Extracting features from given URL. Please wait...
| Model | Outcome | Probability | ||
|---|---|---|---|---|
| {{ x[0] }} | {% if x[1] == 'Phishing' %}{{ x[1] }} | {% else %}{{ x[1] }} | {% endif %}{{ x[2] }} | |
| Overall estimation | {% if overall[0] == 'Phishing' %}{{ overall[0] }} | {% elif overall[0] == 'Legitimate' %}{{ overall[0] }} | {% else %}{{ overall[0] }} | {% endif %}{{overall[1]}} |
This project is constructed of 4 types of features
(1) Domain-based features. Such as WHOIS information, domain and its sections, days after the domain was registered and remaining days before the domain expires.
(2) Webpage-based features and JS properties. Such as disabled right click.
(3) Lexical Features. Such as the number of dots in URL, number of parameters, TLD length.
(4) HTTP Headers. Such as if a cookie is being set.
All 63 features used in this system are list below:
TABLE 1
The description of all 63 features
|
Type |
feature |
description |
|
Domain |
dns_record |
DNS record in WHOIS database. |
|
check_age_of_domain |
Days since the domain was registered in WHOIS database. |
|
|
check_ssl |
Check for valid SSL certificate. |
|
|
days_till_expiration_domain |
Days till expiration of the SSL certificate |
|
|
qty_redirects |
Number of redirects till the final URL. |
|
|
url_shortened |
Check if the url is shortened. |
|
|
Webpage based |
favicon |
If the favicon is loaded from another domain. |
|
iFrame |
IFrame tag. |
|
|
rightClick |
If the rightClick is disabled. |
|
|
onmouseover |
If the mouseOver property show different URL than the redirected. |
|
|
check_URL_of_anchor |
If a tags direct to different domain or nowhere. |
|
|
sfh |
No actions after submitting form. |
|
|
a_tags_count |
Number of a tags in the html of the webpage. |
|
|
form_tags_count |
Number of form tags in the html of the webpage. |
|
|
email_tags_count |
Number of email tags in the html of the webpage. |
|
|
pass_tags_count |
Number of password tags in the html of the webpage. |
|
|
hidden_tags_count |
Number of hidden tags in the html of the webpage. |
|
|
actions_tags_count |
Number of action tags in the html of the webpage. |
|
|
signin_tags_count |
Number of signin tags in the html of the webpage. |
|
|
signup_tags_count |
Number of signup tags in the html of the webpage. |
|
|
Lexical |
double_slash |
More that 1 occurance of "//" in the URL. |
|
qty_dot_url |
Number of "." in the URL. |
|
|
qty_hyphen_url |
Number of "-" in the URL. |
|
|
qty_questionmark_url |
Number of "?" in the URL. |
|
|
qty_at_url |
Number of "@" in the URL. |
|
|
qty_hashtag_url |
Number of "#" in the URL. |
|
|
qty_dollar_url |
Number of "$" in the URL. |
|
|
qty_percent_url |
Number of "%" in the URL. |
|
|
TLD_length |
Number of letters of the TLD(Top Level Domain) |
|
|
TLD_count |
Number of sub-TLDs |
|
|
URL_length |
Length of the whole URL |
|
|
email_in_url |
If there is an email in the URL. |
|
|
word_script_in_url |
If the word "script" is in the URL. |
|
|
check_https_in_url |
If "https" is in the URL. |
|
|
qty_dot_domain |
Number of "." in the Domain. |
|
|
qty_hyphen_domain |
Number of "-" in the Domain. |
|
|
count_vowels |
Number of vowels in the Domain |
|
|
Domain_length |
Length of the Domain. |
|
|
Ip_in_domain |
Ip in Domain. |
|
|
Client_or_Server_in_domain |
Words "client" or "server" in Domain. |
|
|
qty_dot_directory |
Number of "." in the Directory. |
|
|
qty_hyphen_directory |
Number of "-" in the Directory. |
|
|
qty_at_directory |
Number of "@" in the Directory. |
|
|
qty_slash_directory |
Number of "/" in the Directory. |
|
|
qty_percent_directory |
Number of "%" in the Directory. |
|
|
directory_length |
Length of the Directory. |
|
|
qty_dot_File |
Number of "." in the File. |
|
|
qty_hyphen_File |
Number of "-" in the File. |
|
|
qty_at_File |
Number of "@" in the File. |
|
|
qty_percent_File |
Number of "%" in the Directory. |
|
|
File_length |
Length of the File. |
|
|
qty_dot_params |
Number of "." in the Parameters. |
|
|
qty_hyphen_params |
Number of "-" in the Parameters. |
|
|
qty_at_params |
Number of "@" in the Parameters. |
|
|
qty_underline_params |
Number of "_" in the Parameters. |
|
|
qty_hashtag_params |
Number of "#" in the Parameters. |
|
|
qty_dollar_params |
Number of "$" in the Parameters. |
|
|
qty_percent_params |
Number of "%" in the Parameters. |
|
|
params_length |
Length of the Parameters. |
|
|
tld_params |
If there is a TLD in the Parameters |
|
|
count_params |
How many parameters are being set. |
|
|
HTTP Headers |
cookie |
If a cookie is being set. |
|
strict_trans_sec |
Existance of Strict_Trans_Sec header. |
All features are numeric.


The JavaTM Virtual Machine Tools Interface (JVM TI) is a native tool interface provided in JDK 5.0 and newer. Native libraries that use JVM TI and are loaded into the Java Virtual Machine via the -agentlib, -agentpath, or -Xrun (deprecated) interfaces, are called Agents.
JVM TI was designed to work with the Java Native Interface (JNI), and eventually displace the Java Virtual Machine Debugging Interface (JVMDI) and the Java Virtual Machine Profiling Interface (JVMPI).
We have created a set of demonstration agents that should help show many of the features and abilities of the interface. This list of demonstration agents will change over time. They are provided as educational tools and as starting points for Java tool development.
These agents are built with every JDK build and some basic testing is performed on a regular basis, but no extensive testbases currently exist for these agents. Every JDK installation should include all the pre-built binaries and sources for all these agents, just look in the demo/jvmti directory of your JDK.
Using these agents will require the VM to locate the shared library file before any actual Java code is run. The JDK installation should contain all the agent libraries in the ${JAVA_HOME}/demo/jvmti/agent-name/lib directories. The Solaris 64bit version would be contained in the sparcv9 or amd64 subdirectory. If 'java' complains that it can't find the library, you may need to add the directory containing the library into the LD_LIBRARY_PATH environment variable (Unix), or the PATH environment variable (Windows). This is system and platform specific. If you are using 64bit Solaris (e.g. 'java -d64'), you should use LD_LIBRARY_PATH64. Some agents such as hprof (heap/cpu profiler) and jdwp (debugger backend) are located inside the primary JDK directories and will always be found in those locations.
The agents that instrument classfiles (i.e. BCI, usually through the java_crw_demo library) such as hprof, heapTracker, mtrace, and minst, also need to have the Java classes they use available in the bootclasspath. The one used by hprof is already in the bootclasspath, and the other agents will make attempts at automatically adding their jar file (e.g. heapTracker.jar, mtrace.jar, or minst.jar) to the bootclasspath with AddToBootstrapClassLoaderSearch from JVM TI at startup (see the agent_util code). This is done by locating this jar file at ${JAVA_HOME}/demo/jvmti/agent-name where JAVA_HOME is obtained by calling GetSystemProperty from JVM TI with "java.home". We recognize that this is not ideal, but felt that as just demonstration code it was acceptable. Ideally the agent could find out the actual directory it came from and locate the jar file relative to that location. Our demonstration agents currently do not do this.
If you choose to modify or change these agents, the above information is important in making everything is found. It is recommended that you change the name of the agent when you modify it to avoid conflicts with the existing demo agents. Or better yet, go to http://jdk.dev.java.net and submit your changes to the agent as an RFE to the JDK.
All libraries loaded into java are assumed to be MT-safe (Multi-thread safe). This means that multiple threads could be executing the code at the same time, and static or global data may need to be placed in critical sections. See the Raw Monitor interfaces for more information.
All native libraries loaded into the Java Virtual Machine, including Agent libraries, need to be compiled and built in a compatible way. Certain native compilation options or optimizations should be avoided, and some are required. More information on this options is available in the man pages for the various compilers.
Some native compiler and linker options can create fatal or erroneous behavior when native agent libraries are operating inside the Java Virtual Machine. It would take too many words to describe all the possible issues with all the native compiler options, optimizations, and settings. Here are some recommendations on the basic compiler and linker options we recommend:
cc -xO2 -mt -xregs=no%appl -xmemalign=4s -xarch=v8 -KPIC -c *.c
cc -mt -xarch=v8 -z defs -ztext -G -o libXXX.so *.o -lc
cc -xO2 -mt -xregs=no%appl -xarch=v9 -KPIC -c *.c
cc -mt -xarch=v9 -z defs -ztext -G -o libXXX.so *.o -lc
cc -xO2 -mt -xregs=no%frameptr -KPIC -c *.c
cc -mt -z defs -ztext -G -o libXXX.so *.o -lc
cc -xO2 -mt -xregs=no%frameptr -xarch=amd64 -KPIC -c *.c
cc -mt -xarch=amd64 -z defs -ztext -G -o libXXX.so *.o -lc
-xarch=v8
,
for SPARC 64bit use -xarch=v9
,
for X86 (32-bit)
leave the option off or use -xarch=generic
,
and for AMD64 (64bit) use -xarch=amd64
with both C and C++.
-KPIC -mt
with both C and C++.
-xregs=no%appl
and for X86 and AMD64 use -xregs=no%frameptr
with both C and C++.
-xmemalign=4
with both C and C++.
ldd -r LibraryName
.
ldd
can be used to verify that all dependent libraries
have been satisfied, and all externs can be found.
If ldd
says anything is missing, it is very likely that the JVM will also
be unable to load this library.
This usually means that you missed some -lname
options when building the library, or perhaps forgot a -R path
option that tells the library where to look for libraries at runtime.
gcc -O2 -fPIC -pthread -DLINUX -c *.c
gcc -z defs -static-libgcc -shared -o libXXX.so *.o -lc
gcc -O2 -fPIC -pthread -DLINUX -D_LP64=1 -c *.c
gcc -z defs -static-libgcc -shared -o libXXX.so *.o -lc
-fPIC -pthread
.
-fno-omit-frame-pointer
.
-xregs=no%frameptr
option.
ldd -r LibraryName
.
cl /O1 /MD /D _STATIC_CPPLIB /c *.c
link /dll /opt:REF /out:XXX.dll *.obj
cl /O1 /MD /D _STATIC_CPPLIB /c *.c
link /dll /opt:REF /out:XXX.dll *.obj
/opt:REF
when building the dll.
/MD /D _STATIC_CPPLIB
option.
dumpbin /exports
and the VC++ "Dependency Walker".
ldd
.
Remember, the complete source to all these agents is contained in the JDK installations at demo/jvmti.
For more detailed information on JVM TI, refer to http://java.sun.com/j2se/latest/docs/guide/jvmti.
More information on using JNI and building native libraries refer to: http://java.sun.com/j2se/latest/docs/guide/jni.
Additional information can also be found by doing a search on "jvmti" at http://java.sun.com/j2se. Various technical articles are also available through this website. And don't forget the Java Tutorials at http://java.sun.com/docs/books/tutorial for getting a quick start on all the various interfaces.
Comments regarding JVM TI or on any of these demonstrations should be sent through http://java.sun.com/mail/


--- title: "Markdown Syntax and Styling" lastmod: 2019-03-06T00:00:00.000Z draft: false type: docs maths: true output: blogdown::html_page: toc: true linktitle: "Markdown Syntax and Styling" menu: docs: parent: Content Management weight: 80 ---
Sometimes there are situations in which you want to escape the RMarkdown syntax. For example, if you want to have *text with asterisks* and not have it be in itallics like this. To do this use a backslash (\) behind each character with special meaning.
An example is:
\* text \*
which will render like:
*text*
Headings are rendered by using a # before the heading content. There are six heading levels which are triggered using more #. So a level four heading would be done like this:
#### Heading
Which would appear like this:
Note: The table of contents for the Methods101 site will only pick up on heading levels 1 through 3 when generating.
For a Markdown cheat sheet go here.
Some useful RMarkdown formatting commands (these are the same as Markdown):
Bold text: Use a double ** before and after the text like this *bold text* which will render like this bold text
Itallic text: Use a single * before and after the text like this *itallic text* which will render like this itallic text
Lists are either ordered or unordered.
Unordered lists are created like this:
* List
* List
* List
And render like this:
List
List
List
Ordered lists are created (and rendered) like this:
List
List
List
If you would like to indent the text like this:
Indented text
Then use for each space you would like the text to be indented by (the above was six spaces). This can also be done using HTML.
RMarkdown cannot style the text. Instead, to style the text you need to insert HTML into the RMD document.
To colour the text use the following:
 Coloured text
Which will render like this:
Coloured text
Some available colours can be found here .
Instead of colour any of the numerous CSS styling options can be inserted. More options can be found here and elsewhere with a quick google search.
Problem:
\$
or \\$
worked.Solution:
$
So for example, this text renders correctly:
Code:
"How do you insert a dollar sign into text, such as US$50?"
Renders as:
“How do you insert a dollar sign into text, such as US$50?”
We need to use HTML symbols (between tags) for most symbols.
This is a useful website where you can easily look up HTML tags for symbols
The following text adds borders to images, if included after the YAML in each page.

Latex Maths is the best way to render formulas.
You use a single dollar sign $ for inline formulas, and a double dollar sign $$ for formulas that appear in the middle of the page on their own line.
I (Nick) have found that it is better to use the single dollar signs, and the formula listed below, as it allows you to layout the formulas and the definitions of terms in a more tight and neat manner.
Note that the & sign indicated the part of each line that should be aligned with the others. Also \text
is a useful command, as it allows you to put text and spaces into the lines of Latex maths.
The double backslash \\
means end of line.
$\begin{aligned}
r = &\frac{\sum_{i=1}^n (x_i - \bar x)(y_i - \bar y)}{(N-1)s_x s_y} \\
\\
\text{Where:} \\
\bar x = &\text{ mean of x} \\
\bar y = &\text{ mean of y} \\
\bar N = &\text{ number of observations} \\
s_x = &\text{ standard deviation of x} \\
s_y = &\text{ standard deviation of y} \\
\end{aligned}$
$\begin{aligned}
y = &b_1 x_1 + b_2 x_2 + b_3 x_3 + ... + b_0 + e \\
\\
\text{Where:} \\
y=&\text{ dependent variable (outcome variables)} \\
x_1 , x_2 , \text{ ... }x_n = &\text{ independent variables (predictor variables)} \\
b_1 , b_2 , \text{ ... }b_n = &\text{ slope of relationship between }y\text{ and }x_1 , x_2 , \text{ ... }x_n \\
b_0 = &\text{ intercept (i.e. value of }y \text{ when all }x=0 \text{)} \\
\end{aligned}$
\(\begin{aligned} \\ \\ r = &\frac{\sum_{i=1}^n (x_i - \bar x)(y_i - \bar y)}{(N-1)s_x s_y} \\ \\ \text{Where:} \\ \bar x = &\text{ mean of x} \\ \bar y = &\text{ mean of y} \\ N = &\text{ number of observations} \\ s_x = &\text{ standard deviation of x} \\ s_y = &\text{ standard deviation of y} \\ \end{aligned}\)
\(\begin{aligned} \\ \\ y = &b_1 x_1 + b_2 x_2 + b_3 x_3 + ... + b_0 + e \\ \\ \text{Where:} \\ y=&\text{ dependent variable (outcome variables)} \\ x_1 , x_2 , \text{ ... }x_n = &\text{ independent variables (predictor variables)} \\ b_1 , b_2 , \text{ ... }b_n = &\text{ slope of relationship between }y\text{ and }x_1 , x_2 , \text{ ... }x_n \\ b_0 = &\text{ intercept (i.e. value of }y \text{ when all }x=0 \text{)} \\ \end{aligned}\)


ALEX KLINGER
BIO
PROJECTS
CONTACT
other work with physical computing, code, and design.
Infinity Mirror
Wearable tech
Graphics


About
Exploration
Basic Concepts
Variables
Basic Visual Tools
Histograms
Details
Central Tendency
More Visual Tools
Order Statistics
Variability
Correlation
Spurious Correlations
Correlation
Graphical Exploration
Correlation Measurements
Linear Regression
Prediction
Model Fit Assessment
Outliers: Assessment of Influence
Hans Rosling
Spurious Correlations
Odd examples
http://tylervigen.com/spurious-correlations
Aníbal Granada González
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License


Please cycle forward for my CV!
As part of the R&D team, I build software for machine learning with Python and TypeScript. I've acted as the lead developer in a project including as many as seven of my colleagues at at time and participated in numerous meetings with our clients to better understand their needs.
As AI engineer, I help clients build machine learning solutions. I've also been actively involved in recruitment by carrying out tech interviews.
Our technology stack includes technologies such as Django, Vue.js, Apache Kafka, Postgres, OpenAPI, NGINX, Docker, and Kubernetes.
I was actively involved in defining vision, mission as well as research and product roadmaps for the company.
With my colleagues we created front-ends, backends, command-line tools, databases, logging, monitoring as well as analytics solutions to power our build-measure-learn cycle and various products.
We wrote code mostly in TypeScript and Python, using tools such as PyTorch, Amazon SageMaker, GraphQL, Next.js, Gatsby, GraphQL and Prisma.
I developed radio positioning algorithms using Matlab and implemented them in production using Java and Scala with Apache Spark and Cassandra. I also lead the bluetooth positioning project.
I stored algorithm performance metrics to ElasticSearch and created a front-end UI for comparing algorithms.
I was the Data team lead responsible for processing high-volume end-user positioning data and exposing data through a REST API and front-end UI.


A bug is never a mistake.
It represents something bigger.
an error of thinking.
That makes who you are


Sweet Free Stuff
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The post Free Laura Mercier Smooth Finish Flawless Fluide (In-store)
appeared first on SweetFreeStuff.com.
///////////////////////////////////////////
Free Dominos Gift Cards
Posted: 10 Sep 2014 06:14 AM PDT
http://feedproxy.google.com/&edburner&utm_medium=email
From their site: We’re at it again with another opportunity to grab one of
over 50,000 Domino’s gift cards* sometime soon. This time, were giving away
over $150,000 in FREE pizza! Just click the ‘I Want In’ button to be
notified when the fun begins. The promotion will go live sometime before
September 30th, so []
The post Free Dominos Gift Cards appeared first on SweetFreeStuff.com.
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Free GUM Proxabrush Go-Between Cleaners (Refer 5 Friends)
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Enter their giveaway on Facebook and refer 5 friends for Free GUM
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The post Free GUM Proxabrush Go-Between Cleaners (Refer 5 Friends) appeared
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Posted: 09 Sep 2014 10:01 AM PDT
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Free Demi mp3 album download from Google Play
The post Free Demi Lovato: Demi Album Download appeared first on
SweetFreeStuff.com.
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Free Heart Attack Wallet Card
The post Free Heart Attack Wallet Card appeared first on SweetFreeStuff.com.


Class ColorScales
Static collection of color scales based on well-known scales
Inheritance
System.Object
ColorScales
Inherited Members
System.Object.Equals(System.Object)
System.Object.Equals(System.Object, System.Object)
System.Object.GetHashCode()
System.Object.GetType()
System.Object.MemberwiseClone()
System.Object.ReferenceEquals(System.Object, System.Object)
System.Object.ToString()
Namespace: CatsHelpers.ColorScales
Assembly: CatsHelpers.dll
Syntax
public static class ColorScales
Fields
| Improve this Doc View SourceInferno
The Inferno color scale https://github.com/BIDS/colormap/blob/master/colormaps.py
Declaration
public static readonly ColorScale Inferno
Field Value
| Type | Description |
|---|---|
| ColorScale |
Remarks
Get the 256 values (readonly) from ColorData property
Magma
The Magma color scale https://github.com/BIDS/colormap/blob/master/colormaps.py
Declaration
public static readonly ColorScale Magma
Field Value
| Type | Description |
|---|---|
| ColorScale |
Remarks
Get the 256 values (readonly) from ColorData property
Plasma
The Plasma color scale https://github.com/BIDS/colormap/blob/master/colormaps.py
Declaration
public static readonly ColorScale Plasma
Field Value
| Type | Description |
|---|---|
| ColorScale |
Remarks
Get the 256 values (readonly) from ColorData property
Turbo
Declaration
public static readonly ColorScale Turbo
Field Value
| Type | Description |
|---|---|
| ColorScale |
Remarks
Get the 256 values (readonly) from ColorData property
Viridis
The Viridis color scale https://github.com/BIDS/colormap/blob/master/colormaps.py
Declaration
public static readonly ColorScale Viridis
Field Value
| Type | Description |
|---|---|
| ColorScale |
Remarks
Get the 256 values (readonly) from ColorData property


“Coleridge is one of our great men who require many footnotes, for there are characteristics of his which need all the extenuation they can get. How comes it, for instance, that he could write, and not only write but publish, in the same decade, and sometimes in the same year, poetry which is of our very best, and some which for frozen inanity it would be hard to equal anywhere?  And finally, of what quality was the talk of one whose social life was entirely monologue?” — Maurice Hewlett, In A Green Shade


Blog Posts
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Call it a ticktee and next step
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Start new rails project: Ticktee
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Complete new look of my realm
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New site and new post. It's awesome!
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Jan 30, 14 »
Trouble shooting: org.hibernate.StaleStateException: Batch update returned unexpected row count from update [0]; actual row count: 0; expected: 1
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Selectboxize Selectboxize is a simple and lightweight JavaScript library for styling and replacing default selectboxes. The library is heavily based on previous work by Krzysztof Suszyński. Regular selectbox Afghanistan Aland Islands Albania Algeria American Samoa Andorra Angola Anguilla Antarctica Antigua and Barbuda Argentina Armenia Aruba Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bermuda Bhutan Bolivia, Plurinational State of Bonaire, Sint Eustatius and Saba Bosnia and Herzegovina Botswana Bouvet Island Brazil British Indian Ocean Territory Brunei Darussalam Bulgaria Burkina Faso Burundi Cambodia Cameroon Canada Cape Verde Cayman Islands Central African Republic Chad Chile China Christmas Island Cocos (Keeling) Islands Colombia Comoros Congo Congo, The Democratic Republic of The Cook Islands Costa Rica Cote D'ivoire Croatia Cuba Curacao Cyprus Czech Republic Denmark Djibouti Dominica Dominican Republic Ecuador Egypt El Salvador Equatorial Guinea Eritrea Estonia Ethiopia Falkland Islands (Malvinas) Faroe Islands Fiji Finland France French Guiana French Polynesia French Southern Territories Gabon Gambia Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guadeloupe Guam Guatemala Guernsey Guinea Guinea-bissau Guyana Haiti Heard Island and Mcdonald Islands Holy See (Vatican City State) Honduras Hong Kong Hungary Iceland India Indonesia Iran, Islamic Republic of Iraq Ireland Isle of Man Israel Italy Jamaica Japan Jersey Jordan Kazakhstan Kenya Kiribati Korea, Democratic People's Republic of Korea, Republic of Kuwait Kyrgyzstan Lao People's Democratic Republic Latvia Lebanon Lesotho Liberia Libya Liechtenstein Lithuania Luxembourg Macao Macedonia, The Former Yugoslav Republic of Madagascar Malawi Malaysia Maldives Mali Malta Marshall Islands Martinique Mauritania Mauritius Mayotte Mexico Micronesia, Federated States of Moldova, Republic of Monaco Mongolia Montenegro Montserrat Morocco Mozambique Myanmar Namibia Nauru Nepal Netherlands New Caledonia New Zealand Nicaragua Niger Nigeria Niue Norfolk Island Northern Mariana Islands Norway Oman Pakistan Palau Palestinian Territory, Occupied Panama Papua New Guinea Paraguay Peru Philippines Pitcairn Poland Portugal Puerto Rico Qatar Reunion Romania Russian Federation Rwanda Saint Barthelemy Saint Helena, Ascension and Tristan da Cunha Saint Kitts and Nevis Saint Lucia Saint Martin (French part) Saint Pierre and Miquelon Saint Vincent and The Grenadines Samoa San Marino Sao Tome and Principe Saudi Arabia Senegal Serbia Seychelles Sierra Leone Singapore Sint Maarten (Dutch part) Slovakia Slovenia Solomon Islands Somalia South Africa South Georgia and The South Sandwich Islands South Sudan Spain Sri Lanka Sudan Suriname Svalbard and Jan Mayen Swaziland Sweden Switzerland Syrian Arab Republic Taiwan, Province of China Tajikistan Tanzania, United Republic of Thailand Timor-leste Togo Tokelau Tonga Trinidad and Tobago Tunisia Turkey Turkmenistan Turks and Caicos Islands Tuvalu Uganda Ukraine United Arab Emirates United States United Kingdom United States Minor Outlying Islands Uruguay Uzbekistan Vanuatu Venezuela, Bolivarian Republic of Viet Nam Virgin Islands, British Virgin Islands, U.S. Wallis and Futuna Western Sahara Yemen Zambia Zimbabwe $('#countries-1').selectboxize(); Restricted width The width is restricted by applying width: 150px on the <select> definition in HTML. Afghanistan Aland Islands Albania Algeria American Samoa Andorra Angola Anguilla Antarctica Antigua and Barbuda Argentina Armenia Aruba Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bermuda Bhutan Bolivia, Plurinational State of Bonaire, Sint Eustatius and Saba Bosnia and Herzegovina Botswana Bouvet Island Brazil British Indian Ocean Territory Brunei Darussalam Bulgaria Burkina Faso Burundi Cambodia Cameroon Canada Cape Verde Cayman Islands Central African Republic Chad Chile China Christmas Island Cocos (Keeling) Islands Colombia Comoros Congo Congo, The Democratic Republic of The Cook Islands Costa Rica Cote D'ivoire Croatia Cuba Curacao Cyprus Czech Republic Denmark Djibouti Dominica Dominican Republic Ecuador Egypt El Salvador Equatorial Guinea Eritrea Estonia Ethiopia Falkland Islands (Malvinas) Faroe Islands Fiji Finland France French Guiana French Polynesia French Southern Territories Gabon Gambia Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guadeloupe Guam Guatemala Guernsey Guinea Guinea-bissau Guyana Haiti Heard Island and Mcdonald Islands Holy See (Vatican City State) Honduras Hong Kong Hungary Iceland India Indonesia Iran, Islamic Republic of Iraq Ireland Isle of Man Israel Italy Jamaica Japan Jersey Jordan Kazakhstan Kenya Kiribati Korea, Democratic People's Republic of Korea, Republic of Kuwait Kyrgyzstan Lao People's Democratic Republic Latvia Lebanon Lesotho Liberia Libya Liechtenstein Lithuania Luxembourg Macao Macedonia, The Former Yugoslav Republic of Madagascar Malawi Malaysia Maldives Mali Malta Marshall Islands Martinique Mauritania Mauritius Mayotte Mexico Micronesia, Federated States of Moldova, Republic of Monaco Mongolia Montenegro Montserrat Morocco Mozambique Myanmar Namibia Nauru Nepal Netherlands New Caledonia New Zealand Nicaragua Niger Nigeria Niue Norfolk Island Northern Mariana Islands Norway Oman Pakistan Palau Palestinian Territory, Occupied Panama Papua New Guinea Paraguay Peru Philippines Pitcairn Poland Portugal Puerto Rico Qatar Reunion Romania Russian Federation Rwanda Saint Barthelemy Saint Helena, Ascension and Tristan da Cunha Saint Kitts and Nevis Saint Lucia Saint Martin (French part) Saint Pierre and Miquelon Saint Vincent and The Grenadines Samoa San Marino Sao Tome and Principe Saudi Arabia Senegal Serbia Seychelles Sierra Leone Singapore Sint Maarten (Dutch part) Slovakia Slovenia Solomon Islands Somalia South Africa South Georgia and The South Sandwich Islands South Sudan Spain Sri Lanka Sudan Suriname Svalbard and Jan Mayen Swaziland Sweden Switzerland Syrian Arab Republic Taiwan, Province of China Tajikistan Tanzania, United Republic of Thailand Timor-leste Togo Tokelau Tonga Trinidad and Tobago Tunisia Turkey Turkmenistan Turks and Caicos Islands Tuvalu Uganda Ukraine United Arab Emirates United States United Kingdom United States Minor Outlying Islands Uruguay Uzbekistan Vanuatu Venezuela, Bolivarian Republic of Viet Nam Virgin Islands, British Virgin Islands, U.S. Wallis and Futuna Western Sahara Yemen Zambia Zimbabwe $('#countries-2').selectboxize(); Restricted number of items rolled-out When selectbox is clicked and rolled out only 5 items are visible (default is 15). Afghanistan Aland Islands Albania Algeria American Samoa Andorra Angola Anguilla Antarctica Antigua and Barbuda Argentina Armenia Aruba Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bermuda Bhutan Bolivia, Plurinational State of Bonaire, Sint Eustatius and Saba Bosnia and Herzegovina Botswana Bouvet Island Brazil British Indian Ocean Territory Brunei Darussalam Bulgaria Burkina Faso Burundi Cambodia Cameroon Canada Cape Verde Cayman Islands Central African Republic Chad Chile China Christmas Island Cocos (Keeling) Islands Colombia Comoros Congo Congo, The Democratic Republic of The Cook Islands Costa Rica Cote D'ivoire Croatia Cuba Curacao Cyprus Czech Republic Denmark Djibouti Dominica Dominican Republic Ecuador Egypt El Salvador Equatorial Guinea Eritrea Estonia Ethiopia Falkland Islands (Malvinas) Faroe Islands Fiji Finland France French Guiana French Polynesia French Southern Territories Gabon Gambia Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guadeloupe Guam Guatemala Guernsey Guinea Guinea-bissau Guyana Haiti Heard Island and Mcdonald Islands Holy See (Vatican City State) Honduras Hong Kong Hungary Iceland India Indonesia Iran, Islamic Republic of Iraq Ireland Isle of Man Israel Italy Jamaica Japan Jersey Jordan Kazakhstan Kenya Kiribati Korea, Democratic People's Republic of Korea, Republic of Kuwait Kyrgyzstan Lao People's Democratic Republic Latvia Lebanon Lesotho Liberia Libya Liechtenstein Lithuania Luxembourg Macao Macedonia, The Former Yugoslav Republic of Madagascar Malawi Malaysia Maldives Mali Malta Marshall Islands Martinique Mauritania Mauritius Mayotte Mexico Micronesia, Federated States of Moldova, Republic of Monaco Mongolia Montenegro Montserrat Morocco Mozambique Myanmar Namibia Nauru Nepal Netherlands New Caledonia New Zealand Nicaragua Niger Nigeria Niue Norfolk Island Northern Mariana Islands Norway Oman Pakistan Palau Palestinian Territory, Occupied Panama Papua New Guinea Paraguay Peru Philippines Pitcairn Poland Portugal Puerto Rico Qatar Reunion Romania Russian Federation Rwanda Saint Barthelemy Saint Helena, Ascension and Tristan da Cunha Saint Kitts and Nevis Saint Lucia Saint Martin (French part) Saint Pierre and Miquelon Saint Vincent and The Grenadines Samoa San Marino Sao Tome and Principe Saudi Arabia Senegal Serbia Seychelles Sierra Leone Singapore Sint Maarten (Dutch part) Slovakia Slovenia Solomon Islands Somalia South Africa South Georgia and The South Sandwich Islands South Sudan Spain Sri Lanka Sudan Suriname Svalbard and Jan Mayen Swaziland Sweden Switzerland Syrian Arab Republic Taiwan, Province of China Tajikistan Tanzania, United Republic of Thailand Timor-leste Togo Tokelau Tonga Trinidad and Tobago Tunisia Turkey Turkmenistan Turks and Caicos Islands Tuvalu Uganda Ukraine United Arab Emirates United States United Kingdom United States Minor Outlying Islands Uruguay Uzbekistan Vanuatu Venezuela, Bolivarian Republic of Viet Nam Virgin Islands, British Virgin Islands, U.S. Wallis and Futuna Western Sahara Yemen Zambia Zimbabwe $('#countries-3').selectboxize({ 'listboxMaxSize': 5 }); Callback upon a value selection The following example will display an alert modal dialog upon selecting a value. Afghanistan Aland Islands Albania Algeria American Samoa Andorra Angola Anguilla Antarctica Antigua and Barbuda Argentina Armenia Aruba Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bermuda Bhutan Bolivia, Plurinational State of Bonaire, Sint Eustatius and Saba Bosnia and Herzegovina Botswana Bouvet Island Brazil British Indian Ocean Territory Brunei Darussalam Bulgaria Burkina Faso Burundi Cambodia Cameroon Canada Cape Verde Cayman Islands Central African Republic Chad Chile China Christmas Island Cocos (Keeling) Islands Colombia Comoros Congo Congo, The Democratic Republic of The Cook Islands Costa Rica Cote D'ivoire Croatia Cuba Curacao Cyprus Czech Republic Denmark Djibouti Dominica Dominican Republic Ecuador Egypt El Salvador Equatorial Guinea Eritrea Estonia Ethiopia Falkland Islands (Malvinas) Faroe Islands Fiji Finland France French Guiana French Polynesia French Southern Territories Gabon Gambia Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guadeloupe Guam Guatemala Guernsey Guinea Guinea-bissau Guyana Haiti Heard Island and Mcdonald Islands Holy See (Vatican City State) Honduras Hong Kong Hungary Iceland India Indonesia Iran, Islamic Republic of Iraq Ireland Isle of Man Israel Italy Jamaica Japan Jersey Jordan Kazakhstan Kenya Kiribati Korea, Democratic People's Republic of Korea, Republic of Kuwait Kyrgyzstan Lao People's Democratic Republic Latvia Lebanon Lesotho Liberia Libya Liechtenstein Lithuania Luxembourg Macao Macedonia, The Former Yugoslav Republic of Madagascar Malawi Malaysia Maldives Mali Malta Marshall Islands Martinique Mauritania Mauritius Mayotte Mexico Micronesia, Federated States of Moldova, Republic of Monaco Mongolia Montenegro Montserrat Morocco Mozambique Myanmar Namibia Nauru Nepal Netherlands New Caledonia New Zealand Nicaragua Niger Nigeria Niue Norfolk Island Northern Mariana Islands Norway Oman Pakistan Palau Palestinian Territory, Occupied Panama Papua New Guinea Paraguay Peru Philippines Pitcairn Poland Portugal Puerto Rico Qatar Reunion Romania Russian Federation Rwanda Saint Barthelemy Saint Helena, Ascension and Tristan da Cunha Saint Kitts and Nevis Saint Lucia Saint Martin (French part) Saint Pierre and Miquelon Saint Vincent and The Grenadines Samoa San Marino Sao Tome and Principe Saudi Arabia Senegal Serbia Seychelles Sierra Leone Singapore Sint Maarten (Dutch part) Slovakia Slovenia Solomon Islands Somalia South Africa South Georgia and The South Sandwich Islands South Sudan Spain Sri Lanka Sudan Suriname Svalbard and Jan Mayen Swaziland Sweden Switzerland Syrian Arab Republic Taiwan, Province of China Tajikistan Tanzania, United Republic of Thailand Timor-leste Togo Tokelau Tonga Trinidad and Tobago Tunisia Turkey Turkmenistan Turks and Caicos Islands Tuvalu Uganda Ukraine United Arab Emirates United States United Kingdom United States Minor Outlying Islands Uruguay Uzbekistan Vanuatu Venezuela, Bolivarian Republic of Viet Nam Virgin Islands, British Virgin Islands, U.S. Wallis and Futuna Western Sahara Yemen Zambia Zimbabwe $('#countries-4').selectboxize({ 'callback': function(item, e) { alert("You have selected '" + $(item).text() + "' with value of '" + $(item).data('value') + "'."); } });


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Ruvu Shooting: Simba SC not so indomitable
by Michael MwebeRUVU Shooting will be out to chase a first victory over Vodacom Premier League defending champions, Simba, when the teams meet at Uhuru Stadium in Dar es Salaam today afternoon.
The Coast Region-based club registered their fourth loss of the league season when they were beaten 2-1 by Namungo FC at Majaliwa Stadium in Lindi before the international break on November 6.
Ruvu Shooting have claimed 15 points from 11 matches in the 2019/20 season.
Ruvu Shooting may be up against 19-time league champions but the former’s head coach Salum Mayanga is confident of good results.
He has challenged his side to end the winless run against the Msimbazi Street club when they meet in today’s showdown.
Ruvu Shooting are yet to register a win against Simba, nicknamed ‘Msimbazi Reds’, in the Vodacom Premier League since September 2010 – which is a run of 15 losses and a draw.
“Simba are not so indomitable though they are rightly praised for having a very strong squad this season. We are having the same preparation we had against Yanga early this season, why wouldn’t we take maximum point against them?’’ he asked.
He confidently added: “All taboos are made to be broken, this is the year to end our winless run against Simba and Yanga, whether we play them at home or away.”
On the opening day of the season Mayanga managed to help Ruvu Shooting end their 16-match winless run against Yanga when a solitary goal netted by Sadat Nanguo gave them a 1-0 victory at Uhuru Stadium.
Simba, meanwhile, head into the clash with doubts lingering over the future of head coach Patrick Aussems.
Aussems is widely believed to be the next Vodacom Premier League coach on the chopping block.
The sentiment has been strengthened by the 56-year old Belgian tactician’s decision to dodge questions about his future this week in the wake of his employers saying he travelled out of the country without following due procedure.
Aussems is rumoured to have gone to South Africa formalize talks with the country’s Premier Soccer League side, Polokwane City.
Be that as it may, Simba's chief executive officer, Senzo Mbatha, has since moved to dismiss speculations, it is only a matter of when not if Aussems will become the latest coaching casualty this season.
The back-to-back champions are four points clear atop the standings but they know rivals, Young Africans (Yanga), have enough matches in hand to make up the points difference.
Mainland Premier League Fixtures:
Saturday
Ruvu Shooting v Simba (Uhuru Stadium, Dar es Salaam, 4pm), Mbao FC v Azam FC (CCM Kirumba Stadium, Mwanza, 4pm), Mbeya City v Singida United (Sokoine Stadium, Mbeya, 4pm


velocyto.diffusion module¶
-
class
velocyto.diffusion.
Diffusion
→ None[source]¶ Bases:
object
-
compute_transition_matrix2
(x0: numpy.ndarray, v: numpy.ndarray, sigma: float = 0.0, reverse: bool = False) → scipy.sparse.csr.csr_matrix[source]¶ Compute a right-stochastic matrix representing transition probabilities from each node
Parameters: - Embedding positions (x0) –
- Velocities on the embedding (n_cells, n_dims (v) –
- The kernel size (sigma) –
- Compute the reverse transition matrix (reverse) –
- Remarks:
- Computes a Markov transition matrix for the KNN graph. The probability of transition along an edge is proportional to the scalar projection of the velocity vector onto that edge, times the reciprocal of the edge length. Edges that get negative scalar projections are clipped to zero and the total non-zero outgoing edges are normalized to a sum of 1.0.
-
compute_transition_matrix
(knn: scipy.sparse.coo.coo_matrix, x: numpy.ndarray, v: numpy.ndarray, epsilon: float = 0.0, reverse: bool = False) → scipy.sparse.csr.csr_matrix[source]¶ Compute a right-stochastic matrix representing transition probabilities from each node
Parameters: - KNN graph (knn) –
- Embedding positions (x) –
- Velocities on the embedding (v) –
- Compute the reverse transition matrix (reverse) –
- Remarks:
- Computes a Markov transition matrix for the KNN graph. The probability of transition along an edge is proportional to the scalar projection of the velocity vector onto that edge, times the reciprocal of the edge length. Edges that get negative scalar projections are clipped to zero and the total non-zero outgoing edges are normalized to a sum of 1.0.
-


There are
chars in
lines.


Oxygen is a modern and elegant Onepage HTML template. Every single detail is carefully designed in order to create a wonderful user experience.
Oxygen is very easy to set up and customize and comes with a well documented help file, which will assist you configure the template in minutes.
Open the index.html file using any text editor. We recommend Sublime Text. Now look for the following code and remove them.

Save the file and refresh your browser.
From the sendemail.php file just replace the email address and save the file.
<?php
$name = @trim(stripslashes($_POST['name']));
$from = @trim(stripslashes($_POST['email']));
$subject = @trim(stripslashes($_POST['subject']));
$message = @trim(stripslashes($_POST['message']));
$to = 'email@email.com';//replace with your email
$headers = array();
$headers[] = "MIME-Version: 1.0";
$headers[] = "Content-type: text/plain; charset=iso-8859-1";
$headers[] = "From: {$name} <{$from}>";
$headers[] = "Reply-To: <{$from}>";
$headers[] = "Subject: {$subject}";
$headers[] = "X-Mailer: PHP/".phpversion();
mail($to, $subject, $message, $headers);
die;
Open index.html file and look for the code

From the above code just replace your data-latitude and data-longitude value.
Javascript
Images
Finally thank you very much for choosing this template. Please keep that in mind that we are working very hard to providing better quality in coming days.
If you love your work then appreciate us by sharing this product in social media like twitter or facebook.


Best Practices in Client-side Development
Projected Time
About 20-30 minutes
Prerequisites
HTML and CSS
Motivation
- During development, we always focus on writing runnable code to complete our goal but, we ignore the best practices to make our code more readable & manageable.
- New contributors and repository/project maintainers can coordinate easily if they use common coding practices.
- Best practices are used to improve the quality of the software product.
Objectives
Participants will be able to:
- Understand the importance of dummy content during development.
Specific Things to Learn
- Importance of Lorem ipsum text and images
Lesson
- About dummy text Lorem ipsum (10 min) - Lorem Ipsum refers to text that developer/designer use as replacement text when the real text is not available. The purpose of Lorem Ipsum is to create a natural looking block of text (sentence, paragraph, page, etc.) that doesn’t distract from the layout. Similar there is Lorem Picsum which refers to images that developer/designer use as filler images when the real images are not available.
- A developer uses Lorem Ipsum/Picsum in their project, when the developer creates an initial version of his project then he uses Lorem Ipsum as a placeholder for that.
- When designer designs something then he uses Lorem Ipsum/Picsum in mockup design to choose font-family and font colors for the real text in the final design. Link to pick up dummy text : Lorem Ipsum Link to pick up dummy images :Lorem Picsum
Supplemental Materials


Civil Engineering
For more than a decade, Protech Construction and Development Corporation is committed in delivering robust and global standards compliant vertical and horizontal structures. Swiftly accomplishing projects without compromising quality.
ISO 9001 : 2015 Certified. Protech Construction and Development Corporation abides and passed all quality requirements of ISO 9001.
Extended Capabilites
We invested heavily on equipments and machineries to extended our engineering capabilities and offer complete, effective and efficient engineering solutions to our clients.
Getting the job done
Accomplishing projects on-time without comprimising safety is our utmost goal. Having satisfied clients and comfort for the end-user is our ambition.
Innovation is in our DNA
We aim to be the best
provider of quality infrastructures in the Philippines.
To achieve these, we commit continuous
training, provide excellent needs, moral and just treatment of employees and implement
regulatory requirement of government agencies, execute pro-active safety.
Quality, Efficiency
We are a team of experienced Engineers, Consultants and Multi-Skilled Workers whose service are available.
These Engineers had their varying degree and experience from Engineering Construction and other
Building services.
01.
Planning
02.
Execution
03.
Support
Design is making ideas real.
Human centered design is at the core of product development. Empathetic communication with the client is a key part of the development process from the beginning until the product launch and support phases.
Design thinking is iterative, and cyclic. Combining raw creative out with theoretical structure is the best way to deliver high quality products to clients. Listening and guiding are core communication principles between the developer and client.
When developing new sites and applications our job as a contractor is to meet client needs through empathetic research and interaction. Listening to the client is key when solving in an unfamiliar domain of expertise. Guiding must be approached as a craft of finess to bridge the gulf between possible and not possible.
Engineering and Development Thrive on Strong Design.
Using current development technologies and proven best practices in civil engineering, coupled with a formal background in mechanical science drives and delivers high quality civil development solutions.
Adaptive development methods ensure cross-device and cross-platform consistent solutions.
Understanding client levels of technical knowledge is important. We understand that some clients require to be more involved in the development process than others. Transparency is a key factor which addresses security and technical issues across domains. When working with clients from the science and engineering field open communication and input regarding technology is welcome. We are always open to learning and compormise.
Support is Trust. Product Life Cycle Beyond Development.
Client support is rooted in the mindset of client empathy and need. Delivering emerging technologies to strengthen the product and both user and client experience are integral to our support role.
Security features are updated to protect against current threats to protect the business, technology, and users. Best practices are communicated and implemented with the client and user in mind.
Support is an ongoing role which extends the development period of the software. Scale, security and usability are key support concepts which we deliver in our product support role.


--- title: Info For Newcomers ---
Welcome to SIGPwny! We are glad that you found us, and we hope you are ready to start hacking!
Our second meeting of the year will generally be "Introduction to Shells". If you're joining us after that, please learn what a shell is and make sure you have a bash one on your computer.
Here are some other learning resources for getting started:
learn shell (good for starting): http://overthewire.org/wargames/bandit/


Introduction to Mealy automata, Grigorchuk group and the Burnside problem
26 Jun 2018Hello! After a quite long pause, semidoc comes back, with the long-awaited post by Thibault Godin about his research. Thibault is currently postdoc in Turku, Finland, but was PhD student when he gave a talk at the PhD seminar. After this post, Victor Lanvin replaces me as ``maintainer’’ of this blog. Enjoy!
During my PhD, I have been mostly looking at drawings like this one:
Theses drawings are called Mealy automata, and in this note we will see how they can be used to solve important problems arising from group theory. More precisely we aim to prove that the group generated by the automaton above solves Burnside Problem, i.e. is on the edge between finite and infinite groups. We will first explain how this automaton can represent a group, then why is this group infinite and finally why are every elements of this group of finite order.
Mealy automata and groups
We see that the graph of the first figure has vertices labelled by letters and edges (called transitions) of the form $x|y$ with $x,y \in \lbrace 0,1 \rbrace$. We are going to call $a,b,c,d,e$ the states of the automaton, $\lbrace 0,1 \rbrace$ its alphabet, $x$ the input letter of the transition, and $y$ the output letter of the transition.
As for a classical automaton, the main move is, from a state, to read a letter. For instance reading $0$ from the state $b$ leads us to $a$ outputting $0$, because the transition is $b \xrightarrow{ 0\mid 0} a $. This action can be easily extended, and from a state we can read a word of letter. For instance if we want to read, from the state $b$, the word $0100$, we start as before by following the transition $b \xrightarrow{ 0\mid 0} a $, outputting $0$. What left to do is to read the word $100$, now from $a$, so we follow the transition $a \xrightarrow{ 1\mid 0} e $, and we iterate this process until there is no more letter to be read. To summarise we have went through the states $b,a,e$ and $e$, outputting $0000$. This can be read as a path in the automaton:
or equivalently
As we see, $b$ transforms $0100$ into $0000$. As we can do this for any word, we can say that $b$ induces a transformation $\rho_b$ from $ \lbrace 0, 1 \rbrace^* $ to itself. Hence we get one function from word to word per state. Moreover, since these functions have the same domain and codomain, we can compose them as we want. Note that the composition corresponds in the automaton to the plug-in of the output of a run to the input of another. Namely $\rho_{ab} = \rho_b \circ \rho_a$ can be seen as
This structure where object can be compose together is called a semigroup. The most well known semigroup is certainly the set of positive integer (because the addition of two such number is always a positive integer), but in computer science we also use quite often the semigroup of words (the concatenation of two words is also a word), and we can think to many other examples. The theory of semigroups is a wide area intertangling math and informatics, but one is generally more familiar with group theory, where the elements can always be inversed.
In our setting, generating a group means that each function has to be bijective, i.e. that every state induces a function that can be inverted.
This can be easily verified on the automaton: it is equivalent to require that every state induces a permutation on the alphabet. This is the case for the Grigorchuk automaton (for instance $a$ flips $0$ and $1$), so we can study the group generated by the Grigorchuk automaton, henceforth called the Grigorchuk group.
Infiniteness of the Grigorchuk group
For the Grigorchuk group lots of properties are known. For instance we can prove that it infinite :
First, we can see that $e = \mathbb{1}_{\Sigma^*}$ because $e$ is a sink state which copies the input word on the output.
We are going to construct an infinite number of elements via a morphism~$\eta$ defined by:
Lemma The elements $\eta^{\ell}(a)$ are pairwise different in the Grigorchuk group.
Proof We show that the $\eta^{\ell}(a)$ act differently on $1^\omega$. We have:
So, as $e$ acts like the identity in the group, it can be ignored when it appears in a word, we have:
hence every $\eta^\ell(a)$ acts differently on $1^\omega$, so they represent different elements in the group.
We have proved:
Corollary: The Grigorchuk group is infinite
The Burnside Problem
Now, why would one wants to study such groups? Because it is an infinite Burnside group. Let’s elaborate:
the order of a element $g$ is the smallest positive integer~$n$ such that $g^n$ is the identity in the group. When such an integer exists we say that $g$ has finite order, infinite otherwise.
For instance in $(\mathbb{Z}/12\mathbb{Z},+)$, $5$ has order $12$ because $5+5=10$, $10+5 = 3$, $3+5=8$, $8+5=1$, $1+5=6$, $6+5=11$, $11+5 = 4$, $4+5 = 9$, $9+5=2$, $2+5=7$, $7+5=0=e$. In the same fashion $2$ has order 6 and $8$ has order $3$.
On the other hand, for the group of integers $\mathbb{Z}$, zero is the only element of finite order since the repeated sum of the same integer goes to plus or minus infinity.
It is quite clear that if a group has an element of infinite order (and hence contains a copy of $\mathbb{Z}$ has a subgroup), then it has to be infinite (if $g$ has infinite order, then $\lbrace g^k, k \in \mathbb{Z} \rbrace$ is infinite). The reciprocal gives that a finite group has only elements of finite order.
At the beginning of the XX${}^{th}$ century, people only knew finite groups and infinite groups with elements of infinite order.1 Hence the question of Burnside:
Question, Burnside (1902): Can a finitely generated group have all elements of finite order and be infinite?
This question became central in group theory and was solved for several classes of groups (for instance it is not hard to see that when the group is commutative the answer is no).
The solution was found in 1964 by Golod and Shafarevich, who gave an explicit example of a finitely generated group with all elements of finite order and infinite (henceforth called infinite Burnside group. However this example is very complicated and requires deep results in field theory, and, as these groups are on the edge between finiteness and infiniteness, people continued to look for examples.
We are now going to prove that the group generated by the Grigorchuk automaton is an infinite Burnside group.
One of the crucial observation for our proof is that the subgroup generated by $b,c,d$ is finite: $\langle b,c,d \rangle = \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$. The relations are:
$bc=cb=d ~;~ bd=db=c ~;~ cd=dc= b.$
The proof is a simple verification and can be done with cross diagrams or via computer assisted computations.
Let us recall that the conjugate of $g$ by $h$ is the group element $h^{-1}gh$. We need the small lemma:
Lemma If $g$ has finite order $n$, then so does each of its conjugates.
Proof: We compute:
$(h^{-1}gh)^n = h^{-1}ghh^{-1}gh … h^{-1}gh = h^{-1}g^nh =h^{-1}e h = e$.
So $h^{-1}gh$ has order less than $n$, we get the other inequality by symmetry: $g$ is conjugate to $h^{-1}gh$ by $h^{-1}$.
We now have all the tools we need to prove
Theorem: The group $\langle\mathcal{G}\rangle$ has every element of finite order.
Proof: Let $g \in \langle\mathcal{G}\rangle$. We are going to do an induction on the length of the shortest representative of $g$ on $Q^*$. Let $\ell$ be this shortest length and $\mathbf{w}$ be a word on $Q$ of length $\ell$ representing $g$ in $\langle\mathcal{G}\rangle$. As the product of two element of $S := Q \setminus \lbrace a \rbrace$ is an element of $S$, we can assume that $\mathbf{w}$ is written as an alternation of an $a$ and a letter of $S$. One can show2 for initialisation, that if $\ell < 3$, then $g$ has finite order.
Assume $\ell$ is odd. If $\mathbf{w}$ starts with an $a$, then $\mathbf{w}= a\mathbf{u}a = {\mathbf{u}}^{a}$ (since $a^{-1}=a$), with $\mathbf{u}$ a word on $Q$ of length $\ell - 2$. Hence we can use the induction of $u$, and since conjugation does not change the order (Lemma above), $g$ has finite order. If $\mathbf{w}$ starts with $p \in S$, then $\mathbf{w} = p\mathbf{u}q$, $q\in S$. We can conjugate by $p^{-1}$ : ${g}^{p^{-1}} = p^{-1}p \mathbf{u} q p$. The word $\mathbf{u}r$ has length at most $\ell -1$ (since $q.p = r \in S$), whence the order of $g$ (which is equal to the order of $\mathbf{u}r$) is finite order using the induction hypothesis.
Now is $\ell$ is even. By conjugation we can assume that $\mathbf{w}$ starts with an $a$. We are going to split the analysis into sub-cases depending on the length of $\mathbf{w}$. If $4$ divides $\ell$, then $\mathbf{w} = a w_1 a u_1 a w_2 a … a w_{\ell/4} a u_{\ell /4} $ and we can group the letters of $w$ into blocks $a w_i a$ and $w_j$. As $\mathbf{w}$ has an even number of $a$, $\mathbf{w}$, can be decomposed as $ (\mathbf{w_{ 0}},\mathbf{w_{ 1}})()$3 where $\mathbf{w_\epsilon}$ ($\epsilon \in \lbrace 0, 1 \rbrace$) have length at most $\ell/2$, since blocks $aw_ia$ can be decomposed as $aw_ia = (s,t)$ with $s,t \in Q$. So, the order of $g$ is the lowest common multiple of the orders of $\mathbf{w_\epsilon}$, finite by the induction. Finally, if $\ell= 4j-2$, we consider $g^2$, represented by $\mathbf{ww}$.
- if $\mathbf{w}$ contains a letter $d$, then the length of $(w_{\epsilon})$ is lesser or equal to $ 4j-3$ and we can conclude.
- if $\mathbf{w}$contains a letter $ c$ then the words $\mathbf{w_{\epsilon}}$ are either of size lesser or equal to $4j-3$, or contain a $d$, and we conclude using the previous case on $\mathbf{w_\epsilon}$.
- otherwise, the word $\mathbf{w}$ is a power $ab$, hence of finite order.
Using the corollary above, we get:
Theorem: The group $\langle\mathcal{G}\rangle$ generated by the Grigorchuk automaton $\mathcal{G}$ is an infinite Burnside group.
Conclusion
Among the interests of this proof are its shortness and elementariness: we have not used any theorem that goes further a first lecture in group theory.
Moreover, these groups generated by Mealy automata have given several other interesting examples, among which are the first groups with intermediate growth (solving Milnor Problem), non uniform exponential growth (solving Gromov Problem), or Amenability but not exponentially amenability (solving Day Problem).
On the computer science side, some graphs associated with Mealy automata are conjectured to by families of expander graphs.
My research involves linking the structure of the automaton and the properties of the group it generates. With co-authors we proved that some shapes in the Mealy automaton forbids the group it generates to be infinite~Burnside.
Footnotes
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To be precise this is true when the group is finitely generated, i.e. when there exists a finite set such that each element of the group can be written as a product on this set. Otherwise it is easy to build counterexamples in the spirit $\prod_{\mathbb{Z}} \mathbb{Z}/2\mathbb{Z}$. ↩
-
Using computer or by hand. ↩
-
i.e. $\mathbf{w}$ acts like $\mathbf{w}_0$ after reading a 0 and as $\mathbf{w}_1$ after reading a 1, and that the first letter read is not modified by $\mathbf{w}$. ↩


Sisters arrested for theft
Accused targeted people in crowded spo
by Staff ReporterTwo sisters have been arrested for their alleged involvement in cases of theft in south Delhi, the police said on Saturday.
DCP (South) Atul Kumar Thakur said that the women — Lalita (25) and her younger sister Damini (22) are from Madhya Pradesh.
The police said that the first case was registered on November 5 at Kotla Mubarakpur police station in which the complainant reported a theft of ₹50,000 inside a bank. The second case was reported from a temple in Chhatarpur the same day in which the complainant stated that he withdrew ₹50,000 after which he went to the temple and while returning, he found the money missing. A case was registered at Mehrauli police station.
CCTV footage was scrutinised and two women were found moving in a suspicious manner. The suspects were identified and surveillance was mounted. “A tip-off was received that the women were in Pushp Vihar after which a trap was laid and they were apprehended,” Mr. Thakur said, adding that the stolen money was recovered from them.
During interrogation, they allegedly told the police that they visited cities during festival and marriage seasons and targeted people in crowded places.
“Accused Lalita disclosed that she was apprehended in a theft case in Delhi and sent to Jail about 15-16 months ago,” the officer added.


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| Vendor Name: | Deloitte LLP |
|---|---|
| Reference Number: | C2014-077 |
| Contract Date: | 2014-02-26 |
| Description of work: | 0491 - Management Consulting |
| Item Procured: | Professional Services |
| Contract Period: | 2014-03-03 to 2014-03-31 |
| Original Contract Value: | $24,154.32 |
| Contract Value: | |
| Comments: | |
| Former Public Servant: | No |


Exploitation is when the action preferred by the model is
chosen. The model preference is based on the context and past interactions.
Experiment ResponseExploration
65%
Exploration is when, despite the model's preference, an
alternative action is chosen. This is crucial to discover new trends and learn the best
policy.