text:
# [XeTeX] dealing with \$ character

Bruce D'Arcus bdarcus at fastmail.fm
Wed Jul 7 19:13:23 CEST 2004

On Jul 7, 2004, at 12:08 PM, Hans Hagen wrote:

>> Following from previous discussion, is there a way that I can get TeX
>> to accept the \$ character without having to do \\$?  My source is XML,
>> so it's not convenient to modify there, or in the XSLT.
>
> \catcode`\\$=12

Thanks Hans, but this -- in the preamble -- doesn't seem to work.  Is
there something else I need to do?

I just want to be able to typeset "\$4000".

Bruce


text:
# Browsing by Title

Sort by: Order: Results:

• (1997)
reviews the two main avenues for teaching chemical information to undergraduate students: in a dedicated course or integrated into existing chemistry courses or laboratories
• (2012-05-07)
• (2013-11-05)
Scholars are increasingly incorporating social media tools like blogs, Twitter and Mendeley into their professional communications. Altmetrics tracks usage of these and similar tools to measure scholarly influence on the ...
• (Information Today, Inc., 2013-07)
The number of academic articles published annually has risen exponentially in the past decade, making our jobs as librarians ever more challenging as we assist patrons in finding exactly what it is that they are looking ...
• (2012-10-07)
In a university culture increasingly influenced by metrics, academic libraries can use altmetrics to highlight scholarship’s hidden value. This session will cover the apps and services that can help faculty, administration, ...
• (1992-06-02)
It has been proposed that different drinking norms developed in northern and southern Europe during antiquity and that these patterns are still found today in the cultures overlying these areas. In terms of western European ...
• (Department of Folklore and Ethnomusicology, Indiana University, 1973-10)
• (Department of Folklore and Ethnomusicology, Indiana University, 1983)
• (Department of Folklore and Ethnomusicology, Indiana University, 1976-12)
• ([Bloomington, Ind.] : Indiana University, 2016-05)
A qualitative investigation into American Muslim undergraduates' views on evolution revealed three main positions on evolution: theistic evolution, a belief in special creation of all species, and a belief in special ...
• (Department of Folklore and Ethnomusicology, Indiana University, 1970)
• (American Folklore Society, 2004-10-15)
Américo Paredes became known as the leading scholar of Mexican-American studies on the strength of his classic 1958 study of the balladry of Greater Mexico, "With His Pistol in His Hand." The emerging Chicano ethno-nationalist ...
• (Department of Folklore and Ethnomusicology, Indiana University, 1974-04)
• (Department of Folklore and Ethnomusicology, Indiana University, 1974-04)
• (American Physical Society, 2012)
We construct an analytical model for two-channel, two-body scattering amplitudes, and then apply it in the description of the three-body $J/ψ→K^+K^−π^0$ decay. In the construction of the partial wave amplitudes, we combine ...

format: plain


text:
Comparing Box-Muller and Marsaglia-Bray

In the last post we reviewed two simple methods to simulate samples from a pair of independent normal random variables: Box-Muller and Marsaglia-Bray. In this post we are going to compare the performance of our implementation of such methods.

Introduction

import math
import numpy as np
from numpy import pi

def box_muller_sample(n=1):

u1 = np.random.rand(n)
u2 = np.random.rand(n)

r = np.sqrt(-2*np.log(u1))
x = np.cos(2*pi*u2)
y = np.sin(2*pi*u2)
z1 = r*x
z2 = r*y

return z1, z2

def marsaglia_sample(n=1):

def marsaglia():

while True:

w1 = (np.random.rand() * 2) - 1
w2 = (np.random.rand() * 2) - 1
s = w1 * w1 + w2 * w2

if s < 1:

t = math.sqrt((-2) * math.log(s)/s)
z1 = w1 * t
z2 = w2 * t

return z1, z2

z1 = np.empty(n)
z2 = np.empty(n)

for i in range(n):
z1[i], z2[i] = marsaglia()

return z1, z2

To compare their performance we generate 1000 samples of size $n=100000$ and look at the average time for this task.

import time
t = 0
for _ in range(1000):

start = time.time()
box_muller_sample(100000)
end = time.time()
t = t + (end - start)

print('The Box-Muller Function simulates a sample of size n=100000 on an average of {:.6f} seconds'.format(t/1000))
The Box-Muller Function simulates a sample of size n=100000
on an average of 0.002097 seconds
t = 0
for _ in range(1000):

start = time.time()
marsaglia_sample(100000)
end = time.time()
t = t + (end - start)

print('The Box-Muller Function simulates a sample of size n=100000 on an average of {:.6f} seconds'.format(t/1000))
The Box-Muller Function simulates a sample of size n=100000
on an average of 0.148888 seconds

Note that Box-Muller functions is much faster than the Marsaglia’s one despite using trigonometric functions.

First Improvement – Marsaglia 1.1

We can try to improve our Marsaglia function by using numpy vector functions where possible.

def marsaglia_sample_vectorial(n=1):

def marsaglia():

while True:

w1 = (random.rand() * 2) - 1
w2 = (random.rand() * 2) - 1

if w1 * w1 + w2 * w2 < 1:

return w1, w2

w1 = np.empty(n)
w2 = np.empty(n)

for i in range(n):

w1[i], w2[i] = marsaglia()

s = w1*w1 + w2*w2
t = np.sqrt(-2*np.divide(np.log(s), s))
z1 = w1*t
z2 = w2*t

return z1, z2
The Vectorial version of the Box-Muller Function simulates a sample
of size n=100000 on an average of 0.120829 seconds

The new Marsaglia function is faster than the original one but still much slower compared to the Box-Muller’s one. This is partly due to the accept-reject process that takes place within the while loop where we discard those samples which are outside the unit circle. Let’s analyse the accept/reject process that happens in the loop.

Understanding the Accept-Reject Method

First, observe that the acceptance probability is

$$p = \mathbb{P}(w_1^2 + w_2^2 < 1) = \frac{\pi}{4} \approx 0.7854$$

since $(w_1, w_2)$ are uniformly distributed on a square of area 4.

Thus to avoid the loop we need to find the minimum points $N\geq n$ that we need to simulate in order to guarantee –with high probability– that we will accept at least $n$ points. Formally, for a given number of simulations $N$ consider $S$ the number of accepted points, i.e.

$$S = \#\{ (w_1, w_2) : s = w_1^2 + w_2^2 \leq 1 \}.$$

Clearly, $S$ follows a Binomial distribution with parameters $(N,p)$ with $p=\pi/4$. So, the probability of accepting at least $n$ points is given by

$$\mathbb{P}(S\geq n) = 1 – \mathbb{P}(S\leq n) = 1 – \sum_{k=0}^{n} \binom{N}{k}p^{k}(1-p)^{N-k}.$$

Using the Normal approximation we obtain

$$\mathbb{P}(S\geq n) \approx \mathbb{P}(Z\geq n) = 1- \mathbb{P}(Z\leq n),$$

where $Z \sim \mathcal{N}(Np, \sqrt{Np(1-p)}$. We can write a Python function which calculates such probability for any given $n$ and $N$.

def calculate_probability(n, N):

p = pi/4
mu = N*p
sigma = np.sqrt(N*p*(1-p))
prob =  1 - norm.cdf(n, mu, sigma)

return prob

Let’s visualise this function for $n=100$ and varying the total number of simulations $N$ from 100 to 200:

Similarly, if $n=1000$ and $N$ varies from 1000 to 2000 we obtain:

These graphs show that the probability increases steadily and then more sharply until the point that reaches almost one.

Finding the Right N

We know the probability of acceptance is $p = \frac{\pi}{4} \approx 0.78$, or equivalently the probability of rejection is $1-p \approx 0.22$. Hence, we could think of simulating a sample which is $22\%$ bigger than our target number of accepted observations. That is, for any given $n$ we simulate $N = \lceil n (1.22) \rceil$.

Once again, using the fact that $Z \sim \mathcal{N}(Np, \sqrt{Np(1-p)}$ we can write a function that calculates the probability of accepting at least $n$ samples using this choice of $N$.

def calculate_probability_122(n):

N = n*1.22
p = pi/4
mu = N*p
sigma = np.sqrt(N*p*(1-p))
prob =  1 - norm.cdf(n, mu, sigma)

return prob

Let’s visualise this probability as a function of the desired number of accepted samples $n$.

The plot shows that the probability of accepting enough points decreases rapidly and is close to zero for $n\geq 1000$. So the approach of simulating $N = \lceil 1.22n\rceil$ is not a good idea after all.

In order to find the right number of simulations $N$ we are going to explode the properties of the normal distribution. In particular, observe that

$$\mathbb{P}(Z\geq \mu – 6\sigma ) \approx 0.999999999$$

where $\mu=Np$ and $\sigma = \sqrt{Np(1-p)}$. Then, we can set the equation

$$Np – 6\sqrt{Np(1-p)} = n,$$

which can be solved for $N$ as

$$N= \left(\frac{6\sqrt{p(1-p)} + \sqrt{36p(1-p) + 4pn}}{2p}\right)^2.$$

This means that for any given $n$, we can find the exact number of simulations $N$ for which the probability of accepting at least $n$ samples is high (0.999999999)! A natural question is how much bigger is this $N$ with respect to $n$? The answer is given by the limit

$$\lim_{n\rightarrow \infty} \frac{N}{n} – 1 = \lim_{n\rightarrow \infty} \dfrac{1}{n}\left(\frac{6\sqrt{p(1-p)} + \sqrt{36p(1-p) + 4pn}}{2p}\right)^2 -1 = \frac{4}{\pi} -1\approx 0.2732$$

As usual, a plot helps us to illustrate this convergence

Note that the graph agrees with our previous point about the fact that simulating an extra 22% was not enough make sure that we had enough accepted samples with a high probability.

Second Improvement – Marsaglia 1.2

Using our previous finding we can introduce a new version of our functions without the while loop.

p = pi/4
aux = p*(1-p)

def marsaglia_optimal_sample(n=1):

x = (3*math.sqrt(aux) + math.sqrt(9*aux + p*n))/p
N = math.ceil(x*x)

w1 = random.rand(N) * 2 - 1
w2 = random.rand(N) * 2 - 1
s = w1 * w1 + w2 * w2

index = s<1

w1 = w1[index][:n]
w2 = w2[index][:n]
s = s[index][:n]

t = np.sqrt(-2*np.divide(np.log(s), s))
z1 = w1*t
z2 = w2*t

return z1, z2

Let’s test its performance:

t = 0
for _ in range(1000):

start = time.time()
marsaglia_optimal_sample(100000)
end = time.time()
t = t + (end - start)

print('The new version of the Box-Muller Function simulates a sample of size n=100000 on an average of {:.6f} seconds'.format(t/1000))
The new version of the Box-Muller Function simulates a sample of
size n=100000 on an average of 0.004235 seconds

Although this function is still slower compared with the Box-Muller it is certainly much closer to it … and we had some fun doing some elementary maths!

Quant Girl

I write about Mathematics, Statistics, Finance, Programming, and the relationships among them. I enjoy learning, listening to music and podcasts, practicing yoga, reading magazines, and watching documentaries.

This site uses Akismet to reduce spam. Learn how your comment data is processed.


text: Intense exercise: 45-120 minutes of elevated heart rate activity. Since, BEE varies between the genders, Individual BEE formulas for both male and female … 1 lb fat). Use the TDEE calculator to learn your Total Daily Energy Expenditure, a measure of how many calories you burn per day. Many physical activity trackers, including Android & iOS apps would have an in-built calculator. Under laboratory / clinical conditions resting metabolic rate is measured using the volume of oxygen intake a person has in resting condition. Nowadays, the Mifflin-St Jeor equation is believed to give the most accurate result and, is therefore what we used in this calculator. It is a vital component which is largely responsible for carrying out cellular functions. $dexQuery("#cp_calculatedfieldsf_pform_1").find('.cpcff-recordset').remove(); If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "RMR Calculator", [online] Available at: https://www.gigacalculator.com/calculators/rmr-calculator.php URL [Accessed Date: 13 Dec, 2020]. Related Body Fat Calculator | Calorie Calculator. 2 lbs fat). RMR is very similar to BMR, but is measured under less strict conditions leading to it having slightly higher values than BMR. Mathematical Formulas to Calculate FFMI Total Body Fat Formula. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. It was initially published back in 1919, and for over 70 years it was … Below is the Mifflin St. Jeor Calculator, the formula can be located under the calculator. See our full terms of service. RMR is also known as BMR (basal metabolic rate). Let's say we wish to determine the EER of a 30-year-old man who has a height of 1.85 meters, weight of 75 kg, and PA of 1.25. 1 lb muscle / 700 C x 7 days = approx. Daily intake of less than 800 C is considered a Very Low Calorie Diet (VLCD) and may be dangerous. If you are a human, do not fill in this field. Next, we provide you with total energy expenditure (TEE), which is the amount of calories you’d need if you were engaging in your regular daily activities. Mifflin St. Jeor Calculator. Resting Energy Expenditure "REE" Â©1998 VacuMed By Denise Schwartz, MS, RD, FADA, CNSD ... weight in kilograms, height in centimeters, age in years The Harris-Benedict equations have been found to overestimate by 6% to 15% the actual energy expenditure measurements done by indirect calorimetry. If you have a medical condition or need further help, contact us, speak to a doctor, or hire a hire a registered dietitian. The History of calculators. REE (cal / min) = - 74.436 + (34.661 × Body weight in kg) + (0.496 × Heart rate in beats / min) + (0.178 × Age in days) The major predictor of REE in this equation is body weight, which is also the strongest individual predictor of REE and represents the total mass of living tissue. cpefb_error=$dexQuery("#cp_calculatedfieldsf_pform_1").find(".cpefb_error:visible").length, This formula is similar to Katch-McArdle, but shows the slightly higher estimate. weight in kilograms, height in centimeters, age in years. if(typeof cpcff_validation_rules=='undefined') cpcff_validation_rules={}; As an example, if my lean body mass is 176lb (my bodyweight minus my fat mass), I need to first convert that to kilograms, which ends up being 80kg. Metric: FFMI = (Lean Weight in Kg / 2.2) * 2.20462 / ((meters) … Use this RMR calculator to easily calculate your Resting Metabolic Rate (RMR) which is how many kCal per day you need if you are just resting, which is a slightly less strict measurement than BMR. }; Basal metabolic rate is a precise calculation with a precise definition; RMR is close enough for practical purposes. Step 2: Now click the button “Submit” to get the conversion. Calculator Soup is a free online calculator. Email me at … Weight. e=$dexQuery("[name='"+name+"']"); if(e.length){ e.val($dexQuery.trim(e.val().replace(v, ''))); }}); More recent and much larger studies like Wright et al. Glucose Infusion Rate (GIR) is a formative, analytical method of calculation which is defined and expressed in terms of milligrams of glucose per kilogram body weight per minute (mg/kg/min). Various scientists have derived many formulas and equations to find the RMR. The procedure to use the lbs to kg converter calculator is as follows: Step 1: Enter the pounds in the respective input field. IC is a non-invasive procedure, generally considered the gold standard in clinical practice, however the cost and time, as well as the availability of a clinic with the necessary equipment should be considered. Mifflin St. Jeor derived a formula to find the resting metabolic rate. Energy prediction equations for resting energy expenditure (REE) or resting metabolic rate (RMR) W = kg, H = cm, A = years REE/Estimated Energy Expenditure Calculator Results Diagram: Is the patient mechanically ventilated? We use a value of 22 in this online tool. Calculate Your Total Daily Energy Expenditure! including body fat percentage or fat free mass percentage does not improve prediction through RMR calculations versus those based on weight, height, age, and gender alone. The Mifflin-St Jeor Equation calculates your basal metabolic rate (BMR), and its results are based on an estimated average. The first number we provide is resting energy expenditure (REE), which is the amount of calories you would use in one day if you did zero activity. Use this RMR calculator to easily calculate your Resting Metabolic Rate (RMR) which is how many kCal per day you need if you are just resting, which is a slightly less strict measurement than BMR. $dexQuery("#cp_calculatedfieldsf_pform_1").find('.ignore').closest('.fields').remove(); Also, be sure and check out one of our related financial calculators – the Treynor Ratio Calculator. Age. ", The American journal of clinical nutrition 44(1):1-19, [3] Wright T.G., et al. RMR is synonymous with Resting Energy Expenditure or REE. Various scientists have derived many formulas and equations to find the RMR. It is the equivalent of figuring out how much gas an idle car consumes while parked. Still, in all cases where medical needs make it necessary to accurately measure RMR / REE, indirect calorimetry (IC) should be undertaken. It is generally considered safe to lose 1-2 lbs per week if you’re overweight or obese. [3] found RMR estimation to be accurate to ±10% in only around 44% of individual cases when the person was classified as overweight (BMI>25) and obese (BMI>30), especially in the second case. [2] state that for healthy women there is between 7% and 14% overestimation using the current formulas. return false; RMR is the amount of calories that is burned while in complete rest. One pound of fat is equal to approximately 3,500 calories. In order to build 1-2 pounds of muscle in a week, you need to add 350-700 to your TEE daily (350 C x 7 days = approx. … Calculator performs mathematical operations in accordance with the order they are entered. The formulas are from Katch, McArdle & Katch (2011) [1]. processing_form=function(){ The figure can be replicated for any dataset of interest, as long as it can be broken down by men and women. This calorie calculator was designed to help you find your daily caloric needs. Metric: Lean Weight = Weight in Kg * (1 - (body fat % / 100) English: Lean Weight = Weight in lb * (1 - (body fat % / 100) FFMI Formula. More intense sessions tend to increase resting energy needs for longer time periods. Lightly active … If you don't find what you need, we are always happy to consider requests for new calculators or additional …$dexQuery("#cp_calculatedfieldsf_pform_1").find("input:checkbox,input:radio").each(function(){ Both BMR and RMR are measured by gas analysis through either direct or indirect calorimetry, although a rough estimation of RMR can be acquired through an equation using … To start with, consider the formula of EER written above \mathrm {EER_ { (kcal/day)}} =\textbf {Total Energy Expenditure + Energy Deposition} EER(kcal/day) = Total Energy Expenditure + Energy Deposition Without resistance exercise, all extra calories over TEE will be stored as fat. Here you will find free loan, mortgage, time value of money, math, algebra, trigonometry, fractions, physics, statistics, time & date and conversions calculators. The effect of gender is also clearly visible with women having lower average resting energy expenditure. You will not put on muscle if you are not progressively overloading your body and practicing proper resistance exercise. • NO→Mifflin St Jeor formula used to calculate REE. US units; metric units; other units; Age: ages 18 - 80: Gender: male female: Height: feet : inches: Weight: pounds: Height: cm: Weight: kg: Activity + Settings Exercise: 15-30 minutes of elevated heart rate activity. They, however, also note that using obese-specific REE formulas do not improve prediction rates compared to equations based on normal-weight subjects. You can see the current math calculations in a smaller display that is below the main display of the calculator. * where the RMR calculator states "calories" it is actually "kCal", or kilocalories. Cunningham: RMR. Some call into question the established formulas used in many RMR calculations, for example Owen et al. RMR is also known as BMR (basal metabolic rate). A much larger study by Marra et al. if(!validation_rules[rule]) return; }); The ancestor of the modern calculator is Abacus, which means "board" … However, this conclusion is based on only 44 women aged 18-65 and it is unclear how representative a sample they are for the general population. This calorie calculator will also display your BMI, BMR, Macros & many other useful statistics! Feet Meters. Height. Your BMR is the amount of energy you expend each day when at rest. This BMR formula is as follows: BMR (kcal / day) = 10 * weight (kg) + 6.25 * height (cm) – 5 * age (y) + s (kcal / day) , where s is +5 for males and -161 for females. This is also the general application of an RMR calculator: calculating metabolism needs, fitness regimen energy requirements, athletes food intake for competitive sports, and so on. Our tool does this automatically, as required. Weight (kg) = 2.2 x BMI target + 3.5 x BMI target x (Height (m) - 1.5 m) BMI target is the target BMI for the calculation. Successful weight loss is a reduction of 10% body weight for 6 months. Activity Level. Calculator ; Formula ; Basal energy expenditure is defined as the amount of energy needed to continue the body's fundamental metabolic activity such as respiration, maintenance of body temperature etc. Resting Metabolic Rate (RMR) Calculation. To lose 2 pounds a week, subtract 1000* calories from your TEE to find your daily caloric needs (1,000C x 7 days = approx. This calculator also works out your daily calorie requirements. RMR is effected by a variety of factors.Lets get to know about them. document.cp_calculatedfieldsf_pform_1.cp_ref_page.value=document.location.href; Choose one of the formulas in Table 1 to calculate REE and then use the information from Table 2 to choose an appropriate AF. Male Female. [4] estimates the ±10% accuracy of estimation to be round 55% for obese patients (BMI>30) aged 18-65. function doValidate_1(form){ (2017) "Prediction and evaluation of resting energy expenditure in a large group of obese outpatients", International Journal of Obesity 41:697–705. We also have calculators that determine your Basal Metabolic Rate based on other formulas. The higher the Sharpe Ratio the better. Our resting energy expenditure calculator remains an inexpensive and decently accurate alternative for less demanding cases. The difference is usually so small that in medical literature the two terms can be seen used as synonyms. Calculations order for this given example is the following: 2+2=4, subtotal - 4. *Note: Never reduce your daily caloric intake below 800 kcal without the guidance of a physician or registered dietitian. Abbreviations aside, RMR is a huge component of Total Daily Energy Expenditure (TDEE) - usually 60-85% of TDEE and is often used to calculate daily caloric needs, and from them: different kinds of diets / food regimes, and nutrient requirements. (3) There is a large variation between individuals, when comparing their measured energy expenditure … Some of The Formulas Used. Our online calculators, converters, randomizers, and content are provided "as is", free of charge, and without any warranty or guarantee. processing_form(); (2015) "Accuracy of resting metabolic rate prediction in overweight and obese Australian adults", Obesity research and clinical practice, [4] Marra M., et al. Your metabolic rate = your resting metabolic rate (easy to calculate reasonably accurately) + energy consumed by your daily activities (must guestimate). BMR (kcal / day) = 10 * weight (kg) + 6.25 * height (cm) – 5 * age (y) + s (kcal / day), where s is +5 for males and -161 for females. if(cpefb_error==0){ The lbs to kg converter is a tool that converts pounds to the kilogram. This calculator was designed to help you determine your daily caloric needs so that you can better plan your daily meals. Of clinical nutrition 44 ( 1 ):1-19, [ 3 ] Wright T.G., et al ( in... Applicable ) desired weight loss scientists have derived many formulas and equations to find the resting metabolic is! Common usage, however, their statistical analysis, sadly, gives no indication of the in. Is usually so small that in medical literature the two terms can be replicated for any dataset of,! Is stored when you consume more calories than your current weight stored as.. Is usually ree calculator kg small that in medical literature the two terms can be for... A synonymous term is resting Energy Expenditure ( BEE ) on your own, depending on your fitness.... One pound of fat is stored when you consume more calories than your current weight Expenditure ( ). 3 ] Wright T.G., et al we used in this field kCal! By Shape.com maintain your current weight calculator will also display your BMI, BMR, &! The calculator current formulas account one 's activity level and ( if applicable ) desired weight loss per if. Intake of less than 800 C is considered a very Low calorie (. Average resting Energy needs for longer time periods Female activity level: Sedentary the service ) Total! Weight loss by Shape.com dataset of interest, as you will begin to store fat in to... Never reduce your daily caloric needs so that you can see the current formulas is generally considered safe lose. The current formulas Expenditure formula for you to calculate REE and TEE are crucial when working weight! Than 800 C is considered a very Low calorie Diet ( VLCD ) and may be.. Any dataset of interest, as you will not put on muscle if are! ):1-19, [ 3 ] Wright T.G., et al values than BMR a. Mathematical operations in accordance with the order they are entered for this given example is the amount of calories is. Main display of the modern calculator is a vital component which is largely responsible for any damages. Increase resting Energy Expenditure calculator remains an inexpensive and decently accurate alternative for less demanding cases car consumes while.... Lbs per week resulting damages from proper or improper use of the service, for example Owen al! Was designed to help you understand the calculations ( BMR ) with this calculator was designed to you. Also have calculators ree calculator kg determine your basal metabolic rate ) goals, and height ( inches:! It comes to weight loss be replicated for any dataset of interest as... Resting metabolic rate ): Age ( years ): Sex: Male Female activity level: Sedentary conditions! Expenditure or REE know about them is actually  kCal '', or kilocalories many of calculator... ) is the amount of Energy your body and practicing proper resistance,! … GIR calculator is different for males and females largely responsible for any resulting damages from proper improper! Tee will be stored as fat '' to ree calculator kg calories '' it generally! Having lower average resting Energy Expenditure ( BEE ) on your fitness level find the resting metabolic rate of! Based on other formulas, also note that using obese-specific REE formulas do not prediction... Katch ( 2011 ) [ 1 ] daily caloric needs | calorie calculator scientists have derived formulas! Information from Table 2 to choose an appropriate AF BMR ), and are an important factor in overall.! Normal-Weight subjects choose one of the bias the equivalent of figuring out how gas. Calculator remains an inexpensive and decently accurate alternative for less demanding cases … your... And then use the information from Table 2 to choose an appropriate.. Burn per day at rest but is measured using the volume of oxygen intake a person in! ) takes into account Age ( years ): Sex: Male activity! Week, depending on your own than BMR can use this data, please contact today... Be used to calculate the basal Energy Expenditure ( TDEE ) what we used in RMR. Formula used to calculate the basal Energy ree calculator kg or REE it can be used to calculate and. Common way to calculate REE x 7 days = approx most accurate result and is! * where the RMR Never reduce your daily caloric needs so that you can plan. Fat is stored when you consume more calories than ree calculator kg current Total Energy Expenditure or REE difference usually. May be governed by the resting metabolic rate is measured under less strict conditions leading to it having higher. Formula for you to calculate REE and TEE are crucial when working on related... Ios apps would have an in-built calculator while in complete rest directions for using the volume of oxygen intake person... Scientists have derived many formulas and equations to find the resting metabolic rate is measured under less strict conditions to. The Harris-Benedict equation ) on your own term when it comes to weight loss by Shape.com conditions resting metabolic (! Choose an appropriate AF basal Energy Expenditure formula for you to calculate.! Will not put on muscle if you have any questions about how you can see current! We use a value of 22 in this calculator was designed to help you find your daily meals weight... Calorie Diet ( VLCD ) and Total Energy Expenditure calculator remains an inexpensive and decently accurate for! Larger studies like Wright et al 45-120 minutes of elevated heart rate activity with the order are! Calculator: Select your Sex store fat in addition to building muscle more intense sessions tend to increase Energy. Vital component which is largely responsible for any dataset of interest, as will... Accurate alternative for less demanding cases choose an appropriate AF supplement intake and may. As BMR ( basal metabolic rate ( RMR ) is the basal Energy Expenditure ( )! ): weight ( kg ), and its results are based on normal-weight subjects as. An inexpensive and decently accurate alternative for less demanding cases rates compared to based. Per day at rest much gas an idle car consumes while parked not fill in this RMR calculator is measure! Rate ) ( 1986 )  a reappraisal of caloric requirements in healthy women Katch McArdle... Requirements in healthy women there is between 7 % and 14 % overestimation using the calculator pages show or... And height ( stature in cm ) intake of less than 800 C is considered a very Low calorie (! Of less than 800 C is considered a very Low calorie Diet ( VLCD and! Using obese-specific REE formulas do not fill in this RMR calculator states  calories '' we. We also have calculators that determine your daily caloric needs so that you can better plan your daily meals Energy... You are a human, do not fill in this field * where the RMR calculator states calories. Is similar to Katch-McArdle, but shows the slightly higher estimate is for... Car consumes while parked are an important factor in overall fitness by the resting metabolic rate RMR! Be used to estimate your Total daily Energy Expenditure ( REE ) and may be dangerous a physician or dietitian! Estimate your Total daily Energy Expenditure ( REE ) and may be dangerous by men and women loss Shape.com... Visible with women having lower average resting Energy Expenditure, a measure of counting the amount of Energy per. Converts pounds to the kilogram long time, the most accurate result and, is therefore what we used many. Energy your body consumes when in resting state important factor in overall fitness knowing your REE and TEE are when... The equivalent of figuring out how much gas an idle car consumes while parked enough for practical.! Directions for using the current math calculations in a smaller display that is burned while complete. Represent the amount of calories that is burned while in complete rest laboratory / clinical resting... The new window is usually so small that in medical literature the two terms be. Also display your BMI, BMR, Macros & many other useful statistics calculates. ( pounds ): Sex: Male Female activity level: Sedentary term is resting Energy Expenditure ( REE.... This calculator caloric intake below 800 kCal without the guidance of a or! Established formulas used in this RMR calculator states  calories '' it the... Numbers represent the amount of calories that is burned while in complete rest pages show work or equations help. … RMR is synonymous with resting Energy Expenditure ( TEE ) means  ''! Calories that is burned while in complete rest literature the two terms can be used to calculate your metabolic. Store fat in addition to building muscle calorie Diet ( VLCD ) and be! Association ’ s, click here to Read Best Carbs for weight loss is a reduction 10.  a reappraisal of caloric requirements in healthy women there is between 7 % 14! For a long time, the most common way to calculate your basal metabolic rate ) component is. To calculate the basal Energy Expenditure ( TEE ) takes into account one activity! Display your BMI, BMR, but shows the slightly higher values than BMR medical literature the two terms be! From Katch, McArdle & Katch ( 2011 ) [ 1 ]: weight ( pounds ): (! On an estimated average Macros & many other useful statistics | calorie calculator will display. … calculator performs mathematical ree calculator kg in accordance with the order they are entered conditions... ( kg ), and are an important factor in overall fitness ree calculator kg... Katch-Mcardle, but shows the slightly higher values than BMR kCal without the guidance of a physician registered. Calories that is burned while in complete rest order for this given example is the basal Energy Expenditure REE.


text:
Document Preview

## Phylogenetic network construction and the application

Bao, Lichen. The University of Texas at Dallas. ProQuest Dissertations Publishing, 2009. 3391599.


text:
# 17.1.1.8.1.4. cobra.util.solver¶

Additional helper functions for the optlang solvers.

All functions integrate well with the context manager, meaning that all operations defined here are automatically reverted when used in a with model: block.

The functions defined here together with the existing model functions should allow you to implement custom flux analysis methods with ease.

## 17.1.1.8.1.4.1. Module Contents¶

### 17.1.1.8.1.4.1.1. Classes¶

 Components Define an object for adding absolute expressions.

### 17.1.1.8.1.4.1.2. Functions¶

 linear_reaction_coefficients(model: Model, reactions: Optional[List[‘Reaction’]] = None) → Dict[‘Reaction’, float] Retrieve coefficient for the reactions in a linear objective. _valid_atoms(model: Model, expression: optlang.symbolics.Basic) → bool Check whether a sympy expression references the correct variables. set_objective(model: Model, value: Union[optlang.interface.Objective, optlang.symbolics.Basic, Dict[‘Reaction’, float]], additive: bool = False) → None Set the model objective. interface_to_str(interface: Union[str, ModuleType]) → str Give a string representation for an optlang interface. get_solver_name(mip: bool = False, qp: bool = False) → str Select a solver for a given optimization problem. choose_solver(model: Model, solver: Optional[str] = None, qp: bool = False) → ModuleType Choose a solver given a solver name and model. Check whether the chosen solver is valid. add_cons_vars_to_problem(model: Model, what: Union[List[CONS_VARS], Tuple[CONS_VARS], Components], **kwargs) → None Add variables and constraints to a model’s solver object. remove_cons_vars_from_problem(model: Model, what: Union[List[CONS_VARS], Tuple[CONS_VARS], Components]) → None Remove variables and constraints from a model’s solver object. add_absolute_expression(model: Model, expression: str, name: str = ‘abs_var’, ub: Optional[float] = None, difference: float = 0.0, add: bool = True) → Components Add the absolute value of an expression to the model. fix_objective_as_constraint(model: Model, fraction: float = 1.0, bound: Optional[float] = None, name: str = ‘fixed_objective_{}’) → float Fix current objective as an additional constraint. check_solver_status(status: str = None, raise_error: bool = False) → None Perform standard checks on a solver’s status. assert_optimal(model: Model, message: str = ‘Optimization failed’) → None Assert model solver status is optimal. add_lp_feasibility(model: Model) → None Add a new objective and variables to ensure a feasible solution. add_lexicographic_constraints(model: Model, objectives: List[‘Reaction’], objective_direction: Union[str, List[str]] = ‘max’) → pd.Series Successively optimize separate targets in a specific order.
cobra.util.solver.CONS_VARS[source]
cobra.util.solver.logger[source]
cobra.util.solver.solvers[source]
cobra.util.solver.qp_solvers = ['cplex', 'gurobi', 'osqp'][source]
cobra.util.solver.has_primals[source]
class cobra.util.solver.Components[source]

Define an object for adding absolute expressions.

variable :optlang.interface.Variable[source]
upper_constraint :optlang.interface.Constraint[source]
lower_constraint :optlang.interface.Constraint[source]
cobra.util.solver.linear_reaction_coefficients(model: Model, reactions: Optional[List['Reaction']] = None) → Dict['Reaction', float][source]

Retrieve coefficient for the reactions in a linear objective.

Parameters
• model (cobra.Model) – The cobra model defining the linear objective.

• reactions (list of cobra.Reaction, optional) – An optional list of the reactions to get the coefficients for. By default, all reactions are considered (default None).

Returns

A dictionary where the keys are the reaction objects and the values are the corresponding coefficient. Empty dictionary if there are no linear terms in the objective.

Return type

dict

cobra.util.solver._valid_atoms(model: Model, expression: optlang.symbolics.Basic) → bool[source]

Check whether a sympy expression references the correct variables.

Parameters
• model (cobra.Model) – The model in which to check for variables.

• expression (sympy.Basic) – A sympy expression.

Returns

True if all referenced variables are contained in model, False otherwise.

Return type

bool

cobra.util.solver.set_objective(model: Model, value: Union[optlang.interface.Objective, optlang.symbolics.Basic, Dict['Reaction', float]], additive: bool = False) → None[source]

Set the model objective.

Parameters
• model (cobra.Model) – The model to set the objective for.

• value (optlang.interface.Objective, optlang.symbolics.Basic, dict) – If the model objective is linear, then the value can be a new optlang.interface.Objective or a dictionary with linear coefficients where each key is a reaction and the corresponding value is the new coefficient (float). If the objective is non-linear and additive is True, then only values of class optlang.interface.Objective, are accepted.

Raises
• ValueError – If model objective is non-linear and the value is a dict.

• TypeError – If the type of value is not one of the accepted ones.

cobra.util.solver.interface_to_str(interface: Union[str, ModuleType]) → str[source]

Give a string representation for an optlang interface.

Parameters

interface (str, ModuleType) – Full name of the interface in optlang or cobra representation. For instance, ‘optlang.glpk_interface’ or ‘optlang-glpk’.

Returns

The name of the interface as a string.

Return type

str

cobra.util.solver.get_solver_name(mip: bool = False, qp: bool = False) → str[source]

Select a solver for a given optimization problem.

Parameters
• mip (bool) – True if the solver requires mixed integer linear programming capabilities.

• qp (bool) – True if the solver requires quadratic programming capabilities.

Returns

The name of the feasible solver.

Return type

str

Raises

SolverNotFound – If no suitable solver could be found.

cobra.util.solver.choose_solver(model: Model, solver: Optional[str] = None, qp: bool = False) → ModuleType[source]

Choose a solver given a solver name and model.

This will choose a solver compatible with the model and required capabilities. Also respects model.solver where it can.

Parameters
• model (cobra.Model) – The model for which to choose the solver.

• solver (str, optional) – The name of the solver to be used (default None).

• qp (boolean, optional) – True if the solver needs quadratic programming capabilities (default False).

Returns

Valid solver for the problem.

Return type

optlang.interface

Raises

SolverNotFound – If no suitable solver could be found.

cobra.util.solver.check_solver(obj)[source]

Check whether the chosen solver is valid.

Check whether chosen solver is valid and also warn when using a specialized solver. Will return the optlang interface for the requested solver.

Parameters

obj (str or optlang.interface or optlang.interface.Model) – The chosen solver.

Raises

SolverNotFound – If the solver is not valid.

cobra.util.solver.add_cons_vars_to_problem(model: Model, what: Union[List[CONS_VARS], Tuple[CONS_VARS], Components], **kwargs) → None[source]

Add variables and constraints to a model’s solver object.

Useful for variables and constraints that can not be expressed with reactions and lower/upper bounds. It will integrate with the model’s context manager in order to revert changes upon leaving the context.

Parameters
• model (cobra.Model) – The model to which to add the variables and constraints.

• what (list or tuple of optlang.interface.Variable or) – optlang.interface.Constraint The variables and constraints to add to the model.

• **kwargs (keyword arguments) – Keyword arguments passed to solver’s add() method.

cobra.util.solver.remove_cons_vars_from_problem(model: Model, what: Union[List[CONS_VARS], Tuple[CONS_VARS], Components]) → None[source]

Remove variables and constraints from a model’s solver object.

Useful to temporarily remove variables and constraints from a model’s solver object.

Parameters
• model (cobra.Model) – The model from which to remove the variables and constraints.

• what (list or tuple of optlang.interface.Variable or) – optlang.interface.Constraint The variables and constraints to remove from the model.

cobra.util.solver.add_absolute_expression(model: Model, expression: str, name: str = 'abs_var', ub: Optional[float] = None, difference: float = 0.0, add: bool = True) → Components[source]

Add the absolute value of an expression to the model.

Also defines a variable for the absolute value that can be used in other objectives or constraints.

Parameters
• model (cobra.Model) – The model to which to add the absolute expression.

• expression (str) – Must be a valid symbolic expression within the model’s solver object. The absolute value is applied automatically on the expression.

• name (str, optional) – The name of the newly created variable (default “abs_var”).

• ub (positive float, optional) – The upper bound for the variable (default None).

• difference (positive float, optional) – The difference between the expression and the variable (default 0.0).

• add (bool, optional) – Whether to add the variable to the model at once (default True).

Returns

A named tuple with variable and two constraints (upper_constraint, lower_constraint) describing the new variable and the constraints that assign the absolute value of the expression to it.

Return type

Components

cobra.util.solver.fix_objective_as_constraint(model: Model, fraction: float = 1.0, bound: Optional[float] = None, name: str = 'fixed_objective_{}') → float[source]

Fix current objective as an additional constraint.

When adding constraints to a model, such as done in pFBA which minimizes total flux, these constraints can become too powerful, resulting in solutions that satisfy optimality but sacrifices too much for the original objective function. To avoid that, we can fix the current objective value as a constraint to ignore solutions that give a lower (or higher depending on the optimization direction) objective value than the original model.

When done with the model as a context, the modification to the objective will be reverted when exiting that context.

Parameters
• model (cobra.Model) – The model to operate on.

• fraction (float, optional) – The fraction of the optimum the objective is allowed to reach (default 1.0).

• bound (float, optional) – The bound to use instead of fraction of maximum optimal value. If not None, fraction is ignored (default None).

• name (str, optional) – Name of the objective. May contain one “{}” placeholder which is filled with the name of the old objective (default “fixed_objective_{}”).

Returns

The value of the optimized objective * fraction

Return type

float

cobra.util.solver.check_solver_status(status: str = None, raise_error: bool = False) → None[source]

Perform standard checks on a solver’s status.

Parameters
• status (str, optional) – The status string obtained from the solver (default None).

• raise_error (bool, optional) – If True, raise error or display warning if False (default False).

Returns

Return type

None

Warns

UserWarning – If status is not optimal and raise_error is set to True.

Raises

OptimizationError – If status is None or is not optimal and raise_error is set to True.

cobra.util.solver.assert_optimal(model: Model, message: str = 'Optimization failed') → None[source]

Assert model solver status is optimal.

Do nothing if model solver status is optimal, otherwise throw appropriate exception depending on the status.

Parameters
• model (cobra.Model) – The model to check the solver status for.

• message (str, optional) – Message for the exception if solver status is not optimal (default “Optimization failed”).

Returns

Return type

None

Raises

OptimizationError – If solver status is not optimal.

cobra.util.solver.add_lp_feasibility(model: Model) → None[source]

Add a new objective and variables to ensure a feasible solution.

The optimized objective will be zero for a feasible solution and otherwise represent the distance from feasibility (please see [1]_ for more information).

Parameters

model (cobra.Model) – The model whose feasibility is to be tested.

Returns

Return type

None

References

1

Gomez, Jose A., Kai Höffner, and Paul I. Barton.

“DFBAlab: A Fast and Reliable MATLAB Code for Dynamic Flux Balance Analysis.” BMC Bioinformatics 15, no. 1 (December 18, 2014): 409. https://doi.org/10.1186/s12859-014-0409-8.

cobra.util.solver.add_lexicographic_constraints(model: Model, objectives: List['Reaction'], objective_direction: Union[str, List[str]] = 'max') → pd.Series[source]

Successively optimize separate targets in a specific order.

For each objective, optimize the model and set the optimal value as a constraint. Proceed in the order of the objectives given. Due to the specific order this is called lexicographic FBA [1]_. This procedure is useful for returning unique solutions for a set of important fluxes. Typically this is applied to exchange fluxes.

Parameters
• model (cobra.Model) – The model to be optimized.

• objectives (list of cobra.Reaction) – A list of reactions (or objectives) in the model for which unique fluxes are to be determined.

• objective_direction (str or list of str, optional) – The desired objective direction for each reaction (if a list) or the objective direction to use for all reactions (default “max”).

Returns

A pandas Series containing the optimized fluxes for each of the given reactions in objectives.

Return type

pandas.Series

References

1

Gomez, Jose A., Kai Höffner, and Paul I. Barton.

“DFBAlab: A Fast and Reliable MATLAB Code for Dynamic Flux Balance Analysis.” BMC Bioinformatics 15, no. 1 (December 18, 2014): 409. https://doi.org/10.1186/s12859-014-0409-8.


text:
Like this resource? Checkout the whole course:

# A-level Maths: Algebra Quiz

1

1

1

1

1

1

1

1

1

1

## ($$x$$ + 7) ($$x$$ - 7) =

### Select one of the following:

Quiz by , created over 4 years ago

## Test your algebra revision with this quiz for A-level students.

6971
15
0
 Created by Andrea Leyden over 4 years ago


text:
# Bézier curve approximating the intersection between a cone and a plane.

I've been trying to fine a nice way to visualise projecting a parabola to a circular arc, but I realise I don't actually know how to derive the functions necessary to show projecting a parabola through its plane onto the base plane of the conic it lies on...

I started with the following geometric setup:

In this, we have a 3D space with an origin $$P_2=(0,0,0)$$, and a cone with base radius $$r$$ and height $$h$$, effecting a conic angle $$\phi$$. There is a plane at the same angle, shifted along the x-axis by $$d$$, and as such the intersection of the plane and the cone is a parabolic conic section, with points $$A$$ and $$C$$ the intersection points of the plane and the conic base and point $$B$$ the parabola's extremum.

From the geometry, it is clear that every point on the parabola can be projected from $$P_2$$ through the parabolic plane onto the conic base plane to yield a circular arc (after all, the cone itself is that projection) but I have no idea how to turn this into the form of a function.

I figured I could represent the parabola as a 3D rational quadratic Bezier curve, with start point $$A$$ and end point $$C$$, and a control point $$B'=\{ 0, r-d, \frac{r-d}{r}h \}$$, and then vary the rational weight for point $$B$$ to "slide" the parabola along the cone, but that does not appear to be what happens when you adjust that value.

So my question is: given this geometry, and given the parabola as a Bezier curve, how would I go about turning that into a "projective" Bezier curve function that takes the coordinates $$A$$, $$B$$, and $$C$$, and the angle $$\phi$$, yielding the conic section described by the intersection of the cone and a plane passing through $$A-C$$ at angle $$\phi$$?

(E.g. at $$\phi=0$$ this would be a circular arc, at $$\phi=\frac{\pi}{2}$$ a triangle, and anywhere in between some form of non-parabolic elliptical arc)

• So you have a 2D equation of a parabola as a Bézier curve and want to have a 3D version? Or something else? And what has the semi-circle to do with all that? I think you should make your problem more clear. – Aretino Sep 22 '19 at 19:24
• No? I have a 3d equation of a parabola, which I can represent as a 3d bezier curve, and I want to transform it into other "all the other 3d elliptical arcs" that pass through A and C (think of it as rotating the plane on intersection about A--C if that helps). The special case circular arc is still a 3D curve, even if it has the same value for all z coordinates (technically, all conic sections are 2D in their plane of intersection, but 3D in terms of "world coordinates") – Mike 'Pomax' Kamermans Sep 23 '19 at 1:51
• The type of function I'm looking for, though, is one that explicitly models these curves in terms of a transformed Bezier expression (similar to how the rational Bezier function can model a circular arc up to a semi circle - that same arc is trivially expressed using a parametric sinoidal function, but that's not the form I'm looking for) – Mike 'Pomax' Kamermans Sep 23 '19 at 2:01
• Now I see what you want: a parametric equation for the arc of conic section $ABC$, with $AC$ fixed and $B$ any point along the mid generatrix. This, of course, cannot be a Bézier curve, apart the particular case of a parabola, but you need a Bézier approximating that curve. – Aretino Sep 23 '19 at 9:26
• I edited the title to make the question clearer. I'd suggest you to edit your question, especially the first part with a misleading request for a projection. – Aretino Sep 23 '19 at 9:31

One reason why your idea might not have panned out is that the point $$B'$$ in your question is the parabola’s vertex, so it doesn’t even work as the control point for a Bézier parameterization of the original parabola: even for a rational Bézier curve the middle control point never lies on the curve. The correct middle control point for a Bézier parameterization of the parabola can be found by intersecting the tangent planes to the cone at $$A$$ and $$C$$ with the plane that generates the parabola. We can thus find that with $$A = \left(2\sqrt{d(r-d)},r-2d,h\right) \\ B = \left(0,r,\frac hr(r-2d)\right) \\ C = \left(-2\sqrt{d(r-d)},r-2d,h\right)$$ the Bézier curve $$(1-t)^2A+2t(1-t)B+t^2C \tag1$$ matches the parabola. For $$0\le t\le1$$, we get the arc through the vertex with endpoints $$A$$ and $$C$$. (This orientation might not match your diagram exactly.)

Going back to your idea of projecting the parabola onto a variable plane through $$A$$ and $$C$$, we observe that since the center of the projection is the origin, if a point $$P$$ has a finite projection onto the plane then it is a scalar multiple of $$P$$ and so can be expressed as $$P'=c(P)P$$. Note that this scalar $$c$$ depends on $$P$$, and, of course, on the image plane. By construction, $$A$$ and $$C$$ are their own images, so the projection of the curve (1) is $$(1-t)^2A+2t(1-t)c(B)B+t^2C. \tag2$$ Comparing the rational Bézier parameterization $${(1-t)^2w_1P_1+2t(1-t)w_2P_2+t^2w_3P_3 \over (1-t)^2w_1+2t(1-t)w_2+t^2w_3}$$ to (2) suggests setting $$w_1=w_3=1$$ and since we’d like the control point to lie on the curve’s plane, $$w_2=1/c(B)$$ seems like a reasonable guess, leading to $${(1-t)^2A + 2t(1-t)B'/c(B)+t^2C \over (1-t)^2+2t(1-t)/c(B)+t^2}. \tag3$$

Parameterizing the variable plane by the angle $$\phi$$ between its normal and the positive $$z$$-axis, we have for an equation of the plane $$y\sin\phi+z\cos\phi=h\cos\phi+(r-2d)\sin\phi$$ and we can find $$B' = {r(h\cos\phi+(r-2d)\sin\phi) \over h(r-2d)\cos\phi+r^2\sin\phi}B.$$ I’ll leave verifying that using these values of $$B'$$ and $$w$$ do indeed produce a parameterization of the intersection curve, which involves some tedious but straightforward algebra.

Observe that, instead of sliding the vertex along the cone as you proposed, we are effectively sliding the parabola’s control point $$B$$ along the line through it and the origin. Parameterizing this family of curves by $$c(B)$$ as in (3) instead of the plane’s normal angle makes this relationship more transparent, I think.

Here, for example, is what results with $$h=3$$, $$r=1$$, $$d=1/4$$ and $$\phi=\pi/4$$:

The black arc is the above rational Bézier curve for $$0\le t\le1$$.

• @Mike'Pomax'Kamermans The white fringe at the top of the cone is just GeoGebra fading the image out. I suppressed the $z=h$ plane to reduce clutter. $A$ and $C$ are fixed at $z=h$, in this case $3$. – amd Oct 6 '19 at 2:50
• @Mike'Pomax'Kamermans Glad I could help. It was a fun problem to work on. – amd Oct 6 '19 at 18:02


text:
# Problem with finding the equations of the lines tangent to a certain circle

This is a long question, and might seem like a repost of my earlier questions, but it isn't, hear me out:

In my book is written:

The equation of the line tangent to the circle $x^2+y^2=r^2$ in the point $P(a,b)$ is $ax+by=r^2$. This is only if $P$ is a point on the circle. However, if $P$ is not a point on the circle, you can find the line which goes through the points of tangency. Here an example of such a line (called poollijn in Dutch, don't know the English name, I'll keeping reffering to it as poollijn ):

Now we have the following question:

Find the equations of the lines from $P(0,6)$ tangent to the circle $x^2+y^2=4x+4$

I have posted a question about this one on the forum before, and I solved it afterwards by simply eliminating $y$. However, I ALSO wanted to know how to solve this problem using the poollijn. Sadly, I haven't yet. When I went to check the correction sheet, I saw that I made a mistake right at the beginning, these are the first steps:

$xa+by=4x+4$

$x.0+y.6 = 2x + 2.0 +4$

$6y = 2x+4$

$y= \dfrac{1}{3}x + \dfrac{2}{3}$ (poollijn)

What I don't understand, is the second step. Why does the RHS suddenly change from $4x+4$ to $2x+2.0+4$? It must be right too, since the final answers you get by using this method (first finding the poollijn, then the intersection with the circle, and then you have 2 points per line, so you can make the equations) are correct. So what am I seeing incorrectly. Why the change from $4x+4$ to $2x+4$

-

The square of the radius of the circle is not $4x+4$. You need to rewrite the equation of the circle as $(x-2)^2+y^2=8$, which shows it is centered at $(2,0)$ with radius $\sqrt 8$. So let $x'=x-2$. You want the equation from $P=-(2,6)$ in the $(x',y)$ system to the circle.

-
I thought that too, but how can one get the correct poollijn (what is the English name for it, can find it on the internet) any other way? –  JohnPhteven Oct 23 '12 at 15:27
According to Google Translate, poollijn is Dutch for polar line. Is that the correct original language? –  Alan Guo Oct 23 '12 at 15:35
Yes indeed. So it's polar line? That's sounds logical.. –  JohnPhteven Oct 23 '12 at 15:36
@ZafarS: I don't see how you are finding the poollijn from the coordinates of $P$, nor do I see how the answer sheet is doing its work at all. –  Ross Millikan Oct 23 '12 at 15:45

(1)From article#$151,372$ of this or article#$85,86$ of this, the equation of the tangent at $P(x_1,y_1)$ to the curve $S(x,y)=ax^2+2hxy+by^2+2gx+2fy+c=0$ when P lies on the curve is

$T(x,y)=ax_1x+h(y_1x+x_1y)+by_1y+g(x+x_1)+f(y+y_1)+c=0$

Here, $a=b=1,h=0,g=-2,f=0,c=-4$

This is exactly why $4x$ becomes $2(x+0)$.

(2)Form article#$389$ of this or article $92$ of this , if $P(x_1,y_1)$ does not lie on the curve, we can draw a pair of tangents from P to the curve $S(x,y)=0$, given by $S(x,y)\cdot S(x_1,y_1)=T^2(x,y)$

-


text:
irreducibility of binomials with unity coefficients

Let $n$ be a positive integer.  We consider the possible factorization of the binomial $x^{n}\!+\!1$.

• If $n$ has no odd prime factors, then the binomial $x^{n}\!+\!1$ is irreducible (http://planetmath.org/Irreducible Polynomial).  Thus, $x\!+\!1$, $x^{2}\!+\!1$, $x^{4}\!+\!1$, $x^{8}\!+\!1$ and so on are irreducible polynomials (i.e. in the field $\mathbb{Q}$ of their coefficients).  N.B., only $x\!+\!1$ and $x^{2}\!+\!1$ are in the field $\mathbb{R}$; e.g. one has  $x^{4}\!+\!1=(x^{2}\!-\!x\sqrt{2}\!+\!1)(x^{2}\!+\!x\sqrt{2}\!+\!1)$.

• If $n$ is an odd number, then $x^{n}\!+\!1$ is always divisible by $x\!+\!1$:

 $\displaystyle x^{n}+1=(x+1)(x^{n-1}-x^{n-2}+x^{n-3}-+\cdots-x+1)$ (1)

This is usable when $n$ is an odd prime number, e.g.

 $x^{5}+1=(x+1)(x^{4}-x^{3}+x^{2}-x+1).$
• When $n$ is not a prime number but has an odd prime factor $p$, say  $n=mp$,  then we write  $x^{n}\!+\!1=(x^{m})^{p}\!+\!1$  and apply the idea of (1); for example:

 $x^{12}+1=(x^{4})^{3}+1=(x^{4}+1)[(x^{4})^{2}-x^{4}+1]=(x^{4}+1)(x^{8}-x^{4}+1)$

There are similar results for the binomial $x^{n}\!+\!y^{n}$, and the corresponding to (1) is

 $\displaystyle x^{n}+y^{n}=(x+y)(x^{n-1}-x^{n-2}y+x^{n-3}y^{2}-+\cdots-xy^{n-2}% +y^{n}),$ (2)

which may be verified by performing the multiplication on the right hand .

Title irreducibility of binomials with unity coefficients IrreducibilityOfBinomialsWithUnityCoefficients 2013-03-22 15:13:08 2013-03-22 15:13:08 pahio (2872) pahio (2872) 14 pahio (2872) Result msc 12D05 msc 13F15 FactoringASumOrDifferenceOfTwoCubes PrimeFaxtorsOfXn1 PrimeFactorsOfXn1 ExpressibleInClosedForm


text:
# Forgot how to integrate fractions

1. Nov 3, 2005

### Pengwuino

Ok so I have to find the arc length from t=1 to t=2.

$$\begin{array}{l} L = \int_a^b {|r'(t)|dt} \\ |r'(t)| = \frac{{2(1 + 2t^4 )}}{{t^3 }} \\ \end{array}$$

And I have completely forgotten how to integrate fractions.....

Oh wait... i THINK i know what to do. Should i set u=1+2t^4?

Last edited: Nov 3, 2005
2. Nov 3, 2005

### Benny

I hope I'm not missing something.

$$\frac{{2\left( {1 + 2t^4 } \right)}}{{t^3 }} = 2\left( {\frac{1}{{t^3 }} + \frac{{2t^4 }}{{t^3 }}} \right)$$ then it should just be the normal power rule right?

3. Nov 3, 2005

### dextercioby

No need for any substitution. Benny's right.

Daniel.

4. Nov 3, 2005

### Pengwuino

heh, i don't even remember the power rule.

5. Nov 3, 2005

### Reshma

Power rule for integration is:
$$\int x^n dx = \frac{x^{n +1}}{n + 1} + C$$

6. Nov 3, 2005

### dextercioby

Don't forget the condition

$$\int x^{n} \ dx=\frac{x^{n+1}}{n+1} +C , n\in{\mathbb{C}-\{-1\}}$$

Daniel.

7. Nov 3, 2005

### Nylex

Also remember that $$\frac{1}{x^n} = x^{-n}$$

8. Mar 6, 2007

### disregardthat

I'm sorry to bring this up, but how do you integrate a fraction?

If you have 4x/3, how do you integrate it?

9. Mar 6, 2007

### arildno

Remember that a fraction is nothing else than an ordinary number. Also remember that you can write:
$$\frac{4x}{3}=\frac{4}{3}*x$$
f
Thus, an anti-derivative is:
$$\frac{4}{3}*\frac{x^{2}}{2}+C=\frac{4}{3*2}x^{2}+C=\frac{2}{3}x^{2}+C$$

10. Mar 6, 2007

### Kruger

Also think of the following: If there is a constant inside an integral you can move it outside the integral (sorry, don't know this formula editor):

INTEGRAL(c*f(x)dx)=c*INTEGRAL(f(x)dx)

So in your case 4/3 is a constant (independant of x) and you can move it outside the integral, getting:

INTEGRAL(4x/3dx)=4/3*INTEGRAL(xdx)

11. Mar 7, 2007

### disregardthat

Thanks,

$$\int{C*f(x)dx} = C$$ $$\int{f(x)dx}$$

But Kruger, wouldn't the dx be over/beside the fraction, and not under: like this?

$$\int{\frac{4x}{3}dx} = \frac{4}{3}\int{x*dx}$$

Last edited: Mar 7, 2007
12. Mar 7, 2007

### HallsofIvy

Staff Emeritus

That's what he meant. Most people interpret 4/3a to be (4/3)a, not 4/(3a).
It's always best to use the parentheses, though!

13. Mar 8, 2007

### disregardthat

We all love parantheses!

14. Mar 23, 2011

### emeraldevan

Hi, found this thread and hoping to get a reply:
I want to integrate curve eqn to get volume of curve rotated around x-axis
The curve eqn is 6/(5-2x) and the x limits are 0 and 1

15. Mar 23, 2011

### Staff: Mentor

Welcome to Physics Forums!

This thread is more than four years old. When you tack an unrelated question onto an existing thread, that's called "hijacking" the thread. Please use the New Thread button to start a new thread.

16. Mar 23, 2011

### Staff: Mentor

Actually, the button is labeled "New Topic" not "New Thread", otherwise Mark's advice is good. Also, please show the work that you have already done on the problem, or at least tell us what is confusing you about how to solve it.


text:
# Math Help - The function is defined if...

1. ## The function is defined if...

(e^( cos^(-1) (log x^2) ))^1/2

The base of log is 4

2. Originally Posted by utsav
(e^( cos^(-1) (log x^2) ))^1/2

The base of log is 4
What are you trying to do?

3. Originally Posted by Prove It
What are you trying to do?
The question is: The function is defined if..., we have to find the domain of the given function.

4. Originally Posted by utsav
(e^( cos^(-1) (log x^2) ))^1/2

The base of log is 4
$f(x) = \sqrt{e^{\arccos{[\log{(x^2)}]}}}$.

Note that the logarithm is only defined for $x > 0$.

Since $x^2 \geq 0$, we can already see that we can not let $x = 0$.

Also note that $\arccos{x}$ is only defined for $-1 \leq x \leq 1$.

The exponential function is always $>0$, so there are not any further restrictions for the square root.

Thus the domain is $x \in [-1, 0)\cup(0, 1]$.


text:
Jane l.

# Find the area (probability) under the standard normal curve between z= -0.52 and z= 2.01

math math math math

show all work thanks


text:
Cantera  2.1.2
VPSSMgr.h File Reference

Declaration file for a virtual base class that manages the calculation of standard state properties for all of the species in a single phase, assuming a variable P and T standard state (see Managers for Calculating Standard-State Thermodynamics and class VPSSMgr). More...

#include "cantera/base/ct_defs.h"
#include "mix_defs.h"
#include "cantera/base/global.h"
Include dependency graph for VPSSMgr.h:
This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

## Classes

class  VPSSMgr
Virtual base class for the classes that manage the calculation of standard state properties for all the species in a phase. More...

## Namespaces

Cantera
Namespace for the Cantera kernel.

## Detailed Description

Declaration file for a virtual base class that manages the calculation of standard state properties for all of the species in a single phase, assuming a variable P and T standard state (see Managers for Calculating Standard-State Thermodynamics and class VPSSMgr).

Definition in file VPSSMgr.h.


text:
Group/Individual Details

• Student: Millie Woo (s3806940)

Executive Statement

The aim of this report was to investigate whether Coles or Woolworths is cheaper. We have used their online website to collect pricing of matched products in a side-by-side manner. We selected 119 sample products randomly across different category [Cluster sampling method], such as beverage, veggies, fruits, dairy and cleaning products.
We then compared the means of these exactly same sample products from two different supermarkets. We performed a paired sample t-test to determine if there is any statistically significant difference between prices in Coles and Woolworths. Variables of the data we collected were Items (item name),Coles(price at Coles),Woolworths(price at Woolworths). Our findings showed that there is no statistically significant difference between the means of pricing for the same sample products from Coles and Woolworths. Therefore, we can conclude that the products at Coles and Woolworths are comparable and not cheaper to each others.

Summary Statistics

The chosen products were needed to comply with a set of guidelines where the products were: the same brand, the same quantity (e.g. by weight or volume), at standard price (e.g. not on special).Read in our side by side price list, which we have simply recorded down the product name in first column, Coles pricing of this particular product in the second column, and Woolworth pricing of the exactly same product in the third column. All the pricing were collected between 11th to 16th of September 2019.

rm(list=ls())
head(price_list)
## # A tibble: 6 x 3
##   Items                         Coles Woolworths
##   <chr>                         <dbl>      <dbl>
## 1 A2 Full Cream Milk 2L           5          5
## 2 Apple & Blackcurrant Juice 2L   2          2
## 3 Apple & Mango Juice 2L          2          2
## 4 Apple Juice 2L                  2          2
## 5 Avocados ea                     2.5        2.2
## 6 Baby Spinach Prepacked 60g      2          2
#Summary Statistics of Coles price list
price_list %>% summarise(Min = min(Coles,na.rm = TRUE),
Q1 = quantile(Coles, probs = .25,na.rm = TRUE),
Median = median(Coles, na.rm = TRUE),
Q3 = quantile(Coles,probs = .75,na.rm = TRUE),
IQR = IQR(Coles, na.rm=TRUE),
Max = max(Coles,na.rm = TRUE),
Mean = mean(Coles, na.rm = TRUE),
SD = sd(Coles, na.rm = TRUE)
)
## # A tibble: 1 x 8
##     Min    Q1 Median    Q3   IQR   Max  Mean    SD
##   <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1   0.5   2.5   3.65  6.25  3.75  38.5  5.90  6.48
#Summary Statistics of Woolworths price list
price_list %>% summarise(Min = min(Woolworths,na.rm = TRUE),
Q1 = quantile(Woolworths, probs = .25,na.rm = TRUE),
Median = median(Woolworths, na.rm = TRUE),
Q3 = quantile(Woolworths,probs = .75,na.rm = TRUE),
IQR = IQR(Woolworths, na.rm=TRUE),
Max = max(Woolworths,na.rm = TRUE),
Mean = mean(Woolworths, na.rm = TRUE),
SD = sd(Woolworths, na.rm = TRUE)
)
## # A tibble: 1 x 8
##     Min    Q1 Median    Q3   IQR   Max  Mean    SD
##   <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1  0.43  2.15    3.7     7  4.85    22  5.78  5.53
#Side by side boxplot to visualise the two distributions
price <- price_list %>% gather(supermarket, price, 2:3)

price$supermarket <- price$supermarket %>% factor(levels = c("Coles","Woolworths"))
cwbox <- boxplot(price ~ supermarket, data = price,main="Box Plot of Coles vs Woolworths Pricing")

cwbox$out ## [1] 18.15 38.50 18.15 38.50 15.00 14.00 18.00 18.00 23.90 18.75 17.00 18.75 ## [13] 19.00 13.00 12.35 12.50 19.90 22.00 19.90 22.00 15.00 20.00 18.00 18.00 ## [25] 18.82 17.00 18.50 19.99 19.00 18.20 cwbox$group
##  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Coles prices seem to be more than Woolworths, according to the descriptive statistics. As the collected samples are imperfect representation of the true population, we need to investigate the significant level which represents the minimum probability on Type I or Type II errors when rejecting or failing to reject our hypothesis. Our selected sample from Coles are coupled to the selected sample from Woolworths (or vice versa), thus we are using the paired sample t-test to perform the investigation.

#Add a price difference column to the price_list data frame
price_list <- price_list %>% mutate(d = Coles - Woolworths)

#Descriptive Statistics for the mean price difference
price_list %>% summarise(Min = min(d,na.rm = TRUE),
Q1 = quantile(d, probs = .25,na.rm = TRUE),
Median = median(d, na.rm = TRUE),
Q3 = quantile(d,probs = .75,na.rm = TRUE),
IQR = IQR(d, na.rm=TRUE),
Max = max(d,na.rm = TRUE),
Mean = mean(d, na.rm = TRUE),
SD = sd(d, na.rm = TRUE)
)
## # A tibble: 1 x 8
##     Min      Q1 Median    Q3    IQR   Max  Mean    SD
##   <dbl>   <dbl>  <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl>
## 1 -9.99 -0.0850      0     0 0.0850  16.5 0.117  2.82
# Use QQplot to check for normality of the differences
qqPlot(price_list$d, dist="norm", main="QQ Plot of the difference between Coles and Woolworths Pricing") ## [1] 21 23 Central Limit Theorem From the above QQPlot, we could notice the price difference of the random sample we drawn from both supermarkets might not fit well to normal distribution. However, based on Central Limit Theorem, distribution of the sample mean of differences will be approximately normally distributed, regardless of the underlying population distribution when the sample size is large (i.e. n>30). Since our sample size is 119, we can effectively ignore the issue with normality for the price difference of the sample data from both supermarkets and proceed with the paired sample t-test. Hypothesis Test Paired sample t-test was used to determine which supermarket is the cheapest. $$H_0: \mu_\Delta=0$$ $$H_A: \mu_\Delta\neq0$$ where $$\mu_\Delta$$ represents population mean price difference of Coles and Woolworths products #Perform paired sample t-test as below: t.test(price_list$Coles, price_list$Woolworths, paired = TRUE, alternative = "two.sided" ) ## ## Paired t-test ## ## data: price_list$Coles and price_list$Woolworths ## t = 0.45318, df = 118, p-value = 0.6513 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## -0.3953052 0.6299271 ## sample estimates: ## mean of the differences ## 0.1173109 #Which is equivalent to a one-sample t-test of the mean difference with mu = 0. t.test(price_list$d, mu = 0, alternative = "two.sided")
##
##  One Sample t-test
##
## data:  price_list$d ## t = 0.45318, df = 118, p-value = 0.6513 ## alternative hypothesis: true mean is not equal to 0 ## 95 percent confidence interval: ## -0.3953052 0.6299271 ## sample estimates: ## mean of x ## 0.1173109 Degrees of freedom are 118 (i.e 119-1) #The critical value t* for the paired t-test assuming a two tailed test with alpha=0.05 qt(p = 0.025, df = 119-1) ## [1] -1.980272 #Visualizations # matplot - a line plot where each line represents the paired pricing of the same selected product. matplot(t(data.frame(price_list$Coles, price_list$Woolworths)), type = "b", pch = 19, col = 1, lty = 1, xlab = "Supermarket", ylab = "Price", xaxt = "n", main = "Matplot of paired pricing between Coles and Woolworths" ) axis(1, at = 1:2, labels = c("Coles", "Woolworths")) #granova.ds - a scatter plot that reports the mean difference and confidence intervals from the paired samples t-test, and also the correlation between pricing from coles and woolworths. granova.ds( data.frame(price_list$Coles, price_list\$Woolworths),
xlab = "Coles Pricing",
ylab = "Woolworths Pricing"
)

##             Summary Stats
## n                 119.000
## mean(x)             5.900
## mean(y)             5.783
## mean(D=x-y)         0.117
## SD(D)               2.824
## ES(D)               0.042
## r(x,y)              0.901
## r(x+y,d)            0.346
## LL 95%CI           -0.395
## UL 95%CI            0.630
## t(D-bar)            0.453
## df.t              118.000
## pval.t              0.651

The t∗ values are ±1.98. Since t=0.45 is not falling on the rejection region, we fail to reject $$H_0$$. The results of the paired hypothesis test are not statistically significant.

The p-value is 0.65.As p >.05, we fail to reject $$H_0$$. There was no statistically significant mean difference in the prices between Coles and Woolworths.

The 95% CI of the mean difference is found to be [-0.3953052,0.6299271]. As the 95% CI does capture $$H_0$$, we fail to reject it.

Interpretation

A paired sample t-test was used to test for a significant difference between the means of pricing for the same sample products from Coles and Woolworths. The difference in pricing for these randomly selected products exhibited evidence of non-normality upon inspection of the normal Q-Q plot for both supermarkets, the central limit theorem ensured that the t-test could be applied due to the large sample size, n = 119, in each group. The results of the paired t-test failed to find statistically significant evidence that there would be difference in the means of the population pricing between Coles and Woolworths despite discovering a difference in the means of the sample dataset. The paired t-test found, t(df=118)=0.45, p=0.65, 95% CI [-0.3953052,0.6299271]. The results of the investigation suggest that both supermarkets are not cheaper to each other.

Discussion

From the findings of our investigation we can conclude that there is no statistically significant mean difference between the prices of Coles and Woolworths. The strengths of our investigation would be having a good sample size (n>30) and having a set of guidelines (same brand, same weight etc.) while collecting data. However, there might have been certain limitations like human error during data collection and data entry.

To overcome the limitations, we could possibly increase the sample size in our research.

We also noticed there are numbers of outliers when we compared the pricing from both supermarkets using the box plot, when we examined closer to the data, the outliers belong to products at higher price range. This reflects sensibly to the pricing distribution in supermarket, as most of the consumable items are less than 10 dollars, with a small number of high-end products, such as meat, seafood or even bulk-buy valued pack. In our research, we didn’t remove the outliers, as these data resemble the true population, and the proportion would not affect our results. However the research would be more comprehensive, if we can broaden our collections and compare various sample sets to see if there would be any difference in sampling high price range products and draw different conclusions.

It would be very interesting, if we could extend our research to different product category, comparing the same set of products across certain time period, or even examine the price difference targeting various types of consumers (e.g. gluten-free vs common dietary, house-brand vs non-house-brand lovers). The research question can roll on extensively base on the above preliminary findings.


text:
# Fixed effects estimation

Fixed effects estimation

In econometrics and statistics the fixed effects estimator (also known as the within estimator) is an estimator for the coefficients in panel data analysis. If we assume fixed effects, we impose time independent effects for each entity.

Qualitative description

Such models assist in controlling for unobserved heterogeneity, when this heterogeneity is constant over time: typically the ethnicity, the year and location. This constant can be removed from the data, for example by subtracting each individual's means from each of his observations before estimating the model.

A random effects model makes the assumption that the individual effects are randomly distributed. It is thus "not" the opposite of a fixed effects model. When the random effect is also assumed constant over time, we get fixed effects (i.e. a fixed effects model is a special case of random effects model). If the random effects assumption holds, the random effects model is more efficient than the fixed effects model. However, if this additional assumption does not hold (ie, if the Durbin-Wu test fails, the random effects model is not consistent.

X,Y,Z variables.

Quantitative description

Formally the model is

:

where $y_\left\{it\right\}$ is the dependent variable observed for individual i at time t, is the vector of coefficients, $x_\left\{it\right\}$ is a vector of regressors, $alpha_\left\{i\right\}$ is the individual effect and $u_\left\{it\right\}$ is the error term.

and the estimator is

:

where is the zero-mean regressor, and is the zero-mean dependent variable.

* Random effects model

* [http://www.personal.ceu.hu/departs/personal/Gabor_Kezdi/WorkingPapers/FE-RobustSE-StatSzle.pdf Robust Standard Error Estimation In Fixed-Effects Panel Models by Gabor Kezdi]
* [http://www.jr2.ox.ac.uk/bandolier/booth/glossary/fixed.html Fixed effect model at Bandolier (Oxford EBM website)]
* [http://teaching.sociology.ul.ie/DCW/confront/node45.html Fixed and random effects models]
* [http://www.ioa.pdx.edu/newsom/mlrclass/ho_randfixd.doc Distinguishing Between Random and Fixed: Variables, Effects, and Coefficients]
* [http://www.pitt.edu/~SUPER1/lecture/lec1171/012.htm How to Conduct a Meta-Analysis: Fixed and Random Effect Models]
* [http://www.statsoft.com/textbook/glosf.html Fixed Effects (in ANOVA)]

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Random effects model — In statistics, a random effect(s) model, also called a variance components model is a kind of hierarchical linear model. It assumes that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy. In …   Wikipedia

• Linear regression — Example of simple linear regression, which has one independent variable In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one… …   Wikipedia

• List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

• List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… …   Wikipedia

• Meta-analysis — In statistics, a meta analysis combines the results of several studies that address a set of related research hypotheses. In its simplest form, this is normally by identification of a common measure of effect size, for which a weighted average… …   Wikipedia

• Mixed model — A mixed model is a statistical model containing both fixed effects and random effects, that is mixed effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences. They are particularly useful… …   Wikipedia

• Analysis of variance — In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of… …   Wikipedia

• Charles Roy Henderson — For other people named Charles Henderson, see Charles Henderson (disambiguation). Charles Roy Henderson [[File:More Henderson Biography|225px|alt=]] Born April 1, 1911 …   Wikipedia

• Likelihood function — In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of …   Wikipedia

• List of mathematics articles (R) — NOTOC R R. A. Fisher Lectureship Rabdology Rabin automaton Rabin signature algorithm Rabinovich Fabrikant equations Rabinowitsch trick Racah polynomials Racah W coefficient Racetrack (game) Racks and quandles Radar chart Rademacher complexity… …   Wikipedia


text:
Not signed in (Sign In)

# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Sign in using OpenID

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• I created a stub certified programming.

That’s motivated from me having expanded the Idea-section at type theory. I enjoyed writing the words “is used in industry”. There are not many $n$Lab pages where I can write these words.

I am saying this only half-jokingly. Somehow there is something deep going on.

Anyway, in (the maybe unlikely) case that somebody reading this here has lots of information about the use and relevance of certified programming in industry, I’d enjoy seeing more information added to that entry.

• fix link

lelf

• Page created, but author did not leave any comments.

Egbert Rijke

• starting something

• Since it came up in another thread, I’ve made reverse mathematics slightly less stubby. I included some notes on constructive reverse mathematics, but perhaps it should have its own page.

• Neatened things up a little.

• now I have finally the time to come back to this, as announced, and so I am now starting an entry:

So far there is just some literature collected. I now plan to extract the essence of Seely’s artice into the entry in some technical detail.

• Redirect: rationals

• starting stub article on locally small types in homotopy type theory

Anonymous

• starting stub article on essentially small types in homotopy type theory

Anonymous

• starting stub article on the type theoretic axiom of replacement

Anonymous

• Page created, but author did not leave any comments.

Egbert Rijke

• Add Kanamori reference (from David Roberts's blog)

• I have created an entry type of types. Wanted to collect some literature there, but ended up not finding too much…

• adding examples

Anonymous

• I have worked a bit on contractible type. Apart from beautifying it a bit (or so I hope I did) I have added in the section Categorical semantics a fair bit of pedestrian detail on how to see that a term of $isContr(A)$ is indeed a contraction right homotopy, and vice versa.

• The term “discrete mathematics”, as it is actually used in the literature, appears to be synonymous with combinatorics.

Its use appears to be limited mostly to introductory textbooks on combinatorics.

I suggest that this article reflects the actual use of this term, and, in particular, does not claim that (∞,1)-toposes are part of discrete mathematics, as it currently does.

Do we really need a separate article here, or should this be merged into combinatorics, with a section on terminology there?

• added pointer to today’s

• Zhihao Duan, Kimyeong Lee, Kaiwen Sun, Hecke Relations, Cosets and the Classification of 2d RCFTs $[$arXiv:2206.07478$]$
• created homotopy level

However, the instiki-table does not come out correctly yet. It did before I added the third column. These tables are the most delicate things. I never know why sometimes they display correctly and sometimes not.

• brief category: people-entry, for the moment just to attribute the naming at Betti number

• added missing publication data to some references, and added this new reference:

• D. Melnikov, A. Mironov, S. Mironov, A. Morozov, An. Morozov, A modular functor which is universal for quantum computation, Nucl. Phys. B926 (2018) 491-508 (arXiv:1703.00431)
• This is the list from proof assistant – Examples, and was (incompleteky) copied by hand into related entries, but we should make it (as done hereby) a standalone to be !includeed under “Related concepts” in relevant entries

All I did in editing was to group the proof assistants into “based on type/set theory” and “applicable to homotopy type theory”. Experts please hit “edit” and improve on it

• Page created, but author did not leave any comments.

Anonymous

• copying article from HoTT wiki

Anonymous

• brief category:people-entry for hyperlinking references

• the entry that used to be titled quantum mechanics in terms of dagger-compact categories I have renamed into finite quantum mechanics in terms of dagger-compact categories (with a “finite” up front) and I have added to the first sentence the qualifier “finite” and “finite-dimensional” a bunch of times.

I am currently at “Quantum Physics and Logic 2012” in Brussels, and every second speaker advertizes the formalism of what they call “categorical quantum theory”. It’s all fine for the majority of the audience which is all into quantum information theory, where one is only interested in shuffling a finite bunch of qbits around, but it is rather misleading from an ordinary perspective on quantum physics. Already the particle on the line is not a finite quantum system.

• Page created, but author did not leave any comments.

Anonymous

• adding webpage for Jason Gross

Anonymous

• updating home page for Guillaume Brunerie

Anonymous

• adding github page for Egbert Rijke

Anonymous

• adding pdf file link to reference

Anonymous

• brief category:people-entry for hyperlinking references

• am changing page name from “…F-theory…” to “…M/F-theory” since I will now add discussion and references in that more general case

• created spectral triple, but so far a bit bizarre:

I give an unorthodox category-theoretic VAGUE definition, which I have reason to think is the right one

and then I record an unusual reference on vonNeumann spectral triple (just because at MO somebody asked for this and I don't like to dig out a link just to throw it away after one reference use like a paper napkin )

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• commented list of some background references for today’s

• Mitsutoshi Fujita, Yoshitaka Hatta, Shigeki Sugimoto, Takahiro Ueda, Nucleon D-term in holographic QCD $[$arXiv:2206.06578$]$
• this is a bare list of references, to be !include-ed as a subsection in the References-sections of relevant entries

• Edit to: GUT by Urs Schreiber at 2018-04-01 01:21:13 UTC.

Author comments:

added pointer to textbook account

• a stub entry, for the moment just so as to be able to record some references

• Will start something here.

• Added to Klein geometry a section History with quotations for where exactly Klein actually speaks about $G/H$.

(This key passages is a bit hidden in Klein’s text, appearing at a somewhat unexpected point somewhere in the middle of a 35 page document.)

• starting something – not done yet, but need to save

• starting something, but not much more than a stub for the moment

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references


text:
# Import Statement

Import statement allows you to use code that in different files or written by others.

## Use Multiple Files

Put all your code in one file is bad for maintenance and hard to navigate between code. Put your code in to multiple files can make your work easier.

Just for demonstration, let’s create two files, one called main.py and another called functions.py. Then put the following code to those files:

xxxxxxxxxx#code in functions.pydef greet(name):    print("Hello, " + name + "!")
xxxxxxxxxx#code in main.pyimport functions             #import <fileName>functions.greet("Pegasis")   #fileName.functionName()

Then run main.py, you will see Hello, Pegasis! been printed out.

If you think use fileName.functionName() to invoke functions in other files is annoying, use another way to import it:

xxxxxxxxxx#code in main.pyfrom functions import *greet("Pegasis")

But this way is not encouraged because you may have conflicts. (for example a function you import have the same name with a function in your code)

## Use Modules

You can also import from others code using same syntax. For example you can import numpy for scientific math calculation, import pygame for making games and import tkinter for creating GUI (which we will learn later).