| < Day Day Up > |
Software Versions and AvailabilityWriting a MySQL book has proven to be quite a challenge. One reason is that MySQL is a moving target. In the two-plus years since Jeremy first wrote the outline for this book, numerous releases of MySQL have appeared. MySQL 4.0 went from testing to stable, and as we go to press, MySQL 4.1 and 5.0 are both available as alpha versions. We had to revise the older text occasionally to remove references to limitations that were fixed after the fact.[2]
We didn't use a single version of MySQL for this book. Instead, we used a handful of MySQL 4.0 and 4.1 releases, while occasionally looking back at how things used to be in the 3.23 days. MySQL 5.0 is still in so much flux that we simply could not attempt to cover it in the first edition. The same is true for the (currently) new MySQL Administrator GUI tool. Throughout this book, we assume a baseline version of MySQL 4.0.14 and have made an effort to note features or functionality that may not exist in older releases or that may exist only in the 4.1 series. However, the definitive reference for mapping features to specific versions is the MySQL documentation itself. We expect that you'll find yourself visiting the annotated online documentation (http://www.mysql.com/doc/) from time to time as you read this book. Another great aspect of MySQL is that it runs on all of today's popular platforms: Mac OS X, Windows, Linux, Solaris, FreeBSD: you name it! However, our experience is heavily skewed toward Linux and FreeBSD. When possible, we've tried to note differences Windows users are likely to encounter, which tend to come in two flavors. First, file paths are completely different. Chapter 1 contains numerous references to C:\mysql and the location of configuration files on Windows. Perl is the other rough spot when dealing with MySQL on Windows. MySQL comes with several useful utilities that are written in Perl and certain chapters in this book present example Perl scripts that form the basis of more complex tools you'll build. However, Windows doesn't come with Perl. In order to use these scripts, you'll need to download a Windows version of Perl from ActiveState and install the necessary add-on modules (DBI and DBD::mysql) for MySQL access. |
| < Day Day Up > |


5. The execute
script
The place to start investigating a workflow
is the
execute
script,
which has the steps that the workflow will execute:
- setup (install)
- run the workflow application
- wait for completion of the run
- postprocess results
- wait for completion of postprocess
- validate results
The
execute
script shows the steps that are run.
In the case of a workflow run on a target HPC system, the script
would look like this:
#!/bin/bash
source bootstrap.env
source pantheon/env.sh
./sbang.sh setup/install-deps.sh
./sbang.sh run/run.sh
./sbang.sh run/wait_for_completion.sh
./sbang.sh postprocess/postprocess.sh
./sbang.sh postprocess/wait_for_completion.sh
./sbang.sh validate/validate.sh
When run on a supercomputer, the steps are executed
by submitting an application job to a queue. The
wait_for_completion
steps then monitor the
queue to provide feedback on the state of the job. This allows
the workflow to run continuously until completion.


Pegawai-pegawai Kecamatan.
Graphic design is a process of visual and problem solving through the use of type, space.
Vision dominates a lot of our subconscious interpretation of the world around us.
The development of your business plan will be executed by our brilliant team who will indicate.
Web design agencies is the ability to offer the most User Friendly Experience.


A cat-lovers travelers companion. Users can find local pet sitters & join a homeshare community. A desktop app, that is currently being adapted for mobile use. Technologies: ruby on rails, html, css, bootstrap, javascript, jquery.
a comparison game that matches up two foods and their nutritional content. easy, useable format for adults & children. technologies: react, html, css, jquery, usda api.
company website for a yoga studio. technologies: html, css, javascript, original photography, photoshop.
Style mockup for a website re-design project. Gives client an overall feel for future site, from fonts to images. technologies: photoshop.
so you've gotta catch them all. but how much do you know about your favorite characters? this app uses the Pokeapi to show details and photos of each beloved creature. technologies: ruby on rails, html, css, jquery, ajax.
mini music player made with the Spotify api. technologies: ruby on rails, html, css, ajax.
Landing page mockup with email capture. technologies: illustrator, photoshop.
concert network allows users to create & post concerts in their areas. technologies: react, html, css, jquery, usda api.
landing page mockup for a food delivery service. intended for either mobile or web app. technologies: illustrator, photoshop.


JNU Administration Condemns, Warns to Take Stringent Action Over Defacement of Vivekananda Statue
Speaking to news agency ANI, a JNU staff said, "Condemn the vandalism done by students. Everything has been recorded. Chief Proctor Office will take stringent action possible against those who will be found guilty."
New Delhi: The Jawaharlal Nehru University (JNU) administration on Sunday condemned the acts of vandalism by students, including the recent defacement of Swami Vivekananda statue in the campus. A police complaint was filed by JNU professor and chairman of the Swami Vivekananda Statue Installation Committee, Buddha Singh, over the ‘defacement’ of the yet-to-be-unveiled Vivekananda statue.
“Condemn the vandalism done by students. Everything has been recorded. Chief Proctor Office will take stringent action possible against those who will be found guilty,” a JNU administration staff was quoted by news agency ANI as saying on November 17.
The Vivekananda statue was installed at JNU’s administration block on January 5, 2019 in order “to pay homage to Swami Vivekananda and his ideologies”, noted Singh in his police complaint, according to news agency PTI. Notably, some JNU students had allegedly defaced the statue on early November 14, he added.
The complaint, as quoted by news agency PTI, further read: “I, along with other officials, reached the location to see that the base of the statue has been vandalised with objectionable messages and the cloth with which the statue is covered has been partially torn off.”
For breaking news and live news updates, like us on Facebook or follow us on Twitter and Instagram. Read more on India Latest News on India.com.
Story Timeline
- 16 Nov 2019 Despite Massive Fee hike, JNU Still Has Cheapest Hostels
- 14 Nov 2019 Will Continue Protest Until Complete Rollback of Fee Hike: JNU Students' Union
- 13 Nov 2019 After JNU Partially Roll backs Fee Hike, Teachers And Students Say Changes Are 'Cosmetic'
- 13 Nov 2019 Great Relief For Students as JNU Partially Rolls Back Fee Hike Amid Massive Protests
- 11 Nov 2019 HRD Minister Leaves AICTE Office After Being Stuck Inside For Six Hours Following JNU Protest
Comments - Join the Discussion


Michael Jackson beaten by Taylor Swift as artist with most American Music Awards of all time
Swift now has 29 awards to her name
by Clémence MichallonMichael Jackson is no longer the artist with the most American Music Awards to his name.
Taylor Swift beat the late singer during Sunday’s ceremony, during which she picked up six new awards.
This brings her total to 29, surpassing Jackson’s 24 wins.
Swift notably won the Artist of the Year award on Sunday, as well as Favourite Pop/Rock Album.
The latter was the one that enabled her to initially tie with Jackson before scoring additional wins.
Swift performed a medley of her hits before accepting the Artist of the Decade award, which came amid her ongoing conflict with music executive Scooter Braun.
The singer said the last year had “the most amazing times and some of the hardest things I have gone through in my life,” but that she felt lucky.
On Sunday, she also collected the Favourite Music Video, Favourite Pop/Rock Female Artist, and Favourite Adult Contemporary Artist awards.
Swift won her first American Music Award in 2008 and collected more trophies in 2009, 2010, 2011, 2012, 2013, 2014, 2015, and 2018.


Referencing DOM nodes in Angular expressions is disallowed! Expression: {0}
Occurs when an expression attempts to access a DOM node.
AngularJS restricts access to DOM nodes from within expressions since it's a known way to execute arbitrary Javascript code.
This check is only performed on object index and function calls in Angular expressions. These are places that are harder for the developer to guard. Dotted member access (such as a.b.c) does not perform this check - it's up to the developer to not expose such sensitive and powerful objects directly on the scope chain.
To resolve this error, avoid access to DOM nodes.
The $parse:isecdom
error also occurs when an event handler invokes a function that returns a DOM
node.
<button ng-click="iWillReturnDOM()">click me</button>
$scope.iWillReturnDOM = function() {
return someDomNode;
}
To fix this issue, avoid returning DOM nodes from event handlers.
Note: This error often means that you are accessing DOM from your controllers, which is usually a sign of poor coding style that violates separation of concerns.
This error can occur more frequently when using CoffeeScript, which has a feature called implicit returns. This language feature returns the last dereferenced object in the function when the function has no explicit return statement.
The solution in this scenario is to add an explicit return statement. For example return false
to
the function.


The body of a comment can be written in GitHub Flavored Markdown. issues, issue comments, pull request comments, and the gist comments APIs all accept these same media types:
application/vnd.github.VERSION.raw+json
Return the raw markdown body. Response will include body
. This is
the default if you do not pass any specific media type.
application/vnd.github.VERSION.text+json
Return a text only representation of the markdown body. Response will include
body_text
.
application/vnd.github.VERSION.html+json
Return HTML rendered from the body's markdown. Response will include
body_html
.
application/vnd.github.VERSION.full+json
Return raw, text and HTML representations. Response will include
body
, body_text
, and body_html
:


--- layout: archive title: Zulip Chat Archive permalink: /stream/113488-general/topic/bug.20with.20refine.20.2B.20rw.html ---
example (H : (0 = 0 → 0 = 1) → true) : true := begin refine H (λ h, _), rw h --fails /- rewrite tactic failed, lemma is not an equality nor a iff state: H : (0 = 0 → 0 = 1) → true, h : 0 = 0 ⊢ 0 = 1 -/ end example (H : (0 = 0 → 0 = 1) → true) : true := begin refine H _, intro h, rw h --works end
and also workaround:
example (H : (0 = 0 → 0 = 1) → true) : true := begin refine H (λ h, _), change _ at h, rw h --works end
Last updated: Apr 24 2020 at 19:02 UTC


| /[Apache-SVN]/jakarta/ecs/tags/RELEASE_1_4/xdocs |
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Battle Points are the in-game currency used in PlayerUnknown's Battlegrounds. You receive it when the match ends. The amount varies depending the amount of kills you have made, how long you managed to survive and and the total damage dealt to other players.
Points for Winning:
Solo: 820 BP
Duo: 400 BP
Squad: 20 BP
Points per Kill:
Solo: 20 BP
Duo: 15 BP
Squad: 10 BP
Squad: 10 BP
Points per Damage:
Approx. 1BP per 5 damage BP


Fixed: Unable to close chatter list after opening it with the chat header turned off.
3.5.497
Fixed: Position of player controls in theater mode.
Fixed: Unnecessary bottom border under the player in theater mode.
3.5.496
Fixed: Input handling.
Fixed: Minimal Chat Header not hiding the chat header.
3.5.495
Fixed: Game Purchase share messages in chat.
3.5.494
Added: By default, messages from moderators will no longer be removed if they contain banned words. Configurable via Chat Filtering > Remove Messages from Moderators.
Fixed: Bits UI breaking when you switch chat rooms.
Fixed: Incorrect fullscreen and theater mode states when resetting the player.
3.5.493
Changed: Tag Vodcasts in the navigation bar's Following tooltip and the enhanced tooltips for live channels on the social bar.
Fixed: New logviewer messages coming in would erase the name history tab of mod cards and display chat instead.


Hello {{ context.username }},
Someone with access to your account has violated our community guidelines.
As a result, your account has been banned. You will no longer be able to
comment, react or report comments. If you think this has been done in error,
please contact our community team at
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September 23 2014
This is a blog post. Here's what a really long title looks like if you need it.
 Ground round t-bone swine shoulder, cow bacon sausage, turkey meatloaf. Tongue ball tip corned beef turkey.  Capicola shankle ham, sirloin billtong pork chop ribeye brisket shank chuck. Turducken bresaola ball tip pork loin. rump kevin porchetta, brisket pork tri-tip shank ribeye chicken chuck, andouille bacon bresaola jowl.
Written by Emily Davis / Posted in WordPress / 2 comments
September 20, 2014
This is an image blog post.
 Ground round t-bone swine shoulder, cow bacon sausage, turkey meatloaf. Tongue ball tip corned beef turkey. Leberkas shoulder pork chop doner venison meatball
Written by Emily Davis / Posted in WordPress / No comments
September 18, 2014
This is a video blog post.
Written by Emily Davis / Posted in Videos / No comments
September 14, 2014
This is a quote post.
"Whatever the problem, be part of the solution.
- Tina fey
Written by Emily Davis / Posted in Quotes / No comments


A Contract Logistics Service Provider
We are a privately owned company that provides top-notch Contract Logistics.
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The transportation and logistics industry is ever changing and is becoming even more
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We are third party logistics provider company that operates primarily
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In order to best fulfill your needs, we offer services in contract logistics namely, Logistics,
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We are determined to continuously improve our service
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time staying ahead of the competition.
The word “advance” is critical to our Mission statement. This speaks to the fact that our
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We continuously develop progressive supply chain strategies for the changing world.
We build credibility as the recognized leader by developing, publishing and speaking on new
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We help our clients navigate complex challenges and respond with agility to the changing
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Our expertise, and ability to deliver 4PL services, helps create the harmony,
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Our overland transport operations provide competitive solutions to customers seeking cross border and domestic trucking services across a range of fleet types and delivery capabilities. We manage the end to end service, including clearance facilitation of truck movement across the region for a variety of products.
Our logistics experts have years of experience in assembling agile networks that keep costs low while making sure the right products get to shelves at exactly the right time.
Value added activities in the warehouse and the open stock yard provide customers with
the ability to change, enhance and consolidate product before distributing to retails
and end users.
We provide a range of value-added services to meet our customers specific needs and
promotional activities.
We manage and operate both owned fleet and network of partners including last mile
delivery.
The company has tie ups with third party transporters and have its own fleet of vehicles
to manage both FTL and part load shipments.
Irrespective of the size of the shipment and its destination, with our extensive
tracking system and the information available at our disposal, we choose the most
efficient transporter and the size of the shipment to ensure that your shipment reaches
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Through the use of economies of scale Panther Empire Limited is able to pass on the
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The warehouses offer a range of storage methods – from palletized storage to shelving
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Our proximity to both the port of Mombasa and the ICD hub of Nairobi routes allows us to
offer agile distribution networks for all manners of goods, including fast moving retail
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We have enough fleet of trucks and equipment's that are operated by highly professional
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Panther Empire Ltd is well known for its “safety-first” policy that guarantees safe
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We have also invested in modern technology, such as car tracking system, which helps
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We offer:
We are a privately owned company that provides top-notch Transport and Distribution
Services.
Headquartered in Nairobi, Kenya.
We have substantial operating capacity, powered by a Operations team that has combined
experience
over 25 years in the industry.
We offer a wide range of value added services, such as free consulting to our clients
regarding a
variety Logistics & Distribution processes and procedures which are guided by stringent
value principles and apply best practices in our daily operations.
We also offer Warehousing services through our partners which makes us a one stops service
and
your choice as the Logistics solution provider.
We’re not driven by quarterly numbers; we’re driven by doing what is best for our customers in
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We’re privately held and our owners are actively engaged in your success, so we can make
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How to compute a gradient, a divergence or a curl#
This tutorial introduces some vector calculus capabilities of SageMath within the 3-dimensional Euclidean space. The corresponding tools have been developed via the SageManifolds project.
The tutorial is also available as a Jupyter notebook, either
passive (nbviewer
)
or interactive (binder
).
First stage: introduce the Euclidean 3-space#
Before evaluating some vector-field operators, one needs to define the arena
in which vector fields live, namely the 3-dimensional Euclidean space
\(\mathbb{E}^3\). In SageMath, we declare it, along with the standard Cartesian
coordinates \((x,y,z)\), via EuclideanSpace
:
sage: E.<x,y,z> = EuclideanSpace()
sage: E
Euclidean space E^3
Thanks to the notation <x,y,z>
in the above declaration, the coordinates
\((x,y,z)\) are immediately available as three symbolic variables x
,
y
and z
(there is no need to declare them via var()
, i.e. to type
x, y, z = var('x y z')
):
sage: x is E.cartesian_coordinates()[1]
True
sage: y is E.cartesian_coordinates()[2]
True
sage: z is E.cartesian_coordinates()[3]
True
sage: type(z)
<class 'sage.symbolic.expression.Expression'>
Besides, \(\mathbb{E}^3\) is endowed with the orthonormal vector frame \((e_x, e_y, e_z)\) associated with Cartesian coordinates:
sage: E.frames()
[Coordinate frame (E^3, (e_x,e_y,e_z))]
At this stage, this is the default vector frame on \(\mathbb{E}^3\) (being the only vector frame introduced so far):
sage: E.default_frame()
Coordinate frame (E^3, (e_x,e_y,e_z))
Defining a vector field#
We define a vector field on \(\mathbb{E}^3\) from its components in the vector frame \((e_x,e_y,e_z)\):
sage: v = E.vector_field(-y, x, sin(x*y*z), name='v')
sage: v.display()
v = -y e_x + x e_y + sin(x*y*z) e_z
We can access to the components of \(v\) via the square bracket operator:
sage: v[1]
-y
sage: v[:]
[-y, x, sin(x*y*z)]
A vector field can evaluated at any point of \(\mathbb{E}^3\):
sage: p = E((3,-2,1), name='p')
sage: p
Point p on the Euclidean space E^3
sage: p.coordinates()
(3, -2, 1)
sage: vp = v.at(p)
sage: vp
Vector v at Point p on the Euclidean space E^3
sage: vp.display()
v = 2 e_x + 3 e_y - sin(6) e_z
Vector fields can be plotted:
sage: v.plot(max_range=1.5, scale=0.5)
Graphics3d Object
For customizing the plot, see the list of options in the documentation of
plot()
.
For instance, to get a view of the orthogonal projection of \(v\) in the plane
\(y=1\), do:
sage: v.plot(fixed_coords={y: 1}, ambient_coords=(x,z), max_range=1.5,
....: scale=0.25)
Graphics object consisting of 81 graphics primitives
We may define a vector field \(u\) with generic components \((u_x, u_y, y_z)\):
sage: u = E.vector_field(function('u_x')(x,y,z),
....: function('u_y')(x,y,z),
....: function('u_z')(x,y,z),
....: name='u')
sage: u.display()
u = u_x(x, y, z) e_x + u_y(x, y, z) e_y + u_z(x, y, z) e_z
sage: u[:]
[u_x(x, y, z), u_y(x, y, z), u_z(x, y, z)]
Its value at the point \(p\) is then:
sage: up = u.at(p)
sage: up.display()
u = u_x(3, -2, 1) e_x + u_y(3, -2, 1) e_y + u_z(3, -2, 1) e_z
How to compute various vector products#
Dot product#
The dot (or scalar) product \(u\cdot v\) of the vector fields \(u\)
and \(v\) is obtained by the method
dot_product()
,
which admits dot()
as a shortcut alias:
sage: u.dot(v) == u[1]*v[1] + u[2]*v[2] + u[3]*v[3]
True
\(s= u\cdot v\) is a scalar field, i.e. a map \(\mathbb{E}^3 \to \mathbb{R}\):
sage: s = u.dot(v)
sage: s
Scalar field u.v on the Euclidean space E^3
sage: s.display()
u.v: E^3 → ℝ
(x, y, z) ↦ -y*u_x(x, y, z) + x*u_y(x, y, z) + sin(x*y*z)*u_z(x, y, z)
It maps points of \(\mathbb{E}^3\) to real numbers:
sage: s(p)
-sin(6)*u_z(3, -2, 1) + 2*u_x(3, -2, 1) + 3*u_y(3, -2, 1)
Its coordinate expression is:
sage: s.expr()
-y*u_x(x, y, z) + x*u_y(x, y, z) + sin(x*y*z)*u_z(x, y, z)
Norm#
The norm \(\|u\|\) of the vector field \(u\) is defined in terms of the dot product by \(\|u\| = \sqrt{u\cdot u}\):
sage: norm(u) == sqrt(u.dot(u))
True
It is a scalar field on \(\mathbb{E}^3\):
sage: s = norm(u)
sage: s
Scalar field |u| on the Euclidean space E^3
sage: s.display()
|u|: E^3 → ℝ
(x, y, z) ↦ sqrt(u_x(x, y, z)^2 + u_y(x, y, z)^2 + u_z(x, y, z)^2)
sage: s.expr()
sqrt(u_x(x, y, z)^2 + u_y(x, y, z)^2 + u_z(x, y, z)^2)
For \(v\), we have:
sage: norm(v).expr()
sqrt(x^2 + y^2 + sin(x*y*z)^2)
Cross product#
The cross product \(u\times v\) is obtained by the method
cross_product()
,
which admits cross()
as a shortcut alias:
sage: s = u.cross(v)
sage: s
Vector field u x v on the Euclidean space E^3
sage: s.display()
u x v = (sin(x*y*z)*u_y(x, y, z) - x*u_z(x, y, z)) e_x
+ (-sin(x*y*z)*u_x(x, y, z) - y*u_z(x, y, z)) e_y
+ (x*u_x(x, y, z) + y*u_y(x, y, z)) e_z
We can check the standard formulas expressing the cross product in terms of the components:
sage: all([s[1] == u[2]*v[3] - u[3]*v[2],
....: s[2] == u[3]*v[1] - u[1]*v[3],
....: s[3] == u[1]*v[2] - u[2]*v[1]])
True
Scalar triple product#
Let us introduce a third vector field, \(w\) say. As a example, we do not pass
the components as arguments of
vector_field()
,
as we did for \(u\) and \(v\); instead, we set them in a second stage, via the
square bracket operator, any unset component being assumed to be zero:
sage: w = E.vector_field(name='w')
sage: w[1] = x*z
sage: w[2] = y*z
sage: w.display()
w = x*z e_x + y*z e_y
The scalar triple product of the vector fields \(u\), \(v\) and \(w\) is obtained as follows:
sage: triple_product = E.scalar_triple_product()
sage: s = triple_product(u, v, w)
sage: s
Scalar field epsilon(u,v,w) on the Euclidean space E^3
sage: s.expr()
-(y*u_x(x, y, z) - x*u_y(x, y, z))*z*sin(x*y*z) - (x^2*u_z(x, y, z)
+ y^2*u_z(x, y, z))*z
Let us check that the scalar triple product of \(u\), \(v\) and \(w\) is \(u\cdot(v\times w)\):
sage: s == u.dot(v.cross(w))
True
How to evaluate the standard differential operators#
The standard operators \(\mathrm{grad}\), \(\mathrm{div}\), \(\mathrm{curl}\), etc.
involved in vector calculus are accessible as methods on scalar fields and
vector fields (e.g. v.div()
). However, to allow for standard mathematical
notations (e.g. div(v)
), let us import the functions
grad()
, div()
,
curl()
and
laplacian()
:
sage: from sage.manifolds.operators import *
Gradient#
We first introduce a scalar field, via its expression in terms of Cartesian coordinates; in this example, we consider some unspecified function of \((x,y,z)\):
sage: F = E.scalar_field(function('f')(x,y,z), name='F')
sage: F.display()
F: E^3 → ℝ
(x, y, z) ↦ f(x, y, z)
The value of \(F\) at a point:
sage: F(p)
f(3, -2, 1)
The gradient of \(F\):
sage: grad(F)
Vector field grad(F) on the Euclidean space E^3
sage: grad(F).display()
grad(F) = d(f)/dx e_x + d(f)/dy e_y + d(f)/dz e_z
sage: norm(grad(F)).display()
|grad(F)|: E^3 → ℝ
(x, y, z) ↦ sqrt((d(f)/dx)^2 + (d(f)/dy)^2 + (d(f)/dz)^2)
Divergence#
The divergence of the vector field \(u\):
sage: s = div(u)
sage: s.display()
div(u): E^3 → ℝ
(x, y, z) ↦ d(u_x)/dx + d(u_y)/dy + d(u_z)/dz
For \(v\) and \(w\), we have:
sage: div(v).expr()
x*y*cos(x*y*z)
sage: div(w).expr()
2*z
An identity valid for any scalar field \(F\) and any vector field \(u\):
sage: div(F*u) == F*div(u) + u.dot(grad(F))
True
Curl#
The curl of the vector field \(u\):
sage: s = curl(u)
sage: s
Vector field curl(u) on the Euclidean space E^3
sage: s.display()
curl(u) = (-d(u_y)/dz + d(u_z)/dy) e_x + (d(u_x)/dz - d(u_z)/dx) e_y
+ (-d(u_x)/dy + d(u_y)/dx) e_z
To use the notation rot
instead of curl
, simply do:
sage: rot = curl
An alternative is:
sage: from sage.manifolds.operators import curl as rot
We have then:
sage: rot(u).display()
curl(u) = (-d(u_y)/dz + d(u_z)/dy) e_x + (d(u_x)/dz - d(u_z)/dx) e_y
+ (-d(u_x)/dy + d(u_y)/dx) e_z
sage: rot(u) == curl(u)
True
For \(v\) and \(w\), we have:
sage: curl(v).display()
curl(v) = x*z*cos(x*y*z) e_x - y*z*cos(x*y*z) e_y + 2 e_z
sage: curl(w).display()
curl(w) = -y e_x + x e_y
The curl of a gradient is always zero:
sage: curl(grad(F)).display()
curl(grad(F)) = 0
The divergence of a curl is always zero:
sage: div(curl(u)).display()
div(curl(u)): E^3 → ℝ
(x, y, z) ↦ 0
An identity valid for any scalar field \(F\) and any vector field \(u\) is
as we can check:
sage: curl(F*u) == grad(F).cross(u) + F*curl(u)
True
Laplacian#
The Laplacian \(\Delta F\) of a scalar field \(F\) is another scalar field:
sage: s = laplacian(F)
sage: s.display()
Delta(F): E^3 → ℝ
(x, y, z) ↦ d^2(f)/dx^2 + d^2(f)/dy^2 + d^2(f)/dz^2
The following identity holds:
as we can check:
sage: laplacian(F) == div(grad(F))
True
The Laplacian \(\Delta u\) of a vector field \(u\) is another vector field:
sage: Du = laplacian(u)
sage: Du
Vector field Delta(u) on the Euclidean space E^3
whose components are:
sage: Du.display()
Delta(u) = (d^2(u_x)/dx^2 + d^2(u_x)/dy^2 + d^2(u_x)/dz^2) e_x
+ (d^2(u_y)/dx^2 + d^2(u_y)/dy^2 + d^2(u_y)/dz^2) e_y
+ (d^2(u_z)/dx^2 + d^2(u_z)/dy^2 + d^2(u_z)/dz^2) e_z
In the Cartesian frame, the components of \(\Delta u\) are nothing but the (scalar) Laplacians of the components of \(u\), as we can check:
sage: e = E.cartesian_frame()
sage: Du == sum(laplacian(u[[i]])*e[i] for i in E.irange())
True
In the above formula, u[[i]]
return the \(i\)-th component of \(u\) as a
scalar field, while u[i]
would have returned the coordinate expression of
this scalar field; besides, e
is the Cartesian frame:
sage: e[:]
(Vector field e_x on the Euclidean space E^3,
Vector field e_y on the Euclidean space E^3,
Vector field e_z on the Euclidean space E^3)
For the vector fields \(v\) and \(w\), we have:
sage: laplacian(v).display()
Delta(v) = -(x^2*y^2 + (x^2 + y^2)*z^2)*sin(x*y*z) e_z
sage: laplacian(w).display()
Delta(w) = 0
We have:
sage: curl(curl(u)).display()
curl(curl(u)) = (-d^2(u_x)/dy^2 - d^2(u_x)/dz^2 + d^2(u_y)/dxdy
+ d^2(u_z)/dxdz) e_x + (d^2(u_x)/dxdy - d^2(u_y)/dx^2 - d^2(u_y)/dz^2
+ d^2(u_z)/dydz) e_y + (d^2(u_x)/dxdz + d^2(u_y)/dydz - d^2(u_z)/dx^2
- d^2(u_z)/dy^2) e_z
sage: grad(div(u)).display()
grad(div(u)) = (d^2(u_x)/dx^2 + d^2(u_y)/dxdy + d^2(u_z)/dxdz) e_x
+ (d^2(u_x)/dxdy + d^2(u_y)/dy^2 + d^2(u_z)/dydz) e_y
+ (d^2(u_x)/dxdz + d^2(u_y)/dydz + d^2(u_z)/dz^2) e_z
A famous identity is
Let us check it:
sage: curl(curl(u)) == grad(div(u)) - laplacian(u)
True
How to customize various symbols#
Customizing the symbols of the orthonormal frame vectors#
By default, the vectors of the orthonormal frame associated with Cartesian coordinates are denoted \((e_x,e_y,e_z)\):
sage: frame = E.cartesian_frame()
sage: frame
Coordinate frame (E^3, (e_x,e_y,e_z))
But this can be changed, thanks to the method
set_name()
:
sage: frame.set_name('a', indices=('x', 'y', 'z'))
sage: frame
Coordinate frame (E^3, (a_x,a_y,a_z))
sage: v.display()
v = -y a_x + x a_y + sin(x*y*z) a_z
sage: frame.set_name(('hx', 'hy', 'hz'),
....: latex_symbol=(r'\mathbf{\hat{x}}', r'\mathbf{\hat{y}}',
....: r'\mathbf{\hat{z}}'))
sage: frame
Coordinate frame (E^3, (hx,hy,hz))
sage: v.display()
v = -y hx + x hy + sin(x*y*z) hz
Customizing the coordinate symbols#
The coordinates symbols are defined within the angle brackets <...>
at the
construction of the Euclidean space. Above we did:
sage: E.<x,y,z> = EuclideanSpace()
which resulted in the coordinate symbols \((x,y,z)\) and in the corresponding
Python variables x
, y
and z
(SageMath symbolic expressions). To
use other symbols, for instance \((X,Y,Z)\), it suffices to create E
as:
sage: E.<X,Y,Z> = EuclideanSpace()
We have then:
sage: E.atlas()
[Chart (E^3, (X, Y, Z))]
sage: E.cartesian_frame()
Coordinate frame (E^3, (e_X,e_Y,e_Z))
sage: v = E.vector_field(-Y, X, sin(X*Y*Z), name='v')
sage: v.display()
v = -Y e_X + X e_Y + sin(X*Y*Z) e_Z
By default the LaTeX symbols of the coordinate coincide with the letters given
within the angle brackets. But this can be adjusted through the optional
argument symbols
of the function EuclideanSpace
, which has to be
a string, usually prefixed by r (for raw string, in order to allow for the
backslash character of LaTeX expressions). This string contains the coordinate
fields separated by a blank space; each field contains the coordinate’s text
symbol and possibly the coordinate’s LaTeX symbol (when the latter is
different from the text symbol), both symbols being separated by a colon
(:
):
sage: E.<xi,et,ze> = EuclideanSpace(symbols=r"xi:\xi et:\eta ze:\zeta")
sage: E.atlas()
[Chart (E^3, (xi, et, ze))]
sage: v = E.vector_field(-et, xi, sin(xi*et*ze), name='v')
sage: v.display()
v = -et e_xi + xi e_et + sin(et*xi*ze) e_ze


CLEAN AND SOBER A film review by Mark R. Leeper Copyright 1988 Mark R. Leeper
Capsule review: Overly long story of an embezzler, alcoholic, and drug addict who is half-heatedly trying to get his life together. A hard-hitting film on this subject is needed, but this film only occasionally has what it would take. Rating: +1.
Back in 1962 Jack Lemmon had a reputation as a comic actor and surprised audiences by playing a dramatic role and being *very* good at it. The film was DAYS OF WINE AND ROSES. The story was of a young couple with everything going for them whose lives are ripped apart by an alcoholism problem. Somehow to audiences who had seen Lemmon in a humorous context, his serious role seemed all the more serious. Well, times have changed since DAYS OF WINE AND ROSES, and while alcoholism is no less a problem drug addiction is much more of a problem today so, perhaps even inspired by WINE AND ROSES, comedy actor Michael Keaton is currently starring in the serious CLEAN AND SOBER.
While DAYS OF WINE AND ROSES concentrated on why a successful young man would get an alcohol problem, it is clear from early on that Daryl Poynter (played by Keaton) is a jerk who deserves the worst that his alcoholism and drug problem will bring him, so the film wastes none of its 124 minutes on how he got into this state. Instead, the film starts with the incident that finally causes Keaton to check himself into a detoxification clinic and tells how even there he tries to sidestep his problem rather than confronting it. Most of the film covers Keaton trying very hard to relapse into being once again the addict who embezzled $92,000 to support his habit. The real heroes are ex-addicts Craig (played by Morgan Freeman) and Richard (played by M. Emmet Walsh), who take no nonsense in trying to straighten out Poynter against his will. Craig runs the rehabilitation clinic; Richard heads up the local chapter of Alcoholics Anonymous.
Where CLEAN AND SOBER goes most astray is in Poynter's romantic attachment to fellow clinic attendee Charlie Standers (played by Kathy Baker). In spite of the fact that both are addicts, Poynter's attempts to get involved in Standers's life are something of a diversion and a distraction from the central theme. It is through his relationship with Standers that Keaton will eventually get serious about his own problem, but the screentime spent on that aspect of the plot is excessive in a film that is overly long anyway. That screentime could have been more effectively used in telling the story of Poynter's problem. It is good to see a serious film, well-acted, on the problem of substance abuse, but a better film than CLEAN AND SOBER really is needed. Rate it a +1 on the -4 to +4 scale.
Mark R. Leeper att!mtgzz!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.
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Related links: index of all rec.arts.movies.reviews reviews


Comments
-
Greg Hurrell
Please see:
-
roksob
Wincent: Your fix worked. Thanks. You might consider displaying a challenge when a user closes the preference window without clicking on "Apply". E.g. "Do you want to apply the changes you have made?" I expected that closing the window would automatically apply my selections.
-
Greg Hurrell
But it already does do that... Do an experiment:
- change any setting - note that the "Apply" button becomes enabled - do not click "Apply" - try to close the preferences window - observe that a sheet comes down advising you of unsaved changes
Note that this is not the same as:
- turning off "Launch at login" (and not clicking "Apply") - turning on "Launch at Login" (and not clicking "Apply")
If you do that you'll see the "Apply" button becomes enabled when you first toggle the setting and then becomes disabled again when you toggle it back; that's because turning something off and then on again is a "no-op" and there's nothing to apply.
-
Greg Hurrell
Ah, one more thing...
The whole "Apply" button thing is getting a bit old fashioned now. This used to be the way things were done in the majority of Mac apps, and Synergy adheres to the model very well.
But for some time now the trend has been for "instant apply" or "real time" preferences; ie. there isn't even an "Apply" button at all and everything takes effect immediately.
The current Synergy preferences UI is the way it is, but if I ever make a new version of it I'll dump the "Apply" paradigm for the "real time" one. Simply because its the dominant trend now and users expect things to work that way, not necessarily because it's the best way to do things (for example, one thing you lose when you go to the "real time" model is the ability to discard you changes and go back to the way things were before you started fiddling; in other words, the good old "Cancel" button).
-
roksob
So it does. I'm just not ready for prime time:) Thanks for your patience.
Add a comment
Comments are now closed for this issue.


Kevin S. Bradley
Democrat
Self-employed Bookseller, and independent contract driver for Skyline Vision Clinic and Laser Center, Colorado Springs
M.I.M. (Master of International Management, Thunderbird*, Glendale AZ)(1985) B.A. (Spanish/Marketing) Metropolitan State College*, Denver, CO)(1981) H.S. Denver East (1976)
81226
I have in addition to the political experience listed, been a Vice President of a small company (sales/marketing), a translator, a teacher, a public relations director, a Speakers Bureau Chairman, an advocate and a fundraiser.
I was elected to positions in college and grad school. I have been a registered Democrat for most of my life. I was briefly a Republican for the 2006 election. I was an active member of Florence City government from 2003-2007 (City Council, Planning Commission). I was the Treasurer(2007-2008) and Chairman(2007-2009) of the Fremont County Democrats from 2007-2009. I was the Democratic Candidate for Congress (2010, CO-5).
I have not been a member of any group (except Colorado Democrats) since November 10, 2015. I volunteer in my community.
I am keenly interested in representation for all communities within Colorado. I participated in 2011, legislative and congressional redistricting in Pueblo and Salida. As a native, and resident for all but about 10 years of my life, been an avid traveler and politically aware Coloradan. I have worked in the government and private sectors, including for contractors to government contracts for the government (Minerals Management Service of the Department of Interior, Civil Division (Aviation and Admiralty and Toxic Torts) of the Department of Justice, and US State Department). Spanish and my love and frequent travel to Latin America are part of my understanding that may be valuable to the Spanish speaking community at home and abroad.
I am a Democrat in Republican dominated Fremont County, I live and breathe in the current 5th Congressional District: Chaffee, El Paso, Fremont, Park, Teller and I ran for office when Lake County was a part of it. I know Colorado, from the Four Corners, to Springfield, to Sterling to Dinosaur National Monument, five generations of my family call Colorado home. I am acutely aware of what it means to be a resident of Denver, and the rural beyond. I have lived in rural Fremont County longer than I have lived anywhere. I want a competitive division of districts that do not punish smaller counties.
I have been a bookseller for more than 30 years. I read and sell a wide variety of books, all kinds, with just enough stock to offend everyone and anyone. I have friends across the world, country, state, county and city that are the scale of human endeavor. I work within deadlines and constraints. I believe learning is lifelong and value it deeply.
Male


WITNESS LIST Business & Commerce Committee February 25, 2003 - 9:00A SB 128 FOR: Beneke, Jim (Self), Austin, TX Edler, Jerry (Self), San Antonio, TX Wadley, Leo (Self), Ft. Worth, TX ON: Ray, Matt (Texas Department of Insurance), Austin, TX Sulak, Tim (TTLA), Austin, TX Registering, but not testifying: For: Cardenas, P. Gus (AARP), San Antonio, TX Davila, Alex (AARP), San Antonio, TX Kelemen, George (AARP), Austin, TX Lambe, Dan (Texas Watch), Austin, TX SB 129 FOR: Becker, Gregory (TDH Mold Task Force and Texas Association for Indoor Air Quality), Houston, TX Dotson, Kyle (The Dotson Group, LLC), Houston, TX Giaramita, Kathi (Service Master), Memphis, TN Heyer, Connie (Building Owners and Managers Association), Austin, TX McAuster, Todd (Texas Air Conditioning Contractors Association), Austin, TX Mintz, David (Texas Apartment Association), Austin, TX Small, Ed (Indoor Air Quality Association Inc.), Austin, TX ON: Kotrla, Claren (Texas Department of Health), Austin, TX Norman, Scott (Texas Association of Builders), Austin, TX Registering, but not testifying: For: Cardenas, P. Gus (AARP), San Antonio, TX Davila, Alex (AARP), San Antonio, TX Kelemen, George (AARP), Austin, TX Lambe, Dan (Texas Watch), Austin, TX


More intuition behind the iteration:
For infinite horizon, Bellman’s optimality condition implies that,
$$
J_{\alpha}(x)=\max_{a\in\mathcal{A}}\sum_{y\in\mathcal{X}}P_a(x, y)\left\{R_a(x,y)+\alpha J_{\alpha}(y)\right\}
$$
If we write the iterative step more explicitly, it turns out to be,
$$
J_{\alpha}^{(i+1)}(x):=\max_{a\in\mathcal{A}}\sum_{y\in\mathcal{X}}P_a(x, y)\left\{R_a(x,y)+\alpha J_{\alpha}^{(i)}(y)\right\}
$$
So if the iteration converges, we get a relation similar to Bellman’s equation.
Infinite horizon
Similarly if we want to find $J_{\alpha}^{\pi}$ for a given policy, we can do a similar iteration:
$$
J_{\alpha}^{\pi,(i+1)}:=T_{\pi}\circ J_{\alpha}^{\pi,(i)}
$$
The major questions are,
-
Do these procedures converge?
-
If yes, how fast?
Q: Does it converge?
Here is a theorem:
For any $\pi$ and $0<\alpha<1$, there is $J^{\pi}\in\mathbb{R}^{\mathcal{X}}$ such that,
For all $J\in\mathbb{R}^{\mathcal{X}}$,
$$
J^{\pi}=\lim_{k\rightarrow\infty}T_{\pi}^{k}J
$$
$J^{\pi}$ is the unique solution to
$$J=T_{\pi}\circ J
$$
Q: Does it converge?
The idea of the proof is as follows:
First we can
show that $T_{\pi}$ is a contraction, i.e., for any $J$ and $J'$,
$$
\lvert\lvert T_{\pi}J-T_{\pi}J'\rvert\rvert_{\infty}\leq\alpha\lvert\lvert J -J'\rvert\rvert_{\infty}
$$
For convergence, note that,
$$
\lvert\lvert T_{\pi}J-J^{\pi}\rvert\rvert_{\infty}\leq \alpha \lvert\lvert J-J^{\pi}\rvert\rvert_{\infty}\\ 0<\alpha<1
$$
Thus the policy iteration converges.
Q: Does it converge?
A similar theorem for optimal value function:
For any $\pi$ and $0<\alpha<1$, there is $J^{\star}\in\mathbb{R}^{\mathcal{X}}$ such that,
For all $J\in\mathbb{R}^{\mathcal{X}}$,
$$
J^{\star}=\lim_{k\rightarrow\infty}T^{k}J
$$
$J^{\pi}$ is the unique solution to
$$J=T\circ J
$$
$J^{\star}=\max_{\pi}J^{\pi}$
and
$J^{\star}=J^{\pi^{\star}}$
Policy Iteration
Instead of iterating over the value function, we can also iterate over the policy.
First note that,
$$
J^{\star}(x)=\sum_{y\in\mathcal{X}}P_{\pi^{\star}(x)}(x,y)\left\{R_{\pi^{\star}(x)}(x,y)+\alpha J^{\star}(y)\right\}\\
\pi^{\star}(x)=\arg\max_{a\in\mathcal{A}}\sum_{y\in\mathcal{X}}P_{a}(x,y)\left\{R_{a}(x,y)+\alpha J^{\star}(y)\right\}
$$
So we can define a Greedy operator $G:\mathbb{R}^{\mathcal{X}}\rightarrow\mathcal{A}^{\mathcal{X}}$ as:
$$
(GJ)(x)=\arg\max_{a\in\mathcal{A}}\mathbb{E}\left[R_0+\alpha J(X_1)\mid X_0=x, A_0=a\right]
$$
Policy Iteration
From the last set of equations, we can think of the following iteration:
$$
J^{(k+1)}(x):=\sum_{y\in\mathcal{X}}P_{\pi^{(i)}(x)}(x,y)\left\{R_{\pi^{(i)}(x)}(x,y)+\alpha J^{(k)}(y)\right\}
$$ until convergence. Call the limit $J^{\pi^{(i)}}$.
Then update the policy with,
$$
\pi^{(i+1)}(x):=\arg\max_{a\in\mathcal{A}}\sum_{y\in\mathcal{X}}P_{a}(x,y)\left\{R_{a}(x,y)+\alpha J^{\pi^{(i)}}(y)\right\}
$$
Policy Iteration
Equivalently,
-
Start with some policy $\pi^{(0)}$
-
Compute $J^{\pi^{(i)}}$ (policy evaluation iteration).
-
Update $\pi$ with the following:
$$
\pi^{(i+1)}=G\circ J^{\pi^{(i)}}
$$
-
If $\pi^{(i+1)}$ changes in the last step, go to step 2.
If $\pi^{(i+1)}$ does not change, then terminate.
Policy Iteration
Like the value iteration, the policy iteration also converges. One theorem says that it terminates in finite number of steps.
Policy iteration generates a sequence of policies with distinct, increasing values, terminating after a finite number of iteration with an optimal policy,
i.e., for some $k$,
$$
J^{\pi^{(0)}}\leq J^{\pi^{(1)}}\leq\ldots\leq J^{\pi^{(k)}}=J^{\star}
$$
Policy Iteration
There are some other variants of policy iteration. For example, in Generalized Policy iteration,
The value updation is done for a fixed number of times (i.e., approx. values):
$$
J^{(i+1)}:=T_{\pi^{i}}^{k}\circ J^{(i)}
$$ and then update the policy,
$$
\pi^{(i+1)}=G\circ J^{(i+1)}$$
Though value ierations look simpler, policy iterations are faster in practice, and terminates after finite steps.
Solution with Linear Programming
Another approach for finding the optimal policies is given by LPP:
Minimize $$\sum_{x\in\mathcal{X}}J(x) \text{ over }J$$
under the consraints,
$$J(x)\geq \sum_{y\in\mathcal{X}}R_a(x,y)P_a(x,y)+\alpha \sum_{z\in\mathcal{X}}P_a(x,z)J(z),\\ \forall a\in\mathcal{A}, x\in\mathcal{X}
$$
The solution will be same as $J^{\star}$.
...
Applications
Many applications. Some are:
-
Finance: deciding how much to invest in stock.
-
Robotics: Dialogue system, navigation system
-
Traditional problems like:
-
Which catalogues to send to individual clients?
-
At what age a vehicle needs to be repaires / replaced?
-
What proportion of fishes should be caught?
-
and many more...
Applications
The main challanges are:
-
Transition probabilities may not be known.
-
Rewards may not be defined explicitly.
-
For all modern problems, state space is huge. Difficult to handle.
-
Sometimes the states are not fully observed. Those are called Partially Observable MDP.
When the parameters are unknown, the decision maker tries to learn those from “experience”. That is called Reinforcement Learning (stay tuned for more on this 🙂).
Here we present two toy examples.
Cart-Pole problem
Classical problem of balancing a pole by applying force on a cart.
We have a system like this:
Want to balance the stick
Cart-Pole problem
Here are the values:
$$M=1kg, m=0.1kg, L=1m,\\ g=9.8ms^{-2}, \Delta t=0.02s$$
After each 0.02s, the decision maker decides to apply a force $F$ on the cart for the next 0.02s. Possible values of $F$ are $-10N, 0N, 10N$
Objectives are:
-
To keep the cart within boundary.
-
To keep the angle of the pole withinn a range ($-12^o$ to $12^o$)
-
To keep the system within these limits upto $200^{th}$ timepoint.
Cart-Pole problem
The dynamics of the system is described by the following:
Define
$$
p(t)=\frac{F+m\omega^2(t)L \sin(\theta(t))}{M+m}
$$
Then,
$$
\frac{d\omega(t)}{dt}=\frac{g\sin(\theta(t))-p(t)\cos(\theta(t))}{L\left(\frac{4}{3}-\frac{m\cos^2(\theta(t))}{M+m}\right)}\\
\frac{dv(t)}{dt}=p(t)-\frac{mL\frac{d\omega(t)}{dt}\cos(\theta(t))}{M+m}
$$
Cart-Pole problem
Given $x, v, \theta, \omega$ at time $t$, we can compute the state for time $t+\Delta t$. And apply the force accordingly.
Yes, the process is deterministic if the precise measurements are given.
But a little child can also balance a pole on his/her hand, without knowing the physics or the precise measurements.
Here we try to mimic the same behaviour. We shall provide only some discrete info about the state and see if we can find a good policy.
Drawback: Markov property may no longer be valid. But let’s see how it goes.
Cart-Pole problem
Some bad policies:
Choose the action randomly:
Mean life: 22.93
Cart-Pole problem
Some bad policies:
Based on position $x$ only:
Mean life: 29.33
Cart-Pole problem
Some bad policies:
Based on angle $\theta$ only:
Mean life: 41.40
Cart-Pole problem
Discrete representation of the states:
-
The whole range of $x$ was divided into three regions: Left-Forbidden, Good, Right-Forbidden
-
Each of $v, \theta, \omega$ was also categorized into 5 regions.
-
So, $\#$ of states$=3\times 5^3=375$
-
At each time point, the continuous observations are collected from the simulator. Then a small amount of random noise is added, and then the observation is categorized.
-
Based on the supplied category, the program has to take a decision which will be sent to the simulator.
Cart-Pole problem
The transition probabilities under each action were estimated beforehand using simulation.
The reward is defined as follows:
$$
R_a(x,y)=
\begin{cases}
-10, & \text{if }y\text{ is a forbidden state}\\
2, & \text{if }y\text{ is a `very good' state}\\
0, & \text{otherwise}
\end{cases}
$$
Cart-Pole problem
Mean life: 195.80
Cart-Pole problem
The result is as follows:
For 100 simulations upto time 200, the following was obtained:
|
Mean Life |
Min. |
Max. |
#(==200) |
|
Random policy
|
22.93
|
9
|
66
|
0
|
|
x-based if-else
|
29.33
|
8
|
56
|
0
|
|
$\theta$-based if-else
|
41.40
|
25
|
59
|
0
|
|
MDP
|
195.8
|
170
|
200
|
61
|
Toy example : 2048
Why $2\times 2$?
-
For $4\times 4$, it is possibe to go to 2048 (possibly more than that), and there are trillions of states.
-
If we consider the $4\times 4$ game upto 64, that has about 40 billion states.
-
For $3\times 3$, it is possible to go upto 1024 and there are about 25 million states.
-
For $2\times 2$, it is possible to reach 32, and there are at most $6^4=1296$ states.
Toy example : 2048
-
After each move, the game randomly chooses a blank tile.
-
In that position, a 4 is placed with probability 0.1, a 2 is placed with probability 0.9
-
If there is no blank space, the game is over.
So we can explicitly calculate the transition probabilities.
Toy example : 2048
Transition probabilities
Toy example : 2048
Reward is defined as follows:
$$R_a(x,y)=
\begin{cases}
+5, & \text{if }y\text{ contains 32}\\
-5, & \text{if move }a\text{ is invalid for state }x\\
0, & \text{otherwise}
\end{cases}
$$
Toy example : 2048
Here is the result:
From 200 simulations, the highest tiles were as following:
Conclusion:
-
The iterative procedures perform pretty well for a simple problem.
-
For real world problems, the probabilities and rewards will be unknown. Those have to be learned by the agent from experience.
-
The main challange is to solve a problem with huge number of states.
-
References:
-
Reinforcement Learning: An Introduction, Richard S. Sutton and Andrew G. Barto
-
Lecture Notes available online
-
Presented by:
-
Riddhiman Saha
-
Souhardya Ray
-
Tamoghna Gupta


- Backup of XDTOXD - Music Collection from my old channel: http://www.nyaa.eu/?page=torrentinfo&tid=315473 Made by Rizlim. Welcome, this channel is mainly focused to share arranges and vocals of Touhou Project, as well as original, non-Touhou songs too. Regarding the old channel, requests from those old uploads are welcome, just try to be specific when you do (like which artist/circle made it, the image that was used in the video or something similar) i can't identify certain songs just by their video title or original theme. Hope you enjoy!
✜【東方アレンジ#003】 『++++』【Malicent vs CORRUPTEDお兄ちゃん】✜
90 views, 4 days ago
◐【TGC:004】 「悔恨コロッセオ」【Team Grimoire】◑
90 views, 4 days ago
◐【TGC:003】 「Anbrosia」【-45】◑
90 views, 4 days ago
◐【TGC:002】 「モンテクリスト」【LUNE】◑
90 views, 4 days ago
Most Epic OSTs Ever: Distant Lands
90 views, 4 days ago
Most Epic OSTs Ever: Disappear
90 views, 4 days ago
Wallpaper: http://animeflow.net/1086/landscape---scenic---sky---space Auto-Replay: http://hdsoundi.com/video-146 From / Album: http://soundcloud.com/JKOL Music By: JKOL x - - - Note: Our Opinion May Differ - - - x AnimeFlow: http://animeflow.net/ Facebook Fan Page: https://www.facebook.com/HDSounDI BackUp Channel: http://www.youtube.com/subscription_center?add_user=thepicore


October 21st
October 21st
Lecture
- Demonstrated a mail sever thing.
- Showed general overview of how javadoc comments work
- Comments should be in format: /** *[comment] *[comment] */
- Click on 'Run Javadoc' under the run menu
- Take a description of the code, for each class
- This chapter according to Leon: (Also pick one to reaserch more into)
- Code division multiplexing: Allows multiple people to 'talk' at once and they can focus only on similar 'languages'/codes to communicate
- More into error detection code
- Ethernet, how they share the system and try to avoid collision
- Niegl:
- NodeJS and Socket.io
- Javascript
- Browser-based (originally)
- High-level, not machine specific, as long as there is an interpreter it will run
- Interpreted language, not compiled
- Untyped: You don't need to declare variable types, just declare it as a variable. (If you don't declaire it it'll be global)
- Dynamic: Can be loaded on the fly, as requested. Not all together at once
- Functional: Can pass functions as arguments, and have functions return functions as variables/results
- Netscape 2.0 in 1995 was first ever javascript implementation
- Internet Explorer 3 in 1996 reversed engineered javascript, arose compatibility issues
- EMCA in 1997 tried to create a stardard attempt (first attempt), wasn't picked up
- Ajax was implemented in Javascript in 2005
- Chrome V8 engine was introduced in 2008 (fast Javascript implementation engine)
- EMCA finally got a starndard (5.0) in 2009. Now on EMCA 2016
- V8 engine
- Made by google
- Open source
- Very fast
- Standalone or embedded system
- in C++
- Node.js
- Created by Ryan Dahl in 2009
- Based on Google's V8 javascript engine
- Event-driven, handles things as events occur (listens for even and then does something)
- Asynchronous, processes things as it happens
- Good for heavy I/O processing
- npm
- Node Packet Manager
- Full of open source javascript libraries
- Largest code repository in the world
- Anyone can publish a package
- Socket.io
- Realtime communication engine
- Uses WebSockets with an AJAX fallback
- Event-driven (like Node.js)
- package.json: every node.js file has this. Expresses libraries, name, version, and description.
- JSON: JavaScript Object Notation, everything is an object, object denoted by brackets. Usually key-value notation. Can also have arrays, denoted by square brackets.
- server.js is the main driver file. Only thing that it really uses
- npm install --save____________________command line to generate the folder for running
-
Lab


Iranian refugee 'free' after six years in Australian detention camp
by AFP, StaffAn Iranian asylum seeker and award-winning author held in an offshore Australian detention camp for more than six years said Thursday he had arrived in New Zealand, and was celebrating "freedom."
Behrouz Boochani was sent to Manus Island in Papua New Guinea after fleeing Iran in 2013. He was picked up on a vessel packed with asylum seekers attempting to reach Australia from Indonesia.
The 36-year-old journalist later won the Victorian Prize for Literature for a book detailing his life under Australia's harsh offshore detention policy.
"I just arrived in New Zealand. So exciting to get freedom after more than six years," Boochani tweeted on Thursday.
"Thank you to all the friends who made this happen."
Under a policy meant to deter asylum-seekers from reaching Australia by boat, Canberra has for years sent arrivals to remote Pacific camps on Nauru and Papua New Guinea's Manus Island for processing, barring them from ever resettling in Australia.
The UN, rights groups and leading health professionals have slammed Canberra for its treatment of detainees, as stories of violent riots, self harm, dire living conditions and even murder have emerged from the camps over the years.


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--- layout: default ---
“A new self-driving car subscription service where you pay a monthly fee, and just request a ride on demand whenever you want to be taken from point A to point B. You request a pickup with an app, whatever car in the area that is available drives itself to your location, then takes you to your destination, and becomes available for someone else to use after that point.”


Project name*Please add name.*Project name in this path already exists.*Project name should contain more than 3 characters.*Project name can't contain only spaces.*Project name can't contain slash (/)*Please add location.Please provide a name longer than 3 charactersCreate in(Create New)"{{targetFolder.value}}" (Create New)


--- layout: post status: publish published: true title: Pro90:Dual Palindromes author: display_name: hippo login: admin email<EMAIL_ADDRESS>url: http://blog.futureme.info author_login: admin author_email<EMAIL_ADDRESS>author_url: http://blog.futureme.info wordpress_id: 33 wordpress_url: http://localhost/?p=29 date: '2012-07-16 12:34:19 +0800' date_gmt: '2012-07-16 12:34:19 +0800' categories: - usaco tags: - usaco - algorithms comments: [] ---
A number that reads the same from right to left as when read from left to right is called a palindrome. The number 12321 is a palindrome; the number 77778 is not. Of course, palindromes have neither leading nor trailing zeroes, so 0220 is not a palindrome.

The number 21 (base 10) is not palindrome in base 10, but the number 21 (base 10) is, in fact, a palindrome in base 2 (10101).

Write a program that reads two numbers (expressed in base 10):

Solutions to this problem do not require manipulating integers larger than the standard 32 bits.

A single line with space separated integers N and S.

3 25

OUTPUT FORMAT
 N lines, each with a base 10 number that is palindromic when expressed in at least two of the bases 2..10. The numbers should be listed in order from smallest to largest.
SAMPLE OUTPUT (file dualpal.out)

26 27 28


|
PART A: Cross-connecting a Player and HTML Form Elements
|
This part of the tutorial will show in the most basic way how one can use the Music Object API's callback capabilities to achieve two-way connection between player instances and elements of an HTML page.
Because of these callback capabilities, it is even possible to create your own elaborate custom interface for player instances that exactly matches the desired aesthetics for your sonified Web pages. Of course, in this tutorial we will only go as far as to demonstrate the principles behind the way callbacks work, and we will leave it up to your imagination to find cool ways to apply these principles in your sonified Web content.


1923 - Born Anna Maria Sofia Cecilia Kalogeropoulou in Manhattan, New York
1937 - Her family moves back to Athens, Greece where Anna Maria was enrolled at the Greek National Conservatoire to study with Maria Trivella
1939 - Auditions at the Athens Conservatoir to study with Elvira de Hidalgo whom became her teacher
1941 - Mades her professional debut in the small role of Beatrice in Franz von Suppé's Boccaccio
1942 - Mades her debut in leading role as Tosca and as Marta in Eugen d'Albert's Tiefland at the Olympia Theatre
1944 - Callas performs the role of Leonore in a Greek language production of Fidelio at the Odeon of Herodes Atticus
1945 - Callas travels back to the United States to audition at the Metropolitan Opera but declines the contract that was offered to her
1946 - Travels to Verona, Italy, where she auditions for La Gioconda at the Arena di Verona and makes her Italian debut
1949 - Marries Giovanni Battista Meneghini, an older, wealthy industrialist, who assumes control of her career and also debuts in Buenos Aires at the Teatro Colón in the Aida, Turandot and Norma roles directed by Tullio Serafin, supported by Mario Del Monaco, Fedora Barbieri and Nicola Rossi-Lemeni
1949 - Takes on the roles of Brünnhilde in Die Walküre and Elvira in I puritani at the same time which set her on a path to leading many other important roles like Lucia di Lammermoor, La traviata, Armida, La sonnambula, Il pirata, Il turco in Italia, Medea, Anna Bolena, and other neglected operas by Cherubini, Bellini, Donizetti and Rossini
1950 - Callas substituts for Renata Tebaldi in the role of Aida which opened the door to her debut at Italy's most prestigious opera house
1951 - Makes her official debut at La Scala in Verdi's I vespri siciliani making La Scala her artistic home throughout the 50s
1952 - Makes her London debut at the Royal Opera House in Norma so successfully that sets her to return for many years
1956 - Finally makes her Metropolitan Opera debut as Norma, opening the Met's seventy-second season
1957 - Gives a concert to inaugurate what then was billed as the Dallas Civic Opera, and helps establish that company with her friends from Chicago, Lawrence Kelly and Nicola Rescigno
1958 - Further consolidates Dallas Civic Opera standings after giving a towering performance as Violetta in La traviata, and that same year, in her only American performances of Medea
1959 - Leaves Meneghini and starts dating Greek shipping magnate Aristotle Onassis
1960 - Callas and Onassis have a child, a boy, who dies hours after he was born
1965 - Performs Tosca opposite to Franco Corelli as Cavaradossi, and Richard Tucker with Tito Gobbi as Scarpia for her final performances at the Met
1966 - Callas renounces her U.S. citizenship at the American Embassy in Paris, to facilitate the end of her marriage to Meneghini
1968 - Onassis leaves Callas to marry Jacqueline Kennedy
1975 - Callas was diagnosed with dermatomyositis, a disease that causes a failure of the muscles and tissues (including the larynx) which leads to her vocal decline and affects heart functions
1977 - Callas dies in isolation of heart failure at her Paris flat at the age of 53
Although her dramatic life and personal tragedy have often overshadowed Callas the artist in the popular press, her artistic achievements were such that Leonard Bernstein called her "the Bible of opera" and her influence so enduring that, in 2006, Opera News wrote of her: "Nearly thirty years after her death, she's still the definition of the diva as artist—and still one of classical music's best-selling vocalists."