Uni{corn|form} Tool Kit
The UTK tool kit aims at providing executables to generate and analyze point sets in unit domains [0,1)^s. It is originally meant to help researchers developing sampling patterns in a numerical integration using Monte Carlo estimators. More precisely, it was developed with the precise question of optimizing image synthesis via Path tracing algorithms.
UTK is a C++ library that implements a large variety of samplers and tools to analyze and compare them (discrepancy evaluation, spectral analysis, numerical integration tests…).
License
The core of the library is available under the BSD license. For some samplers, the library is just a wrapper on some codes with specific license (see the samplers page for details).
Clone and Build
UTK is hosted on a git repository. To install it, the first step is to clone the repository on your computer. This can be done using the following command line:
git clone https://github.com/utk-team/utk.git
The code can be build on a Linux or a Mac environment. The Windows build is not yet supported. To build it, one can use the following commands, assuming the current working directory is the cloned utk repository.
mkdir build
cd build
cmake ..
make
See Using UTK/*
documentation pages for mor information and building options.
External libraries
Main external libraries are downloaded automatically by CMake (spdlog, cli11). When the python binding is enabled (cmake flag UTK_PYTHON
set to true), pybind11 is fetched.
If UTK_USE_FFTW
cmake flag is set to true (the default setting) and if the fftw library is available on your system, the Fourier tools will use it.
Finally, if UTK_USE_CGAL
is set to true, samplers with CGAL as dependency will be built. CGAL and SuiteSparse must be installed on your system.
Authors
The UTK library was developed mainly by
- David Coeurjolly<EMAIL_ADDRESS>- Hélène Perrier<EMAIL_ADDRESS>- Bastien Doignies<EMAIL_ADDRESS>But was also contributed to by
- Victor Ostromoukhov<EMAIL_ADDRESS>- Adrien Pilleboue
- Jean David Genevaux
If you want to refer to UTK in your publications, please use the following bibtex entry:
@Misc{UTK,
title = {Uni(corn|form) tool kit},
note = {url{https://utk-team.github.io/utk/}}
}
Contributing
UTK is an open-source, community driven, project. If you want to help us (typos, documentations issues, new samplers, new tools…), feel free to create a Pull-Request on the Github project.


We all have written/supported an application that had zero logging. It is like playing two sided blindfolded chess in the dark. We didn’t want to pass that on to the users of Highway so logging is backed right into the toolset. We rely on Common.Logging for our logging API, because this allows you, our users, to use your favorite logging facility. I am going to use a simple console logger for these examples, but it could be any Common.Logging adapter.
Example Domain
In all of the examples below, we’ll be working with the following business domain, from our Driver’s Education company:
When you add an item there are several things that could/should happen. Knowing at which point the failure happens is important. This is where Highway Framework makes things easier on you. We want to know where the operations are executing and how the context is operating on a configurable level. This is going to use the standard log levels to get output from the system. Consider the following Test.
123456789101112131415161718192021222324252627
[TestMethod]publicvoidShouldLogAtDebugLevel(){//arrange varlogger=newConsoleOutLogger("Testing",LogLevel.Debug,true,true,true,@"dd/mm/yyyy hh:mm:ss");vartarget=newDataContext(Settings.Default.Connection,newDriversEducationMappings(),logger);//acttarget.Add(newDriver("Devlin","Liles"));target.Add(newDriver("Tim","Rayburn"));target.Add(newDriver("Jay","Smith"));target.Add(newDriver("Brian","Sullivan"));target.Add(newDriver("Cori","Drew"));target.Commit();foreach(vardriverintarget.AsQueryable<Driver>()){target.Remove(driver);}target.Commit();//assertAssert.Inconclusive("We fail here to get the output from console nice and easy");}
You can see that you get the step by step of what the application is doing on Debug but if you want even more information, you can up the game with LogLevel.Trace – This will trace every action start and finish.


Class Event
Common base class for all events.
Inheritance
System.Object
Event
Inherited Members
System.Object.Equals(System.Object, System.Object)
System.Object.GetType()
System.Object.MemberwiseClone()
System.Object.ReferenceEquals(System.Object, System.Object)
Namespace: x2net
Assembly: x2net.dll
Syntax
public class Event : Cell
Constructors
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Event()
Initializes a new instance of the Event class.
Declaration
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Event(Int32)
Initializes a new Event instance with the given fingerprint length.
Declaration
protected Event(int length)
Parameters
| Type |
Name |
Description |
| System.Int32 |
length |
|
Fields
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tag
Per-class type tag to support custom type hierarchy.
Declaration
protected static readonly Event.Tag tag
Field Value
Properties
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_Channel
Gets or sets the name of the hub channel which this event is
assigned to.
Declaration
public string _Channel { get; set; }
Property Value
| Type |
Description |
| System.String |
|
|
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_Handle
Gets or sets the link session handle associated with this event.
Declaration
public int _Handle { get; set; }
Property Value
| Type |
Description |
| System.Int32 |
|
|
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Gets or sets a boolean value indicating whether this event is to be
transformed or not when it is transferred through a link.
Declaration
public bool _Transform { get; set; }
Property Value
| Type |
Description |
| System.Boolean |
|
|
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_WaitHandle
Gets or sets the coroutine wait handle associated with this event.
Declaration
public int _WaitHandle { get; set; }
Property Value
| Type |
Description |
| System.Int32 |
|
|
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TypeId
Gets the type identifier of this event class.
Declaration
public static int TypeId { get; }
Property Value
| Type |
Description |
| System.Int32 |
|
Methods
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Describe(StringBuilder)
Overridden by subclasses to build a ToString chain.
Declaration
protected override void Describe(StringBuilder stringBuilder)
Parameters
| Type |
Name |
Description |
| System.Text.StringBuilder |
stringBuilder |
|
Overrides
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Deserialize(Deserializer)
Overridden by subclasses to build a deserialization chain.
Declaration
public override void Deserialize(Deserializer deserializer)
Parameters
Overrides
|
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EqualsTo(Cell)
Overridden by subclasses to build an equality test chain.
Declaration
protected override bool EqualsTo(Cell other)
Parameters
| Type |
Name |
Description |
| Cell |
other |
|
Returns
| Type |
Description |
| System.Boolean |
|
Overrides
|
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GetFactoryMethod()
Returns the factory method delegate that can create an instance of
this event.
Declaration
public virtual Func<Event> GetFactoryMethod()
Returns
| Type |
Description |
| System.Func<Event> |
|
|
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GetHashCode()
Returns the hash code for the current object.
Declaration
public override int GetHashCode()
Returns
| Type |
Description |
| System.Int32 |
|
Overrides
|
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GetHashCode(Fingerprint)
Overridden by subclasses to build a hash code generator chain.
Declaration
public override int GetHashCode(Fingerprint fingerprint)
Parameters
Returns
| Type |
Description |
| System.Int32 |
|
Overrides
|
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GetHashCode(Fingerprint, Int32)
Returns the hash code for this event based on the specified
fingerprint, assuming the given type identifier.
Declaration
public int GetHashCode(Fingerprint fingerprint, int typeId)
Parameters
| Type |
Name |
Description |
| Fingerprint |
fingerprint |
|
| System.Int32 |
typeId |
|
Returns
| Type |
Description |
| System.Int32 |
|
|
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GetLength(Type, ref Boolean)
Overridden by subclasses to build an encoded length computation chain.
Declaration
public override int GetLength(Type targetType, ref bool flag)
Parameters
| Type |
Name |
Description |
| System.Type |
targetType |
|
| System.Boolean |
flag |
|
Returns
| Type |
Description |
| System.Int32 |
|
Overrides
|
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GetTypeId()
Returns the type identifier of this event.
Declaration
public virtual int GetTypeId()
Returns
| Type |
Description |
| System.Int32 |
|
|
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GetTypeTag()
Returns the custom type tag of this event.
Declaration
public override Cell.Tag GetTypeTag()
Returns
Overrides
|
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IsEquivalent(Cell, Fingerprint)
Overridden by subclasses to build an equivalence test chain.
Declaration
protected override bool IsEquivalent(Cell other, Fingerprint fingerprint)
Parameters
Returns
| Type |
Description |
| System.Boolean |
|
Overrides
|
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New()
Creates a new instance of this event class.
Declaration
public static Event New()
Returns
|
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Serialize(Serializer, Type, ref Boolean)
Overridden by subclasses to build a serialization chain.
Declaration
public override void Serialize(Serializer serializer, Type targetType, ref bool flag)
Parameters
| Type |
Name |
Description |
| Serializer |
serializer |
|
| System.Type |
targetType |
|
| System.Boolean |
flag |
|
Overrides
|
Improve this Doc
View Source
ToString()
Returns a string that describes the current object.
Declaration
public override string ToString()
Returns
| Type |
Description |
| System.String |
|
Overrides
Extension Methods


CASINO
A film review by Merch
Copyright 1996 Merch
***1/2, out of 4
CASINO (1995) is one of those rare movies where everything falls wonderfully into place. The script is magnificent, with nary a weak point in sight. The story follows the rise and fall of two gangsters, played to perfection by Robert De Niro and Joe Pesci as they leave their mid-western gambling roots and literally "take over" Las Vegas. One tries to take the high road by running the Tangiers Hotel and Casino (De Niro), while the other (Pesci) takes the low road, becoming one of the most feared (and sought-after) men in the city. Both try to please the bosses "back home", to varying degrees of success. Marty Scorsese turns in a wonderful job of directing, and will be forever credited for taking Sharon Stone (who plays Ginger, the coke-head alcoholic wife) from the terrible material she has had post-"Basic Instinct" to her Golden Globe win for Best Actress and her subsequent Oscar nomination for this part. The musical score is peppered with over 30 songs from the 70's and 80's, which serve in many cases as narratives (i.e. after Stone and De Niro have a falling out, "I'm Sorry" plays). CASINO is a well done film, and will please many groups of people: fans of the actors (Stone has an especially showy part), lovers of the genre (gangster films), and those who appreciate wonderful atmosphere (you at some points would really swear that this was really filmed during the era it portrays). CASINO is rated R for brief nudity (none, surprisingly, done by Sharon Stone), heavy language, and some very graphic violence. It has a running time of 179 minutes, and also stars Don Rickles, James Woods, Alan King, and Kevin Pollak (A Few Good Men).
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


THSITLab
lite
Hi there, this is the homepage of THSCSLab, or Tsinghua High School Computer Science Lab.
Projects
Homepage - WIP
The webste you are viewing right now.
My Galaxy - WIP
Astrodynamics Simulator
To be continued...
Place your project here, if you have push access to this repo.
Members
Liu Xiaoyi, @CircuitCoder
Low-ranked Osu! Player
Can't even write algorithms
Uses Whitespace as his primary programming language
Doesn't know how to use colors in his websites
Wu Yusong, @bqsgwys
Uses Adobe Premiere instead of Moviemaker
Almost never rebuild his project
Weights more than all members in the lab next door combined
Involved in numerous lab projects, but finished few of them
Dan Ho, @igaryhe
Creator of THSITG
FiC (Father-in-Common) of other lab members
Can manipulate space-time using mind power
Once made a Google Glass application to help users find toliets
Xu Jiazhao, @dsg-god
Weights more than Wu Yusong
Use Photoshop instead of Sketch to design
Specialist of killing chairs
Only use Soldier-76 in Overwatch
FAQ
Q:
Why are these all written is English?
A:
Because there is no good Chinese webfont. Also, Google is great. So yeah.
Q:
What do you guys actually do?
A:
Usually gaming. May code in spare time.
Proof of existence
Gitlab:
http://git.thsitg.org
Github:
https://github.com/THSITG


1) Installation
TagSLAM has been tested on Ubuntu 16.04 and 18.04LTS. You will need a full ROS installation (Kinetic or Melodic). For installation instructions see the tagslam root repository.
TagSLAM has been tested on Ubuntu 16.04 and 18.04LTS. You will need a full ROS installation (Kinetic or Melodic). For installation instructions see the tagslam root repository.


Installation¶
f3 is written in Python. It can be installed using pip with the command:
pip install f3
From Source¶
The source code can be downloaded from GitHub by running
git clone https://github.com/benmontet/f3.git
and then can be built by running
python setup.py install
in the root directory of the source tree.
Dependencies¶
In addition to a Python installation, there are a few other dependencies that are required to run f3:
mahotas will be automagically installed along with f3 by running setup.py (or through pip). As of June 5, 2017, the kplr version available on pip is not sufficient for running f3, you need a version dated June 11, 2016 or newer: the version on github linked above will be sufficient.
You will also need the Full Frame Images themselves, which are 44gb and not a part of the installation package. To get them, run
wget -r -nH -nd -np -R index.html -e robots=off https://archive.stsci.edu/pub/kepler/ffi/
f3 will by default look for these in a subdirectory from your working directory called “ffidata” but they can be placed anywhere.


JOB APPLICATION
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SUBMIT


This was my first submission to Vis, and our team was remote. Yifang and I were in HKUST while Ke was in MSRA. It was a fresh experience in which I improved my research and front-end coding skills fast but also found my shortcomings to address.
Team Work
Both Ke and Yifang are experienced and reliable. Working with them is lucky and comfortable. During this submission, I truly saw the power of teamwork. There is no way to complete all the jobs within three months by myself alone. Ke is a doer, decisive and highly effective. When the design requirements were not clear and data were deficient, he didn’t trap in problems but decided to build the prototype first and find some open source datasets. Yifang designed the style of the system, which I personally think is elegant and harmonious. She pays attention to every detail and pursues perfection. I appreciate their guidance and learned a lot from them, especially their personal qualities.
A lesson I learned is that in remote collaboration it is hard to keep everyone at the same pace as we cannot communicate immediately. I think possible solutions include a higher meeting frequency, daily report and keeping Skype opening the whole day when the deadline is close.
Coding
My front-end coding skill improves a lot in this submission from my point of view. Here are some important tips I learned:
Writing
Apparently, I need to make much more efforts in my writing. My biggest problem is that I attempted to explain everything in the paper but forgot the logic and some common rules of writhing visualization papers.
PQE
When I read related surveys and papers, I found that visualization really solves the pain points of anomaly detection. For instance, anomalies are rarer and have various forms, so it is hard to define and diagnose them only using algorithms. The evidence of the effectiveness of visualization in anomaly detection is strong. This inspires me about my choice of the PQE topic. If my research is about using visualization solve other questions, does visualization straight hit the pain point and is it irreplaceable? If my research is about developing a visualization technique such as data movie, could this technique serve for real application problems and has broad influence?


How Does it Work?
1. Use your phone camera to scan the small QR code in the bottom right corner or visit artonfranklin.com manually in your web browser.
2. From the website, place your phone in front of the black and white box business logo marker to see art pop up on your screen.
3. Touch, swipe, or pinch to rotate, flip, or zoom in on the art on your phone!


Emmott
This page contains an index of all the individuals in the database with the surname of Emmott. Selecting the person’s name will take you to that person’s individual page.
| Given Name | Birth | Death | Partner | Parents |
|---|---|---|---|---|
| 1 girl | c1914 | Emmott, Frederick Dawson, Florence | ||
| ??? | Emmott, William | |||
| Abraham, (Grocer) | c1804 | he had died by 1878 | ????, Margaret | |
| Annie | 1893-03-28 | Emmott, Frederick James Hartley, Emily | ||
| Arthur, married Muriel ?? | 1898-05-08 | 1st Qtr 1981 | Emmott, Frederick James Hartley, Emily | |
| Cecil | 1900 | Emmott, Frederick James Hartley, Emily | ||
| Clara | 1882-12-10 | Berry, Herbert | Emmott, Frederick James Hartley, Emily | |
| Emily | 1884-10-00 | Emmott, Frederick James Hartley, Emily | ||
| Frederick | 1886-12-00 | Dawson, Florence | Emmott, Frederick James Hartley, Emily | |
| Frederick James | 1855-08-21 | Mar Qtr 1929 | Hartley, Emily, Thompson, Alice | Emmott, Abraham (Grocer) ????, Margaret |
| George | 1881-05-23 | Carter, Ann | Emmott, Frederick James Hartley, Emily | |
| Maggie | 1879-10-13 | Emmott, Frederick James Hartley, Emily | ||
| Martha | 1835 | 1901-03-18 | Wilkinson, Eli | Emmott, William Emmott, ??? |
| Wilfred Hartley | 3rd Qtr 1912 | 1942-10-25 | Birch, Frances Sarah | Emmott, Frederick Dawson, Florence |
| William | Emmott, ??? | |||
| [Living] | Emmott, George Carter, Ann |


About Me
My name is Chris Frome. I’m currently a DevOps engineer in the Baltimore, MD area. I graduated with from James Madison University where I majored in Computer Science and minored in Environmental Information Systems. My interests within Computer Science include: software engineering, DevOps, and full stack web development. I first learned about programming starting in high school, and am now working as a DevOps engineer using Amazon Web Services (AWS) for cloud development. Aside from programming and computer science I enjoy cooking, rock climbing (indoor/outdoor), and camping/the outdoors.
Contact Details
Chris Frome DevOps Engineer Mount Airy, Maryland chris@chrisfrome.com


The Faculty * * * (out of * * * * )
Directed by Robert Rodriguez. Cast: Elijah Wood, Josh Hartnett, Clea DuVall, Shawn Hatosy, Jordanna Brewster, Laura Harris, Robert Patrick, Bebe Neuwirth, Famke Janssen, Piper Laurie, Jon Stewart, Salma Hayek, Christopher McDonald, Usher Raymond, Susan Willis, Daniel von Bargen, Louis Black, Megan Gallagher, Joe Hatton, Harry Knowles, Duane Martin, Jason D. May, Katherine Willis, Summer Phoenx. 1998 - 101 minutes. Rated R (for violence, gore, profanity, nudity, and drug use). Reviewed December 27, 1998.
"The Faculty," the heavily-hyped and advertised sci-fi/horror film that has teamed up director Robert Rodriguez (1995's "Desperado" and 1996's "From Dusk Till Dawn") and screenwriter Kevin Williamson (1996's "Scream" and 1997's "Scream 2"), is being called a cross between "Invasion of the Body Snatchers" and "The Breakfast Club," and I don't think I could describe it any better than that.
The film sets up the six central teenage characters who do not seem to have much in common, and then the science-fiction aspect is added, involving the fear that the faculty at Herrington High School are actually aliens who are quickly transforming everyone in the town. The six characters, as in "The Breakfast Club," can be easily labeled as a stereotype, but as they are developed, they become far more complex: Casey (Elijah Wood), the much picked upon nerd; Stokely (Clea DuVall), a goth outcast who hides behind the false facade of being a lesbian so everyone will avoid her; Zeke (Josh Hartnett), a drug dealer who turns out to be a science whiz; Stan (Shawn Hatosy), the star football quarterback who is considering quitting the team to concentrate more on academics; Delilah (Jordanna Brewster), the popular cheerleader and newspaper journalist; and Marybeth (Laura Harris), the sweet 'n southern new girl in town. Although the characters are only slightly connected (i.e. Casey is Delilah's photojournalist assistant; Marybeth tries to become buddies with Stokely, since they both don't have friends, etc.), when they all begin to suspect the teachers due to some grotesque and strange occurrences, the only people they can count on for help is each other, even though they aren't really even sure if they can trust one another.
"The Faculty" is another smart and pop-culturally hip film from Williamson, although it does not equal up to his best film, the original "Scream," and Rodriguez, whose "From Dusk Till Dawn" is still one of the more original genre films of the 90's. Williamson and Rodriguez are so assured at their professions, respectively, that the idea of teaming up together is pretty much a no-brainer. The plotline of "The Faculty," involving aliens taking over other people's bodies, has been done quite a lot before, from "Invasion of the Body Snatchers," to "The Puppet Masters," to "Invaders from Mars," so one of the obstacles that Williamson and Rodriguez had to overcome was to somehow make the idea seem fresh, and by setting the goings-on at a high school and having the protagonists be a group of teens, they were mostly successful. Surely, the conventions of the story are still the same, and the climax was inevitable, but there were a few surprises along the way, including the question of who were the aliens, and who weren't. The epilogue was also a refreshing change-of-pace as it did not set up a sequel but ended on a note that probably could not have been any better.
The performances in "The Faculty" were a treat throughout, since there were so many recognizable actors in roles that were the polar opposite of what they usually do. One exception were the teens, who, aside from Elijah Wood, are not very well-known, but they all aquit themselves nicely, particularly Wood (the seasoned pro), Clea DuVall, and Jordanna Brewster. As members of the faculty, Robert Patrick ("T2: Judgement Day") was creepy as the gym coach; Piper Laurie was amusing and threatening as the drama teacher; Bebe Neuwirth actually was somehow able to look like an alien; and Salma Hayek, as the school nurse with a bad case of the cold, was very funny in a small role. The standout, in my opinion, of the whole cast was Famke Janssen who turns in an oddly touching performance as the shy and meek english teacher who, after turning into an alien, becomes the sex bombshell. If there was any problem I had with the faculty, it was that some of them were given no real payoff in the climactic sequence. Since the teenagers realize that in order to save everyone they must kill the "Queen" alien, many of the faculty members disappear. It might have been more fun if they had to face every one of the teachers, although the finale is still pretty impressive, and includes some showstopping creature effects, especially for a relatively low 15-million-dollar budget.
Although not one of the best horror or science-fiction films I have seen, "The Faculty" is still an exciting and worthy film that Dimension Films was smart to release around the Holiday Season when this type of genre offering is usually not released. While the story is as old as the hills, it is also, in a way, timeless, because everyone, I think, has suspected at one time or another that a certain person simply did not act right, as if they really weren't human. And by putting this idea in the setting of a small-town high school, it perfectly contrasts with the alienation that most teenagers usually go through when relating to adults and other peers.
+ Note: The ad and poster campaign for this film is hugely misleading, as it features R & B artist Usher Raymond as one of the main characters. In actuality, he only has a small role as one of Stan's buddies who becomes quarterback after Stan resigns from the team. If I were one of the heads from Dimension, I would change this advertising at once, since it is unnecessary and rather deceiving.
- Copyright 1998 by Dustin Putman < Dustin Putman's Film Reviews >
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


{% extends "global/Page.html" %} {% load otree %} {% block title %} The world will be fine,... for now {% endblock %} {% block content %}
You have been able to collaborate with others to save the planet. Good job, what is left of your money and belongings is safe, thanks to the common effort of the community.
{% next_button %} {% endblock %}


Let us quickly remind ourselves how we derive the above method.
Perhaps the most celebrated of all one-dimensional root-finding routines is Newton's method, also called the Newton-Raphson method. This method requires the evaluation of both the function \( f \) and its derivative \( f' \) at arbitrary points. If you can only calculate the derivative numerically and/or your function is not of the smooth type, we normally discourage the use of this method.
The Newton-Raphson formula consists geometrically of extending the tangent line at a current point until it crosses zero, then setting the next guess to the abscissa of that zero-crossing. The mathematics behind this method is rather simple. Employing a Taylor expansion for \( x \) sufficiently close to the solution \( s \), we have
$$
f(s)=0=f(x)+(s-x)f'(x)+\frac{(s-x)^2}{2}f''(x) +\dots.
\tag{1}
$$
For small enough values of the function and for well-behaved functions, the terms beyond linear are unimportant, hence we obtain
$$
f(x)+(s-x)f'(x)\approx 0,
$$
yielding
$$
s\approx x-\frac{f(x)}{f'(x)}.
$$
Having in mind an iterative procedure, it is natural to start iterating with
$$
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.
$$
The above is Newton-Raphson's method. It has a simple geometric interpretation, namely \( x_{n+1} \) is the point where the tangent from \( (x_n,f(x_n)) \) crosses the \( x \)-axis. Close to the solution, Newton-Raphson converges fast to the desired result. However, if we are far from a root, where the higher-order terms in the series are important, the Newton-Raphson formula can give grossly inaccurate results. For instance, the initial guess for the root might be so far from the true root as to let the search interval include a local maximum or minimum of the function. If an iteration places a trial guess near such a local extremum, so that the first derivative nearly vanishes, then Newton-Raphson may fail totally
Newton's method can be generalized to systems of several non-linear equations and variables. Consider the case with two equations
$$
\begin{array}{cc} f_1(x_1,x_2) &=0\\
f_2(x_1,x_2) &=0,\end{array}
$$
which we Taylor expand to obtain
$$
\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1
\partial f_1/\partial x_1+h_2
\partial f_1/\partial x_2+\dots\\
0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1
\partial f_2/\partial x_1+h_2
\partial f_2/\partial x_2+\dots
\end{array}.
$$
Defining the Jacobian matrix \( \hat{J} \) we have
$$
\hat{J}=\left( \begin{array}{cc}
\partial f_1/\partial x_1 & \partial f_1/\partial x_2 \\
\partial f_2/\partial x_1 &\partial f_2/\partial x_2
\end{array} \right),
$$
we can rephrase Newton's method as
$$
\left(\begin{array}{c} x_1^{n+1} \\ x_2^{n+1} \end{array} \right)=
\left(\begin{array}{c} x_1^{n} \\ x_2^{n} \end{array} \right)+
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right),
$$
where we have defined
$$
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right)=
-{\bf \hat{J}}^{-1}
\left(\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\ f_2(x_1^{n},x_2^{n}) \end{array} \right).
$$
We need thus to compute the inverse of the Jacobian matrix and it is to understand that difficulties may arise in case \( \hat{J} \) is nearly singular.
It is rather straightforward to extend the above scheme to systems of more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.
The basic idea of gradient descent is that a function \( F(\mathbf{x}) \), \( \mathbf{x} \equiv (x_1,\cdots,x_n) \), decreases fastest if one goes from \( \bf {x} \) in the direction of the negative gradient \( -\nabla F(\mathbf{x}) \).
It can be shown that if
$$
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k),
$$
with \( \gamma_k > 0 \).
For \( \gamma_k \) small enough, then \( F(\mathbf{x}_{k+1}) \leq F(\mathbf{x}_k) \). This means that for a sufficiently small \( \gamma_k \) we are always moving towards smaller function values, i.e a minimum.
The previous observation is the basis of the method of steepest descent, which is also referred to as just gradient descent (GD). One starts with an initial guess \( \mathbf{x}_0 \) for a minimum of \( F \) and computes new approximations according to
$$
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k), \ \ k \geq 0.
$$
The parameter \( \gamma_k \) is often referred to as the step length or the learning rate within the context of Machine Learning.
Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global minimum of the function \( F \). In general we do not know if we are in a global or local minimum. In the special case when \( F \) is a convex function, all local minima are also global minima, so in this case gradient descent can converge to the global solution. The advantage of this scheme is that it is conceptually simple and straightforward to implement. However the method in this form has some severe limitations:
In machine learing we are often faced with non-convex high dimensional cost functions with many local minima. Since GD is deterministic we will get stuck in a local minimum, if the method converges, unless we have a very good intial guess. This also implies that the scheme is sensitive to the chosen initial condition.
Note that the gradient is a function of \( \mathbf{x} = (x_1,\cdots,x_n) \) which makes it expensive to compute numerically.
The gradient descent method is sensitive to the choice of learning rate \( \gamma_k \). This is due to the fact that we are only guaranteed that \( F(\mathbf{x}_{k+1}) \leq F(\mathbf{x}_k) \) for sufficiently small \( \gamma_k \). The problem is to determine an optimal learning rate. If the learning rate is chosen too small the method will take a long time to converge and if it is too large we can experience erratic behavior.
Many of these shortcomings can be alleviated by introducing randomness. One such method is that of Stochastic Gradient Descent (SGD), see below.
Ideally we want our cost/loss function to be convex(concave).
First we give the definition of a convex set: A set \( C \) in \( \mathbb{R}^n \) is said to be convex if, for all \( x \) and \( y \) in \( C \) and all \( t \in (0,1) \) , the point \( (1 − t)x + ty \) also belongs to C. Geometrically this means that every point on the line segment connecting \( x \) and \( y \) is in \( C \) as discussed below.
The convex subsets of \( \mathbb{R} \) are the intervals of \( \mathbb{R} \). Examples of convex sets of \( \mathbb{R}^2 \) are the regular polygons (triangles, rectangles, pentagons, etc...).
Convex function: Let \( X \subset \mathbb{R}^n \) be a convex set. Assume that the function \( f: X \rightarrow \mathbb{R} \) is continuous, then \( f \) is said to be convex if
$$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$
for all \( x_1, x_2 \in X \) and for all \( t \in [0,1] \). If \( \leq \) is replaced with a strict inequaltiy in the definition, we demand \( x_1 \neq x_2 \) and \( t\in(0,1) \) then \( f \) is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \( f(x_1) \) and \( f(x_2) \), the value of the function on the interval \( [x_1,x_2] \) is always below the line as illustrated below.
In the following we state first and second-order conditions which ensures convexity of a function \( f \). We write \( D_f \) to denote the domain of \( f \), i.e the subset of \( R^n \) where \( f \) is defined. For more details and proofs we refer to: S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press.
Suppose \( f \) is differentiable (i.e \( \nabla f(x) \) is well defined for all \( x \) in the domain of \( f \)). Then \( f \) is convex if and only if \( D_f \) is a convex set and
$$f(y) \geq f(x) + \nabla f(x)^T (y-x) $$
holds
for all \( x,y \in D_f \). This condition means that for a convex function
the first order Taylor expansion (right hand side above) at any point
a global under estimator of the function. To convince yourself you can
make a drawing of \( f(x) = x^2+1 \) and draw the tangent line to \( f(x) \) and
note that it is always below the graph.
Assume that \( f \) is twice differentiable, i.e the Hessian matrix exists at each point in \( D_f \). Then \( f \) is convex if and only if \( D_f \) is a convex set and its Hessian is positive semi-definite for all \( x\in D_f \). For a single-variable function this reduces to \( f''(x) \geq 0 \). Geometrically this means that \( f \) has nonnegative curvature everywhere.
This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition.
The next result is of great importance to us and the reason why we are going on about convex functions. In machine learning we frequently have to minimize a loss/cost function in order to find the best parameters for the model we are considering.
Ideally we want the global minimum (for high-dimensional models it is hard to know if we have local or global minimum). However, if the cost/loss function is convex the following result provides invaluable information:
Consider the problem of finding \( x \in \mathbb{R}^n \) such that \( f(x) \) is minimal, where \( f \) is convex and differentiable. Then, any point \( x^* \) that satisfies \( \nabla f(x^*) = 0 \) is a global minimum.
This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum.
Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).
Before we proceed, we would like to discuss the approach called the standard Steepest descent, which again leads to us having to be able to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).
The success of the CG methodfor finding solutions of non-linear problems is based on the theory of conjugate gradients for linear systems of equations. It belongs to the class of iterative methods for solving problems from linear algebra of the type
$$
\begin{equation*}
\hat{A}\hat{x} = \hat{b}.
\end{equation*}
$$
In the iterative process we end up with a problem like
$$
\begin{equation*}
\hat{r}= \hat{b}-\hat{A}\hat{x},
\end{equation*}
$$
where \( \hat{r} \) is the so-called residual or error in the iterative process.
When we have found the exact solution, \( \hat{r}=0 \).
The residual is zero when we reach the minimum of the quadratic equation
$$
\begin{equation*}
P(\hat{x})=\frac{1}{2}\hat{x}^T\hat{A}\hat{x} - \hat{x}^T\hat{b},
\end{equation*}
$$
with the constraint that the matrix \( \hat{A} \) is positive definite and symmetric. This defines also the Hessian and we want it to be positive definite.
We denote the initial guess for \( \hat{x} \) as \( \hat{x}_0 \). We can assume without loss of generality that
$$
\begin{equation*}
\hat{x}_0=0,
\end{equation*}
$$
or consider the system
$$
\begin{equation*}
\hat{A}\hat{z} = \hat{b}-\hat{A}\hat{x}_0,
\end{equation*}
$$
instead.
One can show that the solution \( \hat{x} \) is also the unique minimizer of the quadratic form
$$
\begin{equation*}
f(\hat{x}) = \frac{1}{2}\hat{x}^T\hat{A}\hat{x} - \hat{x}^T \hat{x} , \quad \hat{x}\in\mathbf{R}^n.
\end{equation*}
$$
This suggests taking the first basis vector \( \hat{r}_1 \) (see below for definition) to be the gradient of \( f \) at \( \hat{x}=\hat{x}_0 \), which equals
$$
\begin{equation*}
\hat{A}\hat{x}_0-\hat{b},
\end{equation*}
$$
and \( \hat{x}_0=0 \) it is equal \( -\hat{b} \).
We can compute the residual iteratively as
$$
\begin{equation*}
\hat{r}_{k+1}=\hat{b}-\hat{A}\hat{x}_{k+1},
\end{equation*}
$$
which equals
$$
\begin{equation*}
\hat{b}-\hat{A}(\hat{x}_k+\alpha_k\hat{r}_k),
\end{equation*}
$$
or
$$
\begin{equation*}
(\hat{b}-\hat{A}\hat{x}_k)-\alpha_k\hat{A}\hat{r}_k,
\end{equation*}
$$
which gives
$$
\alpha_k = \frac{\hat{r}_k^T\hat{r}_k}{\hat{r}_k^T\hat{A}\hat{r}_k}
$$
leading to the iterative scheme
$$
\begin{equation*}
\hat{x}_{k+1}=\hat{x}_k-\alpha_k\hat{r}_{k},
\end{equation*}
$$
#include <cmath>
#include <iostream>
#include <fstream>
#include <iomanip>
#include "vectormatrixclass.h"
using namespace std;
// Main function begins here
int main(int argc, char * argv[]){
int dim = 2;
Vector x(dim),xsd(dim), b(dim),x0(dim);
Matrix A(dim,dim);
// Set our initial guess
x0(0) = x0(1) = 0;
// Set the matrix
A(0,0) = 3; A(1,0) = 2; A(0,1) = 2; A(1,1) = 6;
b(0) = 2; b(1) = -8;
cout << "The Matrix A that we are using: " << endl;
A.Print();
cout << endl;
xsd = SteepestDescent(A,b,x0);
cout << "The approximate solution using Steepest Descent is: " << endl;
xsd.Print();
cout << endl;
}
Vector SteepestDescent(Matrix A, Vector b, Vector x0){
int IterMax, i;
int dim = x0.Dimension();
const double tolerance = 1.0e-14;
Vector x(dim),f(dim),z(dim);
double c,alpha,d;
IterMax = 30;
x = x0;
r = A*x-b;
i = 0;
while (i <= IterMax){
z = A*r;
c = dot(r,r);
alpha = c/dot(r,z);
x = x - alpha*r;
r = A*x-b;
if(sqrt(dot(r,r)) < tolerance) break;
i++;
}
return x;
}
import numpy as np
import numpy.linalg as la
import scipy.optimize as sopt
import matplotlib.pyplot as pt
from mpl_toolkits.mplot3d import axes3d
def f(x):
return 0.5*x[0]**2 + 2.5*x[1]**2
def df(x):
return np.array([x[0], 5*x[1]])
fig = pt.figure()
ax = fig.gca(projection="3d")
xmesh, ymesh = np.mgrid[-2:2:50j,-2:2:50j]
fmesh = f(np.array([xmesh, ymesh]))
ax.plot_surface(xmesh, ymesh, fmesh)
And then as countor plot
pt.axis("equal")
pt.contour(xmesh, ymesh, fmesh)
guesses = [np.array([2, 2./5])]
Find guesses
x = guesses[-1]
s = -df(x)
Run it!
def f1d(alpha):
return f(x + alpha*s)
alpha_opt = sopt.golden(f1d)
next_guess = x + alpha_opt * s
guesses.append(next_guess)
print(next_guess)
What happened?
pt.axis("equal")
pt.contour(xmesh, ymesh, fmesh, 50)
it_array = np.array(guesses)
pt.plot(it_array.T[0], it_array.T[1], "x-")
In the CG method we define so-called conjugate directions and two vectors \( \hat{s} \) and \( \hat{t} \) are said to be conjugate if
$$
\begin{equation*}
\hat{s}^T\hat{A}\hat{t}= 0.
\end{equation*}
$$
The philosophy of the CG method is to perform searches in various conjugate directions of our vectors \( \hat{x}_i \) obeying the above criterion, namely
$$
\begin{equation*}
\hat{x}_i^T\hat{A}\hat{x}_j= 0.
\end{equation*}
$$
Two vectors are conjugate if they are orthogonal with respect to this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is conjugate to \( \hat{t} \), then \( \hat{t} \) is conjugate to \( \hat{s} \).
An example is given by the eigenvectors of the matrix
$$
\begin{equation*}
\hat{v}_i^T\hat{A}\hat{v}_j= \lambda\hat{v}_i^T\hat{v}_j,
\end{equation*}
$$
which is zero unless \( i=j \).
Assume now that we have a symmetric positive-definite matrix \( \hat{A} \) of size \( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
$$
\begin{equation*}
\hat{x}_{i+1}=\hat{x}_{i}+\alpha_i\hat{p}_{i}.
\end{equation*}
$$
We assume that \( \hat{p}_{i} \) is a sequence of \( n \) mutually conjugate directions. Then the \( \hat{p}_{i} \) form a basis of \( R^n \) and we can expand the solution $ \hat{A}\hat{x} = \hat{b}$ in this basis, namely
$$
\begin{equation*}
\hat{x} = \sum^{n}_{i=1} \alpha_i \hat{p}_i.
\end{equation*}
$$
The coefficients are given by
$$
\begin{equation*}
\mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
\end{equation*}
$$
Multiplying with \( \hat{p}_k^T \) from the left gives
$$
\begin{equation*}
\hat{p}_k^T \hat{A}\hat{x} = \sum^{n}_{i=1} \alpha_i\hat{p}_k^T \hat{A}\hat{p}_i= \hat{p}_k^T \hat{b},
\end{equation*}
$$
and we can define the coefficients \( \alpha_k \) as
$$
\begin{equation*}
\alpha_k = \frac{\hat{p}_k^T \hat{b}}{\hat{p}_k^T \hat{A} \hat{p}_k}
\end{equation*}
$$
If we choose the conjugate vectors \( \hat{p}_k \) carefully, then we may not need all of them to obtain a good approximation to the solution \( \hat{x} \). We want to regard the conjugate gradient method as an iterative method. This will us to solve systems where \( n \) is so large that the direct method would take too much time.
We denote the initial guess for \( \hat{x} \) as \( \hat{x}_0 \). We can assume without loss of generality that
$$
\begin{equation*}
\hat{x}_0=0,
\end{equation*}
$$
or consider the system
$$
\begin{equation*}
\hat{A}\hat{z} = \hat{b}-\hat{A}\hat{x}_0,
\end{equation*}
$$
instead.
One can show that the solution \( \hat{x} \) is also the unique minimizer of the quadratic form
$$
\begin{equation*}
f(\hat{x}) = \frac{1}{2}\hat{x}^T\hat{A}\hat{x} - \hat{x}^T \hat{x} , \quad \hat{x}\in\mathbf{R}^n.
\end{equation*}
$$
This suggests taking the first basis vector \( \hat{p}_1 \) to be the gradient of \( f \) at \( \hat{x}=\hat{x}_0 \), which equals
$$
\begin{equation*}
\hat{A}\hat{x}_0-\hat{b},
\end{equation*}
$$
and \( \hat{x}_0=0 \) it is equal \( -\hat{b} \). The other vectors in the basis will be conjugate to the gradient, hence the name conjugate gradient method.
Let \( \hat{r}_k \) be the residual at the \( k \)-th step:
$$
\begin{equation*}
\hat{r}_k=\hat{b}-\hat{A}\hat{x}_k.
\end{equation*}
$$
Note that \( \hat{r}_k \) is the negative gradient of \( f \) at \( \hat{x}=\hat{x}_k \), so the gradient descent method would be to move in the direction \( \hat{r}_k \). Here, we insist that the directions \( \hat{p}_k \) are conjugate to each other, so we take the direction closest to the gradient \( \hat{r}_k \) under the conjugacy constraint. This gives the following expression
$$
\begin{equation*}
\hat{p}_{k+1}=\hat{r}_k-\frac{\hat{p}_k^T \hat{A}\hat{r}_k}{\hat{p}_k^T\hat{A}\hat{p}_k} \hat{p}_k.
\end{equation*}
$$
We can also compute the residual iteratively as
$$
\begin{equation*}
\hat{r}_{k+1}=\hat{b}-\hat{A}\hat{x}_{k+1},
\end{equation*}
$$
which equals
$$
\begin{equation*}
\hat{b}-\hat{A}(\hat{x}_k+\alpha_k\hat{p}_k),
\end{equation*}
$$
or
$$
\begin{equation*}
(\hat{b}-\hat{A}\hat{x}_k)-\alpha_k\hat{A}\hat{p}_k,
\end{equation*}
$$
which gives
$$
\begin{equation*}
\hat{r}_{k+1}=\hat{r}_k-\hat{A}\hat{p}_{k},
\end{equation*}
$$
Vector ConjugateGradient(Matrix A, Vector b, Vector x0){
int dim = x0.Dimension();
const double tolerance = 1.0e-14;
Vector x(dim),r(dim),v(dim),z(dim);
double c,t,d;
x = x0;
r = b - A*x;
v = r;
c = dot(r,r);
int i = 0; IterMax = dim;
while(i <= IterMax){
z = A*v;
t = c/dot(v,z);
x = x + t*v;
r = r - t*z;
d = dot(r,r);
if(sqrt(d) < tolerance)
break;
v = r + (d/c)*v;
c = d; i++;
}
return x;
}
The optimization problem is to minimize \( f(\mathbf {x} ) \) where \( \mathbf {x} \) is a vector in \( R^{n} \), and \( f \) is a differentiable scalar function. There are no constraints on the values that \( \mathbf {x} \) can take.
The algorithm begins at an initial estimate for the optimal value \( \mathbf {x}_{0} \) and proceeds iteratively to get a better estimate at each stage.
The search direction \( p_k \) at stage \( k \) is given by the solution of the analogue of the Newton equation
$$
B_{k}\mathbf {p} _{k}=-\nabla f(\mathbf {x}_{k}),
$$
where \( B_{k} \) is an approximation to the Hessian matrix, which is updated iteratively at each stage, and \( \nabla f(\mathbf {x} _{k}) \) is the gradient of the function evaluated at \( x_k \). A line search in the direction \( p_k \) is then used to find the next point \( x_{k+1} \) by minimising
$$
f(\mathbf {x}_{k}+\alpha \mathbf {p}_{k}),
$$
over the scalar \( \alpha > 0 \).
Stochastic gradient descent (SGD) and variants thereof address some of the shortcomings of the Gradient descent method discussed above.
The underlying idea of SGD comes from the observation that a given function, which we want to minimize, can almost always be written as a sum over \( n \) data points \( \{\mathbf{x}_i\}_{i=1}^n \),
$$
C(\mathbf{\beta}) = \sum_{i=1}^n c_i(\mathbf{x}_i,
\mathbf{\beta}).
$$
This in turn means that the gradient can be computed as a sum over \( i \)-gradients
$$
\nabla_\beta C(\mathbf{\beta}) = \sum_i^n \nabla_\beta c_i(\mathbf{x}_i,
\mathbf{\beta}).
$$
Stochasticity/randomness is introduced by only taking the gradient on a subset of the data called minibatches. If there are \( n \) data points and the size of each minibatch is \( M \), there will be \( n/M \) minibatches. We denote these minibatches by \( B_k \) where \( k=1,\cdots,n/M \).
As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \) and we choose to have \( M=5 \) minibathces, then each minibatch contains two data points. In particular we have \( B_1 = (\mathbf{x}_1,\mathbf{x}_2), \cdots, B_5 = (\mathbf{x}_9,\mathbf{x}_{10}) \). Note that if you choose \( M=1 \) you have only a single batch with all data points and on the other extreme, you may choose \( M=n \) resulting in a minibatch for each datapoint, i.e \( B_k = \mathbf{x}_k \).
The idea is now to approximate the gradient by replacing the sum over all data points with a sum over the data points in one the minibatches picked at random in each gradient descent step
$$
\nabla_{\beta}
C(\mathbf{\beta}) = \sum_{i=1}^n \nabla_\beta c_i(\mathbf{x}_i,
\mathbf{\beta}) \rightarrow \sum_{i \in B_k}^n \nabla_\beta
c_i(\mathbf{x}_i, \mathbf{\beta}).
$$
Thus a gradient descent step now looks like
$$
\beta_{j+1} = \beta_j - \gamma_j \sum_{i \in B_k}^n \nabla_\beta c_i(\mathbf{x}_i,
\mathbf{\beta})
$$
where \( k \) is picked at random with equal probability from \( [1,n/M] \). An iteration over the number of minibathces (n/M) is commonly referred to as an epoch. Thus it is typical to choose a number of epochs and for each epoch iterate over the number of minibatches, as exemplified in the code below.
import numpy as np
n = 100 #100 datapoints
M = 5 #size of each minibatch
m = int(n/M) #number of minibatches
n_epochs = 10 #number of epochs
j = 0
for epoch in range(1,n_epochs+1):
for i in range(m):
k = np.random.randint(m) #Pick the k-th minibatch at random
#Compute the gradient using the data in minibatch Bk
#Compute new suggestion for
j += 1
Taking the gradient only on a subset of the data has two important benefits. First, it introduces randomness which decreases the chance that our opmization scheme gets stuck in a local minima. Second, if the size of the minibatches are small relative to the number of datapoints (\( M < n \)), the computation of the gradient is much cheaper since we sum over the datapoints in the \( k-th \) minibatch and not all \( n \) datapoints.
A natural question is when do we stop the search for a new minimum? One possibility is to compute the full gradient after a given number of epochs and check if the norm of the gradient is smaller than some threshold and stop if true. However, the condition that the gradient is zero is valid also for local minima, so this would only tell us that we are close to a local/global minimum. However, we could also evaluate the cost function at this point, store the result and continue the search. If the test kicks in at a later stage we can compare the values of the cost function and keep the \( \beta \) that gave the lowest value.
Another approach is to let the step length \( \gamma_j \) depend on the number of epochs in such a way that it becomes very small after a reasonable time such that we do not move at all.
As an example, let \( e = 0,1,2,3,\cdots \) denote the current epoch and let \( t_0, t_1 > 0 \) be two fixed numbers. Furthermore, let \( t = e \cdot m + i \) where \( m \) is the number of minibatches and \( i=0,\cdots,m-1 \). Then the function
$$\gamma_j(t; t_0, t_1) = \frac{t_0}{t+t_1} $$
goes to zero as the number of epochs gets large. I.e. we start with a step length \( \gamma_j (0; t_0, t_1) = t_0/t_1 \) which decays in time \( t \).
In this way we can fix the number of epochs, compute \( \beta \) and evaluate the cost function at the end. Repeating the computation will give a different result since the scheme is random by design. Then we pick the final \( \beta \) that gives the lowest value of the cost function.
import numpy as np
def step_length(t,t0,t1):
return t0/(t+t1)
n = 100 #100 datapoints
M = 5 #size of each minibatch
m = int(n/M) #number of minibatches
n_epochs = 500 #number of epochs
t0 = 1.0
t1 = 10
gamma_j = t0/t1
j = 0
for epoch in range(1,n_epochs+1):
for i in range(m):
k = np.random.randint(m) #Pick the k-th minibatch at random
#Compute the gradient using the data in minibatch Bk
#Compute new suggestion for beta
t = epoch*m+i
gamma_j = step_length(t,t0,t1)
j += 1
print("gamma_j after %d epochs: %g" % (n_epochs,gamma_j))
# Importing various packages
from math import exp, sqrt
from random import random, seed
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import SGDRegressor
x = 2*np.random.rand(100,1)
y = 4+3*x+np.random.randn(100,1)
xb = np.c_[np.ones((100,1)), x]
theta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
print("Own inversion")
print(theta_linreg)
sgdreg = SGDRegressor(n_iter = 50, penalty=None, eta0=0.1)
sgdreg.fit(x,y.ravel())
print("sgdreg from scikit")
print(sgdreg.intercept_, sgdreg.coef_)
theta = np.random.randn(2,1)
eta = 0.1
Niterations = 1000
m = 100
for iter in range(Niterations):
gradients = 2.0/m*xb.T.dot(xb.dot(theta)-y)
theta -= eta*gradients
print("theta frm own gd")
print(theta)
xnew = np.array([[0],[2]])
xbnew = np.c_[np.ones((2,1)), xnew]
ypredict = xbnew.dot(theta)
ypredict2 = xbnew.dot(theta_linreg)
n_epochs = 50
t0, t1 = 5, 50
m = 100
def learning_schedule(t):
return t0/(t+t1)
theta = np.random.randn(2,1)
for epoch in range(n_epochs):
for i in range(m):
random_index = np.random.randint(m)
xi = xb[random_index:random_index+1]
yi = y[random_index:random_index+1]
gradients = 2 * xi.T.dot(xi.dot(theta)-yi)
eta = learning_schedule(epoch*m+i)
theta = theta - eta*gradients
print("theta from own sdg")
print(theta)
plt.plot(xnew, ypredict, "r-")
plt.plot(xnew, ypredict2, "b-")
plt.plot(x, y ,'ro')
plt.axis([0,2.0,0, 15.0])
plt.xlabel(r'$x$')
plt.ylabel(r'$y$')
plt.title(r'Random numbers ')
plt.show()
You can however use codes we have adapted from the text Numerical Recipes in C++, see chapter 10.7. Here we present a program, which you also can find at the webpage of the course we use the functions dfpmin and lnsrch. This is a variant of the Broyden et al algorithm discussed in the previous slide.
Below we show only excerpts from the main program. For the full program, see the above link.
// Main function begins here
int main()
{
int n, iter;
double gtol, fret;
double alpha;
n = 1;
// reserve space in memory for vectors containing the variational
// parameters
Vector g(n), p(n);
cout << "Read in guess for alpha" << endl;
cin >> alpha;
gtol = 1.0e-5;
// now call dfmin and compute the minimum
p(0) = alpha;
dfpmin(p, n, gtol, &iter, &fret, Efunction, dEfunction);
cout << "Value of energy minimum = " << fret << endl;
cout << "Number of iterations = " << iter << endl;
cout << "Value of alpha at minimum = " << p(0) << endl;
return 0;
} // end of main program
The functions Efunction and dEfunction compute the expectation value of the energy and its derivative. They use the the quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) It uses the first derivatives only. The BFGS algorithm has proven good performance even for non-smooth optimizations. These functions need to be changed when you want to your own derivatives.
// this function defines the expectation value of the local energy
double Efunction(Vector &x)
{
double value = x(0)*x(0)*0.5+1.0/(8*x(0)*x(0));
return value;
} // end of function to evaluate
// this function defines the derivative of the energy
void dEfunction(Vector &x, Vector &g)
{
g(0) = x(0)-1.0/(4*x(0)*x(0)*x(0));
} // end of function to evaluate
You need to change these functions in order to compute the local energy for your system. I used 1000 cycles per call to get a new value of \( \langle E_L[\alpha]\rangle \). When I compute the local energy I also compute its derivative. After roughly 10-20 iterations I got a converged result in terms of \( \alpha \).


This document describes how to run BBN Curveball, after it has been installed, on Ubuntu 12.04, with the quilt-client and quilt-server.
A "quilt" is a single BBN Curveball connection constructed from one or more connections, such as BBN Curveball connections [0]. A quilt can be constructed from any combination of multiple concurrent or sequential connections. The connections may appear (to the RAT) to be between the client and multiple decoys, and to use multiple protocols.
The quilt software consists of two applications:
The quilt-client is the client software that runs on the client host. It provides a SOCKS proxy [1].
The quilt-server is a server that runs on the quilt host somewhere on the network beyond the control of any adversary trying to monitor the quilt. The quilt-server implements the backend of the quilt protocol, and uses a local SOCKS proxy (danted) on the quilt host to proxy the requests from the quilt clients.
Note that the order in which the software is started matters.
These steps must be done after installing BBN Curveball and after the DR and DP servers have been started, and after the HTTP/HTTPS servers have been started on the decoy and covert hosts, as described in the instructions for running BBN Curveball.
sudo /opt/curveball/scripts/quilt-server
The quilt-server commandline options are similar to those for cb-dp. It is particularly important to make sure that the --permitted-subnet and --outbound-dev parameters are chosen correctly.
sudo /opt/curveball/scripts/quilt-client
The quilt-client commandline parameters are described below.
Note curveball-client and quilt-client MUST NOT be run at the same time on the same client [1].
A comma-separated list of decoy hosts and the protocols to use to reach them. For example:
-d decoy0:https,decoy1:https,decoy0:http,decoy2:http-uni
means that the quilt should use decoy0 via HTTP and HTTPS, decoy1 only via HTTPS, and decoy2 only via HTTP-UNI.
Quilting can also use non-Curveball tunnels; for example
-d quilt:sock
means that the quilt should connect directly via a socket the quilt host, rather than using Curveball.
QUILTHOST is the name of the host on which the quilt-server is running. The default is "quilt".
The logging level to use for diagnostic messages. If set to 0, all logging is disabled. The lowest level (most verbose) is 1; the highest level (critical errors only) is 5.
The number of concurrent channels that the quilt should try to keep open at the same time. If the requested number of concurrent channels is larger than the number of decoy host/protocol pairs specified with the -d option, the quilt-client will refuse to start. To specify that quilting is permitted to open more than one connection using the same decoy and protocol, include this host/protocol pair more than once in the -d option.
The number of seconds that each channel is permitted to live before it is closed.
Note: If the quilt server crashes or is blocked, paused, or stopped for any reason the quilt client will become unresponsive. The quilt client cannot distinguish between a quilt server that is crashed or dead from one that is unresponsive, and therefore lets the user decide whether or not to quit.
The quilting architecture permits new channels to be developed and added to quilt-client and quilt-server in order to support new connection types (for example, Tor or SONATA). These new channels can also implement different traffic patterns, for example to mimic web browsing, or video streaming, or VOIP.
A key property of the architecture is that the individual channels are autonomous, and decide when to send data and control messages (including sending padding when there is no application traffic to send).
The current version of quilting does not illustrate this feature: it only provides one default channel, with the following behavior:
This product includes software developed in part by support from the Defense Advanced Research Project Agency (DARPA) Contract No. N66001-11-C-4017.


JNDI Concepts
JNDI technology enables Java programs to gain access to a wide variety of naming
and directory services in a consistent, Java-centric way. The following
picture shows a Java application using JNDI to access a directory service.
The role that each part plays is summarized below:
- Application class.
A class that calls the methods of a JNDI service provider to connect
to naming and directory services and perform operations such as querying
the service or binding new entries.
- JNDI Service Provider.
A Java class that can communicate with a naming
or directory service. JDK 1.3 includes service providers for the following:
- Network Information Service (NISCtxFactory)
- Cos Naming Services (CNCtxFactory)
- LDAP directory services (LdapCtxFactory)
- File system (RefFSCtxFactory)
- RMI Registry (RegistryContextFactory)
- Naming and Directory Service.
Software that manages name to object bindings.
A comprehensive account of JNDI is outside the scope of this document.
If you are developing programs that use JNDI and you are not familiar with
the technology, you will do well to look at any of the books that have
been written on JNDI.
Legal Notices


|
Knight's Tour Generator
Tourneys and the Fast Generation and Obfuscation of Closed Knight's Tours
|
Neural network tourney generator. More...
#include <TakefujiLee.h>
Public Member Functions | |
| CTakefujiLee (int w, int h, int seed) | |
| Constructor. More... | |
| void | Generate (CBoard &b) |
| Generate a tourney. More... | |
| Public Member Functions inherited from CNeuralNet | |
| CNeuralNet (UINT n, int seed) | |
| Constructor. More... | |
| void | InsertNeuron (UINT i, UINT j) |
| Insert a neuron. More... | |
| Public Member Functions inherited from CGraph | |
| CGraph (const UINT n) | |
| Constructor. More... | |
| ~CGraph () | |
| Destructor. More... | |
| void | InsertEdge (const UINT i, const UINT j) |
| Insert an edge. More... | |
| UINT | BFSF (std::vector< UINT > &result) |
| Breadth-first spanning forest. More... | |
| void | PrintGraph () |
| Print the graph to a text file. More... | |
Private Member Functions | |
| bool | Update () |
| Update all neurons. More... | |
| void | GetAdjacentVertices (std::vector< CVertex * > &v, CVertex *p) |
| Get adjacent vertices. More... | |
| bool | IsStable () |
| Stability test. More... | |
| bool | HasDegree2 () |
| Degree test. More... | |
| void | Reset () |
| Reset. More... | |
| void | RandomizeEdgeList () |
| Randomize the edge list. More... | |
| void | GraphToBoard (CBoard &b) |
| Convert graph to board. More... | |
Private Attributes | |
| int | m_nWidth = 0 |
| Board width. | |
| int | m_nHeight = 0 |
| Board height. | |
| int | m_nSize = 0 |
| Board size. | |
Additional Inherited Members | |
| Protected Attributes inherited from CGraph | |
| std::vector< CEdge * > | m_vEdgeList |
| Edge list. | |
| UINT | m_nNumEdges = 0 |
| Number of edges. | |
| CVertex * | m_pVertexList = nullptr |
| Vertex list. | |
| UINT | m_nNumVerts = 0 |
| Number of vertices. | |
| std::queue< CVertex * > | m_qBFSQueue |
| Queue for breadth-first search. | |
| CRandom | m_cRandom |
| Random number generator. | |
Neural network tourney generator by Takefuji and Lee, see Takefuji and Lee, "Neural network computing for knight's tour problems", Neurocomputing, 4(5):249–254, 1992. Unfortunately the paper doesn't completely specify the method used, so I've taken best guesses in a couple of places. This method is slow at generating closed knight's tours (for more details, see Parberry, "Scalability of a neural network for the knight's tour problem", Neurocomputing, 12:19-34, 1996), but it's much faster at generating tourneys. It's essentially just a Hopfield network with a custom update function, so convergence is guaranteed.
Definition at line 47 of file TakefujiLee.h.
| CTakefujiLee::CTakefujiLee | ( | int | w, |
| int | h, | ||
| int | seed | ||
| ) |
Initialize the neural network.
| w | Board width. |
| h | Board height. |
| seed | PRNG seed. |
Definition at line 41 of file TakefujiLee.cpp.
| void CTakefujiLee::Generate | ( | CBoard & | b | ) |
Get vector of vertices adjacent to a given vertex.
| p | Pointer to a vertex. |
| v | [out] Vector of vertices adjacent to the vertex pointed to by p. |
Definition at line 237 of file TakefujiLee.cpp.
|
private |
Assuming the neural network has converged, convert the outputs of its neurons to a move table.
| b | [out] Chessboard for the results. |
Definition at line 175 of file TakefujiLee.cpp.
|
private |
The neural network may converge to a state in which not all vertices have degree 2, which is a requirement for knight's tours and tourneys.
Definition at line 123 of file TakefujiLee.cpp.
|
private |
The network is stable if all neurons are stable.
Definition at line 111 of file TakefujiLee.cpp.
|
private |
Permute the edge list into pseudorandom order for update.
Definition at line 252 of file TakefujiLee.cpp.
|
private |
Reset all neuron outputs to zero and all neuron states to a random value.
Definition at line 70 of file TakefujiLee.cpp.
|
private |
Update all neurons.
Definition at line 83 of file TakefujiLee.cpp.


|
Bullet Collision Detection & Physics Library
|
Classes | |
| class | DMul |
| class | Edge |
| class | Face |
| class | Int128 |
| class | IntermediateHull |
| class | Point32 |
| class | Point64 |
| class | PointR128 |
| class | Pool |
| class | PoolArray |
| class | Rational128 |
| class | Rational64 |
| class | Vertex |
Public Member Functions | |
| void | compute (const void *coords, bool doubleCoords, int stride, int count) |
| btVector3 | getCoordinates (const Vertex *v) |
| btScalar | shrink (btScalar amount, btScalar clampAmount) |
Public Attributes | |
| Vertex * | vertexList |
Private Types | |
| enum | Orientation { NONE, CLOCKWISE, COUNTER_CLOCKWISE } |
Private Member Functions | |
| Edge * | findMaxAngle (bool ccw, const Vertex *start, const Point32 &s, const Point64 &rxs, const Point64 &sxrxs, Rational64 &minCot) |
| void | findEdgeForCoplanarFaces (Vertex *c0, Vertex *c1, Edge *&e0, Edge *&e1, Vertex *stop0, Vertex *stop1) |
| Edge * | newEdgePair (Vertex *from, Vertex *to) |
| void | removeEdgePair (Edge *edge) |
| void | computeInternal (int start, int end, IntermediateHull &result) |
| bool | mergeProjection (IntermediateHull &h0, IntermediateHull &h1, Vertex *&c0, Vertex *&c1) |
| void | merge (IntermediateHull &h0, IntermediateHull &h1) |
| btVector3 | toBtVector (const Point32 &v) |
| btVector3 | getBtNormal (Face *face) |
| bool | shiftFace (Face *face, btScalar amount, btAlignedObjectArray< Vertex *> stack) |
Static Private Member Functions | |
| static Orientation | getOrientation (const Edge *prev, const Edge *next, const Point32 &s, const Point32 &t) |
Private Attributes | |
| btVector3 | scaling |
| btVector3 | center |
| Pool< Vertex > | vertexPool |
| Pool< Edge > | edgePool |
| Pool< Face > | facePool |
| btAlignedObjectArray< Vertex * > | originalVertices |
| int | mergeStamp |
| int | minAxis |
| int | medAxis |
| int | maxAxis |
| int | usedEdgePairs |
| int | maxUsedEdgePairs |
Definition at line 50 of file btConvexHullComputer.cpp.
|
private |
| Enumerator | |
|---|---|
| NONE | |
| CLOCKWISE | |
| COUNTER_CLOCKWISE |
Definition at line 658 of file btConvexHullComputer.cpp.
| void btConvexHullInternal::compute | ( | const void * | coords, |
| bool | doubleCoords, | ||
| int | stride, | ||
| int | count | ||
| ) |
Definition at line 1956 of file btConvexHullComputer.cpp.
|
private |
Definition at line 1205 of file btConvexHullComputer.cpp.
|
private |
Definition at line 1477 of file btConvexHullComputer.cpp.
|
private |
Definition at line 1425 of file btConvexHullComputer.cpp.
Definition at line 2086 of file btConvexHullComputer.cpp.
Definition at line 2091 of file btConvexHullComputer.cpp.
|
staticprivate |
Definition at line 1399 of file btConvexHullComputer.cpp.
|
private |
Definition at line 1660 of file btConvexHullComputer.cpp.
|
private |
Definition at line 1020 of file btConvexHullComputer.cpp.
|
private |
Definition at line 999 of file btConvexHullComputer.cpp.
|
inlineprivate |
Definition at line 781 of file btConvexHullComputer.cpp.
|
private |
Definition at line 2221 of file btConvexHullComputer.cpp.
Definition at line 2100 of file btConvexHullComputer.cpp.
Definition at line 2077 of file btConvexHullComputer.cpp.
|
private |
Definition at line 763 of file btConvexHullComputer.cpp.
Definition at line 765 of file btConvexHullComputer.cpp.
Definition at line 766 of file btConvexHullComputer.cpp.
|
private |
Definition at line 771 of file btConvexHullComputer.cpp.
|
private |
Definition at line 773 of file btConvexHullComputer.cpp.
|
private |
Definition at line 770 of file btConvexHullComputer.cpp.
|
private |
Definition at line 768 of file btConvexHullComputer.cpp.
|
private |
Definition at line 769 of file btConvexHullComputer.cpp.
|
private |
Definition at line 767 of file btConvexHullComputer.cpp.
|
private |
Definition at line 762 of file btConvexHullComputer.cpp.
|
private |
Definition at line 772 of file btConvexHullComputer.cpp.
| Vertex* btConvexHullInternal::vertexList |
Definition at line 830 of file btConvexHullComputer.cpp.
Definition at line 764 of file btConvexHullComputer.cpp.


|
SuanShu, a Java numerical and statistical library | |||||||
| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Object com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction com.numericalmethod.suanshu.analysis.differentiation.univariate.FiniteDifference
public class FiniteDifference
A finite difference (divided by a small increment) is an approximation of the derivative of a function.
The accuracy of central difference is the best while those of forward and backward differences are more or less the same.
In general, for finite difference the higher an order of a derivative, the less accurate it gets. For example, approximating the 5-th derivative is much less accurate than approximating the 1st derivative. Also, the accuracy depends on the function to take the derivative of.
| Nested Class Summary | |
|---|---|
static class |
FiniteDifference.Type
the types of finite difference available |
| Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function |
|---|
Function.EvaluationException |
| Field Summary | |
|---|---|
UnivariateRealFunction |
f
the univariate function to take the derivative of |
int |
order
the order of the derivative |
FiniteDifference.Type |
type
the type of finite difference chosen |
| Constructor Summary | |
|---|---|
FiniteDifference(UnivariateRealFunction f,
int order,
FiniteDifference.Type type)
Construct an approximation of the derivative function for f using finite difference. |
| Method Summary | |
|---|---|
double |
df(double x,
double h)
Compute the finite difference for f at x with an increment h
for the n -th order
using either forward, backward, or central difference. |
double |
evaluate(double x)
Numerically evaluate the derivative of f at point x . |
double |
evaluate(double[] x,
double h)
Numerically evaluate the derivative of f at point x with step size h . |
| Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction |
|---|
dimension4Domain, dimension4Range, evaluate |
| Methods inherited from class java.lang.Object |
|---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Field Detail |
|---|
public final UnivariateRealFunction f
public final int order
public final FiniteDifference.Type type
| Constructor Detail |
|---|
public FiniteDifference(UnivariateRealFunction f, int order, FiniteDifference.Type type)
f
using finite difference.
f
- a univariate functionorder
- the order of the derivativetype
- the type of finite difference type to use, c.f., FiniteDifference.Type
| Method Detail |
|---|
public double evaluate(double x)
f
at point x
.
evaluate
in class UnivariateRealFunction
x
- the point to evaluate the derivative at
f
at point x
public double evaluate(double[] x, double h)
f
at point x
with step size h
.
Automatically determining the step size h
could be challenging, esp. when |x| is near 0.
An analysis that involves f'
and f''
may be needed to determine the proper step size.
User may want to experiment with different h
's by calling this function.
x
- the point to evaluate the derivative of f
at.
Although it is a double[] array, only x[0]
is used (f
is univariate).h
- step size
f
at point x
using step size h
public double df(double x, double h)
f
at x
with an increment h
for the n
-th order
using either forward, backward, or central difference.
x
- evaluate the function at x
h
- the increment
dnh[f](x)
|
SuanShu, a Java numerical and statistical library | |||||||
| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |


Developer
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Remove Developer Mode


ACM Symposium on Applied Computing Data Streams Track
in conjunction with ACM Symposium on Applied Computing: The 37th Annual ACM Symposium on Applied Computing in Brno, Czech Republic, April 25 - April 29, 2022.
Track Chairs:
Albert Bifet,
Carlos Ferreira,
João Gama,
Heitor Murilo Gomes
For the past thirty years, the ACM Symposium on Applied Computing has
been a primary gathering forum for applied computer scientists,
computer engineers, software engineers, and application developers
from around the world.
SAC 2022 is sponsored by the
ACM Special Interest Group on Applied Computing,
The goal of DS track is to promote a meeting point and a discussion forum for researchers interested in any aspect of Data Stream processing.
Submission Deadline Extended: 31 OctoberImportant Dates
- Paper Submission: October 31, 2021
- Author Notification: December 10, 2021
- Camera-ready Copy: December 21, 2021
Motivation
The rapid growth in Big Data information science and technology in general and the complexity and volume of data in particular have introduced new challenges for the research community. Many sources produce data continuously. Examples include the Internet of Things (IoT), Smart Cities, Urban Computing, sensor networks, wireless networks, radio frequency identification (RFID), customer click streams, telephone records, multimedia data, scientific data, sets of retail chain transactions, etc. These sources are called data streams. A data stream is an ordered sequence of instances that can be read only once or a small number of times using limited computing and storage capabilities. These sources of data are characterized by being open-ended, flowing at high-speed, and generated by non stationary distributions.
Data streams are increasingly important in the research community, as new algorithms are needed to process this streaming data in reasonable time. Many researchers coming from different areas (data mining, machine learning, OLAP, databases, etc.) are designing new approaches or adapting some of the traditional algorithms to data streams. The number of researchers in this field also is growing considerably, and in many conferences data streams are becoming a consolidated topic (ICML, KDD, IJCAI, ICDM, SAC, ECML, etc).
Topics
We are looking for original, unpublished work related to algorithms, methods and applications on big data streams and large scale machine learning. Topics include (but are not restricted) to:
- Real-Time Analytics
- Data Stream Models
- Big Data Mining
- Large Scale Machine Learning
- Languages for Stream Query
- Continuous Queries
- Clustering from Data Streams
- Decision Trees from Data Streams
- Association Rules from Data Streams
- Decision Rules from Data Streams
- Bayesian networks from Data Streams
- Feature Selection from Data Streams
- Visualization Techniques for Data Streams
- Incremental on-line Learning Algorithms
- Single-Pass Algorithms
- Temporal, spatial, and spatio-temporal data mining
- Scalable Algorithms
- Real-Time and Real-World Applications using Stream data
- Distributed Stream Mining
- Social Network Stream Mining
- Urban Computing, Smart Cities
- Internet of Things (IoT)
Paper Submission
Authors are invited to submit original papers in all topics related to data streams.
All papers should be submitted in ACM 2-column camera ready format for
publication in the symposium proceedings.
ACM SAC follows a double blind review process. Consequently, the
author(s) name(s) and address(s) must NOT appear in the body of the
submitted paper, and self-references should be in the third
person. This is to facilitate double blind review required by ACM. All
submitted papers must include the paper identification number provided
by the eCMS system when the paper is first registered. The number must
appear on the front page, above the title of the paper.
The paper length is 8 pages + 2 pages at an extra charge (max of 10 pages).
There is a set of templates to support the required paper
format for a number of document preparation systems at
https://www.sigapp.org/sac/sac2022/authorkit.html
Submission guidelines must be strictly followed. A paper cannot be
submitted to more than one track. Papers should be submitted in PDF
using the SAC 2022 Webpage.
The maximum number of pages allowed for the final papers is 8 pages
(about 5000 words), with the option (at additional expense) to add
two (2) more pages. Accepted papers in all categories will be
published in the ACM SAC 2022 proceedings.
Paper registration is required, allowing the inclusion of papers, posters, or SRC abstracts in the conference proceedings. An author or a proxy attending SAC MUST present the work. This is a requirement for the presented work to be included in the ACM/IEEE digital library. No-show of registered papers, posters, and SRC abstracts will result in excluding them from the ACM/IEEE digital library.
Important notice:
1. Please submit your contribution via SAC 2022 Webpage: https://www.softconf.com/m/sac2022/
2. Paper registration is required, allowing the inclusion of the paper, poster, or SRC abstract in the conference proceedings. An author or a proxy attending SAC MUST present the paper. This is a requirement for including the work in the ACM/IEEE digital library. No-show of registered papers, posters, and SRC abstracts will result in excluding them from the ACM/IEEE digital library.
Program Committee (to be confirmed)
- Annalisa Appice, Università degli Studi di Bari, Italy
- Maroua Bahri, Télécom Paris - Institut Polytechnique de Paris, France
- Jean Paul Barddal, Pontificia Universidade Catolica do Parana, Brazil
- Vicent Becker, ETH Zurich, Switzerland
- Albert Bifet, UoW, New Zealand and Telecom Paris, France
- Christian Bockermann, University Dortmund, Germany
- Douglas Cardoso, Universidade Federal do Rio de Janeiro, Brazil
- André Carvalho, University of Sao Paulo (USP), Brazil
- Raja Chiky, ISEP, France
- Carlo Combi, University of Verona, Italy
- Alfredo Cuzzocrea, ICAR-CNR and University of Calabria, Italy
- José de Campo Avila, Universidad de Málaga, Spain
- Hadi Fanaee, University of Porto, Portugal
- Carlos Ferreira, Institute of Engineering of Porto, Portugal
- Mohamed Gaber, Tasmanian ICT Centre, Australia
- João Gama, University of Porto, Portugal
- Ricard Gavaldà, Universitat Politècnica de Catalunya, Spain
- Heitor Murilo Gomes, University of Waikato, New Zealand
- João Gomes, Institute for Infocomm Research, Singapore
- Marwan Hassani, Eindhoven University of Technology, Netherlands
- Geoff Holmes, University of Waikato, New Zealand
- Elena Ikonomovska, Josef Stefan Institute, Slovenia
- Petr Kosina, University of Porto, Portugal
- Shonali Krishnaswamy, Monash University, Australia
- Cyril Labbe, University Grenoble, France
- Mark Last, Ben Gurion University, Israel
- Byung Suk Lee, University Vermont, US
- Florent Masseglia, INRIA, France
- Rodrigo Mello, University of Sao Paulo, Brazil
- Gabriele Mencagli, University of Pisa, Italy
- João Moreira, University of Porto, Portugal
- Irene Ntoutsi, LMU Munich, Germany
- Marcia Oliveira, University of Porto, Portugal
- Mykola Pechenizkiy, Eindhoven University of Technology, The Netherlands
- Bernhard Pfahringer, University of Waikato, New Zealand
- Felipe Pinage, Federal University of Amazonas, Brazil
- Jesse Read, Ecole Polytechnique, France
- Pedro Rodrigues, University of Porto, Portugal
- Josep Roure, Universitat Politècnica de Catalunya, Spain
- Elaine Sousa, University of Sao Paulo, Brasil
- Eduardo Spinosa, Federal University of Parana, Brazil
- Shazia Tabassum, INESC TEC, Portugal
- Philip Yu, University of Illinois at Chicago, US
- Wenbin Zhang, Carnegie Mellon University, US
- Indrė Žliobaitė, Aalto University, Finland


WOTV Guild Info
Guild Rankings
Rank
Name
Tokens
Wins
Losses
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American boutique hotel brand, The Standard, has landed in the Maldives and it looks amazing
by Coco TravelAmerican boutique hotel brand, The Standard, has opened up for business in the Maldives and based on a quick visual tour of the premises, it looks like the tropical, idyllic island destination of our dreams — with a funky, fresh aesthetic that The Standard is known for, making for a fun twist on the typical, ahem, standard bungalow-look we’re used to seeing for Maldives properties.
Although it’s called The Standard, the small chain, known for its cool locations in New York City, LA, and Miami Beach, its style is anything but conventional and boring. The brand’s island destination, which just officially opened up on November 1, seems to follow suit, keeping the aesthetic funky and fresh — for instance, there’s a disco ball above the bathtub in each villa.
Situated between the Raa and Baa Atolls on a naturally protected island, The Standard Huruvalhi Maldives has 115 villas, that are a mix of beachside and over-water, each with their own infinity plunge pool, private deck and — the best part in our opinion — direct lagoon, ocean, or beach access.
Getting there is a small adventure in and of itself and involves taking a 35-minute sea plane from Velana International Airport. Alternatively, you can get there from a 20-minute domestic flight to Dharavandhoo and 35-minute speedboat ride to the resort.
Have a look around and try not to drool too much (ngl, we’re salivating):
Notice how those waters are clear AF? The reef around the resort is protected and makes a prime snorkeling spot. (Looks like the resort takes its obligation to conservation seriously as it has its own lagoon coral nursery with over 3,000 juvenile corals; tip of the hat to them for that.) Snorkeling and diving excursions from the resort are also an option for the more adventurous, as well as boat trips to uninhabited islands. Meanwhile, there’s recreational equipment available like glass bottom kayaks, jet skis, and windsurfers for the more active traveler. For the family, there’s an 82-square meter inflatable water park that can be reached by pontoon (and there’s also a kids club for parents in need of some R&R). Plus, there’s pool parties for those feeling social. And of course, there’s a spa for some self-care time (um, yes please!).
Being on a little island, you would think there’s not exactly a bunch of dining options around, but the resort actually has six different restaurants to meet different needs and tastes. Some of the ingredients are even sourced from the resort’s own island farm. If you want to get some culture in, prioritize eating at GUDUGUDA, a Maldivian restaurant, said to be the first of its kind. Food there is made by Maldivian “aunties”. Think locally caught, seafood, coconut-milk curries, and aromatic rice dishes. Also in the restaurant lineup is a beachside BBQ shack — called Shak — for grilled seafood, along with a poolside bar, a another bar featuring craft cocktails, and and adults-only over-water-club.
As the resort is still in its opening phase, they are offering special rates from US$395 a night in one of the private villas along with buffet breakfast included.
FIND IT:
The Standard Huruvalhi Maldives
Huruvalhi Island Raa Atoll
+960 658 5555
More Coco Travel content to stoke your wanderlust here.


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Eric. B Arrested On 17-Year-Old Warrant
by Kyle EusticeHackensack, NJ – Eric Barrier — better known as Eric B. of the revered Hip Hop duo Eric B. & Rakim — was reportedly just released from Bergen County Jail in Hackensack, New Jersey jail after spending two weeks behind bars.
According to NBC New York, the legendary turntablist was arrested on October 28 after turning himself into authorities on a 17-year-old warrant.
In 2002, he pleaded guilty to aggravated assault and resisting arrest/eluding for an incident that happened in Ridgefield Park, New Jersey on September 27, 2001. But because he failed to appear in court, a judge issued a bench warrant.
Bergen County Jail records confirm he was taken into custody last month.
Eric B.’s lawyer Patrick Toscano sent a letter to the court last week and explained Eric B’s former attorney told the tenured producer at the time “there was no need to appear on the sentencing date.”
“Mr. Bergrin told Mr. Barrier that his case was ‘dismissed’ because he was accepted into PTI (pre-trial intervention),” he wrote.
Eric B. also said he received no notice from the court about his failure to appear. Toscano called Eric B.’s ex-counsel as “flawed, fraudulent, unethical and deceptive, through no fault of Mr. Barrier” and was adamant any further punishment would be “draconian and unfair.” He admitted Eric B. “was literally at wits end and overcome with anxiety.”
He’s expected back in court on November 22.


It's the ranch retreat designed with downtime in mind. Ocio Ranch offers visitors an opportunity to escape daily life, disconnect, and take in the beauty that a central Texas ranch has to offer.
This site was built using a Squarespace content management system. It is easily updateable by the business owners at all levels, allowing owners to update imagery across the site and add new blog posts whenever needed. For this site, I was also responsible for all creative and photography.


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Resistance - The First Anonymous DEX and Privacy-Oriented Blockchain Resistance is an anonymous, decentralized exchange and privacy-oriented blockchain that combines Proof of Work and Proof of Research for block rewards.
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I am a student of computer science & enginnering in national institute of technology Raipur.
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I am starting my graduation from NIT Raipur in computer science and engineering branch.I will be graduated in 2022.
I started my education from my village upto class 8th then after I went to govt. higher secondry school Nariyara(CG).
I completed my class 11th and 12th from HSM Global Public School Dayalband Bilaspur chhattisgarh.
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Package io.ebean.config.dbplatform
Database platform specific support
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Interface Summary Interface Description BasicSqlLimiter Simple SQL limiter for use with SqlQuery.DbEncrypt Defines DB encryption support for encrypting and decrypting data using DB encryption features.DbEncryptFunction DbHistorySupport History support for the database platform.ExtraDbTypes Integer codes for the extra types beyond java.sql.Types.PlatformIdGenerator Generates unique id's for objects.SqlExceptionTranslator Used to translate SQLExceptions to specific persistence exceptions.SqlLimiter Adds SQL limiting to a query (such as LIMIT OFFSET).SqlLimitRequest The request object for the query that can have sql limiting applied to it (such as a LIMIT OFFSET clause). -
Class Summary Class Description AbstractDbEncrypt Base type for DB platform specific Encryption.BasicSqlAnsiLimiter Adds ANSI based OFFSET FETCH NEXT clauses to a SQL query.BasicSqlLimitOffset Adds LIMIT OFFSET clauses to a SQL query.DatabasePlatform Database platform specific settings.DbDefaultValue DB Column default values mapping to database platform specific literals.DbIdentity Defines the identity/sequence behaviour for the database.DbPlatformType Represents a DB type with name, length, precision, and scale.DbPlatformTypeMapping Used to map bean property types to DB specific types for DDL generation.DbStandardHistorySupport SQL2011 based history support using 'as of timestamp' type clause appended as part of the the from or join clause.DbViewHistorySupport Database view based implementation of DbHistorySupport.LimitOffsetSqlLimiter Adds LIMIT OFFSET clauses to a SQL query.SequenceBatchIdGenerator Database sequence based IdGenerator using Sequence Step 1 but batch fetch many sequence values.SequenceIdGenerator Database sequence based IdGenerator.SequenceStepIdGenerator Database sequence based IdGenerator using Sequence Step (e.g.SimpleSequenceIdGenerator A very simple Database sequence based IdGenerator.SqlCodeTranslator Translate SQLException based on SQLState codes.SqlErrorCodes Used to build a SQLCodeTranslator given DB platform specific codes.SqlLimitResponse The resulting SQL from a SqlLimit process. -
Enum Summary Enum Description DatabasePlatform.OnQueryOnly Behavior used when ending a query only transaction (at read committed isolation level).DataErrorType Specific persistence error types we wish to map.DbType The known DB types that are mapped.IdType The types of Identity generation that can be defined.


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