Constrained Optimization
Constrained Optimization
$$\min_{x \in R^n} f(x)$$
subject to: $$c_i (x) = 0, i \in E \text{(equality constraints)}$$ $$c_i (x) \geq 0, i \in I \text{(inequality constraints)}$$
Feasible Set $\Omega = { x_i | c_i(x) = 0, i \in E \text{ and } c_i(x) \geq 0, i \in I}$.
Case 1
$\min_{x \in R^n} f(x)$ subject to $c_1 (x) = 0$
x is local minimum if x + s $\notin \Omega$ or f(x+s) $\geq$ f(x).
Now, assume the opposite. Suppose s is a small step, $c_1(x+s) = c_1(x)$ and $f(x+s) < f(x)$
Using Taylor Series Expansion:
$$c_1(x+s) \approx c_1(x) + \nabla c_1(x)^T s = 0$$
So
$$\nabla c_1(x)^T s = 0$$
Also, since $f(x+s) < f(x)$, then
$$0 > f(x+s) - f(x) \approx \nabla f(x)^T s$$
Therefore, $\exists s$ when
\begin{align} \nabla c_1(x)^T s &= 0 \newline \nabla f(x)^T s &< 0 \end{align}
However, this is not possible when $\nabla f(x) = \lambda \nabla c(x)$. If $\nabla f(x)$ and $\nabla c(x)$ lie parallely, s will be perpendicular to $\nabla f(x)$ as well, making dot product 0 instead of <0.
$\therefore$ the optimality condition are $\nabla f(x) = \lambda \nabla c(x)$.

Then
$$c_1(x+s) \approx c_1(x) + \nabla c_1(x)^T s \geq 0 \text{ (a)}$$
$$f(x+s) = f(x) + \nabla f(x)^T s < f(x) \text{ (b)}$$
Any s satisfy the equation (a), and $\exists$ s that satisfy (b) unless $\nabla f(x) = 0$.
$\therefore$ optimality conditions: $\nabla f(x) = 0, c_1(x) > 0$.
Subcase 2.b
$c_1(x) = 0$
If x is not local optimal, then $\exists$ s that $c_1(x+s) \geq 0$ and $f(x+s) < f(x)$.
Again by Taylor series expandsion
$$c_1(x+s) \approx c_1(x) + \nabla c_1(x)^T s \geq 0 \text{ (a)}$$
$$f(x+s) = f(x) + \nabla f(x)^T s < f(x) \text{ (b)}$$
Because $c_1(x) = 0$, then we have
$$\nabla c_1(x)^T s \geq 0 \text{ (a)}$$
$$\nabla f(x)^T s < 0 \text{ (b)}$$
$\exists$ no s that satisfy both a and b iff $\nabla f(x) = \lambda \nabla c_1(x)$ for $\lambda \geq 0$
The Lagrangian function:
$$L(x, \lambda) = f(x) - \sum_{i \in \epsilon \cup I} \lambda_i c_i(x)$$
where $\lambda$ is called Lagrangian variable.
Karush-Kahn-Tucker (KKT) Conditions
At a local solution $x^* $, under some conditions, $\exists$ a Lagrange multiplier $\lambda^* $ s.t.
\begin{align} \nabla L(x^*, \lambda^*) &= 0 \newline c_i(x^*) &= 0, \forall i \in E \newline c_i(x^*) &\geq 0, \forall i \in I \newline \lambda_i^* &\geq 0, \forall i \in I \newline \lambda_i c_i(x^*) &= 0, \forall i \in E \cap I \newline \end{align}
The last is called complementary conditions (either $\lambda_i = 0$ or $c_i(x^*) = 0$ when $c_i(x^*) > 0$) based on rule 3 and 2.


This diagram illustrates the effects of absolutely positioning a box with respect to the initial containing block.
A document window is shown, with 8 lines (numbered 1 to 8), each 24px high. All body and "outer" text has been flowed into lines into lines 1, 2, and 3. The "inner" box has been positioned at "-100, 200" relative to the "0, 0" coordinates (the upper left corner of the document window). Most of the "inner" box contents are therefore rendered outside the document window.
In the following PRE element, each 24 pixel line is simulated by two lines, the second beginning with the appropriate number. The text that is to the left of the line numbers lies outside the initial containing block. The lines, as they appear in the image, contain approximately:
1 Beginning of body contents. [@]Start 2 of outer contents. End of outer 3 contents. End of body contents. 4 Inner 5 Conte 6 nts 7 8
The default text color is black. "Start of outer contents" is red. The "nts" in "Inner contents" is blue. "End of outer contents" is red.


|
Charbrary
2.0.0
|
Represents a circle. More...
#include <Circle.h>
Public Member Functions | |
| Circle () | |
| Constructs a new circle with default values. More... | |
| Circle (const vec_t &position_, float radius_) | |
| Constructs a new Circle from a vector and a radius. More... | |
| float | diameter () const |
| Computes the diameter of the circle. More... | |
| float | circumference () const |
| Computes the circumference of the circle. More... | |
| float | area () const |
| Computes the area of the circle. More... | |
| void | operator= (const Circle &toCopy) |
| Overload of the assignment operator. More... | |
Public Attributes | |
| vec_t | pos |
| float | radius |
Represents a circle.
This class contains member functions that perform common mathematical operations done with circles (computing the area, perimeter, circumference) and also to help dealing with collision detection. Circles are defined by a position (the center) and a radius.
| ch::Circle::Circle | ( | ) |
Constructs a new circle with default values.
The new circle will be positioned at 0,0 and have a radius of 0.
| ch::Circle::Circle | ( | const vec_t & | position_, |
| float | radius_ | ||
| ) |
Constructs a new Circle from a vector and a radius.
| position | Position of the center of the circle. |
| radius_ | Radius of the circle. |
| float ch::Circle::area | ( | ) | const |
Computes the area of the circle.
| float ch::Circle::circumference | ( | ) | const |
Computes the circumference of the circle.
| float ch::Circle::diameter | ( | ) | const |
Computes the diameter of the circle.
| void ch::Circle::operator= | ( | const Circle & | toCopy | ) |
Overload of the assignment operator.
| toCopy | Circle whose values will be copied into the current circle. |
| vec_t ch::Circle::pos |
The circle's center position.
| float ch::Circle::radius |
The circle's radius.


Gateway
BOT
21-Apr-19 10:02 AM
[dscrd-hush] <Inevitability> Means mining HUSH now - that doesn't make any sense?
[dscrd-hush] <Inevitability> I means HUSH/HUSH3
[dscrd-hush] <ComputerGenie - ChickenPool> @Inevitability Would it help if we typed in a different language? Perhaps there's a translation issue?
[dscrd-hush] <Inevitability> No I understand.
[dscrd-hush] <ComputerGenie - ChickenPool> doesn't think you do, but OK
[dscrd-hush] <Inevitability> Start mining)
[dscrd-hush] <ComputerGenie - ChickenPool> started mining the new chain 7 days ago
(edited)
[dscrd-hush] <Inevitability> cool
[dscrd-hush] <dukeleto> @Inevitability many people are mining the new HUSH chain
[dscrd-hush] <dukeleto> only people with no idea what is going on are mining the old chain
[dscrd-hush] <dukeleto> mining the old chain are worthless coins
[dscrd-hush] <dukeleto> you cannot trade them for new HUSH coins that have value
[dscrd-hush] <dukeleto> Safe.trade and Graviex, the current 2 exchanges which are open, are on HUSH3. There is no way to mine the old chain and turn that into anything of value. Those are worthless coins
[dscrd-hush] <dukeleto> We gave people months of notice, but some miners don't check for updates
[dscrd-hush] <dukeleto> Some mining pools don't check for updates, which is really quite wasteful
[dscrd-hush] <dukeleto> We won't automatically turn off nodes like ZEC, that is not our jive. So people running full nodes can be adults and upgrade or do whatever they are doing, as described in the whitepaper. We don't force a chain on people, they can choose between the old insecure unsupported Hush v2 or the new shiny, secure Hush v3
[dscrd-hush] <Inevitability> There is no possibility to exchange for new coins - there is no possibility yet. Waiting for updates for Agama
[dscrd-hush] <dukeleto> Cryptocoins is an active sport
[dscrd-hush] <dukeleto> @Inevitability if you are willing to use the CLI, it's possible right now. But I am not sure that is best if you are not familiar with it
[dscrd-hush] <Inevitability> I'm not familiar with it)
[dscrd-hush] <Inevitability> But familiar with Agama )
[dscrd-hush] <dukeleto> @ComputerGenie - ChickenPool 3358 blocks mined on the old chain, and counting, can you imagine
[dscrd-hush] <ComputerGenie - ChickenPool>
[dscrd-hush] <dukeleto> think of the kittens
[dscrd-hush] <dukeleto> @ComputerGenie - ChickenPool the deprecation height was set to some crazy time in the far future, and the Hush v2 network might just run until then
[dscrd-hush] <dukeleto> like, years
[dscrd-hush] <dukeleto> even mainnet is decentralized!!!
[dscrd-hush] <ComputerGenie - ChickenPool> an estimated 1.90 MSol/s still on old chain; as a miner, I'm fine with that, more profits for me
[dscrd-hush] <dukeleto> yep, great for smart miners who are on the correct chain. Small miners have this advantage
[dscrd-hush] <dukeleto> huge miners cannot deal with changes like this in short timeframes
[dscrd-hush] <ComputerGenie - ChickenPool> It amazes me when miners marry a coin and then pay 0 attention to what goes on with it
[dscrd-hush] <dukeleto> yeah, we are talking about ASIC miners
[dscrd-hush] <dukeleto> what is going on, is a few pools didn't care and tons of users are still sending hash to those pools
[dscrd-hush] <dukeleto> i hope this isn't solo miners
[dscrd-hush] <dukeleto> because i would tisk-tisk them
[dscrd-hush] <Inevitability> Do you mine old HUSH? And then what will you do with it? you just told me there's no point in it!
[dscrd-hush] <ComputerGenie - ChickenPool> even GPU miners....  It has no financial value.
[dscrd-hush] <dukeleto> private keys which contains funds at block 500,000 from HUSH v2, those have value. Those same funds are waiting for you on HUSHv3, unlocked by same private key.
[dscrd-hush] <Inevitability> "ComputerGenie - ChickenPoolСегодня в 13:18
an estimated 1.90 MSol/s still on old chain; as a miner, I'm fine with that, more profits for me"
[dscrd-hush] <dukeleto> every address on Hush v2 has an equivalent but different-looking address on HUSH v3
[dscrd-hush] <Inevitability> !?!
[dscrd-hush] <dukeleto> @Inevitability he meant to say "because people are mining the wrong chain, i have less competition on correct chain"
[dscrd-hush] <dukeleto> language barriers @ComputerGenie - ChickenPool , go easy
[dscrd-hush] <Inevitability> ok
[dscrd-hush] <ComputerGenie - ChickenPool> @Inevitability
as a miner, I'm happy that that much hashrate is on the wrong chain, I make more money that way
as an investor, I don't understand those people
[dscrd-hush] <Inevitability> understand
[dscrd-hush] <dukeleto> @Inevitability backup your wallet.dat, like a few times
[dscrd-hush] <dukeleto> and soon we will have instructions
[dscrd-hush] <dukeleto> and agama wallet and web wallet will hopefully be working soon, and HUSHmate gui swing wallet
[dscrd-hush] <dukeleto> lots of things cooking
[dscrd-hush] <Heno1974> 1300 sat/hush?
[dscrd-hush] <ComputerGenie - ChickenPool> time to shut this thing down for a bit
new cooler and larger data SSD
[dscrd-hush] <Inevitability> Where ZelCore keep wallet.dat ?
[dscrd-hush] <dukeleto> @Inevitability you gonna need to ask their discord
[dscrd-hush] <dukeleto> that is a closed source unsupported wallet
[dscrd-hush] <dukeleto> we don't give support for it, nor suggest anybody use it


Uber uses an algorithm to calculate the surge price during peak times, when the demand for drivers are high in a certain area. This might have several impacts on both customers and drivers. According to a Washington Post article, these may include: a reduction in the demand for cars (less people want a ride for a higher price), creation of new supply (providing an incentive for new drivers to hit the road), and shifts in supply (drivers) to areas of higher demand. We propose to present a visualization of these data to help users understand how surge multiplier works and how to optimize trip planning, especially when travelling to popular events or during peak times.
Working with another 3 designer and developers. We make the web app for this visualization project using D3.js.
Below is one part I made for the "customer's view". The idea is to show the information the customer might be interest, such as price, waiting time, as well as total trip duration in one single window.
Provide "Overview-plus-Detail" so that the user can see the overall pattern of cost&time variation, as well as the detailed waiting time and trip duration at a specific hour
Link the data from various views, which is the so-called "Brushing and Linking" technique in information visualization.
For bar chart, since each bar is an individual svg element, I can bind the data directly to the svg elements.
For the line chart, since the line is a continuous svg element, I have to use invert scale to match the mouse position with data point.
Use the built-in transition function from D3 library to add animation effect to the svg element so as to enhance the user experience.
The detailed project document can be found on google doc.


hello!
Am David kamau kuria, a student in moringa school pursuring software developer.
my career dream is to become a great developer and give the best in field.
venturing in my career is my passion ready to provide world with solutions and new technology.
fellow my website to understand the world.
enjoy exploring as i shine hihger in programming programming


Full-Stack or Bust
The Elevator Pitch
JD with start-up, business development and organizational strategy experience, I hope to become a web developer and bring dreams to reality. I value creative, honest and collaborative approaches to problem solving. My motivation is to do what I love and help people do what they love.
Frequently Asked Questions
Q1: What are you currently trying to accomplish?
A1: I want to change my career path and become a web developer. I want to harness my personal passion for tech to help bring ideas to life and eventually have the technical knowledge and ability myself to build a social networking start-up.
Q2: Favorite food?
A2: I am a big fan of all kinds of food but if I had to pick one, it would be the burrito. It's like a wrapped present you can eat. I am partial to Chipotle.
Q3: What are some of your hobbies?
A3: I love technology so I'm in front of my computer a lot. When I'm not, I love to be outside hiking or playing on a beach. I'm also still slightly obsessed with Legos and Calvin and Hobbes.
Q4: Favorite smell?
A4: Freshly cut lawn and gasoline in a relative mixture of 95/5.
Q5: What's the photo of your site's header?
A5: Part of the Atlas Detector at the Large Hadron Collider... the ultimate Lego model.
Contact Me
To stay in touch you can email me at<EMAIL_ADDRESS>or call<PHONE_NUMBER>.


public class InternalSettingsPreparer
extends java.lang.Object
| 限定符和类型 | 字段和说明 |
|---|---|
static java.lang.String |
SECRET_PROMPT_VALUE |
static java.lang.String |
TEXT_PROMPT_VALUE |
| 构造器和说明 |
|---|
InternalSettingsPreparer() |
| 限定符和类型 | 方法和说明 |
|---|---|
static Environment |
prepareEnvironment(Settings input,
Terminal terminal)
Prepares the settings by gathering all elasticsearch system properties, optionally loading the configuration settings,
and then replacing all property placeholders.
|
static Environment |
prepareEnvironment(Settings input,
Terminal terminal,
java.util.Map<java.lang.String,java.lang.String> properties,
java.nio.file.Path configPath)
Prepares the settings by gathering all elasticsearch system properties, optionally loading the configuration settings,
and then replacing all property placeholders.
|
static Settings |
prepareSettings(Settings input)
Prepares the settings by gathering all elasticsearch system properties and setting defaults.
|
public static final java.lang.String SECRET_PROMPT_VALUE
public static final java.lang.String TEXT_PROMPT_VALUE
public static Settings prepareSettings(Settings input)
public static Environment prepareEnvironment(Settings input, Terminal terminal)
Terminal
is provided and configuration settings are loaded,
settings with a value of ${prompt.text}
or ${prompt.secret}
will result in a prompt for
the setting to the user.input
- The custom settings to use. These are not overwritten by settings in the configuration file.terminal
- the Terminal to use for input/outputSettings
and Environment
as a Tuple
public static Environment prepareEnvironment(Settings input, Terminal terminal, java.util.Map<java.lang.String,java.lang.String> properties, java.nio.file.Path configPath)
Terminal
is provided and configuration settings are loaded,
settings with a value of ${prompt.text}
or ${prompt.secret}
will result in a prompt for
the setting to the user.input
- the custom settings to use; these are not overwritten by settings in the configuration fileterminal
- the Terminal to use for input/outputproperties
- map of properties key/value pairs (usually from the command-line)configPath
- path to config directory; (use null to indicate the default)Settings
and Environment
as a Tuple


You are on the way to opening a demo account with GMG. We just need a few more details from you before you can start trading.


Welcome To Our Website!You can understand what we are doing by Pvon.com, thanks for your coming.
Date: July 2014 ~ July 2016
Members: 范耀中教授、施宗呈、何青祐、廖志豪
Co-organizer: National Chung Hsing University
Project Name
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Start Bootstrap's Agency theme is based on Golden, a free PSD website template built by Mathavan Jaya. Golden is a modern and clean one page web template that was made exclusively for Best PSD Freebies. This template has a great portfolio, timeline, and meet your team sections that can be easily modified to fit your needs.
You can download the PSD template in this portfolio sample item at FreebiesXpress.com.
Project Name
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Escape is a free PSD web template built by Mathavan Jaya. Escape is a one page web template that was designed with agencies in mind. This template is ideal for those looking for a simple one page solution to describe your business and offer your services.
You can download the PSD template in this portfolio sample item at FreebiesXpress.com.
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Dreams is a free PSD web template built by Mathavan Jaya. Dreams is a modern one page web template designed for almost any purpose. It’s a beautiful template that’s designed with the Bootstrap framework in mind.
You can download the PSD template in this portfolio sample item at FreebiesXpress.com.


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Save 100% when you buy ONE (1) 4 oz. Ben Jerrys® Mini Cup. Expires
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Load the coupon to your shoppers card today only (2/13) and use by 2/28.
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Use your right hand to play Rock Paper Scissor (RPS)!
Using artificial intelligence (deep learning) to recognize your hand pose to play RPS
0
0


Vehicle and details
Pictures
Car availability
LIST MY CAR
Step 1: Vehicle and details
Brand
Brand 1
Brand 2
Brand 3
Category
Category 1
Category 2
Category 3
Year
2017
2016
2015
Gaz type
Gaz 1
Gaz 2
Gaz 3
Color
Color 1
Color 2
Color 3
Model
Model 1
Model 2
Model 3
Odometer
Odometer 1
Odometer 2
Odometer 3
Transmission
Transmission 1
Transmission 2
Transmission 3
Number of passenger
5
6
7
LIST MY CAR
Step 2: Pictures
List my car
Step 3: Car availability
*** Please note that you car needs to be available for at least 24 hours ***
My car is available any days at any time
Select Maximum km allowed per day
0 to 100km
100 to 200km
200 to 300km
300 to 500km
Auto-confirm reservation when someone rent my car within the selected days of availability


Welcome to Marcus Willock 30.04.1 LTS (GNU/Linux 4.15.0-34-generic x86_64)
Below tells the story of an open source enthusiast who is passionate about development. Recently, I have focused on developing in Go, but I am well versed in Python as well and I am starting to really like JavaScript.
* Blog: https://crazcalm.github.io/blog
* Github: https://github.com/crazcalm
* Resume: https://crazcalm.org/resume
* List of open source projects that I have contributed to:
- vmware ---> https://github.com/vmware/purser/pulls
- selenium (Go client) ---> https://github.com/tebeka/selenium/pulls
- Go ---> https://github.com/golang/go/pulls
- go-csv-tag ---> https://github.com/artonge/go-csv-tag/pulls
- qri ---> https://github.com/qri-io/qri/pulls
- awesome-go ---> https://github.com/avelino/awesome-go/pulls
- code-buddies ---> https://github.com/codebuddies/codebuddies/pulls
- pygotham ---> https://github.com/PyGotham/pygotham/pulls
* List of sites I created just for fun:
- Pokemon Card Search ---> https://crazcalm.org/pokemon
* List of the Talks I have given:
Wrapping Go in Python ---> https://youtube.com/wrappingGoInPythonTalk
Modify Golang's Default File Server to hide dotfiles ---> https://github.com/golangnyc/meetups/talks
2 packages can be updated {Career & Goals}.


Transaction fee: {{calculatedFee / 100000000 | number:'1.8-8'}} MONA
After sending, you will have {{(getAvailableNumber(assetControl.value) - amountControl.value - calculatedFee / 100000000) | number:'1.8-8'}} MONA remaining at this address.
After sending, you will have {{(getAvailableNumber(assetControl.value) - calculatedFee / 100000000) | number:'1.8-8'}} MONA remaining at this address.


Meetups
Neurotech
NeuroTech #HackNights
Wednesday, 7:00 PM (Weekly)
Location : Faubourg Tower on Guy and Ste Catherine, 6th Floor, Montréal
More Info


version 2.0 changes¶
Code base changes.
1. Pep8 compliance¶
The cf-plot code has been made pep8 compliant using the pep8 online checker http://pep8online.com and the Python autopep8 program. After running the code through autopep8 --in-place --aggressive cfplot.py the code was then run through the online checker and manually changed where needed. The code is now much easier to read and the logic easier to follow.
Done
2. Regression testing¶
Regression code has been added so that new releases are more robust. The gallery plots are compared to a series of previous plots using python md5 checksums. If tany plots are different the plots are passed through the Imagemagick compare routine and the differences displayed on the screen.
Done
3. Merge all X,Y,T vs Z contour code¶
The three X,Y,T vs Z contour code sections were merged together to reduce code sprawl.
Done


Welcome
My Info:
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userType:


--- layout: default title: Home ---
'the divinity in me bow to the divinity in you'
Hello, I am Sourav. Samhita is a Sanskrit word for collection of texts. Here I intend to write about by my experiences on topics that interest me. I have a lot of interests primary of which is development. A pythonista by code. I love and advocate GNU/Linux. I code backend, android and static sites. I involve myself in good UI/UX discussions and like reading engineering blogs.
Other than development I also love reading up on startups, entrepreneurship, capital markets, sports, history and cultures.
My latest post : {{ site.posts[0].title }}


Welcome to my Animation Lab
Sprite Animation
Transform Animation
Translate Animation
go
your
own
way
- Fleetwood Mac


2 Kings 14:20
And they brought him on horses: and he was buried at Jerusalem with his fathers in the city of David.


The registration fees for useR! 2018 include access to talks and poster sessions, welcome reception, lunches, morning and afternoon tea each day. There are three levels of registration, industry, academic and student, each with early bird rates. The conference programme will run from Wednesday lunch time through Friday late afternoon. Tutorials are provided at a modest additional cost Tuesday all day and Wednesday morning. The conference dinner and childcare are available for extra fees, and have limited places.
Early bird registration closes Mar 30, 2018. All prices are in AUD.
When you sign up for tutorials, enter your preferences for each session here
Publisher’s booths (3mx2m) are also available for a cost of $1500, including one free registration. Contact organisers for details.
- Academic registration includes (1) people affiliated with an academic institution, and can use their institution email address (“.edu") to register, and also (2) self-employed or industry self-funded people, who’s company is not paying for their registration. We trust you, but if your registration email is not from a “.edu” domain, we ask that you send an email to<EMAIL_ADDRESS>with a few sentences letting us know why you have registered at the academic rate.
- Student status covers current or recently graduated undergraduate or graduate students at an academic institution. You need to use your institution email address (“.edu") and have a letter from your head of department or academic advisor to upload to the registration page.
- There are three possible times for tutorials, Tues morning and afternoon, Wed morning. There will be beginner and intermediate tracks, with a range of topics in each. There will be 6 concurrent tutorials in each session. Each person can sign up for a maximum of 3 tutorials, one for each time slot. Choice of tutorials will be provided when that programme is finalised.
- Contemporary Australian cuisine, three course dinner and unlimited drinks for four hours, with tea/coffee and chocolates. $140pp value.
- High quality child care will be provided by Charlton Brown.
Registration will not be available on-site. Registration will close in June, or earlier if all places are filled.


mt.benjamini_hochberg¶
-
benjamini_hochberg
(maxima, alpha, plot=False)[source]¶ Select a subset of the maxima to be candidates to Point Source.
It applies the procedure in multiple testing called Benjamini-Hochberg procedure.
- Parameters
maxima (pd.DataFrame) – Pandas DataFrame with the information of the maxima. Has to contain at least the column ‘pvalue’.
alpha (float) – Parameter alpha of the Benjamini-Hochberg procedure. Should be between 0 and 1.
plot (bool, optional) – If
True
, the function prints the expected number of sources for the intensities of the maxima versus the actual number of maxima at that intensity, along with the threshold (expected*alpha). Two plots are given: one with all the detections plus 5; and one with all the maxima.
- Returns
The same Pandas DataFrame as the input
maxima
, but only with the candidates to be point sources.- Return type
pd.DataFrame


# -*- coding: utf-8 -*-
# Copyright 2018, IBM.
#
# This source code is licensed under the Apache License, Version 2.0 found in
# the LICENSE.txt file in the root directory of this source tree.
"""
A two-ways dict that represent a layout.
Layout is the relation between virtual (qu)bits and physical (qu)bits.
Virtual (qu)bits are tuples (eg, `(QuantumRegister(3, 'qr'),2)`.
Physical (qu)bits are numbers.
"""
from qiskit import QiskitError
[ドキュメント]class Layout(dict):
""" Two-ways dict to represent a Layout."""
def __init__(self, input_=None):
dict.__init__(self)
if isinstance(input_, dict):
self.from_dict(input_)
if isinstance(input_, list):
self.from_list(input_)
[ドキュメント] def from_dict(self, input_dict):
"""
Populates a Layout from a dictionary.
Args:
input_dict (dict): For example,
{(QuantumRegister(3, 'qr'), 0): 0,
(QuantumRegister(3, 'qr'), 1): 1,
(QuantumRegister(3, 'qr'), 2): 2}
"""
for key, value in input_dict.items():
self[key] = value
[ドキュメント] def from_list(self, input_list):
"""
Populates a Layout from a list.
Args:
input_list (list): For example,
[(QuantumRegister(3, 'qr'), 0), None,
(QuantumRegister(3, 'qr'), 2), (QuantumRegister(3, 'qr'), 3)]
"""
for key, value in enumerate(input_list):
self[key] = value
def __getitem__(self, item):
if isinstance(item, int) and item < len(self) and item not in self:
return None
return dict.__getitem__(self, item)
def __setitem__(self, key, value):
if key in self:
del self[key]
if value in self:
del self[value]
if key is not None:
dict.__setitem__(self, key, value)
if value is not None:
dict.__setitem__(self, value, key)
def __delitem__(self, key):
dict.__delitem__(self, self[key])
dict.__delitem__(self, key)
def __len__(self):
return max([key for key in self.keys() if isinstance(key, int)], default=-1) + 1
# Override dict's built-in copy method which would return a dict instead of a Layout.
[ドキュメント] def copy(self):
return type(self)(self)
[ドキュメント] def add(self, virtual_bit, physical_bit=None):
"""
Adds a map element between `bit` and `physical_bit`. If `physical_bit` is not
defined, `bit` will be mapped to a new physical bit (extending the length of the
layout by one.)
Args:
virtual_bit (tuple): A (qu)bit. For example, (QuantumRegister(3, 'qr'),2).
physical_bit (int): A physical bit. For example, 3.
"""
if physical_bit is None:
physical_bit = len(self)
self[virtual_bit] = physical_bit
[ドキュメント] def add_register(self, reg):
"""
Adds at the end physical_qubits that map each bit in reg.
Args:
reg (Register): A (qu)bit Register. For example, QuantumRegister(3, 'qr').
"""
for bit in reg:
self.add(bit)
[ドキュメント] def set_length(self, amount_of_physical_bits):
"""
Extends the layout length to `amount_of_physical_bits`.
Args:
amount_of_physical_bits (int): The amount of physical_qubits to
set in the layout.
Raises:
LayoutError: If amount_of_physical_bits is used to reduced the
length instead of extending it.
"""
current_length = len(self)
if amount_of_physical_bits < current_length:
raise LayoutError('Lenght setting cannot be smaller than the current amount of physical'
' (qu)bits.')
for new_physical_bit in range(current_length, amount_of_physical_bits):
self[new_physical_bit] = None
[ドキュメント] def idle_physical_bits(self):
"""
Returns a list of physical (qu)bits that are not mapped to a virtual (qu)bit.
"""
idle_physical_bit_list = []
for physical_bit in range(self.__len__()):
if self[physical_bit] is None:
idle_physical_bit_list.append(physical_bit)
return idle_physical_bit_list
[ドキュメント] def get_virtual_bits(self):
"""
Returns the dictionary where the keys are virtual (qu)bits and the
values are physical (qu)bits.
"""
return {key: value for key, value in self.items() if isinstance(key, tuple)}
[ドキュメント] def get_physical_bits(self):
"""
Returns the dictionary where the keys are physical (qu)bits and the
values are virtual (qu)bits.
"""
return {key: value for key, value in self.items() if isinstance(key, int)}
[ドキュメント] def swap(self, left, right):
""" Swaps the map between left and right.
Args:
left (tuple or int): Item to swap with right.
right (tuple or int): Item to swap with left.
Raises:
LayoutError: If left and right have not the same type.
"""
if type(left) is not type(right):
raise LayoutError('The method swap only works with elements of the same type.')
temp = self[left]
self[left] = self[right]
self[right] = temp
[ドキュメント] def combine_into_edge_map(self, another_layout):
""" Combines self and another_layout into an "edge map".
For example::
self another_layout resulting edge map
qr_1 -> 0 0 <- q_2 qr_1 -> q_2
qr_2 -> 2 2 <- q_1 qr_2 -> q_1
qr_3 -> 3 3 <- q_0 qr_3 -> q_0
The edge map is used to compose dags via, for example, compose_back.
Args:
another_layout (Layout): The other layout to combine.
Returns:
dict: A "edge map".
Raises:
LayoutError: another_layout can be bigger than self, but not smaller. Otherwise, raises.
"""
edge_map = dict()
for virtual, physical in self.get_virtual_bits().items():
if physical not in another_layout:
raise LayoutError('The wire_map_from_layouts() method does not support when the'
' other layout (another_layout) is smaller.')
edge_map[virtual] = another_layout[physical]
return edge_map
[ドキュメント]class LayoutError(QiskitError):
"""Errors raised by the layout object."""
[ドキュメント] def __init__(self, *msg):
"""Set the error message."""
super().__init__(*msg)
self.msg = ' '.join(msg)
def __str__(self):
"""Return the message."""
return repr(self.msg)


Table of Contents
Technical Posts
Cultural Posts
| Week 9 | Asking the Right Questions |
| Week 8 | Dealing with Conflict |
| Week 7 | Exploring My values |
| Week 6 | My Thoughts on Stereotype Threat |
| Week 5 | My Thoughts on Pair Programming and Peer Review |
| Week 4 | Computer Security Awareness is no Longer an Option |
| Week 3 | My Thinking Style and Learning |
| Week 1 | My Thoughts on DBC Culture |
Exercises
| Week 8 | JavaScript Object Cheatsheet |
| Week 3 | Play DIVASTATION!! |
| Week 2 | First Pairing Session: Building a Basic Website |
| Week 2 | My Site's Wireframes |
| Week 2 | Responsive Web Design |
| Week 2 | Intermediate HTML & CSS |
| Week 1 | Wireframing |
| Week 1 | HTML & CSS Solo Challenge |
| Week 1 | Beginning HTML & CSS |


Data Science & Professional Experience
Data Scientist
UT Austin — May 2017 to Current
Building dashboard-style website with dynamic visualizations, summary data, and record lookup, with a SQL backend database.
Built dataset with millions of nonprofit IRS returns (100GB+).
Wrote Python code to flatten unstructured xmls into structured csv/SQL data. Wrote R analytics code.
Wrote optimized Linux/Bash code to improve the accuracy of messy csv data processing and reduce run
s from weeks to hours.
Data / Stats Research & Consulting
UT Austin — January 2011 to May 2017
Hired for data/programming skills by 4 Professors during 13 semesters as a Research Assistant.
Built 6 datasets with 100s of GB of data from many data types (structured, unstructured, spatial, network, demographic, temporal sources, etc.)
Fitted and interpreted complex models (network analysis, multi-level/mixed-effects regressions, and survival analysis, etc.).
Wrote R and Stata functions to perform custom calculations (e.g. a genetic algorithm to estimate network core-periphery position of nodes).
Developed a new method for diagnosing and imputing missing data in time-series, network data, using multi-level and Bayesian prediction.
Designed/programmed replicable data visualizations (2D, time-series, network, and maps).
Dissertation Research
UT Austin — January 2012 to May 2017
Built unique dataset by (1) geocoding map data, (2) reducing data of over 150gb, (3) government data in Arabic and French.
Predicted protest and violence during the Tunisian Revolution of 2010-11, with temporal and spatial effects, using time series and survival models.
Wrote up and presented methods/results for non-technical audiences, leading to 4 published, peer-reviewed journal articles.
Collaborated with experts in various fields.
Frequently consulted on data in department.
Stats & Methods Teaching
UT Austin — January 2012 to May 2017
Personally selected by Professors in several departments for expertise to assistant teach stats, programming, and methods for 6 semesters
(4 for Ph.D. students, and 2 for undergrads).
Designed stats programming labs for Stata, still in use by Sociology Department.
Policy & Program Work
United Nations Development Programme — May 2005 to July 2010
Policy & program advisor to high-level UN o cials working on political/economic development in Arab countries. Based in Beirut and New York.
Strategic planning & program management.


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| ||||||||||||||||||||
config(5)
NAMEconfig - OpenSSL CONF library configuration files
DESCRIPTIONThe OpenSSL CONF library can be used to read configuration files. It is used for the OpenSSL master configuration file openssl.cnf and in a few other places like SPKAC files and certificate extension files for the x509 utility. OpenSSL applications can also use the CONF library for their own purposes. A configuration file is divided into a number of sections. Each section starts with a line [ section_name ] and ends when a new section is started or end of file is reached. A section name can consist of alphanumeric characters and underscores. The first section of a configuration file is special and is referred to as the default section this is usually unnamed and is from the start of file until the first named section. When a name is being looked up it is first looked up in a named section (if any) and then the default section. The environment is mapped onto a section called ENV. Comments can be included by preceding them with the # character Each section in a configuration file consists of a number of name and value pairs of the form name=value The name string can contain any alphanumeric characters as well as a few punctuation symbols such as . , ; and _. The value string consists of the string following the = character until end of line with any leading and trailing white space removed. The value string undergoes variable expansion. This can be done by including the form $var or ${var}: this will substitute the value of the named variable in the current section. It is also possible to substitute a value from another section using the syntax $section::name or ${section::name}. By using the form $ENV::name environment variables can be substituted. It is also possible to assign values to environment variables by using the name ENV::name, this will work if the program looks up environment variables using the CONF library instead of calling getenv() directly. It is possible to escape certain characters by using any kind of quote or the \ character. By making the last character of a line a \ a value string can be spread across multiple lines. In addition the sequences \n, \r, \b and \t are recognized.
OPENSSL LIBRARY CONFIGURATIONIn OpenSSL 0.9.7 and later applications can automatically configure certain aspects of OpenSSL using the master OpenSSL configuration file, or optionally an alternative configuration file. The openssl utility includes this functionality: any sub command uses the master OpenSSL configuration file unless an option is used in the sub command to use an alternative configuration file. To enable library configuration the default section needs to contain an appropriate line which points to the main configuration section. The default name is openssl_conf which is used by the openssl utility. Other applications may use an alternative name such as myapplicaton_conf. The configuration section should consist of a set of name value pairs which contain specific module configuration information. The name represents the name of the configuration module the meaning of the value is module specific: it may, for example, represent a further configuration section containing configuration module specific information. E.g. openssl_conf = openssl_init [openssl_init] oid_section = new_oids engines = engine_section [new_oids] ... new oids here ... [engine_section] ... engine stuff here ... Currently there are two configuration modules. One for ASN1 objects another for ENGINE configuration.
ASN1 OBJECT CONFIGURATION MODULEThis module has the name oid_section. The value of this variable points to a section containing name value pairs of OIDs: the name is the OID short and long name, the value is the numerical form of the OID. Although some of the openssl utility sub commands already have their own ASN1 OBJECT section functionality not all do. By using the ASN1 OBJECT configuration module all the openssl utility sub commands can see the new objects as well as any compliant applications. For example: [new_oids] some_new_oid = <IP_ADDRESS> some_other_oid = <IP_ADDRESS> In OpenSSL 0.9.8 it is also possible to set the value to the long name followed by a comma and the numerical OID form. For example: shortName = some object long name, <IP_ADDRESS>
ENGINE CONFIGURATION MODULEThis ENGINE configuration module has the name engines. The value of this variable points to a section containing further ENGINE configuration information. The section pointed to by engines is a table of engine names (though see engine_id below) and further sections containing configuration information specific to each ENGINE. Each ENGINE specific section is used to set default algorithms, load dynamic, perform initialization and send ctrls. The actual operation performed depends on the command name which is the name of the name value pair. The currently supported commands are listed below. For example: [engine_section] # Configure ENGINE named "foo" foo = foo_section # Configure ENGINE named "bar" bar = bar_section [foo_section] ... foo ENGINE specific commands ... [bar_section] ... "bar" ENGINE specific commands ... The command engine_id is used to give the ENGINE name. If used this command must be first. For example: [engine_section] # This would normally handle an ENGINE named "foo" foo = foo_section [foo_section] # Override default name and use "myfoo" instead. engine_id = myfoo The command dynamic_path loads and adds an ENGINE from the given path. It is equivalent to sending the ctrls SO_PATH with the path argument followed by LIST_ADD with value 2 and LOAD to the dynamic ENGINE. If this is not the required behaviour then alternative ctrls can be sent directly to the dynamic ENGINE using ctrl commands. The command init determines whether to initialize the ENGINE. If the value is 0 the ENGINE will not be initialized, if 1 and attempt it made to initialized the ENGINE immediately. If the init command is not present then an attempt will be made to initialize the ENGINE after all commands in its section have been processed. The command default_algorithms sets the default algorithms an ENGINE will supply using the functions ENGINE_set_default_string() If the name matches none of the above command names it is assumed to be a ctrl command which is sent to the ENGINE. The value of the command is the argument to the ctrl command. If the value is the string EMPTY then no value is sent to the command. For example: [engine_section] # Configure ENGINE named "foo" foo = foo_section [foo_section] # Load engine from DSO dynamic_path = /some/path/fooengine.so # A foo specific ctrl. some_ctrl = some_value # Another ctrl that doesn't take a value. other_ctrl = EMPTY # Supply all default algorithms default_algorithms = ALL
NOTESIf a configuration file attempts to expand a variable that doesn't exist then an error is flagged and the file will not load. This can happen if an attempt is made to expand an environment variable that doesn't exist. For example in a previous version of OpenSSL the default OpenSSL master configuration file used the value of HOME which may not be defined on non Unix systems and would cause an error. This can be worked around by including a default section to provide a default value: then if the environment lookup fails the default value will be used instead. For this to work properly the default value must be defined earlier in the configuration file than the expansion. See the EXAMPLES section for an example of how to do this. If the same variable exists in the same section then all but the last value will be silently ignored. In certain circumstances such as with DNs the same field may occur multiple times. This is usually worked around by ignoring any characters before an initial . e.g. 1.OU="My first OU" 2.OU="My Second OU"
EXAMPLESHere is a sample configuration file using some of the features mentioned above. # This is the default section. HOME=/temp RANDFILE= ${ENV::HOME}/.rnd configdir=$ENV::HOME/config [ section_one ] # We are now in section one. # Quotes permit leading and trailing whitespace any = " any variable name " other = A string that can \ cover several lines \ by including \\ characters message = Hello World\n [ section_two ] greeting = $section_one::message This next example shows how to expand environment variables safely. Suppose you want a variable called tmpfile to refer to a temporary filename. The directory it is placed in can determined by the the TEMP or TMP environment variables but they may not be set to any value at all. If you just include the environment variable names and the variable doesn't exist then this will cause an error when an attempt is made to load the configuration file. By making use of the default section both values can be looked up with TEMP taking priority and /tmp used if neither is defined: TMP=/tmp # The above value is used if TMP isn't in the environment TEMP=$ENV::TMP # The above value is used if TEMP isn't in the environment tmpfile=${ENV::TEMP}/tmp.filename
BUGSCurrently there is no way to include characters using the octal \nnn form. Strings are all null terminated so nulls cannot form part of the value. The escaping isn't quite right: if you want to use sequences like \n you can't use any quote escaping on the same line. Files are loaded in a single pass. This means that an variable expansion will only work if the variables referenced are defined earlier in the file.
SEE ALSO | ||||||||||||||||||||


A browser for the discovery and retrieval of Bonjour services available on the network.
Use the Titanium.Network.createBonjourBrowser
method to create a BonjourBrowser
instance.
If your application publishes Bonjour services itself, that service will be discovered
by the browser if necessary; be prepared to perform a check if you do not want to list
local services as available. Bonjour service browsing is an asynchronous operation,
meaning that you should be extremely careful when caching values from the services
property returned by the updatedServices
event. In particular, if you maintain a
local copy of available services and a user tries to connect to one, you should be prepared
to handle failures gracefully; the next updatedServices
event should provide the new
services list, but you should not rely on it being delivered before user input. When
a window which uses Bonjour browsing is closed, if you do not want to continue searching,
you must call the stop() method.
| domain | [String] | The domain the browser is searching in | |
| isSearching | [Boolean] | Whether or not the browser is currently searching | |
| serviceType | [String] | The type of the service the browser searches for |
| updatedServices | This event has been deprecated and renamed updatedservices (lower case). Fired when the discovered services list is updated | |
| updatedservices | Fired when the discovered services list is updated |
Adds the specified callback as an event listener for the named event.
Arguments
| name | [String] | Name of the event. |
| callback | [Callback<Object>] | Callback function to invoke when the event is fired. |
Applies the properties to the proxy.
Arguments
| props | [Dictionary] | A dictionary of properties to apply. |
Fires a synthesized event to any registered listeners.
Arguments
| name | [String] | Name of the event. |
| event | [Dictionary] | A dictionary of keys and values to add to the Titanium.Event object sent to the listeners. |
Gets the value of the domain property.
Gets the value of the isSearching property.
Gets the value of the serviceType property.
Removes the specified callback as an event listener for the named event.
Arguments
| name | [String] | Name of the event. |
| callback | [Callback<Object>] | Callback function to remove. Must be the same function passed to addEventListener. |
Conduct a search for Bonjour services matching the type and domain specified during creation
Sets the value of the domain property.
Arguments
| domain | [String] | New value for the property. |
Sets the value of the isSearching property.
Arguments
| isSearching | [Boolean] | New value for the property. |
Sets the value of the serviceType property.
Arguments
| serviceType | [String] | New value for the property. |
Event properties
| services |
An array of BonjourService objects corresponding to currently available services. If you cache this value, including using it as table data, be aware that it could become out of date at any time due to the asynchronous nature of Bonjour service discovery. |
| source |
[Object] Source object that fired the event. |
| type |
[String] Name of the event fired. |
Event properties
| services |
An array of BonjourService objects corresponding to currently available services. If you cache this value, including using it as table data, be aware that it could become out of date at any time due to the asynchronous nature of Bonjour service discovery. |
| source |
[Object] Source object that fired the event. |
| type |
[String] Name of the event fired. |


https://www.luminousuk.com
The Criminal Contact application was designed and built by Luminous Development Ltd.
© Copyright Luminous Development 2019. All rights reserved.
Distributed under the Apache License 2.0.


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This popup is running on a different domain. With normal Javascript it wouldn't be able to communicate with your domain. However, with PM.js we can. Click the link below to simulate a user authentication, like Facebook and Google's authentication popup, and see the user information in the main domain.


Regularization in Regression
I would suggest you read Chapter 6 and especially section 6.2 of An Introduction to Statistical Learning to get a full treatment of this topic.
If you want to read the sources for the Lasso, check out the paper by Friedman, Hastie and Tibshirani (2010)
Why do I want to talk about this? The Lasso and regularization are a popular technique in data science today that allows you to perform both variable selection and optimized prediction in one algorithm. It also can alleviate some problems of multicollinearity between predictors. The Lasso can be applied to linear, generalized linear, generalized linear mixed models and the Cox model, and there are R packages that provide this functionality.
We will first have a look at the linear model solution and extend it.
The good ol’ (generalized) linear model
Linear regression
The standard linear regression can be written:
\[\hat y = \hat \beta_0 + \sum {\hat \beta_k x_{ik}}\]
where the terms on the right correspond to the linear predictor for the outcome (\(y\)), given the values of the predictors (\(x_k\)). The \(\hat \beta\) values are the unbiased estimates of the regression parameters, for the linear model, typically found by least squares estimation.
Generalized linear model
Extension of the linear modeling concept to non-gaussian outcomes.
Link function \(\eta\) links the mean of the outcome to a linear predictor with a nonlinear function \(\eta\)
E.G. Logistic regression -
\[log \left( \frac{p_i}{1-p_i} \right ) =\eta_i = \sum {\beta_k x_{ik}}\] To get the probability from the model, we use the inverse logit transform: \[p_i = \frac{1}{1+exp^{\eta}}\]
Model estimation
Find the parameters of the model so that the model Deviance is minimized. In the linear regression context, Deviance is the same as the Residual Squared Error or Residual Sums of Squares
\[\text{Deviance} = \sum (y_i - \sum{\hat{\beta_k x_{ik}}}) ^2 \]
The problem is when there are parameters in the model that are zero or nearly zero, the model may have higher deviance than it could if some of those parameters were not in the model.
The question is how to go about doing this?
You may have seen methods of regression subsetting via stepwise, forward or backward selection. These methods iteratively insert or remove predictor variables from the model, and in this process the models are scored via either their RSS or AIC or some other information criteria.
Here is an example where we fit a linear model and the perform variable subset selection.
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
## Warning: Number of logged events: 655
A common data science approach would be to fit a model with all predictors included, and then winnow the model to include only the significant predictors. We start with this type of model:
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
X<-scale(model.matrix(e0total~. , data=prb2))
dat<-data.frame(X[,-1])
dat$y<-prb2$e0total
fm<-glm(y~., data=dat)
summary(fm)
##
## Call:
## glm(formula = y ~ ., data = dat)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.3470 -1.0362 0.1334 0.9305 8.1069
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.95694 0.12294 552.744 < 2e-16 ***
## continentAsia 0.07720 0.20327 0.380 0.7045
## continentEurope 0.22202 0.29448 0.754 0.4519
## continentNorth.America 0.39021 0.19561 1.995 0.0475 *
## continentOceania -0.10322 0.17471 -0.591 0.5554
## continentSouth.America 0.24651 0.16210 1.521 0.1301
## population. -0.07920 0.13370 -0.592 0.5543
## cbr -6.23299 3.19702 -1.950 0.0527 .
## cdr -2.37212 1.31148 -1.809 0.0721 .
## rate.of.natural.increase 5.53259 2.88553 1.917 0.0568 .
## net.migration.rate -0.11659 0.20356 -0.573 0.5675
## imr -2.37542 0.42992 -5.525 1.12e-07 ***
## womandlifetimeriskmaternaldeath 0.06185 0.21018 0.294 0.7689
## tfr 0.77591 0.87183 0.890 0.3746
## percpoplt15 -0.97796 0.78461 -1.246 0.2142
## percpopgt65 3.02097 0.45506 6.639 3.49e-10 ***
## percurban -0.10826 0.23176 -0.467 0.6410
## percpopinurbangt750k 0.30498 0.21709 1.405 0.1618
## percpop1549hivaids2007 -1.75795 0.27465 -6.401 1.26e-09 ***
## percmarwomcontraall -0.11868 0.38931 -0.305 0.7608
## percmarwomcontramodern 0.60254 0.33495 1.799 0.0737 .
## percppundernourished0204 -0.28350 0.20518 -1.382 0.1687
## motorvehper1000pop0005 0.37047 0.31006 1.195 0.2337
## percpopwaccessimprovedwatersource 0.33456 0.24727 1.353 0.1777
## gnippppercapitausdollars 0.82764 0.35362 2.341 0.0203 *
## popdenspersqkm 0.30807 0.20080 1.534 0.1267
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 3.159121)
##
## Null deviance: 25164.61 on 208 degrees of freedom
## Residual deviance: 578.12 on 183 degrees of freedom
## AIC: 859.76
##
## Number of Fisher Scoring iterations: 2
## [1] 26
One traditional approach would then be to do some sort of variable selection, what people used to be taught was stepwise (backward or forward) elmination to obtain the best subset of predictors:
Stepwise selection model
##
## Call:
## glm(formula = y ~ continentNorth.America + continentSouth.America +
## cbr + cdr + rate.of.natural.increase + imr + percpopgt65 +
## percpopinurbangt750k + percpop1549hivaids2007 + percmarwomcontramodern +
## percpopwaccessimprovedwatersource + gnippppercapitausdollars,
## data = dat)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.5939 -1.1511 0.1894 0.9632 8.0198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.9569 0.1213 560.321 < 2e-16 ***
## continentNorth.America 0.3215 0.1300 2.473 0.0142 *
## continentSouth.America 0.2095 0.1317 1.591 0.1132
## cbr -6.2002 3.0472 -2.035 0.0432 *
## cdr -2.2039 1.2497 -1.764 0.0794 .
## rate.of.natural.increase 5.5896 2.7241 2.052 0.0415 *
## imr -2.4789 0.3761 -6.590 3.96e-10 ***
## percpopgt65 3.6290 0.3294 11.016 < 2e-16 ***
## percpopinurbangt750k 0.2849 0.1498 1.902 0.0586 .
## percpop1549hivaids2007 -1.8568 0.2070 -8.971 2.37e-16 ***
## percmarwomcontramodern 0.3689 0.1699 2.172 0.0311 *
## percpopwaccessimprovedwatersource 0.4307 0.2304 1.870 0.0630 .
## gnippppercapitausdollars 1.2547 0.1883 6.665 2.62e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 3.074258)
##
## Null deviance: 25164.61 on 208 degrees of freedom
## Residual deviance: 602.55 on 196 degrees of freedom
## AIC: 842.41
##
## Number of Fisher Scoring iterations: 2
## [1] 13
Sure enough, there are fewer predictors in the model, and those that remain have small p values.
We can also see the relative model fits of the two models:
## [1] 859.7625
## [1] 842.4147
This shows that the original model had 26 parameters, while the model that used AIC to find the best subset had 13 parameters, and the relative model fit, in terms of AIC went from 859.762467 for the saturated model to<PHONE_NUMBER> for the stepwise model.
An alternative to stepwise selection is called Best Subset Regression and considers all possible combinations of variables from the data, and scores the model based on seeing all possible predictors.
## Loading required package: leaps
yx<-data.frame(cbind(X[,-1],prb2$e0total))
b1<-bestglm(yx,IC = "AIC", family=gaussian, method = "exhaustive")
summary(b1$BestModel)
##
## Call:
## lm(formula = y ~ ., data = data.frame(Xy[, c(bestset[-1], FALSE),
## drop = FALSE], y = y))
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5939 -1.1511 0.1894 0.9632 8.0198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.9569 0.1213 560.321 < 2e-16 ***
## continentNorth.America 0.3215 0.1300 2.473 0.0142 *
## continentSouth.America 0.2095 0.1317 1.591 0.1132
## cbr -6.2002 3.0472 -2.035 0.0432 *
## cdr -2.2039 1.2497 -1.764 0.0794 .
## rate.of.natural.increase 5.5896 2.7241 2.052 0.0415 *
## imr -2.4789 0.3761 -6.590 3.96e-10 ***
## percpopgt65 3.6290 0.3294 11.016 < 2e-16 ***
## percpopinurbangt750k 0.2849 0.1498 1.902 0.0586 .
## percpop1549hivaids2007 -1.8568 0.2070 -8.971 2.37e-16 ***
## percmarwomcontramodern 0.3689 0.1699 2.172 0.0311 *
## percpopwaccessimprovedwatersource 0.4307 0.2304 1.870 0.0630 .
## gnippppercapitausdollars 1.2547 0.1883 6.665 2.62e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.753 on 196 degrees of freedom
## Multiple R-squared: 0.9761, Adjusted R-squared: 0.9746
## F-statistic: 665.8 on 12 and 196 DF, p-value: < 2.2e-16
This creates a parsimonious model, with only 13 coefficients and an AIC of<PHONE_NUMBER> which is slightly lower than the stepwise model.
Model shrinkage
Variable selection methods are one way to approach finding the most parsimonious model in an analysis, but alternative methods also exist. The modern approach to doing this is lumped under the term shrinkage methods
As opposed to the variable selection methods, shrinkage models fit a model that contains all the predictors in the data, and constrains or regularizes the coefficients so that they shrink towards 0, effectively eliminating the unnecessary parameters from the model.
There are two main classes of these methods, Ridge regression and the Lasso.
Ridge regression
Ridge regression is very similar to other regression methods, except the estimates are estimated using a slightly different objective criteria. The estimates of the model coefficient are estimates so that the quantity:
\[\text{Penalized Deviance} = \sum (y_i - \sum{\hat{\beta_k x_k}}) ^2 + \lambda \sum_k \beta_k^2 = \text{Deviance} + \lambda \sum_k \beta_k^2\] is minimized. This looks a lot like the ordinary Deviance for the models above, except it adds a penalization term to the fit criteria. The term \(\lambda\), \(\lambda \geq 0\) is a tuning parameter. The Ridge regression coefficients are those that both fit the data well, and penalize the deviance the least.
Then penalty term is small when the \(\beta\)s are close to 0. As the value of \(\lambda\) increases, the coefficients will be forced to 0. This implies another set of estimation so that the “best” value for \(\lambda\) can be found.
Unlike regular regression, which produces 1 set of regression parameters, the Ridge regression produces a set of regression parameters, each one for a given value of \(\lambda\). The best value for \(\lambda\) is found by a grid search over a range of values.
Here is an example
## Loading required package: Matrix
## Loaded glmnet 4.0-2
x<-X[,-1]
y<-as.matrix(yx[, 26])
ridgemod<-glmnet(x=x,y=y, alpha = 0, nlambda = 100)
plot(ridgemod, label = T, xvar = "lambda")
So, the y axis represents the value of the \(\beta\)’s from the model, and the x axis are the various values of \(\lambda\) for each specific value of \(\lambda\). As you see when \(\lambda\) is 0, the coefficients can be quite large, and as \(\lambda\) increase, the \(\beta\)’s converge to 0. This is nice, but we need to find a “best” value of \(\lambda\). This is done via cross-validation, typically.
##
## Call: cv.glmnet(x = x, y = y, family = "gaussian", alpha = 0)
##
## Measure: Mean-Squared Error
##
## Lambda Measure SE Nonzero
## min 0.9822 4.382 0.5652 25
## 1se 2.2690 4.908 0.4604 25
The plot shows the mean square error for the model with a particular value of log(\(\lambda\)). The dotted lines represent the “best” value and the value of \(\lambda\) that is 1 standard error larger than the true minimum.
Why the two values? Well, the minimum value of \(\lambda\), in this case about -0.0179864, and the minimum + 1se is 0.8193173. The smaller value gives the simplest model, while the 1 se value gives the simplest model that also has high accuracy.
How do the coefficient compare?
##
## Call: glmnet(x = x, y = y, alpha = 0, lambda = s1$lambda.min)
##
## Df %Dev Lambda
## 1 25 97.32 0.9822
## 25 x 1 sparse Matrix of class "dgCMatrix"
## s0
## continentAsia 0.16976947
## continentEurope 0.34553181
## continentNorth America 0.46350047
## continentOceania -0.02282180
## continentSouth America 0.27165406
## population. -0.10805054
## cbr -0.77128773
## cdr -3.19773064
## rate.of.natural.increase 0.74050874
## net.migration.rate -0.19158308
## imr -2.21869216
## womandlifetimeriskmaternaldeath 0.27651883
## tfr -0.35993995
## percpoplt15 -0.65751353
## percpopgt65 1.59794019
## percurban -0.02204929
## percpopinurbangt750k 0.36644454
## percpop1549hivaids2007 -2.34569547
## percmarwomcontraall 0.15264335
## percmarwomcontramodern 0.57816390
## percppundernourished0204 -0.34197021
## motorvehper1000pop0005 0.66058433
## percpopwaccessimprovedwatersource 0.58660140
## gnippppercapitausdollars 0.91519991
## popdenspersqkm 0.46516889
df1<-data.frame(names = names(coef(fm)) , beta=round(coef(fm),4), mod="gm")
df2<-data.frame(names = c(names(coef(fm)[1]), row.names(ridgemod2$beta)), beta=round(as.numeric(coef(s1, s = s1$lambda.min)),4), mod="ridge")
dfa<-rbind(df1, df2)
library(ggplot2)
dfa%>%
ggplot()+geom_point(aes(y=beta,x=names, color=mod))+theme_minimal()+theme(axis.text.x = element_text(angle = 45, vjust = 0.5, hjust=1))
An important note about the ridge regression is that no coefficients are forced to zero, so it is not doing variable selection, only shrinkage of the coefficients. The Lasso, on the other hand can do both.
Lasso
What is the Lasso? Lasso is short for least absolute shrinkage and selection operator. It is designed so that it produces a model that is both strong in the prediction sense, and parsimonious, in that it performs feature (variable) selection as well.
The Lasso is similar to the ridge regression model, in that it penalizes the regression parameter solution, except that the penalty term is not the sum of squared \(\beta\)’s, but the sum of the absolute values of the \(\beta\)’s.
\[ \text{Deviance} + \lambda \sum_k | \beta_k| \]
ridgemod3<-glmnet(x=x,y=y, alpha = 1) #alpha = 1 for Lasso
plot(ridgemod3, label = T, xvar = "lambda")
##
## Call: cv.glmnet(x = x, y = y, family = "gaussian", alpha = 1)
##
## Measure: Mean-Squared Error
##
## Lambda Measure SE Nonzero
## min 0.0646 3.731 0.6382 15
## 1se 0.4559 4.352 0.7667 10
##
## Call: glmnet(x = x, y = y, family = "gaussian", alpha = 1, lambda = s2$lambda.1se)
##
## Df %Dev Lambda
## 1 10 96.97 0.4559
## 25 x 1 sparse Matrix of class "dgCMatrix"
## s0
## continentAsia .
## continentEurope .
## continentNorth America .
## continentOceania .
## continentSouth America .
## population. .
## cbr .
## cdr -4.11173283
## rate.of.natural.increase .
## net.migration.rate .
## imr -3.13251642
## womandlifetimeriskmaternaldeath .
## tfr .
## percpoplt15 -0.25132019
## percpopgt65 2.81422569
## percurban .
## percpopinurbangt750k 0.10711580
## percpop1549hivaids2007 -1.78945838
## percmarwomcontraall .
## percmarwomcontramodern 0.20523750
## percppundernourished0204 .
## motorvehper1000pop0005 0.03841647
## percpopwaccessimprovedwatersource 0.33401182
## gnippppercapitausdollars 1.06967019
## popdenspersqkm .
Elastic net
A third method, the Elastic net regression, blends the shrinkage aspects of the ridge regression with the feature selection of the Lasso. This was proposed by Zou and Hastie 2005
\[\text{Deviance} + \lambda [(1-\alpha) \sum_k |\beta_k| + \alpha \sum_k \beta_k^2]\]
ridgemod4<-glmnet(x=x,y=y, alpha = .5, nlambda = 100) #alpha = .5 for elastic net
plot(ridgemod4, label = T, xvar = "lambda")
##
## Call: cv.glmnet(x = x, y = y, family = "gaussian", alpha = 0.5)
##
## Measure: Mean-Squared Error
##
## Lambda Measure SE Nonzero
## min 0.1292 3.593 0.5248 16
## 1se 0.6284 4.037 0.5181 12
## 25 x 1 sparse Matrix of class "dgCMatrix"
## s0
## continentAsia .
## continentEurope .
## continentNorth America 0.05233114
## continentOceania .
## continentSouth America .
## population. .
## cbr -0.22571539
## cdr -3.79036104
## rate.of.natural.increase .
## net.migration.rate .
## imr -2.84336643
## womandlifetimeriskmaternaldeath .
## tfr .
## percpoplt15 -0.46055079
## percpopgt65 2.31578751
## percurban .
## percpopinurbangt750k 0.23562128
## percpop1549hivaids2007 -2.06460379
## percmarwomcontraall .
## percmarwomcontramodern 0.35690946
## percppundernourished0204 .
## motorvehper1000pop0005 0.28068647
## percpopwaccessimprovedwatersource 0.52328787
## gnippppercapitausdollars 0.99759091
## popdenspersqkm .
In these examples, we will use the Demographic and Health Survey Model Data. These are based on the DHS survey, but are publicly available and are used to practice using the DHS data sets, but don’t represent a real country.
In this example, we will use the outcome of contraceptive choice (modern vs other/none) as our outcome. An excellent guide for this type of literature is this article
library(haven)
dat<-url("https://github.com/coreysparks/data/blob/master/ZZIR62FL.DTA?raw=true")
model.dat<-read_dta(dat)
Here we recode some of our variables and limit our data to those women who are not currently pregnant and who are sexually active.
library(dplyr)
model.dat2<-model.dat%>%
mutate(region = v024,
modcontra= ifelse(v364 ==1,1, 0),
age = cut(v012, breaks = 5),
livchildren=v218,
educ = v106,
currpreg=v213,
wealth = as.factor(v190),
partnered = ifelse(v701<=1, 0, 1),
work = ifelse(v731%in%c(0,1), 0, 1),
knowmodern=ifelse(v301==3, 1, 0),
age2=v012^2,
rural = ifelse(v025==2, 1,0),
wantmore = ifelse(v605%in%c(1,2), 1, 0))%>%
filter(currpreg==0, v536>0, v701!=9)%>% #notpreg, sex active
dplyr::select(caseid, region, modcontra,age, age2,livchildren, educ, knowmodern, rural, wantmore, partnered,wealth, work)
| caseid | region | modcontra | age | age2 | livchildren | educ | knowmodern | rural | wantmore | partnered | wealth | work |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 1 2 | 2 | 0 | (28.6,35.4] | 900 | 4 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
| 1 4 2 | 2 | 0 | (35.4,42.2] | 1764 | 2 | 0 | 1 | 1 | 0 | 0 | 3 | 1 |
| 1 4 3 | 2 | 0 | (21.8,28.6] | 625 | 3 | 1 | 1 | 1 | 0 | 0 | 3 | 1 |
| 1 5 1 | 2 | 0 | (21.8,28.6] | 625 | 2 | 2 | 1 | 1 | 1 | 0 | 2 | 1 |
| 1 6 2 | 2 | 0 | (35.4,42.2] | 1369 | 2 | 0 | 1 | 1 | 1 | 0 | 3 | 1 |
| 1 7 2 | 2 | 0 | (15,21.8] | 441 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
## Loading required package: lattice
set.seed(1115)
train<- createDataPartition(y = model.dat2$modcontra , p = .80, list=F)
dtrain<-model.dat2[train,]
## Warning: The `i` argument of ``[`()` can't be a matrix as of tibble 3.0.0.
## Convert to a vector.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.
Logistic regression
library(glmnet)
library(MASS)
fm<-glm(modcontra~region+factor(age)+livchildren+wantmore+rural+factor(educ)+partnered+work+wealth, data = dtrain, family=binomial)
summary(fm)
##
## Call:
## glm(formula = modcontra ~ region + factor(age) + livchildren +
## wantmore + rural + factor(educ) + partnered + work + wealth,
## family = binomial, data = dtrain)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3727 -0.6498 -0.4970 -0.3590 2.5673
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.80866 0.26506 -10.596 < 0.0000000000000002 ***
## region 0.15475 0.03772 4.103 0.000040825388 ***
## factor(age)(21.8,28.6] 0.44413 0.18439 2.409 0.01601 *
## factor(age)(28.6,35.4] 0.54804 0.19226 2.850 0.00437 **
## factor(age)(35.4,42.2] 0.14667 0.20988 0.699 0.48468
## factor(age)(42.2,49] -0.63063 0.23623 -2.670 0.00760 **
## livchildren 0.18805 0.02976 6.318 0.000000000264 ***
## wantmore -0.16630 0.10204 -1.630 0.10316
## rural -0.62567 0.11323 -5.525 0.000000032859 ***
## factor(educ)1 0.30769 0.13045 2.359 0.01834 *
## factor(educ)2 0.59775 0.13288 4.498 0.000006849378 ***
## factor(educ)3 0.62670 0.24653 2.542 0.01102 *
## partnered 0.28746 0.10467 2.746 0.00603 **
## work 0.16342 0.10386 1.573 0.11561
## wealth2 0.13635 0.14047 0.971 0.33170
## wealth3 0.17350 0.14114 1.229 0.21898
## wealth4 0.24257 0.15013 1.616 0.10614
## wealth5 0.17383 0.18138 0.958 0.33786
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3818.3 on 4128 degrees of freedom
## Residual deviance: 3536.4 on 4111 degrees of freedom
## AIC: 3572.4
##
## Number of Fisher Scoring iterations: 5
stepwise logistic
## Start: AIC=3572.39
## modcontra ~ region + factor(age) + livchildren + wantmore + rural +
## factor(educ) + partnered + work + wealth
##
## Df Deviance AIC
## - wealth 4 3539.2 3567.2
## <none> 3536.4 3572.4
## - work 1 3538.9 3572.9
## - wantmore 1 3539.0 3573.0
## - partnered 1 3543.8 3577.8
## - region 1 3553.0 3587.0
## - factor(educ) 3 3559.4 3589.4
## - rural 1 3566.7 3600.7
## - livchildren 1 3577.1 3611.1
## - factor(age) 4 3609.4 3637.4
##
## Step: AIC=3567.21
## modcontra ~ region + factor(age) + livchildren + wantmore + rural +
## factor(educ) + partnered + work
##
## Df Deviance AIC
## <none> 3539.2 3567.2
## - work 1 3541.7 3567.7
## - wantmore 1 3541.8 3567.8
## + wealth 4 3536.4 3572.4
## - partnered 1 3547.9 3573.9
## - region 1 3555.0 3581.0
## - factor(educ) 3 3564.0 3586.0
## - livchildren 1 3579.4 3605.4
## - rural 1 3590.0 3616.0
## - factor(age) 4 3611.8 3631.8
## (Intercept) region factor(age)(21.8,28.6]
## -2.6270672 0.1501583 0.4524232
## factor(age)(28.6,35.4] factor(age)(35.4,42.2] factor(age)(42.2,49]
## 0.5612389 0.1621533 -0.6103720
## livchildren wantmore rural
## 0.1861566 -0.1651203 -0.6915328
## factor(educ)1 factor(educ)2 factor(educ)3
## 0.3178917 0.6052986 0.6167321
## partnered work
## 0.3043424 0.1621220
Best subset regression
y<-dtrain$modcontra
x<-model.matrix(~factor(region)+factor(age)+livchildren+rural+wantmore+factor(educ)+partnered+work+factor(wealth), data=dtrain)
x<-(x)[,-1]
yx<-as.data.frame(cbind(x[,-1],y))
names(yx)
## [1] "factor(region)3" "factor(region)4" "factor(age)(21.8,28.6]"
## [4] "factor(age)(28.6,35.4]" "factor(age)(35.4,42.2]" "factor(age)(42.2,49]"
## [7] "livchildren" "rural" "wantmore"
## [10] "factor(educ)1" "factor(educ)2" "factor(educ)3"
## [13] "partnered" "work" "factor(wealth)2"
## [16] "factor(wealth)3" "factor(wealth)4" "factor(wealth)5"
## [19] "y"
Logistic ridge regression
## 19 x 1 sparse Matrix of class "dgCMatrix"
## s0
## factor(region)2 0.11736906
## factor(region)3 0.20097363
## factor(region)4 0.15952400
## factor(age)(21.8,28.6] 0.07831211
## factor(age)(28.6,35.4] 0.23721168
## factor(age)(35.4,42.2] 0.06382724
## factor(age)(42.2,49] -0.27968879
## livchildren 0.06545045
## rural -0.33722253
## wantmore -0.09296988
## factor(educ)1 0.13004018
## factor(educ)2 0.27349312
## factor(educ)3 0.28825836
## partnered 0.22401406
## work 0.06631462
## factor(wealth)2 -0.02330795
## factor(wealth)3 0.00422731
## factor(wealth)4 0.13902383
## factor(wealth)5 0.16285245
Logistic Lasso
## 19 x 1 sparse Matrix of class "dgCMatrix"
## s0
## factor(region)2 .
## factor(region)3 0.04882613
## factor(region)4 .
## factor(age)(21.8,28.6] .
## factor(age)(28.6,35.4] 0.17720355
## factor(age)(35.4,42.2] .
## factor(age)(42.2,49] -0.37140425
## livchildren 0.09635800
## rural -0.62095437
## wantmore .
## factor(educ)1 .
## factor(educ)2 0.20666302
## factor(educ)3 .
## partnered 0.26927535
## work .
## factor(wealth)2 .
## factor(wealth)3 .
## factor(wealth)4 .
## factor(wealth)5 .
classification results
Regular GLM
probabilities <- fm %>% predict(dtest, type = "response")
predicted.classes <- ifelse(probabilities > mean(dtest$modcontra, na.rm=T), 1, 0)
# Prediction accuracy
observed.classes <- dtest$modcontra
mean(predicted.classes == observed.classes, na.rm=T)
## [1] 0.6889535
## observed.classes
## predicted.classes 0 1
## 0 605 111
## 1 210 106
stepwise logistic model
probabilities <- predict(smod, dtest, type = "response")
predicted.classes <- ifelse(probabilities > mean(dtest$modcontra, na.rm=T), 1, 0)
# Prediction accuracy
observed.classes <- dtest$modcontra
mean(predicted.classes == observed.classes)
## [1] 0.6860465
## observed.classes
## predicted.classes 0 1
## 0 605 114
## 1 210 103
Logistic ridge regression
x.test <- model.matrix(~factor(region)+factor(age)+livchildren+rural+wantmore+factor(educ)+partnered+work+factor(wealth), data=dtest)
x.test<-(x.test)[,-1]
ytest<-dtrain$modcontra
probabilities <- predict(object=rmod1, newx = x.test, s=s1$lambda.1se, type="response")
predicted.classes <- ifelse(probabilities > mean(dtest$modcontra), 1,0)
# Model accuracy
observed.classes <- dtest$modcontra
mean(predicted.classes == observed.classes)
## [1] 0.7131783
## observed.classes
## predicted.classes 0 1
## 0 646 127
## 1 169 90
Logistic Lasso
probabilities <- predict(object=rmod3, newx = x.test, s=s2$lambda.1se, type="response")
predicted.classes <- ifelse(probabilities > mean(dtest$modcontra), 1,0)
# Model accuracy
observed.classes <- dtest$modcontra
mean(predicted.classes == observed.classes)
## [1] 0.6879845
## observed.classes
## predicted.classes 0 1
## 0 611 118
## 1 204 99
So what?
By doing any type of regression variable selection, you are going to have the computer tell you what variables are going into your models. A lot of people don’t like this, but it is very common in the applied world in order to build the best models, especially in high-dimensional data.
Take aways
- These methods will lead to more parsimonius models with better predictive power
- The models are sensitive to their tuning parameters, so please don’t jump into this without tuning the model parameters.


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Audio Engineer | Aspiring Web Developer | Musician
A native of Northeast Ohio, Matthew was born, raised, and attended highschool in the Cleveland area.
He then went on to earn a B.S. in Sound Recording Technology from the DePaul University School of Music in Chicago, IL.
He currently resides in the Cleveland area, studying through the Free Code Camp program in hopes of developing marketable Front End and Back End development skills, while still maintaining his roots to music and audio recording.
To get in touch with Matthew, feel free to visit the Contact portion of this page, and get in touch through any of his various outlets.
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| string$ = any valid string variable |
| This will let you determine the length (number of letters, spaces, characters, numbers, etc) inside a string. You can use this to ensure the player enters the right number of letters (like 3 letters for a high score table). Quite useful for 'string parsing' with other commands. |
|
name$="Shane Monroe"
Print "There are " + Len(name$) + " characters in your name!" |


Analysis of Epidemic Data
Existing Tools and Methods
Existing literature:
Mainly 3 categories
-
Individual Based Models
-
Mean Field Models
-
Based on Branching process, Birth-Death process
Another type: Analysing network / graph structure (for contact tracing data)
A social network analysis of the spread of COVID-19 in South Korea and policy implications (Nature, April'21)
Objective: Creating an infection network and analysing its structural characteristics.
Data: 3283 patients, January'20 - July'20
For all patients, sources were categorized as personal (972), group (869), overseas (748), unknown (694)
Analysis methods
-
Network analysis
-
Distribution of out-degree
-
Structural changes after removal of nodes
1. Network Analysis
-
Computation of out-degree of each node
-
Mean distance of network
-
Diameter of network
2. Distribution of out-degree
Power-law distribution was fitted on out-degrees. Fitted distribution:
$p\left(x\right)\propto {x}^{-2.70923}$
2. Distribution of out-degree
Hypothesis testing: Power-law against Log-normal, Exponential, Poisson
Using Likelihood-Ratio test, only Log-normal was accepted. Exponenial, Poisson strongly rejected.
3. Network structure change depending on time and policy
Removal of nodes of high-degree and observing how the previously defined measures change.
Out-degree values are: (51, 25, 21, 18, 17, 16, 13, 11, 10, 8, 7, 6, 5, 4, 3, 2, 1)
Regarding partial observed network:
-
Clustering Partially Observed Graphs via Convex Optimization (2014) ..
-
Bayesian analysis for partially observed network data, missing ties, attributes and actors (2013) ..
Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing (Science, 2020)
Detailed analysis on:
Incubation period (Log-normal distribution)
Generation time (Using data on onset of symptoms, exposure time, reporting time and contact)
Posterior probability that transmission was presymptomatic (same data as above)
Infectiousness as a function of time and its decomposition
Modelling and predicting the spatio-temporal spread of COVID-19 in Italy (2020)
Objective: Analyse the diffusion of COVID-19 in Italy, and find spatial and temporal effects
Data: 26th Feb - 31st May'20, 96 days, Cases in Italy
Model: Spatial Generalised Linear Mixed Models (SGLMM)
$Y_{r,t}=$ number of cases in region r on day t, modelled using Negative Binomial, conditional on previous cases
Mean $\mu_{r,t}$ and dispersion $\psi_r$
Mean is decomposed into three parts:
-
Epidemic-within
-
Epidemic-between
-
Endemic
On Identifying and Mitigating Bias in the Estimation of the COVID-19 Case Fatality Rate (2021)


I'm a sports addict, both watching and playing. I swim, run, play football on the weekends, and am training for a marathon. Although it is difficult, I remain an avid Bengals and Reds fan.
Live a block off of Green Lake.
Works part time for Luxe Valet (see me if you want a day of free on-demand valet parking downtown!).


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"use strict";
import {EventManager} from "./EventManager.js";
import {WindowMessage} from "./WindowMessage.js";
/**
* Windows sesstion client is used to store the status of a inter window communication process.
*
* Stores information about the other window e.g. (identification, status etc).
*
* @class
*/
function WindowSession(manager)
{
/**
* The manager attached to this session.
*
* @type {WindowManager}
*/
this.manager = manager;
/**
* Window object of this client, is not always the actual window, but it is the window that contains (directly or indirectly) access to the destination.
*
* The window object is used as a point of communcation. Depending of security configurations the access may be restricted.
*
* @type {Object}
*/
this.window = null;
/**
* URL of the other window.
*
* Only available for windows that were open direclty, for wich a URL is known.
*
* @type {String}
*/
this.url = "";
/**
* UUID to identify the other window.
*
* @type {String}
*/
this.uuid = null;
/**
* Textual type indicator of the other window, used to indetify the type of the other window.
*
* (e.g. "3D", "Main", etc)
*
* @type {String}
*/
this.type = null;
/**
* Counter of messages exchanged between the sessions.
*
* Increased everytime a message is sent.
*
* @type {Number}
*/
this.counter = 0;
/**
* The session object that is used as gateway for this session.
*
* When directly connected to the other window has a null value.
*
* @type {WindowSession}
*/
this.gateway = null;
/**
* Status of the communication.
*
* @type {String}
*/
this.status = WindowSession.WAITING;
/**
* List of all messages received.
*
* Stored the original WindowMessage object contains information about the window of origin and authentication data.
*
* @type {Array}
*/
this.received = [];
/**
* Messages waiting to be sent.
*
* When the status is set to WAITING the messages are held here until it gets to READY status.
*
* @type {Array}
*/
this.queue = [];
/**
* Domains allowed for this session messages.
*
* @type {String}
*/
this.allowdomain = "*";
/**
* On message callback, receives data and authentication as parameters.
*
* Called when a normal message is received from another window, onMessage(data, authentication).
*
* @type {Function}
*/
this.onMessage = null;
/**
* On broadcast message callback, receives data and authentication as parameters.
*
* Called when a broadcast message arrives, onBroadcastMessage(data, authentication).
*
* @type {Function}
*/
this.onBroadcastMessage = null;
/**
* On ready callback, called when the session enters the CLOSED state.
*
* This callback does not receive any parameter.
*
* @type {Function}
*/
this.onClosed = null;
/**
* On ready callback, called when the session enters the READY state.
*
* This callback does not receive any parameter.
*
* @type {Function}
*/
this.onReady = null;
}
/**
* WAITING status means that the window is open but the ready message was not received.
*
* While the window is waiting all messages are stored in a queue waiting for a ready message.
*
* @static
* @attribute {Number}
*/
WindowSession.WAITING = 101;
/**
* READY status means that the window is ready to receive data.
*
* The message gets READY when it receives an ready message from the peer window.
*
* Messages sent before reaching READY state are queued and send only after the session reaches this state.
*
* @static
* @attribute {Number}
*/
WindowSession.READY = 102;
/**
* CLOSED status means that the other window is not available.
*
* @static
* @attribute {Number}
*/
WindowSession.CLOSED = 103;
/**
* Set the status of the window.
*
* Ensures the correct order of the status being set.
*
* @param {Number} status
*/
WindowSession.prototype.setStatus = function(status)
{
if(status <= this.status)
{
console.warn("TabTalk: Invalid status cannot go from " + this.status + " to " + status + ".");
return;
}
this.status = status;
if(this.status === WindowSession.READY)
{
if(this.queue.length > 0)
{
console.warn("TabTalk: Sending queued messages.", this.queue);
}
//Send all queued waiting message
for(var i = 0; i < this.queue.length; i++)
{
var message = this.queue[i];
message.destinationUUID = this.uuid;
this.send(message);
}
this.queue = [];
if(this.onReady !== null)
{
this.onReady();
}
}
else if(this.status === WindowSession.CLOSED)
{
if(this.onClose != null)
{
this.onClose();
}
}
};
/**
* Post data to another window, windows references are stored using their url for later usage.
*
* If the window is unknonwn the opener window is used if available.
*
* @param {String} action Name of the action of this message.
* @param {Object} data Data to be sent (Optional).
* @param {String} authentication Authentication information (Optional).
*/
WindowSession.prototype.send = function(message)
{
if(this.status === WindowSession.CLOSED)
{
console.warn("TabTalk: Session in is closed state, its not possible to send data.", this, message);
return;
}
if(this.window !== null)
{
this.window.postMessage(message, this.allowdomain);
console.log("TabTalk: Sent message.", message);
}
else if(this.gateway !== null)
{
console.log("TabTalk: Message passed to gateway.", message);
this.gateway.send(message);
}
else
{
console.warn("TabTalk: Session has no window attached.");
return;
}
};
/**
* Send a message to another window, if the session is in WAITING status the message will be queued to be send later.
*
* @param {Object} data Data to be sent (Optional).
* @param {String} authentication Authentication information (Optional).
*/
WindowSession.prototype.sendMessage = function(data, authentication)
{
var message = new WindowMessage(this.counter++, WindowMessage.MESSAGE, this.manager.type, this.manager.uuid, this.type, this.uuid, data, authentication);
if(this.status === WindowSession.WAITING)
{
this.queue.push(message);
console.log("TabTalk: Still on waiting status message was queued.", message);
}
else
{
this.send(message);
}
}
/**
* Close this session, send a close message and is possible close the window.
*
* @param {Boolean} closeWindow If set true the session window will be closed (if possible).
*/
WindowSession.prototype.close = function(closeWindow)
{
var message = new WindowMessage(this.counter++, WindowMessage.CLOSED, this.manager.type, this.manager.uuid, this.type, this.uuid);
this.send(message);
if(closeWindow === true && this.window !== null)
{
this.window.close();
}
};
/**
* Send a message to indicate that this session is READY.
*
* Also sends the session metadata for the remote window.
*/
WindowSession.prototype.acknowledge = function()
{
if(this.uuid !== null)
{
this.send(new WindowMessage(this.counter++, WindowMessage.READY, this.manager.type, this.manager.uuid, this.type, this.uuid));
}
else
{
this.send(new WindowMessage(this.counter++, WindowMessage.READY, this.manager.type, this.manager.uuid));
}
};
/**
* Used to indicate the connection intent to remote windows after a positive lookup response.
*
* Works similarly to the ready message.
*/
WindowSession.prototype.connect = function()
{
this.send(new WindowMessage(this.counter++, WindowMessage.CONNECT, this.manager.type, this.manager.uuid, this.type, this.uuid));
};
/**
* Wait for this window to be ready.
*
* When a window is ready it should send a message containing a action property set to WindowMessage.READY.
*
* @param {Function} onReady Callback called when the winow is ready.
*/
WindowSession.prototype.waitReady = function()
{
var self = this;
console.log("TabTalk: Waiting for a ready message.");
var manager = new EventManager();
manager.add(window, "message", function(event)
{
//Ready events can only come from direct messages
if(event.source !== self.window && self.window !== null)
{
console.log("TabTalk: Event from diferent window.", event);
return;
}
var data = event.data;
if(data.action === WindowMessage.READY)
{
console.log("TabTalk: Received ready message.", data, event);
self.type = data.originType;
self.uuid = data.originUUID;
self.manager.sessions[self.uuid] = self;
self.acknowledge();
self.setStatus(WindowSession.READY);
manager.destroy();
}
else
{
console.warn("TabTalk: Not a ready message, waiting for ready.", data, event);
}
});
manager.create();
};
export {WindowSession};


--- layout: default permalink: 404.html title: 404 - Page not found ---
Oops. Seems like the page you're looking for doesn't exist anymore...
Have a look at my recent content and you might get surprised!


Ray data structure. More...
#include <ai_ray.h>
Data Fields | |
| AtUInt16 | type |
Type of ray (AI_RAY_CAMERA , etc) | |
| AtByte | tid |
| Thread ID. | |
| AtByte | level |
| Recursion level (0 for camera rays) | |
| AtByte | diff_bounces |
| Number of diffuse bounces so far. | |
| AtByte | gloss_bounces |
| Number of glossy bounces so far. | |
| AtByte | refl_bounces |
| Number of reflection bounces so far. | |
| AtByte | refr_bounces |
| Number of refraction bounces so far. | |
| int | x |
| Raster-space X coordinate. | |
| int | y |
| Raster-space Y coordinate. | |
| float | sx |
| Image-space X coordinate, in [-1,1) | |
| float | sy |
| Image-space Y coordinate, in [-1,1) | |
| float | px |
| Subpixel X coordinate in [0,1) | |
| float | py |
| Subpixel Y coordinate in [0,1) | |
| AtPoint | origin |
| Ray origin. | |
| AtVector | dir |
| Unit ray direction. | |
| double | mindist |
| Minimum useful distance from the origin. | |
| double | maxdist |
| Maximum useful distance from the origin (volatile while ray is traced) | |
| const AtShaderGlobals * | psg |
| Parent shader globals (last shaded) | |
| void * | light_source |
| For shadow rays only. | |
| AtBucket * | bucket |
| Parent bucket. | |
| float | weight |
| Ray weight, 1.0 for clean camera rays. | |
| float | time |
| Time at which the ray was created, in [0,1) | |
| AtVector | dOdx |
| Partial derivative of ray origin wrt image-space X coordinate. | |
| AtVector | dOdy |
| Partial derivative of ray origin wrt image-space Y coordinate. | |
| AtVector | dDdx |
| Partial derivative of ray direction wrt image-space X coordinate. | |
| AtVector | dDdy |
| Partial derivative of ray direction wrt image-space Y coordinate. | |
| AtString | traceset |
| Trace-set for this ray. More... | |
| bool | inclusive_traceset |
| Is the trace-set inclusive or exclusive? | |
| AtUInt16 | sindex |
| Sub-pixel sample index when supersampling. | |
Ray data structure.
| AtString AtRay::traceset |
Trace-set for this ray.


The following icons are used across our websites, not the applications itself. The application icons will be covered in the Product Design guidelines.
extend your class with #{$icon-prefix}__fixed-width to set icons at a fixed width. Great to use when different icon widths throw off alignment. Especially useful in things like nav lists & list groups.
| Html | |
|---|---|
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
|
| Sass | |
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 |
|
To stack multiple icons, use the #{$icon-prefix}-stack class on the parent, the #{$icon-prefix}-stack-1x for the regularly sized icon, and #{$icon-prefix}-stack-2x for the larger icon. You can even throw larger icon classes on the parent to get further control of sizing.
| Html | |
|---|---|
| 1 2 3 4 |
|
| Sass | |
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
|
Use the #{$icon-prefix}-spin class to get any icon to rotate, and use #{$icon-prefix}-pulse to have it rotate with 8 steps. Works well with spiiner icons.
| Html | |
|---|---|
| 1 2 |
|
| Scss | |
| 1 2 3 4 5 6 7 8 9 10 |
|


We eliminate the guesswork and complexity, so you can be up and running in a few hours.
Security that works with your business
Do it right at the start.
Leverage our platform to build cryptographically sound applications from day one.
Do it right for your customers.
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Leverage out expertise, so you can spend your time on building new products and features.
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Encryption is on hand so your developers can focus their skills on your products and applications getting to market faster vs. spending weeks of precious time and energy engineering data encryption and privacy capabilities.
"Encryption is a proven partner; delivering strong data protection at the fast speeds that our public satefy, law enforcement and ilitary team require."Download Case StudyJeffrey Schweitzer, Asymmetrical Solution Architect, Verizon
We build our APIs to be simple to use, powerful in production, and effortlessly scalable. Because we eliminate needless complexity and rrelevant details, you can quickly enable data encryption and privacy into your application.
We believe data encryption and privacy is a problem rooted (and best solved)in code, not ineffective infrastructure-based security controls. Raise the bar for security and mitigate the risk of today's threads.


For the children and families who’ve come through the clinic, it’s very, very hard to find country conditions materials. Worse, they’ve scarcely a prayer of fling these in a format that comports with the 258-page
Immigration Court Practice Manual. The Child Refugee Network is determined to hand each principal applicant three copies of a pre-fab packet of reports and articles relevant to their asylum claim. Volunteers needn’t be
bilingual, and needn’t be lawyers. Their work could make a big difference.
Please write Paul Zoltan,
<EMAIL_ADDRESS>if you’d be interested in collaborating in the research and compilation of documents relating to gangs, domestic violence and LGBT
rights.


We meet at 7:00pm every first and third Wednesday to solve problems together with Ruby.
IZEA Winter Park Office
480 N. Orlando Avenue, Winter Park, FL 32789
https://github.com/orlandorubydojo