sum of the rolls (i.e. the turn total). At any time during a player's turn, the player is faced with two decisions:
Problem: Given a player's score, simulate a single turn of Pig where a player rolls until a 1 ("pig") is rolled, or the turn total is greater than or equal to 20, or the score plus the turn total is greater than or equal to 100.
Input Format: The input is a single integer representing a Pig player score.
Output Format:
Sample Transcript (input underlined):
Score? 90 Roll: 2 Roll: 3 Roll: 4 Roll: 4 Turn total: 13 New score: 103


{% for s_info in s_infos %}
{{ s_info.i_name.s_name }}
{% endfor %}
Student Info Are Followings:
{% for s_info in s_infos %}
-
Hobby: {{ s_info.i_hobby }}
{% endfor %}
{% for s_info in s_infos %}
-
Age: {{ s_info.i_age }}
{% endfor %}
{% for s_info in s_infos %}
-
Birth: {{ s_info.i_birth }}
{% endfor %}


Please choose an image collection from the above menus. First choose a space and then choose a collection.
Edit Collections
How to Edit Collections
A Collection respresents a group/collection of images within a DuraCloud Space.
Images within a collection must be organized using the following structure:
thumbs (thumbnail images displayed in a grid, all viewable on the page)
previews (larger versions of the thumbnail images, displayed when a thumbnail is clicked)
highres (high resolution images that can be viewed by clicking on the link underneath the blownup preview images)
Example organization structure:
collection1/thumbs/img1.jpg
collection1/thumbs/img2.jpg
collection1/previews/img1.jpg
collection1/previews/img2.jpg
collection1/highres/img1.jpg
collection1/highres/img2.jpg
collection2/thumbs/img1.jpg
collection2/thumbs/img2.jpg
collection2/previews/img1.jpg
collection2/previews/img2.jpg
collection2/highres/img1.jpg
collection2/highres/img2.jpg
A collection can have any name. The above 'collection1', 'collection2' are arbitrary examples.
The images in a collection can have any name, but the corresponding images between thumbs, previews, and highres must have the same name. The above 'img1.jpg', 'img2.jpg' are arbitrary examples.
Spaces can be added by clicking the '+' button. The space must already exist within DuraCloud.
Spaces can be removed by selecting the space to remove from the dropdown menu and then clicking the '-' button.
Adding/Removing collections from a space:
Select the space to add/remove collections to/from.
The current collections will be displayed in the text area below the selected space.
To add a collection, type in the name of the collection on a new line.
To remove a collection, delete the line containing the name of the collection.
Edits are not saved until the 'Save' button is clicked.
Add Space
DuraCloud Image Gallery Tips & Tricks
A few tips and tricks about the DuraCloud image gallery:
When the page is loaded the available spaces and image collections are retrieved and loaded into the dropdown menu. Selecting a space from the dropdown menu triggers the thumbnails in that space to be loaded.
If this is your first time using the image gallery you will most likely not have any spaces or collections availble to select from the dropdown menus. You can set up your available spaces and image collections by clicking the "Edit" button at the top of the screen. There is a "(?) Help" button on the Edit window explaining how to setup your available spaces and image collections.
The thumbnails are displayed in a grid with the name of each image underneath its thumbnail.
Clicking a thumbnail will load a larger version of the image in the foreground.
When viewing a blownup thumbnail:
The blownup image can be zoomed in and out by scrolling on it (mousewheel or trackpad).
A zoomed in image can be panned around by moving the mouse around.
Navigating to the next/previous image can be done by clicking the left or right arrows on either side of the screen or by pressing the left or right arrow keys on the keyboard.
You can exit from viewing the blownup image display by clicking the 'X' at the top-right corner of the screen or by pressing the "Esc" or "x" key on the keyboard.
Clicking the content ID link below the blown up image loads the high-res jpg in a new browser tab/window.
Most of the above functionality works the same on mobile devices.


Drew is a student that programs for fun.
See what Drew is good at
Join this discord to chat with me and suggest improvements https://discord.gg/9mf8ZPt


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This shirt is in remembrance of Dick Assman, a gas station worker turned into a celebrity by David Letterman. God rest his soul. In order to capture his full likeness, I moved the background and the picture of Dick into Adobe Lightroom and merged them together with photoshop.
Next, I made a hat with sublimation printing. The pictures for the hat and Dick Assman were put onto a template in Corel Draw and then exported to be pressed onto the hat and shirt.
The upside to sublimation printing is that it can be done on virtually everything; shirts, mugs, ties, hats. It is also somewhat inexpensive compared to other methods.
Home


India squad vs West Indies announced; Bhuvi returns, Shami makes T20I comeback
The West Indies series consists of three T20Is and three ODI's.
by DECCAN CHRONICLE.Mumbai: The All India Senior Selection Committee met in Kolkata to decide the squad for the Indian cricket team for the West Indies series. The series consists of three T20Is and three ODI's.
Selection committee meets to pick squads for West Indies series
The T20Is will take place in Mumbai on December 6, Thiruvananthapuram on December 8 and Hyderabad on December 11.
The ODIs will take place Chennai on December 15, Visakhapatnam on December 18 and Cuttack on December 22.
India Squad for T20Is:
Virat Kohli (C), Rohit Sharma, Shikhar Dhawan, KL Rahul, Rishabh Pant, Manish Pandey, Shreyas Iyer, Kedar Jadhav, Ravindra Jadeja, Shivam Dube, Yuzvendra Chahal, Kuldeep Yadav, Mohammed Shami, Deepak Chahar and Bhuvneshwar Kumar.
India Squad for ODIs:
Virat Kohli (C), Rohit Sharma, Shikhar Dhawan, KL Rahul, Rishabh Pant, Manish Pandey, Shreyas Iyer, Shivam Dube, Ravindra Jadeja, Washington Sundar, Yuzvendra Chahal, Kuldeep Yadav, Deepak Chahar, Bhuvneshwar Kumar and Mohammed Shami.


;
Chaitanya Ashtekar
Home
Skills
Porfolio
API/Fullstack Projects
Contact
<EMAIL_ADDRESS>+91-9028745967/+917263954367
Chaitanya Ashtekar
I'm a self-taught web developer who loves to code
. I love to learn continuousy so my list of projects is constantly growing.
Check out my work and let me know what you think!
Skillset :
NODE js
JS
JQUERY
Mongodb
HTML
CSS
express js
see me practice javascript on
codewars
||
hackerearth
Portfolio (
Font-End
)
Simon Game
a classic simon game(jquery events)
Pomodoro Clock
i
Github search
by stars/term
wikipedia Search Page
search by term-displays top 10 results
JS Calculator
jquery cal
API / Full Stack Projects
--hosted on
Heroku
It may requie a few seconds to start the
dyno
Time Stamp(
heroku
)
Header Parser(
heroku
)
url Shortner(
github
)
File uploader/Metadata(
github
)
Contact
github.com/chaitanyaashtekar
Codepen
<EMAIL_ADDRESS>+91-9028745967/ +917263954367


I am experienced in leveraging agile frameworks to provide a robust synopsis for high level overviews. Iterative approaches to corporate strategy foster collaborative thinking to further the overall value proposition.
Apart from being a web developer, I enjoy most of my time being outdoors. In the winter, I am an avid skier and novice ice climber. During the warmer months here in Colorado, I enjoy mountain biking, free climbing, and kayaking.
When forced indoors, I follow a number of sci-fi and fantasy genre movies and television shows, I am an aspiring chef, and I spend a large amount of my free time exploring the latest technology advancements in the front-end web development world.


---
title: "32+ M Lok Logo
Pics"
description: "1,000+ vectors, stock photos & psd files."
date: "2020-05-31"
categories:
- "Logo"
images:
- "https://www.aeroprecisionusa.com/media/catalog/product/placeholder/default/NoPhoto_Logo_9.jpg"
featuredImage: "https://cdn.webshopapp.com/shops/44381/files/330581935/890x820x2/metal-5-slot-m-lok-cnc-aluminum-rail.jpg"
featured_image: "https://i0.wp.com/files.constantcontact.com/e8bc7db9001/45481fb7-c4d0-4927-9360-5257c24520c5.jpg"
image: "https://cdn.shopify.com/s/files/1/1395/3677/products/Team_M-LOK_KEYMOD_AMazon_Main_Trans_1024x1024.png?v=1543959456"
---
32+ M Lok Logo
Pics. Designevo's lock logo maker provides lots of lock logo designs for you. Lok logo locação de andaimes e ferramentas para construção.
You can customize them to get a striking logo design in seconds. Lok logo locação de andaimes e ferramentas para construção. Even better, both of these systems also gave gun owners the opportunity to mount small rails directly to their handguards, effectively.
Find & download free graphic resources for m logo.
1,000+ vectors, stock photos & psd files. These gun accessories store developed by ergo are resistant to chemicals and heat to. The following other wikis use this file: ✓ free for commercial use ✓ high quality images.


Lazy real and complex numbers#
These classes are very lazy, in the sense that it doesn’t really do anything but simply sits between exact rings of characteristic 0 and the real numbers. The values are actually computed when they are cast into a field of fixed precision.
The main purpose of these classes is to provide a place for exact rings (e.g. number fields) to embed for the coercion model (as only one embedding can be specified in the forward direction).
- sage.rings.real_lazy.ComplexLazyField()#
Returns the lazy complex field.
EXAMPLES:
There is only one lazy complex field:
sage: ComplexLazyField() is ComplexLazyField() True
- class sage.rings.real_lazy.ComplexLazyField_class#
Bases:
LazyField
This class represents the set of complex numbers to unspecified precision. For the most part it simply wraps exact elements and defers evaluation until a specified precision is requested.
For more information, see the documentation of the
RLF
.EXAMPLES:
sage: a = CLF(-1).sqrt() sage: a 1*I sage: CDF(a) 1.0*I sage: ComplexField(200)(a) 1.0000000000000000000000000000000000000000000000000000000000*I
- construction()#
Returns the functorial construction of
self
, namely, algebraic closure of the real lazy field.EXAMPLES:
sage: c, S = CLF.construction(); S Real Lazy Field sage: CLF == c(S) True
- gen(i=0)#
Return the \(i\)-th generator of
self
.EXAMPLES:
sage: CLF.gen() 1*I sage: ComplexField(100)(CLF.gen()) 1.0000000000000000000000000000*I
- interval_field(prec=None)#
Returns the interval field that represents the same mathematical field as
self
.EXAMPLES:
sage: CLF.interval_field() Complex Interval Field with 53 bits of precision sage: CLF.interval_field(333) Complex Interval Field with 333 bits of precision sage: CLF.interval_field() is CIF True
- class sage.rings.real_lazy.LazyAlgebraic#
Bases:
LazyFieldElement
This represents an algebraic number, specified by a polynomial over \(\QQ\) and a real or complex approximation.

EXAMPLES:
sage: from sage.rings.real_lazy import LazyBinop sage: a = LazyBinop(RLF, 2, 1/3, operator.add) sage: a 2.333333333333334? sage: Reals(200)(a) 2.3333333333333333333333333333333333333333333333333333333333
- depth()#
Return the depth of
self
as an arithmetic expression.This is the maximum number of dependent intermediate expressions when evaluating
self
, and is used to determine the precision needed to get the final result to the desired number of bits.It is equal to the maximum of the right and left depths, plus one.
EXAMPLES:
sage: from sage.rings.real_lazy import LazyBinop sage: a = LazyBinop(RLF, 6, 8, operator.mul) sage: a.depth() 1 sage: b = LazyBinop(RLF, 2, a, operator.sub) sage: b.depth() 2
- eval(R)#
Convert the operands to elements of
R
, then perform the operation on them.EXAMPLES:
sage: from sage.rings.real_lazy import LazyBinop sage: a = LazyBinop(RLF, 6, 8, operator.add) sage: a.eval(RR) 14.0000000000000
A bit absurd:
sage: a.eval(str) '68'
- class sage.rings.real_lazy.LazyConstant#
Bases:
LazyFieldElement
This class represents a real or complex constant (such as
pi
orI
).- eval(R)#
Convert
self
into an element ofR
.EXAMPLES:
sage: from sage.rings.real_lazy import LazyConstant sage: a = LazyConstant(RLF, 'e') sage: RDF(a) # indirect doctest 2.718281828459045 sage: a = LazyConstant(CLF, 'I') sage: CC(a) 1.00000000000000*I
- class sage.rings.real_lazy.LazyField#
Bases:
Field
The base class for lazy real fields.
Warning
LazyField uses
__getattr__()
, to implement:sage: CLF.pi 3.141592653589794?
I (NT, 20/04/2012) did not manage to have
__getattr__
callParent.__getattr__()
in case of failure; hence we can’t use this__getattr__
trick for extension types to recover the methods from categories. Therefore, at this point, no concrete subclass of this class should be an extension type (which is probably just fine):sage: RLF.__class__ <class 'sage.rings.real_lazy.RealLazyField_class_with_category'> sage: CLF.__class__ <class 'sage.rings.real_lazy.ComplexLazyField_class_with_category'>
- Element#
alias of
LazyWrapper
- algebraic_closure()#
Returns the algebraic closure of
self
, i.e., the complex lazy field.EXAMPLES:
sage: RLF.algebraic_closure() Complex Lazy Field sage: CLF.algebraic_closure() Complex Lazy Field
- interval_field(prec=None)#
Abstract method to create the corresponding interval field.
- class sage.rings.real_lazy.LazyFieldElement#
Bases:
FieldElement
- approx()#
Returns
self
as an element of an interval field.EXAMPLES:
sage: CLF(1/6).approx() 0.1666666666666667? sage: CLF(1/6).approx().parent() Complex Interval Field with 53 bits of precision
When the absolute value is involved, the result might be real:
sage: z = exp(CLF(1 + I/2)); z 2.38551673095914? + 1.303213729686996?*I sage: r = z.abs(); r 2.71828182845905? sage: parent(z.approx()) Complex Interval Field with 53 bits of precision sage: parent(r.approx()) Real Interval Field with 53 bits of precision
- continued_fraction()#
Return the continued fraction of self.
EXAMPLES:
sage: a = RLF(sqrt(2)) + RLF(sqrt(3)) sage: cf = a.continued_fraction() sage: cf [3; 6, 1, 5, 7, 1, 1, 4, 1, 38, 43, 1, 3, 2, 1, 1, 1, 1, 2, 4, ...] sage: cf.convergent(100)<PHONE_NUMBER>12646558239761867973501208151173610180916865469/141414466649174973335183571854340329919207428365474086063
- depth()#
Abstract method for returning the depth of
self
as an arithmetic expression.This is the maximum number of dependent intermediate expressions when evaluating
self
, and is used to determine the precision needed to get the final result to the desired number of bits.It is equal to the maximum of the right and left depths, plus one.
EXAMPLES:
sage: from sage.rings.real_lazy import LazyBinop sage: a = LazyBinop(RLF, 6, 8, operator.mul) sage: a.depth() 1
- eval(R)#
Abstract method for converting
self
into an element ofR
.EXAMPLES:
sage: a = RLF(12) sage: a.eval(ZZ) 12
- class sage.rings.real_lazy.LazyNamedUnop#
Bases:
LazyUnop
This class is used to represent the many named methods attached to real numbers, and is instantiated by the
__getattr__
method ofLazyElements
.EXAMPLES:
sage: from sage.rings.real_lazy import LazyNamedUnop sage: a = LazyNamedUnop(RLF, 1, 'arcsin') sage: RR(a) 1.57079632679490 sage: a = LazyNamedUnop(RLF, 9, 'log', extra_args=(3,)) sage: RR(a) 2.00000000000000
- approx()#
Does something reasonable with functions that are not defined on the interval fields.
- eval(R)#
Convert
self
into an element ofR
.
- class sage.rings.real_lazy.LazyUnop#
Bases:
LazyFieldElement
Represents a unevaluated single function of one variable.
EXAMPLES:
sage: from sage.rings.real_lazy import LazyUnop sage: a = LazyUnop(RLF, 3, sqrt); a 1.732050807568878? sage: a._arg 3 sage: a._op <function sqrt at ...> sage: Reals(100)(a) 1.7320508075688772935274463415 sage: Reals(100)(a)^2 3.0000000000000000000000000000
- depth()#
Return the depth of
self
as an arithmetic expression.This is the maximum number of dependent intermediate expressions when evaluating
self
, and is used to determine the precision needed to get the final result to the desired number of bits.It is equal to one more than the depth of its operand.
EXAMPLES:
sage: from sage.rings.real_lazy import LazyUnop sage: a = LazyUnop(RLF, 3, sqrt) sage: a.depth() 1 sage: b = LazyUnop(RLF, a, sin) sage: b.depth() 2
- eval(R)#
Convert
self
into an element ofR
.EXAMPLES:
sage: from sage.rings.real_lazy import LazyUnop sage: a = LazyUnop(RLF, 3, sqrt) sage: a.eval(ZZ) sqrt(3)
- class sage.rings.real_lazy.LazyWrapper#
Bases:
LazyFieldElement
A lazy element that simply wraps an element of another ring.
EXAMPLES:
sage: from sage.rings.real_lazy import LazyWrapper sage: a = LazyWrapper(RLF, 3) sage: a._value 3
- continued_fraction()#
Return the continued fraction of self.
EXAMPLES:
sage: a = RLF(sqrt(2)) sage: a.continued_fraction() [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...]
- depth()#
Returns the depth of
self
as an expression, which is always 0.EXAMPLES:
sage: RLF(4).depth() 0
- eval(R)#
Convert
self
into an element ofR
.EXAMPLES:
sage: a = RLF(12) sage: a.eval(ZZ) 12 sage: a.eval(ZZ).parent() Integer Ring
- class sage.rings.real_lazy.LazyWrapperMorphism#
Bases:
Morphism
This morphism coerces elements from anywhere into lazy rings by creating a wrapper element (as fast as possible).
EXAMPLES:
sage: from sage.rings.real_lazy import LazyWrapperMorphism sage: f = LazyWrapperMorphism(QQ, RLF) sage: a = f(3); a 3 sage: type(a) <class 'sage.rings.real_lazy.LazyWrapper'> sage: a._value 3 sage: a._value.parent() Rational Field
- sage.rings.real_lazy.RealLazyField()#
Return the lazy real field.
EXAMPLES:
There is only one lazy real field:
sage: RealLazyField() is RealLazyField() True
- class sage.rings.real_lazy.RealLazyField_class#
Bases:
LazyField
This class represents the set of real numbers to unspecified precision. For the most part it simply wraps exact elements and defers evaluation until a specified precision is requested.
Its primary use is to connect the exact rings (such as number fields) to fixed precision real numbers. For example, to specify an embedding of a number field \(K\) into \(\RR\) one can map into this field and the coercion will then be able to carry the mapping to real fields of any precision.
EXAMPLES:
sage: a = RLF(1/3) sage: a 0.3333333333333334? sage: a + 1/5 0.5333333333333334? sage: a = RLF(1/3) sage: a 0.3333333333333334? sage: a + 5 5.333333333333334? sage: RealField(100)(a+5) 5.3333333333333333333333333333
sage: CC.0 + RLF(1/3) 0.333333333333333 + 1.00000000000000*I sage: ComplexField(200).0 + RLF(1/3) 0.33333333333333333333333333333333333333333333333333333333333 + 1.0000000000000000000000000000000000000000000000000000000000*I
- construction()#
Returns the functorial construction of
self
, namely, the completion of the rationals at infinity to infinite precision.EXAMPLES:
sage: c, S = RLF.construction(); S Rational Field sage: RLF == c(S) True
- gen(i=0)#
Return the \(i\)-th generator of
self
.EXAMPLES:
sage: RLF.gen() 1
- interval_field(prec=None)#
Returns the interval field that represents the same mathematical field as
self
.EXAMPLES:
sage: RLF.interval_field() Real Interval Field with 53 bits of precision sage: RLF.interval_field(200) Real Interval Field with 200 bits of precision
- sage.rings.real_lazy.make_element(parent, *args)#
Create an element of
parent
.EXAMPLES:
sage: a = RLF(pi) + RLF(sqrt(1/2)) # indirect doctest sage: bool(loads(dumps(a)) == a) True


Title: Professor
Address: 35 Broad St, Red Bank, NJ 07701
Phone:<PHONE_NUMBER>
Email<EMAIL_ADDRESS>Website: janedoe.com
Colleagues: Alice Jones, Bob Smith


Mon Nov 17, 2014
This post contains spoilers (at the end). Read on at your own risk.
Interstellar takes on black holes, relativity, and the politics of space exploration - grounding these topics in an emotional and gut-wrenching family drama. It’s a great movie.
Among the various weighty philosophical questions posed in this Christopher Nolan epic, one stands out - are we alone in the universe? I’d like to frame the movie around this question alone. So, you see, this is only sort of an Interstellar review.
The universe is unimaginably vast, yet we have yet to find any life outside our own planet. Well, that’s not quite true - the “unimaginably” part I mean. Plenty of imaginative thinkers have come up with numbers that will blow your mind. Tim Urban is such a thinker - check out his post for an extremely comprehensive read on this subject. Also check out this i09 post.
So yeah, maybe extinction events are more common than we’d like. Or maybe we are of the first emerging sentient species in the universe. Or maybe we aren’t mature enough to join the United Federation of Planets and the Prime Directive prohibits any superior species from making first contact with us. There are a lot of maybes.
There are a lot of questions too. What are the chances that any intelligent aliens out there are humanoid, animals, or even organic? Or that these aliens have developed a similar cultural and sociological value system that places emphasis on altruism and exploration? Or that their method of interpersonal and interstellar communication even closely resembles ours?
With so much uncertainty about anything that exists beyond our exosphere, there are a lot of theories out there on what is called “The Great Silence”. Personally, I love the theory put forward in The Egg, a wonderful short story by Andy Weir.
 I mean, we threw hundreds of millions of dollars into finding Flight MH370, a plane that disappeared into a relatively defined area of the Indian Ocean, and came up empty-handed. So why assume that we can so easily find intelligent life in an infinite universe?
Now, I don’t know if aliens exist or if Jesus can turn Coke into Pepsi. What I do know is that when we throw reasonable science or dogmatic religion aside and just think outside the box, then we have ourselves some excellent cerebral entertainment. And that’s what Interstellar is.
In Interstellar, a benevolent alien presence opens up a wormhole somewhere in the vicinity of Saturn. This same alien presence manifests itself as a poltergeist in a rambling old farmhouse by throwing books off of shelves and manipulating the downward floating trajectory of dust.
By the end of the movie, we discover that these aliens are actually ourselves in a distant future where we have evolved / transcended into beings of the fifth dimension who can manipulate time and space. Well, technically the protagonist of the movie is actually the ghost because he ends up in a construct of the 5th dimension by flying into a black hole, but I don’t want to overcomplicate it - cause really, it makes sense when you watch it.
But to answer the original question - are we alone in the universe? In Interstellar, it seemed there were intelligent extraterrestrials aiding us, but they were just humans. Or were once humans. So, the answer is yes, we are alone. Although just a movie, this premise seems realistic to us.
The truth is that we are such megalomaniacs, we have an easier time believing that we can become omnipresent gods in the far-flung future than believing there is some sort of alternative intelligence in this universe. An intelligence so far removed from our own that it is simply incomprehensible to us. I’m not sure yet if this is a failure of imagination or an unbridled imagination.
If we ever find Flight MH370, then maybe we can talk about how intelligent we are. In the meantime, just enjoy Interstellar because it actually is a fantastic movie - two thumbs up.


Fits standard and random effects latent class models. The single level random effects model is described in Qu et al <doi:10.2307/2533043> and the two level random effects model in Beath and Heller <doi:10.1177/1471082X0800900302>. Examples are given for their use in diagnostic testing.
| Version: | 1.0-15 |
| Depends: | R (≥ 3.2.0), lattice |
| Imports: | boot, fastGHQuad, Matrix |
| Suggests: | R.rsp |
| Published: | 2018-01-16 |
| Author: | Ken Beath [aut, cre] |
| Maintainer: | Ken Beath <ken.beath at mq.edu.au> |
| Contact: | Ken Beath<EMAIL_ADDRESS>|
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | yes |
| Citation: | randomLCA citation info |
| Materials: | NEWS |
| In views: | Cluster, Psychometrics |
| CRAN checks: | randomLCA results |
| Reference manual: | randomLCA.pdf |
| Vignettes: |
randomLCA: An R Package for Latent Class with Random Effects Analysis |
| Package source: | randomLCA_1.0-15.tar.gz |
| Windows binaries: | r-devel: randomLCA_1.0-15.zip, r-release: randomLCA_1.0-15.zip, r-oldrel: randomLCA_1.0-15.zip |
| OS X binaries: | r-release: randomLCA_1.0-15.tgz, r-oldrel: randomLCA_1.0-15.tgz |
| Old sources: | randomLCA archive |
Please use the canonical form https://CRAN.R-project.org/package=randomLCA to link to this page.


${#/hu/scelight/r/html/help/fragment/playing-session.html}
The
Timelapse Session
tab lists all your
Playing Sessions
, and a session stats row shows statistics for
all
the plays of that particular
session
(contrary to the
Time trend Session
tab which takes one play from each
session
at the most based on the play's position).


PDCM - Perf/Debug Capability MSR
The processor supports the performance and debug feature indication MSR IA32_PERF_CAPABILITIES.


Video on boosting methods by Hastie (the textbook author).
Bagging, voting and random forests. The material on bagging and voting is a repeat from last week and can be found in the slides from week 44. We repeat here the voting approach since this will serve as a motivation for boosting methods later.
The idea behind boosting, and voting as well can be phrased as follows: Can a group of people somehow arrive at highly reasoned decisions, despite the weak judgement of the individual members?
The aim is to create a good classifier by combining several weak classifiers. A weak classifier is a classifier which is able to produce results that are only slightly better than guessing at random.
The basic approach is to apply repeatedly (in boosting this is done in an iterative way) a weak classifier to modifications of the data. In voting we simply apply the law of large numbers while in boosting we give more weight to misclassified data in each iteration.
Decision trees play an important role as our weak classifier. They serve as the basic method.
The simplest case is a so-called voting ensemble. To illustrate this, think of yourself tossing coins with a biased outcome of 51 per cent for heads and 49% for tails. With only few tosses, you may not clearly see this distribution for heads and tails. However, after some thousands of tosses, there will be a clear majority of heads. With 2000 tosses you should see approximately 1020 heads and 980 tails.
We can then state that the outcome is a clear majority of heads. If you do this ten thousand times, it is easy to see that there is a 97% likelihood of a majority of heads.
Another example would be to collect all polls before an election. Different polls may show different likelihoods for a candidate winning with say a majority of the popular vote. The majority vote would then consist in many polls indicating that this candidate will actually win.
The example here shows how we can implement the coin tossing case, clealry demostrating that after some tosses we see the law of large numbers kicking in.
# Common imports
from IPython.display import Image
from pydot import graph_from_dot_data
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split
from sklearn.tree import export_graphviz
from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.compose import ColumnTransformer
from IPython.display import Image
from pydot import graph_from_dot_data
import os
# Where to save the figures and data files
PROJECT_ROOT_DIR = "Results"
FIGURE_ID = "Results/FigureFiles"
DATA_ID = "DataFiles/"
if not os.path.exists(PROJECT_ROOT_DIR):
os.mkdir(PROJECT_ROOT_DIR)
if not os.path.exists(FIGURE_ID):
os.makedirs(FIGURE_ID)
if not os.path.exists(DATA_ID):
os.makedirs(DATA_ID)
def image_path(fig_id):
return os.path.join(FIGURE_ID, fig_id)
def data_path(dat_id):
return os.path.join(DATA_ID, dat_id)
def save_fig(fig_id):
plt.savefig(image_path(fig_id) + ".png", format='png')
# Common imports
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
heads_proba = 0.51
coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)
cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)
plt.figure(figsize=(8,3.5))
plt.plot(cumulative_heads_ratio)
plt.plot([0, 10000], [0.51, 0.51], "k--", linewidth=2, label="51%")
plt.plot([0, 10000], [0.5, 0.5], "k-", label="50%")
plt.xlabel("Number of coin tosses")
plt.ylabel("Heads ratio")
plt.legend(loc="lower right")
plt.axis([0, 10000, 0.42, 0.58])
save_fig("votingsimple")
plt.show()
We can use the voting classifier on other data sets, here the exciting binary case of two distinct objects using the make moons functionality of Scikit-Learn.
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_moons
X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import VotingClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC
log_clf = LogisticRegression(solver="liblinear", random_state=42)
rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
svm_clf = SVC(gamma="auto", random_state=42)
voting_clf = VotingClassifier(
estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
voting='hard')
voting_clf.fit(X_train, y_train)
from sklearn.metrics import accuracy_score
for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
log_clf = LogisticRegression(solver="liblinear", random_state=42)
rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
svm_clf = SVC(gamma="auto", probability=True, random_state=42)
voting_clf = VotingClassifier(
estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
voting='soft')
voting_clf.fit(X_train, y_train)
from sklearn.metrics import accuracy_score
for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_moons
X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import VotingClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC
log_clf = LogisticRegression(random_state=42)
rnd_clf = RandomForestClassifier(random_state=42)
svm_clf = SVC(random_state=42)
voting_clf = VotingClassifier(
estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
voting='hard')
voting_clf.fit(X_train, y_train)
from sklearn.metrics import accuracy_score
for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
log_clf = LogisticRegression(random_state=42)
rnd_clf = RandomForestClassifier(random_state=42)
svm_clf = SVC(probability=True, random_state=42)
voting_clf = VotingClassifier(
estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
voting='soft')
voting_clf.fit(X_train, y_train)
from sklearn.metrics import accuracy_score
for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
Random forests provide an improvement over bagged trees by way of a small tweak that decorrelates the trees.
As in bagging, we build a number of decision trees on bootstrapped training samples. But when building these decision trees, each time a split in a tree is considered, a random sample of \( m \) predictors is chosen as split candidates from the full set of \( p \) predictors. The split is allowed to use only one of those \( m \) predictors.
A fresh sample of \( m \) predictors is taken at each split, and typically we choose $$ m\approx \sqrt{p}. $$
In building a random forest, at each split in the tree, the algorithm is not even allowed to consider a majority of the available predictors.
The reason for this is rather clever. Suppose that there is one very strong predictor in the data set, along with a number of other moderately strong predictors. Then in the collection of bagged variable importance random forest trees, most or all of the trees will use this strong predictor in the top split. Consequently, all of the bagged trees will look quite similar to each other. Hence the predictions from the bagged trees will be highly correlated. Unfortunately, averaging many highly correlated quantities does not lead to as large of a reduction in variance as averaging many uncorrelated quantities. In particular, this means that bagging will not lead to a substantial reduction in variance over a single tree in this setting.
We will grow of forest of say \( B \) trees.
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
from sklearn.svm import SVC
from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import BaggingClassifier
# Load the data
cancer = load_breast_cancer()
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
print(X_train.shape)
print(X_test.shape)
# Logistic Regression
logreg = LogisticRegression(solver='lbfgs')
logreg.fit(X_train, y_train)
print("Test set accuracy with Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
# Support vector machine
svm = SVC(gamma='auto', C=100)
svm.fit(X_train, y_train)
print("Test set accuracy with SVM: {:.2f}".format(svm.score(X_test,y_test)))
# Decision Trees
deep_tree_clf = DecisionTreeClassifier(max_depth=None)
deep_tree_clf.fit(X_train, y_train)
print("Test set accuracy with Decision Trees: {:.2f}".format(deep_tree_clf.score(X_test,y_test)))
#now scale the data
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
# Logistic Regression
logreg.fit(X_train_scaled, y_train)
print("Test set accuracy Logistic Regression with scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
# Support Vector Machine
svm.fit(X_train_scaled, y_train)
print("Test set accuracy SVM with scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
# Decision Trees
deep_tree_clf.fit(X_train_scaled, y_train)
print("Test set accuracy with Decision Trees and scaled data: {:.2f}".format(deep_tree_clf.score(X_test_scaled,y_test)))
from sklearn.ensemble import RandomForestClassifier
from sklearn.preprocessing import LabelEncoder
from sklearn.model_selection import cross_validate
# Data set not specificied
#Instantiate the model with 500 trees and entropy as splitting criteria
Random_Forest_model = RandomForestClassifier(n_estimators=500,criterion="entropy")
Random_Forest_model.fit(X_train_scaled, y_train)
#Cross validation
accuracy = cross_validate(Random_Forest_model,X_test_scaled,y_test,cv=10)['test_score']
print(accuracy)
print("Test set accuracy with Random Forests and scaled data: {:.2f}".format(Random_Forest_model.score(X_test_scaled,y_test)))
import scikitplot as skplt
y_pred = Random_Forest_model.predict(X_test_scaled)
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
plt.show()
y_probas = Random_Forest_model.predict_proba(X_test_scaled)
skplt.metrics.plot_roc(y_test, y_probas)
plt.show()
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
plt.show()
Recall that the cumulative gains curve shows the percentage of the overall number of cases in a given category gained by targeting a percentage of the total number of cases.
Similarly, the receiver operating characteristic curve, or ROC curve, displays the diagnostic ability of a binary classifier system as its discrimination threshold is varied. It plots the true positive rate against the false positive rate.
bag_clf = BaggingClassifier(
DecisionTreeClassifier(splitter="random", max_leaf_nodes=16, random_state=42),
n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)
bag_clf.fit(X_train, y_train)
y_pred = bag_clf.predict(X_test)
from sklearn.ensemble import RandomForestClassifier
rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)
rnd_clf.fit(X_train, y_train)
y_pred_rf = rnd_clf.predict(X_test)
np.sum(y_pred == y_pred_rf) / len(y_pred)
The basic idea is to combine weak classifiers in order to create a good classifier. With a weak classifier we often intend a classifier which produces results which are only slightly better than we would get by random guesses.
This is done by applying in an iterative way a weak (or a standard classifier like decision trees) to modify the data. In each iteration we emphasize those observations which are misclassified by weighting them with a factor.
Boosting is a way of fitting an additive expansion in a set of elementary basis functions like for example some simple polynomials. Assume for example that we have a function $$ f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m), $$
where \( \beta_m \) are the expansion parameters to be determined in a minimization process and \( b(x;\gamma_m) \) are some simple functions of the multivariable parameter \( x \) which is characterized by the parameters \( \gamma_m \).
As an example, consider the Sigmoid function we used in logistic regression. In that case, we can translate the function \( b(x;\gamma_m) \) into the Sigmoid function $$ \sigma(t) = \frac{1}{1+\exp{(-t)}}, $$
where \( t=\gamma_0+\gamma_1 x \) and the parameters \( \gamma_0 \) and \( \gamma_1 \) were determined by the Logistic Regression fitting algorithm.
As another example, consider the cost function we defined for linear regression $$ C(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. $$
In this case the function \( f(x) \) was replaced by the design matrix \( \boldsymbol{X} \) and the unknown linear regression parameters \( \boldsymbol{\beta} \), that is \( \boldsymbol{f}=\boldsymbol{X}\boldsymbol{\beta} \). In linear regression we can simply invert a matrix and obtain the parameters \( \beta \) by $$ \boldsymbol{\beta}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}. $$
In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters \( \beta_m \) and \( \gamma_m \).
The way we proceed is as follows (here we specialize to the squared-error cost function)
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \).
This means that for every iteration \( m \), we need to optimize $$ (\beta_m,\gamma_m) = \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2. $$
We start our iteration by simply setting \( f_0(x)=0 \). Taking the derivatives with respect to \( \beta \) and \( \gamma \) we obtain $$ \frac{\partial {\cal C}}{\partial \beta} = -2\sum_{i}(1+\gamma x_i)(y_i-\beta(1+\gamma x_i))=0, $$ and $$ \frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0. $$ We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma \boldsymbol{x}) \) with \( \boldsymbol{e} \) being the unit vector) $$ \gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0, $$ which gives us \( \beta = \boldsymbol{w}^T\boldsymbol{y}/(\boldsymbol{w}^T\boldsymbol{w}) \). Similarly we have $$ \beta\gamma \boldsymbol{x}^T(\boldsymbol{y}-\beta(1+\gamma \boldsymbol{x}))=0, $$
which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting for \( \beta \) gives us an equation for \( \gamma \). This is a non-linear equation in the unknown \( \gamma \) and has to be solved numerically.
The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma_1 \) leading to the new expression for \( f_1(x) \) as \( f_1(x) = \beta_1(1+\gamma_1x) \). Doing this \( M \) times results in our final estimate for the function \( f \).
Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of observations. We define a classification function \( G(x) \) which produces a prediction taking one or the other of the two values \( \{-1,1\} \).
The error rate of the training sample is then $$ \mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)). $$
The iterative procedure starts with defining a weak classifier whose error rate is barely better than random guessing. The iterative procedure in boosting is to sequentially apply a weak classification algorithm to repeatedly modified versions of the data producing a sequence of weak classifiers \( G_m(x) \).
Here we will express our function \( f(x) \) in terms of \( G(x) \). That is $$ f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m), $$ will be a function of $$ G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x). $$
In our iterative procedure we define thus $$ f_m(x) = f_{m-1}(x)+\beta_mG_m(x). $$
The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the exponential cost/loss function defined as $$ C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}. $$
We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case. This is normally done in two steps. Let us however first rewrite the cost function as $$ C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))}, $$ where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).
First, for any \( \beta > 0 \), we optimize \( G \) by setting $$ G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)), $$ which is the classifier that minimizes the weighted error rate in predicting \( y \).
We can do this by rewriting $$ \exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m, $$ which can be rewritten as $$ (\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0, $$ which leads to $$ \beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}}, $$ where we have redefined the error as $$ \mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m}, $$ which leads to an update of $$ f_m(x) = f_{m-1}(x) +\beta_m G_m(x). $$ This leads to the new weights $$ w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))} $$
The algorithm here is rather straightforward. Assume that our weak classifier is a decision tree and we consider a binary set of outputs with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of observations. Our design matrix is given in terms of the feature/predictor vectors \( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}] \). Finally, we define also a classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).
We have already defined the misclassification error \( \mathrm{err} \) as $$ \mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)), $$ where the function \( I() \) is one if we misclassify and zero if we classify correctly.
With the above definitions we are now ready to set up the algorithm for AdaBoost. The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
Using Scikit-Learn it is easy to apply the adaptive boosting algorithm, as done here.
from sklearn.ensemble import AdaBoostClassifier
ada_clf = AdaBoostClassifier(
DecisionTreeClassifier(max_depth=1), n_estimators=200,
algorithm="SAMME.R", learning_rate=0.5, random_state=42)
ada_clf.fit(X_train, y_train)
from sklearn.ensemble import AdaBoostClassifier
ada_clf = AdaBoostClassifier(
DecisionTreeClassifier(max_depth=1), n_estimators=200,
algorithm="SAMME.R", learning_rate=0.5, random_state=42)
ada_clf.fit(X_train_scaled, y_train)
y_pred = ada_clf.predict(X_test_scaled)
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
plt.show()
y_probas = ada_clf.predict_proba(X_test_scaled)
skplt.metrics.plot_roc(y_test, y_probas)
plt.show()
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
plt.show()
Gradient boosting is again a similar technique to Adaptive boosting, it combines so-called weak classifiers or regressors into a strong method via a series of iterations.
In order to understand the method, let us illustrate its basics by bringing back the essential steps in linear regression, where our cost function was the least squares function.
We start again with our cost function \( {\cal C}(\boldsymbol{y}m\boldsymbol{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i)) \) where we want to minimize This means that for every iteration, we need to optimize $$ (\hat{\boldsymbol{f}}) = \mathrm{argmin}_{\boldsymbol{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2. $$
We define a real function \( h_m(x) \) that defines our final function \( f_M(x) \) as $$ f_M(x) = \sum_{m=0}^M h_m(x). $$
In the steepest decent approach we approximate \( h_m(x) = -\rho_m g_m(x) \), where \( \rho_m \) is a scalar and \( g_m(x) \) the gradient defined as $$ g_m(x_i) = \left[ \frac{\partial {\cal L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{m-1}(x_i)}. $$
With the new gradient we can update \( f_m(x) = f_{m-1}(x) -\rho_m g_m(x) \). Using the above squared-error function we see that the gradient is \( g_m(x_i) = -2(y_i-f(x_i)) \).
Choosing \( f_0(x)=0 \) we obtain \( g_m(x) = -2y_i \) and inserting this into the minimization problem for the cost function we have $$ (\rho_1) = \mathrm{argmin}_{\rho}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i+2\rho y_i)^2. $$
Optimizing with respect to \( \rho \) we obtain (taking the derivative) that \( \rho_1 = -1/2 \). We have then that $$ f_1(x) = f_{0}(x) -\rho_1 g_1(x)=-y_i. $$ We can then proceed and compute $$ g_2(x_i) = \left[ \frac{\partial {\cal L}(y_i, f(x_i))}{\partial f(x_i)}\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i, $$ and find a new value for \( \rho_2=-1/2 \) and continue till we have reached \( m=M \). We can modify the steepest descent method, or steepest boosting, by introducing what is called gradient boosting.
Steepest descent is however not much used, since it only optimizes \( f \) at a fixed set of \( n \) points, so we do not learn a function that can generalize. However, we can modify the algorithm by fitting a weak learner to approximate the negative gradient signal.
Suppose we have a cost function \( C(f)=\sum_{i=0}^{n-1}L(y_i, f(x_i)) \) where \( y_i \) is our target and \( f(x_i) \) the function which is meant to model \( y_i \). The above cost function could be our standard squared-error function $$ C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2. $$
The way we proceed in an iterative fashion is to
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.ensemble import GradientBoostingRegressor
from sklearn.preprocessing import StandardScaler
import scikitplot as skplt
from sklearn.metrics import mean_squared_error
n = 100
maxdegree = 6
# Make data set.
x = np.linspace(-3, 3, n).reshape(-1, 1)
y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
error = np.zeros(maxdegree)
bias = np.zeros(maxdegree)
variance = np.zeros(maxdegree)
polydegree = np.zeros(maxdegree)
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
for degree in range(1,maxdegree):
model = GradientBoostingRegressor(max_depth=degree, n_estimators=100, learning_rate=1.0)
model.fit(X_train_scaled,y_train)
y_pred = model.predict(X_test_scaled)
polydegree[degree] = degree
error[degree] = np.mean( np.mean((y_test - y_pred)**2) )
bias[degree] = np.mean( (y_test - np.mean(y_pred))**2 )
variance[degree] = np.mean( np.var(y_pred) )
print('Max depth:', degree)
print('Error:', error[degree])
print('Bias^2:', bias[degree])
print('Var:', variance[degree])
print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))
plt.xlim(1,maxdegree-1)
plt.plot(polydegree, error, label='Error')
plt.plot(polydegree, bias, label='bias')
plt.plot(polydegree, variance, label='Variance')
plt.legend()
save_fig("gdregression")
plt.show()
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
import scikitplot as skplt
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.model_selection import cross_validate
# Load the data
cancer = load_breast_cancer()
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
print(X_train.shape)
print(X_test.shape)
#now scale the data
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
gd_clf = GradientBoostingClassifier(max_depth=3, n_estimators=100, learning_rate=1.0)
gd_clf.fit(X_train_scaled, y_train)
#Cross validation
accuracy = cross_validate(gd_clf,X_test_scaled,y_test,cv=10)['test_score']
print(accuracy)
print("Test set accuracy with Random Forests and scaled data: {:.2f}".format(gd_clf.score(X_test_scaled,y_test)))
import scikitplot as skplt
y_pred = gd_clf.predict(X_test_scaled)
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
save_fig("gdclassiffierconfusion")
plt.show()
y_probas = gd_clf.predict_proba(X_test_scaled)
skplt.metrics.plot_roc(y_test, y_probas)
save_fig("gdclassiffierroc")
plt.show()
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
save_fig("gdclassiffiercgain")
plt.show()
XGBoost or Extreme Gradient Boosting, is an optimized distributed gradient boosting library designed to be highly efficient, flexible and portable. It implements machine learning algorithms under the Gradient Boosting framework. XGBoost provides a parallel tree boosting that solve many data science problems in a fast and accurate way. See the article by Chen and Guestrin.
The authors design and build a highly scalable end-to-end tree boosting system. It has a theoretically justified weighted quantile sketch for efficient proposal calculation. It introduces a novel sparsity-aware algorithm for parallel tree learning and an effective cache-aware block structure for out-of-core tree learning.
It is now the algorithm which wins essentially all ML competitions!!!
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
import xgboost as xgb
from sklearn.preprocessing import StandardScaler
import scikitplot as skplt
from sklearn.metrics import mean_squared_error
n = 100
maxdegree = 6
# Make data set.
x = np.linspace(-3, 3, n).reshape(-1, 1)
y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
error = np.zeros(maxdegree)
bias = np.zeros(maxdegree)
variance = np.zeros(maxdegree)
polydegree = np.zeros(maxdegree)
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
for degree in range(maxdegree):
model = xgb.XGBRegressor(objective ='reg:squarederror', colsaobjective ='reg:squarederror', colsample_bytree = 0.3, learning_rate = 0.1,max_depth = degree, alpha = 10, n_estimators = 200)
model.fit(X_train_scaled,y_train)
y_pred = model.predict(X_test_scaled)
polydegree[degree] = degree
error[degree] = np.mean( np.mean((y_test - y_pred)**2) )
bias[degree] = np.mean( (y_test - np.mean(y_pred))**2 )
variance[degree] = np.mean( np.var(y_pred) )
print('Max depth:', degree)
print('Error:', error[degree])
print('Bias^2:', bias[degree])
print('Var:', variance[degree])
print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))
plt.xlim(1,maxdegree-1)
plt.plot(polydegree, error, label='Error')
plt.plot(polydegree, bias, label='bias')
plt.plot(polydegree, variance, label='Variance')
plt.legend()
plt.show()
As you will see from the confusion matrix below, XGBoots does an excellent job on the Wisconsin cancer data and outperforms essentially all agorithms we have discussed till now.
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
from sklearn.preprocessing import LabelEncoder
from sklearn.model_selection import cross_validate
import scikitplot as skplt
import xgboost as xgb
# Load the data
cancer = load_breast_cancer()
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
print(X_train.shape)
print(X_test.shape)
#now scale the data
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
xg_clf = xgb.XGBClassifier()
xg_clf.fit(X_train_scaled,y_train)
y_test = xg_clf.predict(X_test_scaled)
print("Test set accuracy with Random Forests and scaled data: {:.2f}".format(xg_clf.score(X_test_scaled,y_test)))
import scikitplot as skplt
y_pred = xg_clf.predict(X_test_scaled)
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
save_fig("xdclassiffierconfusion")
plt.show()
y_probas = xg_clf.predict_proba(X_test_scaled)
skplt.metrics.plot_roc(y_test, y_probas)
save_fig("xdclassiffierroc")
plt.show()
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
save_fig("gdclassiffiercgain")
plt.show()
xgb.plot_tree(xg_clf,num_trees=0)
plt.rcParams['figure.figsize'] = [50, 10]
save_fig("xgtree")
plt.show()
xgb.plot_importance(xg_clf)
plt.rcParams['figure.figsize'] = [5, 5]
save_fig("xgparams")
plt.show()


RandomInteger object generates a random integer every time .get() is called it follows the generator and the distribution type that you provide.
More...
#include <RandomTypes.hpp>
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
class testcaser::maker::types::RandomInteger< Generator, Distribution >
RandomInteger object generates a random integer every time .get() is called it follows the generator and the distribution type that you provide.
- Template Parameters
-
| std::mt19937 | The default Random Number generator to use |
| std::uniform_int_distribution<long | long> The default distribution to use |
◆ RandomInteger() [1/3]
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
Construct a new Random Integer object. Defaults the range to range of Long Long of C++.
◆ RandomInteger() [2/3]
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
Construct a new Random Integer object.
- Parameters
-
| lmt | the limit to set on the range of random number generated |
◆ RandomInteger() [3/3]
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
Construct a new Random Integer object.
- Parameters
-
| lst | the range as a initializer list |
◆ get()
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
returns the random number from this class
- Returns
- long long the value of the random number
- Todo:
- Make get() startegy even better. @body The sampling of the distribution can be inefficent when too many except_intervals are specified. Improve this startegy
◆ get_less_than()
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
Get the random Integer non-strictly less than the value specified.
- Parameters
-
| val | The new upper limit for the distribution to sample from. |
- Returns
- long long The Value less than val but under the limit of this object.
◆ get_more_than()
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
Get the random Integer non-strictly more than the value specified.
- Parameters
-
| val | The new lower limit for the distribution to sample from. |
- Returns
- long long The Value more than val bu under the limit of this object.
◆ reseed_engine()
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
reseeds the generator with a new seed value
- Parameters
-
| seed | the value to seed the generator |
◆ reseed_engine_with_random_device()
template<class Generator = std::mt19937, class Distribution = std::uniform_int_distribution<long long>>
reseed the random number engine with the random value. It uses std::random_device()() for this task.
The documentation for this class was generated from the following file:


Project Overview
In this project, I constructed a vertebrate PAS database, PolyA_DB 3. This database contains PAS identified in several vertebrates, including humans, mouse, rat and chicken, drawn from over 100 datasets. In additions, through systematic bioinformatics analysis, we present the first comprehensive view of conserved cleavage and polyadenylation events in mammals.
Representative publication
- Ruijia Wang, Dinghai Zheng, Ghassan Yehia, Bin Tian: A compendium of conserved cleavage and polyadenylation events in mammalian genes. Genome research 28.10 (2018): 1427-1441. Paper link
- Ruijia Wang, Ram Nambiar, Dinghai Zheng, Bin Tian: PolyA_DB 3 catalogs cleavage and polyadenylation sites identified by deep sequencing in multiple genomes. Nucleic acids research 46, no. D1 (2017): D315-D319. Paper link
Gallery
Figure. PolyA_DB 3 construction and genomic evolution analysis on mammal PAS.
(A) Schematic of PAS identification and presentation in PolyA_DB version 3.
(B) Correlation of aUTR length (left) or cUTR length (right) between human and mouse genes.
A total of 6706 orthologous genes with conserved 3′ UTR APA are included.
3′ UTRs are divided into aUTRs and cUTRs using the first conserved and last conserved PASs (mammal conserved).
Median length value for each species and Pearson correlation coefficient are indicated.
(C) Sequence motifs at the cleavage site, shown as sequence logos.
Two scenarios are considered, as illustrated above the logos.
(Left) Cleavage site is considered to be immediately after a non-A nucleoside (shown as B) and before an adenosine.
(Right) Cleavage site is considered to be immediately after an adenosine and before a B.
(D) Tetramers enriched for 3’UTRs of stable or unstable transcripts.
(E) Odds ratio of miRNA target site distribution between conserved and nonconserved aUTRs for highly conserved miRNA families and moderately conserved miRNA families. miRNA
conservation is defined by TargetScan (“Family Conservation” score = 1 for moderately conserved miRNAs, and = 2 for highly conserved ones).
Author: Ruijia Wang


details
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{% extends 'core/base.html' %} {% block meta %}
Great places are chosen by great chowists
This application replicates core features of Yelp, and adds a couple more bells and whistles to the mix. Please share this website with awesome chowists like yourself!
Learn more {% if user.is_authenticated is False %} Sign up {% endif %}


notes
Technical Reviews
- What Can ResNets Learn Efficiently? [pdf] (for Simons Summer 2019 Reading Group on Generalization Theory)
- Geometry of Optimal Transport [pdf] (for Simons Summer 2019 Reading Group on Optimal Transport)
- Learning to Plan and Hierarchical, Multi-Task Reinforcement Learning [pdf] (for IEOR 8100)
- Generalization from Margins: Connecting Boosting Theory to Neural Nets [pdf–in progress!] (at Columbia DSI Seminar)
- Learning Sparse Polynomials [pdf] (for COMS 6998-5)
- Interactive Clustering [pdf] (for COMS 6998-4)
- Convex Optimization and Randomness [pdf] (for Dave Blei’s Reading Group)
- Tensor Decompositions [pdf] (for ELE 538B)
- Rate Distortion and Unsupervised Learning [pdf] (for COS 598E)
- Matrix Concentration and Applications [pdf] (for ORF 550)
- On Lipschitz Extensions from Finite Sets [pdf] (with Mikhail Khodak, for MAT 529)
- The Structure Theorem for Finitely-Generated Modules over PIDs [pdf] (for MAT 346: Algebra II)
- The Representation of Language in the Brain [pdf] (at Algorithms-Machine Learning Reading Group)
- A Brief Survey on Expander Graphs [pdf] (for Junior Seminar with Zeev Dvir)
Class Notes
For now, I have individual class notes for some classes I’ve taken. Sometimes, lectures are missing or the rest of the notes have been taken by other people — in these events, I direct you to the website of the course, if it exists. If not, take a look at my links page for a list of other resources. At some point in the future, I plan to put together a big document of notes organized by subject.
- COMS 6998-9: Algorithms for Massive Data [pdf] [course website]
- COMS 4995-2: Unsupervised Learning [pdf] [course website]
- STAT 8301: Topics in Probability Theory (taught by Roman Vershynin) [pdf–in progress!] [all notes]
- IEOR 8100: Reinforcement Learning [pdf] [course website]
- STAT 8101: High-dimensional Statistical Inference [pdf–in progress!] [course website]
- COMS 6998-5: Algorithms with a Geometric Lens [scribe notes] [course website]
- COMS 6998-4: Interactive Learning [scribe notes] [course website]
- COS 598E: Unsupervised Learning [scribe notes] [course website]
- ORF 550: Probability in High Dimension [scribe notes] [syllabus] [all notes] (with Xinyi Chen)
- ORF 524: Statistical Theory and Methods [scribe notes] [syllabus]
- MAT 529: Metric Embeddings and Geometric Inequalities (taught by Assaf Naor) [pdf] (with Holden Lee)
- MAT 597/PHY521: Mathematical Physics (taught by Michael Aizenman) [pdf] (with Holden Lee)
- APC 529: Coding Theory and Random Graphs (taught by Emmanuel Abbe) [pdf]
- MAT 340: Applied Algebra (taught by Mark McConnell) [pdf]
- CS 224d: Deep Learning for Natural Language Processing (taught by Richard Socher) [scribe notes]
- COS 511: Theoretical Machine Learning [scribe notes] (with others)
- COS 510: Programming Languages (taught by David Walker) [scribe notes]
- APC 486: Transmission and Compression of Information (taught by Emmanuel Abbe) [scribe notes]
Seminar Notes
- Yann LeCun on The Power and Limits of Deep Learning and AI [pdf]
- Yisong Yue on New Frontiers in Imitation Learning [pdf]
- Tim Roughgarden on How does Computer Science Inform Modern Auction Theory [pdf]
- Yuchen Zhang on Two Approaches to Non-Convex Machine Learning [pdf]
- Ben Recht on What can Deep Learning learn from Linear Regression [pdf]
- Nicholas Boumal on ManOpt: Manifold Optimization [pdf]
- Michael Jordan on Computational Thinking, Inferential Thinking, and Data Science [pdf]
- Joel Tropp on Universality Laws for Randomized Dimension Reduction [pdf]
- Joel Tropp on Finding Structure With Randomness [pdf]
- Michael Jordan on Nonparametric Bayesian and Combinatorial Stochastic Processes [pdf]
- Jacob Steinhardt on Unsupervised Risk Estimation with Only Structural Assumptions [pdf]
- Yuanzhi Li on Weighted Low-Rank Matrix Approximation [pdf]
- Zeyuan Allen-Zhu on Linear Coupling Framework of Gradient and Mirror Descent [pdf]
- Naman Agarwal and Brian Bullins on LiSSA: A Linear Time Second-Order Stochastic Algorithm [pdf]
- Andrew Barron on Computationally Feasible Greedy Algorithms for Neural Networks [pdf]
- Samy Bengio on Neural Image Captioning [pdf]
- Zaid Harchaoui on Convolutional Kernel Neural Networks [pdf]
- Lester Mackey on Divide-and-Conquer Matrix Completion [pdf]
- Gillat Kol on Interactive Information Theory [pdf]
- Sanjeev Arora on Reversible Deep Nets [pdf]
- Santosh Vempala on The Complexity of Detecting Planted Solutions [pdf]
- Amir Ali Ahmadi on Optimizing over Nonnegative Polynomials [pdf]
- Francisco Pereira on Decoding Generic Representations of fMRI [pdf]
- Elad Hazan on Simulated Annealing and Interior Point Methods [pdf]
- Dana Lahat on Joint Independent Subspace Analysis and Blind Source Separation [pdf]
- Barbara Engelhardt on Bayesian Structured Sparsity Using Gaussian Fields [pdf]
- Dimitris Bertsimas on Statistics and Machine Learning from a Modern Optimization Lens [pdf]
- Sébastien Bubeck on Optimal Regret Bounds for the General Convex Multi-Armed Bandit Setting [pdf]
- Han Liu on Nonparametric Graphical Models [pdf]
- Mehryar Mohri on Deep Boosting [pdf]
- Percy Liang on Learning Hidden Computational Processes [pdf]
- Young Kun Ko on The Hardness of Sparse PCA [pdf]
- Tom Griffiths on Rationality, Heuristics, and the Cost of Computation [pdf]
- Anna Choromanska on Optimization for Large-Scale Machine Learning [pdf]
Symposia Notes
- MIT Deep Learning and Nonconvex Optimization (MIFODS MIT Workshop) (Jan. 2019) [page]
- MIT Sublinear Algorithms, Local Algorithms, and Robust Statistics (MIFODS MIT Workshop) (Jun. 2018) [page]
- Bridging Optimization Theory, Information Theory, and Data Science at Princeton (May. 2018) [pdf]
- Mathematics of Deep Learning at Princeton (Mar. 2018) [pdf]
- NYU Mini-Theory Symposium (Feb. 2018) [pdf]


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To install some dependences like CoffeeScript, LessCSS, UglifyJS and Grunt. They are all installed inside the project's directory.
Because it rocks!
Yes, but you will not rock.
Because it rocks as well!
Yes, but you will not rock.
Yes, you can ask questions using the feedback form or by sending an email to: gaeinit at gmail dot com


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Komfo Kolege responds to claim that he is ‘copying’ Mmebusem Ghana Jesus
by Lizbeth BrownPopular Kumawood actor and comedian Komfo Kolege has replied critics over his new ‘Guy Jesus’ tag.
According to Komfo Kolege, he is not in any way imitating Mmebusem ‘Ghana Jesus’ adding that it was just an advertisement he shot for a roofing company.
In an exclusive interview with GhPage TV, the comic actor debunked rumors that he is shooting a new movie or skits with the ‘Guy Jesus’ idea.
He added that he was one of the few people that contacted Mmebusem to congratulate him when he started the ‘Ghana Jesus’ initiative.
Komfo Kolege further stated that he has no intention of competing or copying Mmebusem but was just an advertisement he shot.
He explained that when he received the script, he suggested that Mmebusem will be the right person but they insisted that he (Komfo Kolege) shoots that scene.
Watch the interview below;
Komfo Kolege also added that he has no problem or issue with Mmebusem and that they are in contact and have a very good relationship.
He also disclosed that he has a project with Mmebusem which Ghanaians will love and he is not in competition with anyone.
The comic actor further stated that his aim is only to entertain Ghanaians but not to imitate Mmebusem.


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Pegara will host local information sessions in the New York City area. The local sessions will provide lectures on the latest information about Alzheimer's disease, the MIND Diet, and the Brainsalvation Dietary Program.
1. Facts and figures relating to Alzheimer’s disease
2. The risk factors of Alzheimer’s disease
3. How we can reduce the risk of developing Alzheimer’s disease
4. The MIND Diet
5. Brainsalvation Dietary Program
10-12
Free
Note: These initial sessions are targeted exclusively to women aged 21 to 64.
1. Get a 50% discount on a three month subscription ($149 -> $74)
2. Get the MIND Diet book (subscription signup at the session is required)
3. Try tasty Mind Diet snaks at the session
A Scientific Approach to Enhancing Brain Function and Helping Prevent Alzheimer's and Dementia
26th Sat. Nov
2:00pm – 4:00pm
WEWORK PENN STATION
315 W 36th Street New York NY 10018
28th Mon. Nov
7:00pm – 9:00pm
WEWORK GRAND CENTRAL
450 Lexington Ave New York NY 10017
30th Wed. Nov
6:30pm – 8:30pm
WEWORK TIMES SQUARE
1460 Broadway New York NY 10036
* Participants in each session will be emailed more details on the session location after sign-up
Cori Cohen is a certified Registered Dietitian Nutritionist practicing in New York City. Ms. Cohen is a strong believer in the healing power of food and the undeniable connection between lifestyle choices and optimal wellness. She emphasizes customized nutrition, mindfulness, meditation and purposeful movement as part of a healthy balanced lifestyle.
Over the span of her career Ms. Cohen has counseled a large and diverse population of individuals. She has helped many reach their weight and body composition goals, improve memory, find more energy to enjoy their lives, significantly improve blood sugar and cardiac markers, manage IBS and IBD, navigate life with Celiac disease, and improve overall health by focusing on behavioral changes. In addition to her private practice, Ms. Cohen leads seminars and workshops on a variety of health and nutrition topics.


Pitchfest'17 brings to you a golden opportunity to impress an elite panel of investors and executives with your innovative start-up ideas, and bag a handsome funding from them.
Who is it for?
The competition has two different verticals catering to start-ups in the following phases-
(Start-ups under both categories will be judged by separate independent panels.)
Young start-ups struggling with initial funds- usually student start-ups from educational institutes who might be looking for mentoring,incubationandsmall funding.
Operational start-ups – Start-ups which have started operations (even if at a basic level), which are looking for funding. Start-ups which have already been incubated can also apply under this category.
Note that start-ups applying under both categories should be well past the Ideation stage.
What is at stake?
The most promising start-ups from both categories can hope to get invaluable mentoring and generous funding from our elite panel of investors.
The Early Stage start-ups can also look for the opportunity of being incubated at the Incubation Cell , the Business Incubator of IIT Madras.
The Operational start-ups can look for an attractive funding from the investors.
Prizes worth 75,000 INR will be awarded to the best team across both categories.


This example shows how you can consume service using only Ruby core libraries. You may be interested about using any other community free or third party libraries (gems).
require 'net/http' require 'uri' uri = URI.parse('http://server-host/apirest/bibles') http = Net::HTTP.new(uri.host, uri.port) # Consume service as XML. request = Net::HTTP::Get.new(uri.request_uri) request.add_field "Accept", "application/xml" response = http.request(request) puts response.body # Consume service as JSON. request = Net::HTTP::Get.new(uri.request_uri) request.add_field "Accept", "application/json" response = http.request(request) puts response.body


{% extends "layout.html" %} {% block content %}
Bubble Tea Stores
Provide information about your favorite BubbleTea stores in the world
here
view some of the BubbleTea stores
here
{% endblock %}


Here we are. We have learned how to train a particular kind of neural net: one that transforms our original set of inputs or "features" into several "intermediate features", and then uses those intermediate features to predict our output using logistic regression.
Computing the predictions and ensuring the net learned correctly in this relatively simple case took about 20 separate steps. Clearly, this process will not scale if we want to make nets that are more complex - and, for tasks like recognizing handwritten digits, an extremely complex task for a computer, we will indeed have to build these more complex nets.
To generalize the limited, hard-won understanding we've gained so far into why this process of training neural nets works, we are going to have to change our understanding or what neural nets are - and indeed, we are going to have to leave the comfortable realm of mathematics to learn some of the terminology often used to describe neural nets. Let's dive in.
--
Up until now, we have described neural nets as functions which are composed together as functions are in mathematics. On the "forward" pass of a neural net, these functions take in input and produce output. But what exactly do these functions do on the backwards pass? It isn't clear; it totally depends on the function itself. Therefore, if we want to move toward an understanding of neural nets which involves seeing them as made up of decomposable building blocks, we will need to move past understanding them as merely functions: we will need to understand them differently.
Consider this: the computations in both the forwards and backwards passes of the neural net consist of two different kinds of functions:
This brings us to the conception of neural nets that inspired their original design and is the way most researchers in the field think about them. Going forward, we shall think of neural nets as consisting of "layers". What are "layers", exactly, and what do they do?
This is how we shall think of neural nets going forward.
One note: the layers we have seen so far are only one type of layer. In the terminology of neural nets - and in this case terminology that makes sense intuitively, these layers are:
Later on, we will see the advantages of having layers where this is not the case, especially of having layers which are not fully connected.
These are the concepts. We must now make this precise using code. Neural nets are a complex elephant, and throughout this book, we will have to understnad things at a conceptual, visual, and procedural level, using words, diagrams, and code, respectively. Let's dive into the code.
--
First, we shall have to introduce the notion of a class. I'm not an expert in explaining computer science concepts, so from an amateur's perspective I'd have to say the best explanation of a class I've ever heard is that it is a blueprint: it is a set of instructions on how an object is built, and how it works.
Based on what we know so far, let's try to work out what classes we'll need to ultimately build complex neural nets:
neural_net = [Layer1, Layer2]We'll get into what those "layers" do later. But for now, we know that neural nets will need to work with "layers". Therefore, we know that we can start writing our net as:
class NeuralNetwork: def __init__(self, layers): self.layers = layersWhat will these layers need to do? These layers will need to pass values backwards and forwards. The first layer will take in input and create some "intermediate" quantities, the last layer will take some quantity from the previous layer and output a prediction, and the layers in the middle will simple pass values through the net. Therefore, a forward pass through the net will look like this:
def forwardpass(self, X): """ Calculate an output Y for the given input X. """ X_next = X for layer in self.layers: X_next = layer.fprop(X_next) prediction = X_next return predictionWe'll get to what `fprop` for each layer will look like later. Still, this is an achievement, as it's a general way for a neural net composed of any number of layers to make predictions. Now, once we have a prediction, we should have a way of calculating the loss. Let's write that:
def loss(self, prediction, Y): """ Calculate error on the given data. """ mse = 0.5 * (Y - prediction) ** 2 loss = -1.0 * (Y - prediction) return lossLater on, we may want to be able to make this more general, and able to accomodate different loss functions. Still, we should pat ourselves on the back just for this. Finally, we need to, in a manner similar to the "forwardpass" function, pass this loss back through the network to update the weights.
def backpropogate(self, loss): """ Calculate an output Y for the given input X. """ loss_next = loss for layer in reversed(self.layers): loss_next = layer.bprop(loss_next) return lossAnd that's it - that's the basic structure of our neural net. So far we have changed the way we think about neural nets - instead of thinking of them purely mathematically, we think of them as being composed of layers, which can feed values backwards and forwards. Next week, we will take the complex code we wrote in prior weeks to make the neural net learn and break it down into a "set of layers", each of which has its own "activation function", can send values forwards and backwards based both on this activation function and its derivative, and updates its weights appropriately on the backwards pass. Stay tuned!


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Before Change
Set color of array of lights.
for light in lights:
if is_on(hass, light):
hass.services.call(
LIGHT_DOMAIN, SERVICE_TURN_ON, {
ATTR_XY_COLOR: [x_val, y_val],
ATTR_BRIGHTNESS: brightness,
ATTR_TRANSITION: transition,
ATTR_WHITE_VALUE: brightness,
ATTR_ENTITY_ID: light})
def set_lights_temp(hass, lights, mired, brightness, transition):
Set color of array of lights.
After Change
Set color of array of lights.
for light in lights:
if is_on(hass, light):
service_data = {ATTR_ENTITY_ID: light}
if x_val is not None and y_val is not None:
service_data[ATTR_XY_COLOR] = [x_val, y_val]
if brightness is not None:
service_data[ATTR_BRIGHTNESS] = brightness
service_data[ATTR_WHITE_VALUE] = brightness
if transition is not None:
service_data[ATTR_TRANSITION] = transition
hass.services.call(
LIGHT_DOMAIN, SERVICE_TURN_ON, service_data)
def set_lights_temp(hass, lights, mired, brightness, transition):
Set color of array of lights.