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Distributed Processing¶

This mode assumes that the data set is split into nblocks blocks across computation nodes.

Algorithm Parameters¶

QR decomposition in the distributed processing mode has the following parameters:

Parameter

Default Valude

Description

computeStep

Not applicable

The parameter required to initialize the algorithm. Can be:

• step1Local - the first step, performed on local nodes

• step2Master - the second step, performed on a master node

• step3Local - the final step, performed on local nodes

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

Performance-oriented computation method, the only method supported by the algorithm.

Use the three-step computation schema to compute QR decomposition:

Step 1 - on Local Nodes¶

In this step, QR decomposition accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

data

Pointer to the $$n_i \times p$$ numeric table that represents the $$i$$-th data block on the local node. Note that each data block must have sufficient size: $$n_i > p$$.

Note

The input can be an object of any class derived from NumericTable.

In this step, QR decomposition calculates the results described below. Pass the Partial Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Partial Result ID

Result

outputOfStep1ForStep2

A collection that contains numeric tables each with the partial result to transmit to the master node for Step 2.

Note

By default, these tables are objects of the HomogenNumericTable class, but you can define them as objects of any class derived from NumericTable except the PackedSymmetricMatrix class, CSRNumericTable class, and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

outputOfStep1ForStep3

A collection that contains numeric tables each with the partial result to keep on the local node for Step 3.

Note

By default, these tables are objects of the HomogenNumericTable class, but you can define them as objects of any class derived from NumericTable except the PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

Step 2 - on Master Node¶

In this step, QR decomposition accepts the input from each local node described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

inputOfStep2FromStep1

A collection that contains results computed in Step 1 on local nodes (outputOfStep1ForStep2).

Note

This collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix class and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

key

A key, a number of type int. Keys enable tracking the order in which partial results from Step 1 (inputOfStep2FromStep1) come to the master node, so that the partial results computed in Step 2 (outputOfStep2ForStep3) can be delivered back to local nodes in exactly the same order.

In this step, QR decomposition calculates the results described below. Pass the Result ID or Partial Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Partial Result ID

Result

outputOfStep2ForStep3

A collection that contains numeric tables to be split across local nodes to compute $$Q_1$$.

Note

By default, these tables are objects of the HomogenNumericTable class, but you can define them as objects of any class derived from NumericTable except the PackedSymmetricMatrix class, CSRNumericTable class, and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

Result ID

Result

matrixR

Pointer to the numeric table with the $$p \times p$$ upper triangular matrix $$R_1$$.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except the PackedSymmetricMatrix class, CSRNumericTable class, and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

Step 3 - on Local Nodes¶

In this step, QR decomposition accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

inputOfStep3FromStep1

A collection that contains results computed in Step 1 on local nodes (outputOfStep1ForStep3).

Note

The collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix and PackedTriangularMatrix.

inputOfStep3FromStep2

A collection that contains results computed in Step 2 on local nodes (outputOfStep2ForStep3).

Note

The collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix class and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

In this step, QR decomposition calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Result ID

Result

matrixQ

Pointer to the numeric table with the $$n \times p$$ matrix $$Q_1$$.

Note

By default, the result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.


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# Figuring out the Goo.gl API

### 15 Dec 2009

UPDATE: ‘Fatalis’ has pointed out in the comments that the POST should be made to http://goo.gl/api/url with User-agent set to ‘toolbar’. The code now works, Yay!

Google just announced their own URL shortening service. Their service can only be used from the toolbar or FeedBurner, and I don’t particularly like adding extra toolbars to my browser. Maybe I can figure out a way to use their service from the command line?

I downloaded the toolbar XPI, unzipped it and peeked inside. Horribly indented JS awaited me. Nothing jsbeautifier couldn’t fix though. Few minutes later, I arrived at this readable JS function:

So, I call getUrlShorteningRequestParams("http://www.kix.in/"); to get "[email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */&url=http%3A%2F%2Fwww.kix.in%2F&auth_token=78925814685". I see in their code that they do a POST request to the service to obtain a JSON return value that would contain the short URL. I punch it in using cURL:

Oops! Well, not really, the URL shortener from the toolbar doesn’t work either, I just get the full URL whenever I try to “share” something. Has anybody actually generated a real goo.gl short URL yet?

Their auth_token parameter seems completely superfluous to me as it is generated from the URL itself. Don’t we all know security by obscurity doesn’t work :)

format: plain


text:
Plot the actual repeat transactions and overlay it with the repeat transaction as predicted by the fitted model. Currently, following previous literature, the in-sample unconditional expectation is plotted in the holdout period. In the future, we might add the option to also plot the summed CET for the holdout period as an alternative evaluation metric.

# S3 method for clv.fitted.transactions
plot(
x,
prediction.end = NULL,
newdata = NULL,
cumulative = FALSE,
transactions = TRUE,
label = NULL,
plot = TRUE,
verbose = TRUE,
...
)

# S4 method for clv.fitted.transactions
plot(
x,
prediction.end = NULL,
newdata = NULL,
cumulative = FALSE,
transactions = TRUE,
label = NULL,
plot = TRUE,
verbose = TRUE,
...
)

## Arguments

x The fitted clv model to plot Until what point in time to predict. This can be the number of periods (numeric) or a form of date/time object. See details. An object of class clv.data for which the plotting should be made with the fitted model. If none or NULL is given, the plot is made for the data on which the model was fit. Whether the cumulative expected (and actual) transactions should be plotted. Whether the actual observed repeat transactions should be plotted. Character string to label the model in the legend Whether a plot should be created or only the assembled data is returned. Show details about the running of the function. Ignored

## Value

An object of class ggplot from package ggplot2 is returned by default. If the parameter plot is FALSE, the data that would have been melted and used to create the plot is returned. It is a data.table which contains the following columns:

period.until

The timepoint that marks the end (up until and including) of the period to which the data in this row refers.

Number of Repeat Transactions

The number of actual repeat transactions in the period that ends at period.until. Only if transactions is TRUE.

"Name of Model" or "label"

The value of the unconditional expectation for the period that ends on period.until.

## Details

prediction.end indicates until when to predict or plot and can be given as either a point in time (of class Date, POSIXct, or character) or the number of periods. If prediction.end is of class character, the date/time format set when creating the data object is used for parsing. If prediction.end is the number of periods, the end of the fitting period serves as the reference point from which periods are counted. Only full periods may be specified. If prediction.end is omitted or NULL, it defaults to the end of the holdout period if present and to the end of the estimation period otherwise.

The first prediction period is defined to start right after the end of the estimation period. If for example weekly time units are used and the estimation period ends on Sunday 2019-01-01, then the first day of the first prediction period is Monday 2019-01-02. Each prediction period includes a total of 7 days and the first prediction period therefore will end on, and include, Sunday 2019-01-08. Subsequent prediction periods again start on Mondays and end on Sundays. If prediction.end indicates a timepoint on which to end, this timepoint is included in the prediction period.

Note that only whole periods can be plotted and that the prediction end might not exactly match prediction.end. See the Note section for more details.

The newdata argument has to be a clv data object of the exact same class as the data object on which the model was fit. In case the model was fit with covariates, newdata needs to contain identically named covariate data.

The use case for newdata is mainly two-fold: First, to estimate model parameters only on a sample of the data and then use the fitted model object to predict or plot for the full data set provided through newdata. Second, for models with dynamic covariates, to provide a clv data object with longer covariates than contained in the data on which the model was estimated what allows to predict or plot further. When providing newdata, some models might require additional steps that can significantly increase runtime.

## Note

Because the unconditional expectation for a period is derived as the difference of the cumulative expectations calculated at the beginning and at end of the period, all timepoints for which the expectation is calculated are required to be spaced exactly 1 time unit apart.

If prediction.end does not coincide with the start of a time unit, the last timepoint for which the expectation is calculated and plotted therefore is not prediction.end but the start of the first time unit after prediction.end.

plot for spending models

## Examples

# \donttest{

data("cdnow")

# Fit ParetoNBD model on the CDnow data
pnbd.cdnow <- pnbd(clvdata(cdnow, time.unit="w",
estimation.split=37,
date.format="ymd"))
#> Starting estimation...#> Estimation finished!
# Plot actual repeat transaction, overlayed with the
#  expected repeat transactions as by the fitted model
plot(pnbd.cdnow)
#> Plotting from 1997-01-01 until 1998-07-05.
# Plot cumulative expected transactions of only the model
plot(pnbd.cdnow, cumulative=TRUE, transactions=FALSE)
#> Plotting from 1997-01-01 until 1998-07-05.
# Plot forecast until 2001-10-21
plot(pnbd.cdnow, prediction.end = "2001-10-21")
#> Plotting from 1997-01-01 until 2001-10-21.
# Plot until 2001-10-21, as date
plot(pnbd.cdnow,
prediction.end = lubridate::dym("21-2001-10"))
#> Plotting from 1997-01-01 until 2001-10-21.
# Plot 15 time units after end of estimation period
plot(pnbd.cdnow, prediction.end = 15)
#> Plotting from 1997-01-01 until 1998-01-04.#> Warning: Not plotting full holdout period.
# Save the data generated for plotting
#   (period, actual transactions, expected transactions)
plot.out <- plot(pnbd.cdnow, prediction.end = 15)
#> Plotting from 1997-01-01 until 1998-01-04.#> Warning: Not plotting full holdout period.
# A ggplot object is returned that can be further tweaked
library("ggplot2")
gg.pnbd.cdnow <- plot(pnbd.cdnow)
#> Plotting from 1997-01-01 until 1998-07-05.gg.pnbd.cdnow + ggtitle("PNBD on CDnow")

# }


text:
mersenneforum.org Having a bit of trouble setting up
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 2012-07-19, 08:29 #1 JamesGardiner   Jul 2012 23 Posts Having a bit of trouble setting up I recently got a new laptop (windows 64-bit) and I decided to try to run Prime95 on it. I have managed to get it to run on my old laptop (32-bit) for about a year now. My old one is running prime version 26, my new one I am trying to get on version 27. However, when I extracted the files from the zip folder, there was no worktodo.txt. This seemed wrong, but I went on anyway. I ran the application, but it is just saying 'No work to do at persent time. Waiting' on both worker windows. If anyone can help me or give me the format for the worktodo.txt file so I can make a new one and just do manual testing, that would be great. Just tell me if any further info is required.
 2012-07-19, 10:00 #2 axn     Jun 2003 543610 Posts sounds like you unzipped it into a different folder? if so, just copy the executable to the old folder (overwriting the previous exe) and you should be in business. oh, stop and quit the previous one if it is running.
 2012-07-19, 10:02 #3 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 22·7·367 Posts Can't you connect to the net? It would be much simpler. Just click on "Test/Primenet/Use the server to get work and report results", check it, give a name for the user and computer, click ok. Then go to the "Test/Worker windows" and specify preferred work type. Then connect it to the net, put it in a cooler place, and forget it open with no other daily use for few years If you are talking about recovering old work, then the worktodo is not so useful, more useful would be the temporary files (checkpoints). The worktodo everybody here can make it for you, if you say the expos and the work type you were doing on them. You can recover the expos from the primenet page, login there and look for your assignments. There are tips on the forum about how to recover the (secret) assignment keys, but they are not necessary for completion of the tasks. If you have no temporary files, you can do nothing to recover the (partial) work done on those expos. Do it like in my first paragraph to get new expos, or say the expos here and one would make a worktodo for you faster. About the structure of the worktodo you can read on wiki, if you want to do it by yourself. Last fiddled with by LaurV on 2012-07-19 at 10:10
 2012-07-19, 10:37 #4 axn     Jun 2003 22·32·151 Posts Hmmm... I missed the part about old laptop/new laptop thing. Nevermind what I said before.
 2012-07-19, 14:44 #5 Jwb52z     Sep 2002 5×132 Posts I hope the OP doesn't have the Prime95 program in a location where users aren't allowed to put applications. He should remember to put it in the Users folder under the computer name subfolder, which is usually the best place, or the "My Documents" folder.
 2012-07-19, 20:38 #6 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2012-07-20, 07:11 #7 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 22·7·367 Posts That was my first understanding too, that is why the first paragraph of my post above. At a second thought, he may mean the zip HE MADE HIMSELF from the old laptop, to move it to the new laptop (eventually at an earlier date, HW not accessible anymore) where the file was missing or corrupt. That is why the second part of my post above.
 2012-07-20, 08:43 #8 JamesGardiner   Jul 2012 23 Posts No no no. All I have done on the new laptop is download version 27. It has never run any other version, and it has no files on it from the old laptop. The reason I am trying to get a worktodo.txt file is because it is not getting any work from the server. It just says something like 'No work to do at this time. Waiting'. It has been 'waiting' for about a day now, and it has got nothing. It is definatly connected to the internet, and prime is running and connecting on my old laptop. So I am either looking for the format of the worktodo.txt so I can make one and put some manual work in there, or a way of getting it to get work from the server, when it is refusing to do so.
 2012-07-20, 09:55 #9 axn     Jun 2003 124748 Posts Ah! In that case: Code: Test > Worker Windows... Configure how many workers and what type of work. Then.. Code: Options > CPU Configure your daytime/nighttime memory and run hours Then... Code: Test > Primenet... Check the box. Put in your uname/password, and off you go.
 2012-07-21, 13:30 #10 JamesGardiner   Jul 2012 23 Posts Ok, I'll try that. Also, it may be irrelvant, but everytime I open the prime95 window (having only exited the programe as it isn't working) I have to put in all the stuff that you have to put in when you first start it again, that is, username, computer name, hours it will run, number of workers to run. EDIT: Tried it. The worker threads are still saying 'No work to do at the present time. Waiting' and the comms thread still says 'ERROR: Unable to open spool file.' 'Unable to open log file' Last fiddled with by JamesGardiner on 2012-07-21 at 13:33
2012-07-21, 17:00   #11
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

3·29·83 Posts

Quote:
 Originally Posted by JamesGardiner the comms thread still says 'ERROR: Unable to open spool file.' 'Unable to open log file'
You've never told us that before.

What is often the problem in this case (just a guess) is that you put your Prime95 folder in a spot where Windows won't let it mess with the files. Where is it located ATM?

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\end{equation*}, \begin{equation*} w'(x)=\mathstrut \amp \frac{d}{dx}\left[\sqrt{x}+\tan(x)\right]\\ h'(x) = f'(g(x))g'(x) = -4x^3\sin(x^4)\text{.} State the rule(s) used to find the derivative of each of the following combinations of $$f(x) = \sin(x)$$ and $$g(x) = x^2\text{:}$$. Use the graphs to answer the following questions. \$49.99 New. If you're seeing this message, it means we're having trouble loading external resources on our website. 2020as furniture phone and their helping another situation, and thanks for. 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text:
# Bio

My favourite part of statistics for data science is in conveying a prediction’s uncertainty. All too often, predictions are conveyed deterministically, as though an omniscient expert is broadcasting an inevitability: national GDP will increase by 5% next year; a river will peak to 0.5 meters below the town’s levee in two days. The truth, in reality, is far less certain, and that uncertainty can make the difference when making big decisions such as whether to evacuate a town. My goal, therefore, is to make it easier for all data scientists to establish and communicate uncertainty.

Conveying uncertainty requires the use of probability distributions. This means more than making an elusive Normal assumption, or fitting a test statistic to a t-distribution – it means building realistic distributions as an output, perhaps even using machine learning, and converting that output into something that’s understandable by non-experts. It also means interpreting a deterministic prediction probabilistically, such as by a mean or median. To aid in working with distributions, I’m creating packages for the R Project for Statistical Computing that make it easier to work with distributions. You can find links to these packages on this website.

My main focus these days has been on developing data science initiatives at UBC. I’ve focussed on developing and delivering the Master of Data Science (MDS) program at UBC for its first four years, and am now developing a new minor program in data science at UBC with my colleagues. I also promote the development of sane analyses by continuing to adapt STAT 545. I like to make my work public, much of which you can find from this website.

To give everything context, I like to remain aware of the demands placed on data science by staying in touch with organizations and their data science problems. I usually do this through the MDS capstone course, but I also work with various organizations on the side.

# Career

### Career Philosophy

What is an ideal career to me?

### Teaching Philosophy

What does being an effective teacher mean to me?

### CV

The things I’ve done.

# Teaching

Courses I teach or have taught at UBC.

### STAT 545

Data wrangling, exploration, and analysis with R

Regression II

### DSCI 531

Data Visualization I

### DSCI 551

Descriptive Statistics and Probability for Data Science

### DSCI 511

Programming for Data Science

### DSCI 591

MDS capstone project

# R Packages

R Packages that I am involved with.

### distplyr

Draw powerful insights using distributions.

### rqdist

Build predictive distributions using linear quantile regression.

# Recent Tutorials

Bits and pieces of resources I’ve made for teaching.

⚠ Needs cleaning ⚠

### The squared error has friends, too!

I was invited to the SFU/UBC Joint Seminar in Spring 2019 where I gave this talk. ## Warning: package 'ggplot2' was built under …

### Factor Analysis

## Here's a little tutorial on how to use the factanal function for Factor Analysis. ## Let's make a data frame using actual …

### Contour Plots

This tutorial introduces contour plots, and how to plot them in ggplot2. What is a contour plot? Suppose you have a map of a …

### Mixture distributions

This tutorial introduces the concept of a mixture distribution. We’ll look at a basic example first, using intuition, and then describe …

### Collaboration with Version Control: Git and GitHub

Does this happen to you? What about bouncing files back and forth amongst collaborators through email? Or even keeping track of your …


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# Instrument Turndown (Rangedown)

## Chapter 15 - Basic Principles of Instrument Calibration and Ranging

For example, suppose you were working at a facility where the operations personnel requested a pressure transmitter installed on a process vessel with a measurement range of 50 PSI to 90 PSI. You go to the warehouse where all the new instruments are stocked, and find a pressure transmitter with a (maximum) range of zero to 1000 PSI, and a turndown ratio of 20:1. Dividing the maximum span of 1000 PSI by 20, we arrive at a minimum span of 50 PSI. The span requested by operations for this pressure transmitter is 40 PSI (90 PSI $$-$$ 50 PSI), which means the transmitter you found in the warehouse will not be able to “turn down” that far. At best, we could range it for 50 PSI to 100 PSI, or perhaps for 40 PSI to 90 PSI, but not the 50 PSI to 90 PSI requested by operations. At this point, you could return to the operations personnel to ask if a 50 PSI span would be acceptable – if not, you will have to order a different pressure transmitter with a smaller span (or with a greater turndown ratio).
Another important consideration with turndown is the accuracy of the instrument at the stated turndown. The further an instrument is “turned down” from its maximum span, generally the worse its accuracy becomes at that reduced span. For example, the Micro Motion “ELITE” series of Coriolis mass flowmeters are advertised to perform within an accuracy envelope of $$\pm$$0.05% at turndown ratios up to 20:1, but that measurement uncertainty increases to $$\pm$$0.25% at a turndown of 100:1, and to $$\pm$$1.25% at a turndown of 500:1. It should be noted that the degradation of measurement accuracy at large turndown ratios is not some defect of Micro Motion flowmeters (far from it!), but rather an inescapable consequence of pushing an instrument’s turndown to its limit.


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# Implementing a Heap

November 23, 2013

In this article, we implement a [Heap data structure](http://en.wikipedia.org/wiki/Heap(datastructure)). Since this is a fundamental data structure, the conceptual details of Heaps are discussed in many data structure textbooks. I shall, therefore, not repeat them here. Nonetheless, I shall discuss the Heap implementation with an example usage in mind, so that it is more concrete and provides a way to adapt the implementation for other purposes.

## Usage in mind

I wrote this module while I was a research fellow at Cardiff University. We were trying to find ways in which we could decrease particle simulation time using GPGPU, with the hope that it could be applied to the reduction of radiotherapy dose calculation times.

Within the system that was developed, a Heap data structure named ParticleRepository maintains the particles that are being simulated. Each of these particles are encapsulated by the Particle data structure. To parallelise a simulation using GPU threads, the simulation space represented by a Cuboid is first partitioned orthogonally into multiple subcuboids of equal dimensions. Every particle inside the simulation space therefore belongs to one of these subcuboids, and this is recorded inside a Particle by the unique index subcuboid. The subcuboid index is updated every time a particle leaves the current subcuboid.

Within the particles repository heap, all of the particles are ordered using the subcuboid index. This allows the simulation driver to dispatch particle groups that are inside the same subcuboid to architecturally related group of threads (e.g., CUDA thread block), thus maximising sharing of simulation environment that are common to all particles inside a subcuboid (e.g., CSG models of machine components). The particles repository heap itself is stored in memory as a fixed array of particles, named head, which is an array implementation of a complete binary tree. In the next post, we shall consider the case where we use paging to allow the particles repository heap to grow when the particles simulated no longer fits inside the fixed array.

## Add particle to particle repository

Function heap_insert_fast(pr,t) inserts a new particle t into the particles repository pr. We bubble up the new node to its rightful place using the containing subcuboid as the comparison key. This bubbling is done by climbing up the tree starting at the array position dictated by the array implementation of a complete binary tree, and moving the node from child to parent as we climb up. The insertion is complete when the node is finally placed at its rightful place based on the outcome of the key comparison.

void heap_insert_fast(ParticleRepository *pr, Particle *t)
{
uint32_t p, n; /* indices of parent and current node */
Particle *fp;
fp = pr->head; /* complete binary tree: array of particles */
n = ++pr->count; /* start bubbling from the last node */
p = n >> 1;
while (p > 0) { /* bubble up the tree */
if (fp[p].subcuboid < t->subcuboid)
fp[n] = fp[p];  /* move from parent to child */
else break; /* rightful place found */
n = p; /* climb up the tree */
p = n >> 1;
}
if (0 == t->id)
t->id = pr->pid++; /* give unique id to particle */
fp[n] = *t; /* place node */
}

## Remove particle from particle repository

Function heap_remove_fast(pr,t) removes the particle at the top of the heap representing the particles repository pr, and stores the particle into t. We remove the first node, which is always the top of the heap. We then fill this void by promoting the last node of the complete binary tree to become the root. Finally, we re-balance the heap by bubbling down the root until we find its rightful place, or we find that it has become a leaf. While bubbling down, we move either the left or right subtree root to the current node position as we climb down the tree. This is again based on the outcome of a key comparison.

void heap_remove_fast(ParticleRepository *pr, Particle *t)
{
uint32_t n, l, r, q; /* indices to node, left, right and last */
Particle temp, *fp;
fp = pr->head; /* complete binary tree: array of particles */
*t = fp[1]; /* particle to return */
q = pr->count--;
if (q) {
temp = fp[q]; /* the last node to be promoted */
n = 1; /* start at the root */
l = 2;
/* bubble down the tree choosing left or right subtree */
while (l < q) {
r = l + 1;
if (fp[q].subcuboid < fp[l].subcuboid) {
if (r < q && fp[l].subcuboid < fp[r].subcuboid) {
fp[n] = fp[r];
n = r;
} else {
fp[n] = fp[l];
n = l;
}
} else {
if (r < q && fp[q].subcuboid < fp[r].subcuboid) {
fp[n] = fp[r];
n = r;
} else break; /* rightful place found */
}
l = n << 1; /* go deeper until we have passed a leaf */
}
fp[n] = temp; /* place node */
}
}


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# Question 6cdf0

Jul 14, 2016

Here's how you can do that.

#### Explanation:

Dimensional analysis is all about using conversion factors to go from one unit to another.

In this case, to get from days to seconds you have to use conversion factors that take you from

• days $\to$ hours
• hours $\to$ minutes
• minutes $\to$ seconds

Now, these are all fairly common conversion factors, so I won't go into any detail about them. Starting with $2.5$ days, you can say that you have

2.5 color(red)(cancel(color(black)("days"))) * overbrace((24color(red)(cancel(color(black)("hours"))))/(1color(red)(cancel(color(black)("day")))))^(color(blue)("days to hours")) * overbrace((60 color(red)(cancel(color(black)("minutes"))))/(1color(red)(cancel(color(black)("hour")))))^(color(purple)("hours to minutes")) * overbrace("60 seconds"/(1color(red)(cancel(color(black)("minute")))))^(color(darkgreen)("minutes to seconds")) = "216,000 seconds"

Seeing how you only have two sig figs for the number of days given to you, the answer should be rounded off to

"2.5 days " = color(green)(|bar(ul(color(white)(a/a)color(black)("220,000 seconds")color(white)(a/a)|)))#


text:
nLab cobordism category

Context

Manifolds and Cobordisms

manifolds and cobordisms

Contents

Idea

The notion of cobordism category is an abstract one intended to capture important features of (many variants of) the category of cobordisms and include in the same formalism cobordisms for closed manifolds with various kinds of structure.

The passage from a manifold $M$ to its boundary $\partial M$ has some formal properties which are preserved in the presence of orientation, for manifolds with additional structure and so on. The category of compact smooth manifolds with boundary $D = Diff_c$ has finite coproducts and the boundary operator $\partial:D\to D$, $M\mapsto \partial M$ is an endofunctor commuting with coproducts. (Often these coproducts are referred to as direct sums, and some say that $\partial$ is an additive functor, but $D$ is not actually an additive category). The inclusions $i_M:\partial M\to M$ form a natural transformation of functors $i:\partial\to Id$. Finally, the isomorphism classes of objects in $D$ form a set, so $D$ is essentially small (svelte).

Definition

Axiomatization

Definition

A cobordism category is a triple $(D,\partial,i)$ where

• $D$ is a svelte category

• with finite coproducts (called direct sums, often denoted by $+$),

• including an initial object $0$ (also often denoted by $\emptyset$),

• $\partial:D\to D$ is an additive (direct-sum-preserving) functor

• and $i:\partial\to Id_D$ is a natural transformation such that $\partial\partial M = 0$ for all objects $M\in D$.

Note that $i$ is not required to be a subfunctor of the identity, i.e. the components $i_M$ are not required to be monic, which is however often the case in examples.

Definition

Two objects $M$ and $N$ in a cobordism category $(D,\partial,i)$ are said to be cobordant, written $M\sim_{cob} N$, if there are objects $U,V\in D$ such that $M+\partial U \cong N+\partial V$ where $\cong$ denotes the relation of being isomorphic in $D$.

Remark

In particular, isomorphic objects are cobordant. Being cobordant is an equivalence relation and for any object $M$ in $D$, one has $\partial M\sim_{cob} 0$.

Definition

Objects of the form $\partial M$ where $M$ is an object in $D$ are said to be boundaries and the objects $V$ such that $\partial V = 0$ are said to be closed.

Remark

In particular, every boundary is closed. A direct sum of closed objects (resp. boundaries) is a closed object (resp. a boundary). If an object $M$ is a boundary and $M\cong N$ then $N$ is also a boundary.

Definition

By the above, the relation of being cobordant is compatible with the direct sum, in the sense that the direct sum induces an associative commutative operation on the set of equivalence classes, which hence becomes a commutative monoid called the cobordism semigroup

$\Omega(D,\partial,i) \,,$

of the cobordism category $(D,\partial,i)$.

Properties

The homotopy type of the cobordism category

Topological case

Theorem

There is a weak homotopy equivalence

$\Omega |Cob_d| \simeq \Omega^\infty(MTSO(d))$

between the loop space of the geometric realization of the $d$-cobordism category and the Thom spectrum-kind spectrum

$\Omega^\infty MTSO(d) := {\lim_\to}_{n \to \infty} \Omega^{n+d} Th(U_{d,n}^\perp)$

where

$U_{d,n}^\perp = \{ ... \}$

Geometric case

The Thom group? $\mathcal{N}_*$ of cobordism classes of unoriented compact smooth manifolds is the cobordism semigroup for $D=Diff_c$.

References

A classical reference is

• Robert E. Stong, Notes on cobordism theory, Princeton University Press 1968 (Russian transl., Mir 1973)

The GMTW theorem about the homotopy type of the cobordisms category with topological structures on the cobordisms appears in

A generalization to geometric structure on the cobordisms is discussed in

Revised on July 16, 2014 04:29:57 by Urs Schreiber (89.204.139.73)


text:
$$\require{cancel}$$

# 3.8: Products of Vectors (Part 1)

Learning Objectives

• Explain the difference between the scalar product and the vector product of two vectors.
• Determine the scalar product of two vectors.
• Determine the vector product of two vectors.
• Describe how the products of vectors are used in physics.

A vector can be multiplied by another vector but may not be divided by another vector. There are two kinds of products of vectors used broadly in physics and engineering. One kind of multiplication is a scalar multiplication of two vectors. Taking a scalar product of two vectors results in a number (a scalar), as its name indicates. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector. A quite different kind of multiplication is a vector multiplication of vectors. Taking a vector product of two vectors returns as a result a vector, as its name suggests. Vector products are used to define other derived vector quantities. For example, in describing rotations, a vector quantity called torque is defined as a vector product of an applied force (a vector) and its lever arm (a vector). It is important to distinguish between these two kinds of vector multiplications because the scalar product is a scalar quantity and a vector product is a vector quantity.

## The Scalar Product of Two Vectors (the Dot Product)

Scalar multiplication of two vectors yields a scalar product.

Definition: Scalar Product (Dot Product)

The scalar product $$\vec{A}\; \cdotp \vec{B}$$ of two vectors $$\vec{A}$$ and $$\vec{B}$$ is a number defined by the equation

$\vec{A}\; \cdotp \vec{B} = AB \cos \varphi, \label{2.27}$

where $$\phi$$ is the angle between the vectors (shown in Figure $$\PageIndex{1}$$). The scalar product is also called the dot product because of the dot notation that indicates it.

In the definition of the dot product, the direction of angle $$\varphi$$ does not matter, and $$\varphi$$ can be measured from either of the two vectors to the other because $$\cos \varphi$$ = $$\cos (−\varphi)$$ = $$cos (2 \pi − \varphi)$$. The dot product is a negative number when 90° < $$\varphi$$ ≤ 180° and is a positive number when 0° ≤ $$\phi$$ < 90°. Moreover, the dot product of two parallel vectors is $$\vec{A} \cdotp \vec{B}$$ = AB cos 0° = AB, and the dot product of two antiparallel vectors is $$\vec{A}\; \cdotp \vec{B}$$ = AB cos 180° = −AB. The scalar product of two orthogonal vectors vanishes: $$\vec{A}\; \cdotp \vec{B}$$ = AB cos 90° = 0. The scalar product of a vector with itself is the square of its magnitude:

$\vec{A}^{2} \equiv \vec{A}\; \cdotp \vec{A} = AA \cos 0^{o} = A^{2} \label{2.28}$

Example $$\PageIndex{1}$$: The Scalar Product

For the vectors shown in Figure 2.3.6, find the scalar product $$\vec{A}\; \cdotp \vec{F}$$.

Strategy

From Figure 2.3.6, the magnitudes of vectors $$\vec{A}$$ and $$\vec{B}$$ are A = 10.0 and F = 20.0. Angle $$\theta$$, between them, is the difference: $$\theta = \varphi - \alpha$$ = 110° − 35° = 75°. Substituting these values into Equation \ref{2.27} gives the scalar product.

Solution

A straightforward calculation gives us

$\vec{A}\; \cdotp \vec{F} = AF \cos \theta = (10.0)(20.0) \cos 75^{o} = 51.76 \ldotp$

Exercise 2.11

For the vectors given in Figure 2.3.6, find the scalar products $$\vec{A}\; \cdotp \vec{B}$$ and $$\vec{B}\; \cdotp \vec{C}$$.

In the Cartesian coordinate system, scalar products of the unit vector of an axis with other unit vectors of axes always vanish because these unit vectors are orthogonal:

$\hat{i}\; \cdotp\; \hat{j} = |\hat{i}||\hat{j}| \cos 90^{o} = (1)(1)(0) = 0, \label{2.29}$

$\hat{i}\; \cdotp\; \hat{k} = |\hat{i}||\hat{k}| \cos 90^{o} = (1)(1)(0) = 0,$

$\hat{k} \cdotp\; \hat{j} = |\hat{k}||\hat{j}| \cos 90^{o} = (1)(1)(0) = 0 \ldotp$

In these equations, we use the fact that the magnitudes of all unit vectors are one: $$|\hat{i}| = |\hat{j}| = |\hat{k}|$$ = 1. For unit vectors of the axes, Equation \ref{2.28} gives the following identities:

$\hat{i}\; \cdotp\; \hat{i} = i^{2} = \hat{j}\; \cdotp\; \hat{j} = j^{2} = \hat{k}\; \cdotp\; \hat{k} = 1 \ldotp \label{2.30}$

The scalar product $$\vec{A}\; \cdotp \vec{B}$$ can also be interpreted as either the product of B with the projection A$$_{\parallel}$$ of vector $$\vec{A}$$ onto the direction of vector $$\vec{B}$$ (Figure $$\PageIndex{1}$$(b)) or the product of A with the projection B$$_{\parallel}$$ of vector $$\vec{B}$$ onto the direction of vector $$\vec{A}$$ (Figure $$\PageIndex{1}$$(c)):

$\begin{split} \vec{A}\; \cdotp \vec{B} & = AB \cos \varphi \\ & = B(A \cos \varphi) = BA_{\parallel} \\ & = A(B \cos \varphi) = AB_{\parallel} \ldotp \end{split}$

For example, in the rectangular coordinate system in a plane, the scalar x-component of a vector is its dot product with the unit vector $$\hat{i}$$, and the scalar y-component of a vector is its dot product with the unit vector $$\hat{j}$$:

$\begin{cases} \vec{A}\; \cdotp\; \hat{i} = |\vec{A}||\hat{i}| \cos \theta_{A} = A \cos \theta_{A} = A \cos \theta_{A} = A_{x} \\ \vec{A}\; \cdotp\; \hat{j} = |\vec{A}||\hat{j}| \cos (90^{o} - \theta_{A}) = A \sin \theta_{A} = A_{y} \end{cases}$

Scalar multiplication of vectors is communtative,

$\vec{A}\; \cdotp \vec{B} = \vec{B}\; \cdotp \vec{A}, \label{2.31}$

and obeys the distributive law:

$\vec{A}\; \cdotp (\vec{B} + \vec{C}) = \vec{A}\; \cdotp \vec{B} + \vec{A}\; \cdotp \vec{C} \ldotp \label{2.32}$

We can use the commutative and distributive laws to derive various relations for vectors, such as expressing the dot product of two vectors in terms of their scalar components.

Exercise 2.12

For vector $$\vec{A} = A_{x}\; \hat{i} + A_{y}\; \hat{j} + A_{z}\; \hat{k}$$ in a rectangular coordinate system, use Equation \ref{2.29} through Equation \ref{2.32} to show that $$\vec{A}\; \cdotp \hat{i} = A_{x} \vec{A}\; \cdotp\; \hat{j} = A_{y}$$ and $$\vec{A}\; \cdotp\; \hat{k} = A_{z}$$.

When the vectors in Equation \ref{2.27} are given in their vector component forms,

$\vec{A} = A_{x}\; \hat{i} + A_{y}\; \hat{j} + A_{z}\; \hat{k}\; and \vec{B} = B_{x}\; \hat{i} + B_{y}\; \hat{j} + B_{z}\; \hat{k},$

we can compute their scalar product as follows:

$\begin{split} \vec{A}\; \cdotp \vec{B} & = (A_{x}\; \hat{i} + A_{y}\; \hat{j} + A_{z}\; \hat{k})\; \cdotp (B_{x}\; \hat{i} + B_{y}\; \hat{j} + B_{z}\; \hat{k}) \\ & = A_{x}B_{x}\; \hat{i}\; \cdotp\; \hat{i} + A_{x}B_{y}\; \hat{i}\; \cdotp\; \hat{j} + A_{x}B_{z}\; \hat{i}\; \cdotp\; \hat{k} \\ & + A_{y}B_{x}\; \hat{j} \cdotp\; \hat{i} + A_{y}B_{y}\; \hat{j}\; \cdotp\; \hat{j} + A_{y}B_{z}\; \hat{j} \cdotp\; \hat{k} \\ & + A_{z}B_{x}\; \hat{k}\; \cdotp\; \hat{i} + A_{z}B_{y}\; \hat{k}\; \cdotp\; \hat{j} + A_{z}B_{z}\; \hat{k}\; \cdotp\; \hat{k} \ldotp \end{split}$

Since scalar products of two different unit vectors of axes give zero, and scalar products of unit vectors with themselves give one (see Equation \ref{2.29} and Equation \ref{2.30}), there are only three nonzero terms in this expression. Thus, the scalar product simplifies to

$\vec{A}\; \cdotp \vec{B} = A_{x}B_{x} + A_{y}B_{y} + A_{z}B_{z} \ldotp \label{2.33}$

We can use Equation \ref{2.33} for the scalar product in terms of scalar components of vectors to find the angle between two vectors. When we divide Equation \ref{2.27} by AB, we obtain the equation for cos $$\varphi$$, into which we substitute Equation \ref{2.33}:

$\cos \varphi = \frac{\vec{A}\; \cdotp \vec{B}}{AB} = \frac{A_{x}B_{x} + A_{y}B_{y} + A_{z}B_{z}}{AB} \ldotp \label{2.34}$

Angle $$\varphi$$ between vectors $$\vec{A}$$ and $$\vec{B}$$ is obtained by taking the inverse cosine of the expression in Equation \ref{2.34}.

Example $$\PageIndex{2}$$

Three dogs are pulling on a stick in different directions, as shown in Figure $$\PageIndex{2}$$. The first dog pulls with force $$\vec{F}_{1}$$ = (10.0 $$\hat{i}$$ − 20.4 $$\hat{j}$$ + 2.0 $$\hat{k}$$)N, the second dog pulls with force $$\vec{F}_{2}$$ = (−15.0 $$\hat{i}$$ − 6.2 $$\hat{k}$$)N , and the third dog pulls with force $$\vec{F}_{3}$$ = (5.0 $$\hat{i}$$ + 12.5 $$\hat{j}$$)N . What is the angle between forces $$\vec{F}_{1}$$ and $$\vec{F}_{2}$$?

Strategy

The components of force vector $$\vec{F}_{1}$$ are F1x = 10.0 N, F1y= −20.4 N, and F1z = 2.0 N, whereas those of force vector $$\vec{F}_{2}$$ are F2x = −15.0 N, F2y = 0.0 N, and F2z = −6.2 N. Computing the scalar product of these vectors and their magnitudes, and substituting into Equation \ref{2.34} gives the angle of interest.

Solution

The magnitudes of forces $$\vec{F}_{1}$$ and $$\vec{F}_{2}$$ are

$F_{1} = \sqrt{F_{1x}^{2} + F_{1y}^{2} + F_{1z}^{2}} = \sqrt{10.0^{2} + 20.4^{2} + 2.0^{2}}N = 22.8\; N$

and

$F_{2} = \sqrt{F_{2x}^{2} + F_{2y}^{2} + F_{2z}^{2}} = \sqrt{15.0^{2} + 6.2^{2}}N = 16.2\; N \ldotp$

Substituting the scalar components into Equation \ref{2.33} yields the scalar product

$\begin{split} \vec{F}_{1}\; \cdotp \vec{F}_{2} & = F_{1x}F_{2x} + F_{1y}F_{2y} + F_{1z}F_{2z} \\ & = (10.0\; N)(-15.0\; N) + (-20.4\; N)(0.0\; N) + (2.0\; N)(-6.2\; N) \\ & = -162.4\; N^{2} \ldotp \end{split}$

Finally, substituting everything into Equation \ref{2.34} gives the angle

$\cos \varphi = \frac{\vec{F}_{1}\; \cdotp \vec{F}_{2}}{F_{1}F_{2}} = \frac{-162.4\; N^{2}}{(22.8\; N)(16.2\; N)} = -0.439 \Rightarrow \varphi = \cos^{-1} (-0.439) = 116.0^{o} \ldotp$

Significance

Notice that when vectors are given in terms of the unit vectors of axes, we can find the angle between them without knowing the specifics about the geographic directions the unit vectors represent. Here, for example, the +x-direction might be to the east and the +y-direction might be to the north. But, the angle between the forces in the problem is the same if the +x-direction is to the west and the +y-direction is to the south.

Exercise 2.13

Find the angle between forces $$\vec{F}_{1}$$ and $$\vec{F}_{3}$$ in Example $$\PageIndex{2}$$.

Example $$\PageIndex{3}$$: The Work of a Force

When force $$\vec{F}$$ pulls on an object and when it causes its displacement $$\vec{D}$$, we say the force performs work. The amount of work the force does is the scalar product $$\vec{F}\; \cdotp \vec{D}$$. If the stick in Example $$\PageIndex{2}$$ moves momentarily and gets displaced by vector $$\vec{D}$$ = (−7.9 $$\hat{j}$$ − 4.2 $$\hat{k}$$)cm, how much work is done by the third dog in Example $$\PageIndex{2}$$?

Strategy

We compute the scalar product of displacement vector $$\vec{D}$$ with force vector $$\vec{F}_{3}$$ = (5.0 $$\hat{i}$$ + 12.5 $$\hat{j}$$)N, which is the pull from the third dog. Let’s use W3 to denote the work done by force $$\vec{F}_{3}$$ on displacement $$\vec{D}$$.

Solution

Calculating the work is a straightforward application of the dot product:

$\begin{split} W_{3} & = \vec{F}_{3}\; \cdotp \vec{D} = F_{3x}D_{x} + F_{3y}D_{y} + F_{3z}D_{z} \\ & = (5.0\; N)(0.0\; cm) + (12.5\; N)(-7.9\; cm) + (0.0\; N)(-4.2\; cm) \\ & = -98.7\; N\; \cdotp cm \ldotp \end{split}$

Significance

The SI unit of work is called the joule (J) , where 1 J = 1 N · m. The unit cm · N can be written as 10−2 m · N = 10−2 J, so the answer can be expressed as W3 = −0.9875 J ≈ −1.0 J.

Exercise 2.14

How much work is done by the first dog and by the second dog in Example $$\PageIndex{2}$$ on the displacement in Example $$\PageIndex{3}$$?


text:
Multiplexing UART

I'd like to interface my main microcontroller's hardware serial port to two (or more) devices at the same time. My understanding is that UART on my microcontrollers is based on an active-low 5V TTL.

(I know what I'm explaining here can be technically achieved by using better protocols such as SPI and I2C, but my project requires to only be implemented using UART.)

Here's a pseudo-schematics chart of what I'm trying to achieve:

simulate this circuit – Schematic created using CircuitLab

1. I don't want to use a second UART interface on the master, or any of the slaves.

2. Only one slave at a time is going to transmit or send data on the line to the master. (e.g. If the slave 1 is transmitting data, slave 2 and 3 should remain idle.)

3. Whatever the master is transmitting can, and should be received by all of the slaves.

4. Each slaves should be hot-pluggable, meaning they could be removed or inserted at any time.

5. The RX and TX wires to the master are parallel between each slave, so no daisy chaining.

So, my questions are as follows:

1. Assuming the correct impedance is considered, I shouldn't need an additional circuit to transmit data from the master's TX line to any of the slave's RX line simultaneously. Is this correct?

2. I understand that without current limiting resistors between slaves' TX line and the master's RX line, if any of the devices begin to broadcast data, the line between the devices will short circuit and I risk damaging them. Is this correct?

3. Assuming the items 1 and 2 are correct:

a) Should using just some current limiting resistors be enough?

b) Can I use 74-series logic gates instead of resistors?

4. Between options a and b above, what route should I choose?

5. For a reliable 115200 baud rate connection, will the switching frequency of a 74HC08 AND gate suffice to be incorporated?

EDIT: I'm well aware of other well-suited protocols such as SPI and I2C. There's a reason I'm using UART, and that's because the optiboot bootloader which my master uses communicates over UART, albeit UART s obvious limitations.

Also, while daisy-chaining is certainly a smart approach, by breaking rule 4, it also breaks Arduino bootloader functionality.

The devices could also be USB-to-Serial chips, and using SPI-to-USB or I2C-to-USB would not be feasible in this project.

So, I'd appreciate if you could focus on the 6 questions listed here instead, and share your UART knowledge. :)

• Just for 5, I dont imagine you'll have to worry about the 100ns propagation delay of that and gate – BeB00 Apr 23 '18 at 2:01
• How do you ensure that no two devices are transmitting at the same time? – JimmyB Apr 24 '18 at 11:30
• @JimmyB Simple, the devices only respond on master's request, and the master ensures the previous transmission has ended before requesting a new one. Also, each client can now wether the line is busy or not, by probing the master's RX wire, and comparing it to LOW. – David Refoua Apr 24 '18 at 12:18
• UART or RS-232? The best solution if RS-232 is available, is to implement CTS/RTS lines and use those for chip select purposes. Kind of like /SS in SPI if you will. And then you don't need any icky gates on the data lines. – Lundin Apr 24 '18 at 12:53
• Anyway, if you do end up switching the data lines, you probably don't want to use an AND gate but instead some analog switch/mux. – Lundin Apr 24 '18 at 12:57

1. For three devices no, for more, check the datasheet with regards to input capacitance.
2. Not quite dangerous but certainly it won't work
3. a) No b) yes. With few slaves it would be better with wired AND ( half connections needed) if your slaves are not on the same board.
4. Obviously, the working one, b
5. Yes

Edited to give some details

2 and 3a , even if you ignore "don't connect two outputs together" recommendation everyone agrees, the result of two ones and a zero will never be zero for cmos outputs with almost symmetrical characteristics.

3b You either have a wire from each slave to a N-input (star-like configuration) or at each slave you have an AND from it's output and the chain and use the And output for the next slave chain input.

simulate this circuit – Schematic created using CircuitLab

Obviously the chain configuration is not hot-plug.

Wired AND, you have two options depending on the slave capabilities.

If you have open drain/collector outputs for TX then you can connect them together and add a global pull-up resistor.

If not then a diode on each slave will act as a wired and as follows:

simulate this circuit

You also have a third option, simply to put the slave Tx output to HiZ after answering to a message, a pull up resistor is still needed.

• This is the kind of answer I was hoping to get, so thank you! Wish you could elaborate on 2 and 3. Also, could diodes be used to form an AND gate? – David Refoua Apr 23 '18 at 11:14
• @DRSDavidSoft Yes, this is a wired AND – Dorian Apr 24 '18 at 6:17
• Your second solution with a couple of BAT54C array shotkey diodes seems the way to go, and as such I mark your answer as the accepted one. Thanks for the explanations! – David Refoua Apr 24 '18 at 19:45

Are you married to UART? SPI would handle this better I think. The slave select would give you the multiplexing and you could prioritize one slave more than the other based on whatever the master is doing or expecting from the slaves. Speed should be at least as fast if not faster than UART. This example gets at the idea.

• SPI is coincidentally my favorite protocol, the main issue is that my project requires UART; as I'm not the one married to UART, rather Arduino's bootloader is :) – David Refoua Apr 23 '18 at 11:04
• SPI does not fit well into "Whatever the Arduino is transmitting can, and will be received by all 3 devices". Also, if there was some kind of slave select mechanism (line) available it would just as well work for the USART transmission and solve the problem. – JimmyB Apr 24 '18 at 11:29

You have to ensure they don't transmit at the same time. For example by the master polling the slaves.

Use diodes to connect multiple TXD together, pull up R at master. You can just use firmware if you want, and turn the TXD to input when not transmitting also, but diodes are easier.

All RXD can just be connected.

• I don't plan to transmit from more than one device at the same time, but other than Arduino possibly receiving a corrupted data sequence, would it damage my chips? – David Refoua Apr 23 '18 at 11:08
• Also, does using diodes count as implementing a negative AND gate? – David Refoua Apr 23 '18 at 11:08
• The function is logical OR of negative (0) values. It is nornmally called "wired OR". It is of course electrically same as using AND gate – Henry Crun Apr 23 '18 at 22:59
• You must only transmit from one at a time, otherwise data is corrupted. No other issue. My point being, you must have a way of ensuring it does not happen. Like asking each one for data in turn (polling) – Henry Crun Apr 23 '18 at 23:00
• A tip: put jumpers in the TX lines, so you can disconnect them. It can make debugging much easier when it goes wrong, or one fails – Henry Crun Apr 24 '18 at 22:38

For the line which is driven by the master and received by the slaves, nothing particularly fancy should be required if capacitive loading isn't a problem.

For the line which is driven by slaves, I would suggest that if capacitive loading wouldn't be a problem, you have connect each slave's TX line to the bus through a series resistor, and then set each state's TX pin to float when idle. Make the resistance as low as it can be without allowing an unacceptable or damaging level of current to flow in case of bus conflict.

If the required series resistance to prevent damage, combined with the parasitic capacitance, would limit speeds to be unacceptably slow, then I would suggest using a current-based approach where the slaves source current if they want to transmit. Something like:

simulate this circuit – Schematic created using CircuitLab

The left half is the transmitter, and the right half is the receiver. Note that if the Schottky diode is omitted (or if a non-Schottky diode is substituted) the receiver circuit will not operate nearly as well, since Q2 will be driven into saturation and will take awhile to come out of it. Adding the Schottky diode will prevent Q2 from turning on fully, thus allowing it to turn off faster.

As a practical suggestion, take a look at I2C: it uses the same number of wires as a UART, has similar data rate and implements the bus functionality you need, plus you'll have SW libraries already written for you.

Another protocol which is even more similar to what you're trying to do is LIN, which is basically a UART-based bus with higher signal voltage. If you have 12V available, you could simply plug LIN transceivers in your diagram between each node and the bus, and it would work. You'd have to write your own software though.

Edit: you can also implement pseudo-LIN with your own voltage levels, e.g. 5V. For example:

simulate this circuit – Schematic created using CircuitLab

• Thanks for the suggestion, however using UART is not a matter of wires count limitation, but rather a constraint of the project requirement (see EDIT). Though LIN seems promising, unfortunately I won't be able to interface it with 12V, but I'd like to implement the same functionality with 5V TTL level. – David Refoua Apr 23 '18 at 11:11
• @DRSDavidSoft Hi, I've edited my answer to add an example of a serial-to-bus with arbitrary voltage levels (e.g. 5V) – Dmitry Grigoryev Apr 23 '18 at 13:23
• Is the bus actually a single wire? This LIN protocol seems very promising for some of my other projects, it could enable me to send and receive both data and power using only two wires. Thanks for introducing it to me! – David Refoua Apr 24 '18 at 19:41
• @DRSDavidSoft You need common ground of course, so it will be 3 wires in total. Nevertheless, LIN is a good option for low data rates (20 kB/s or so). You can get higher data rates with your own transceivers (e.g. what my schematic shows), but you will lose the low EM emission property of LIN. – Dmitry Grigoryev Apr 25 '18 at 7:20

If you want to stick to one UART port you can simply daisy chain them (output of one UART go to input of another one). With this approach you don't need any extra hardware, but you need to add code to forward communication from one Arduino to next one.

EDIT I missed hot-swappable requirement so this couldn't work. But if you can guarantee that you wont swap in middle of communication or you can tolerate loss of some packets then you can just short place where you put one of Arduino's UART interface and after swap you remove short for normal operation.

• So you want to transform UART to SPI? Because that's how daisy chained SPI works. – Harry Svensson Apr 23 '18 at 10:15
• That's a clever way to handle it, but unfortunately it breaks the requested notes, and certainly won't work with rule 4 (see question). Still a smart and simple way to do it! – David Refoua Apr 23 '18 at 11:12
• The workaround is also an interesting way to make this work, I'm sure I can use your method in some of my new projects. Thanks! – David Refoua Apr 24 '18 at 12:24


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## 12.5 Latent Variables and the EM Algorithm

At the end of Section 12.3, it was pointed out that the evidence function associated with the regression task in Eq. (12.3), assuming that p(y|θ) and p(θ) are Gaussians of the form given in (12.39), is also Gaussian parameterized via a set of parameters, ξ, where for this case $ξ=[ση2,σθ2]$, and we can write p(y;ξ). Maximizing the evidence with respect to ξ becomes a typical ML task. However, in general, such closed-form expressions for the evidence function are not possible, and the integration in (12.14) is intractable. The main source of difficulty is the fact that our regression model is described ...

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# The amplitude of two waves are in the ratio 5:2. if all other conditions for the two waves are same, then what is the ratio of their energy densities? (a) 5 : 2 (b) 10 : 4 (c) 2.5 : 4 (d) 25 :4

Arun
25763 Points
one year ago

As we learnt in

Intensity of the wave -

$I = \frac{1}{2}\rho \omega ^{2}A^{2}V$

$\rho =$ mass density

$\omega =$ angular frequency

$A =$ Amplitude

$V =$ Wave speed

- wherein

flow of energy per unit area of cross section of the string in the unit time is known as intensity of wave.

Energy density  $\propto \:A^{2}$

$\Rightarrow \:\frac{E_{1}}{E_{2}}=(\frac{A_{1}}{A_{2}})^{2}=(\frac{5}{2})^{2}=25:4$

Vikas TU
14149 Points
one year ago

As sound wave travel through air, the element of air vibrate to produce change in density and pressure along the direction of motion of the wave.

- wherein

sound wave travel through any material medium with a speed that depend on the properties of medium.


text:
Next: The Kirchhoff elastodynamic integral Up: THEORY Previous: THEORY

## A least-squares formalism

Consider a point in the subsurface. I define the reflectivity matrix at the point by the following relation between the incident displacement vector field due to a source at , and the reflected displacement vector field due to a receiver at the position :

 (1)

where all quantities are evaluated locally at the point .The reflectivity matrix is of order (3x3) and, in general, is a scattering matrix which relates to and contains refractions, diffractions and reflections. However, by anticipating that will be simulated as a direct primary incident field, and will be reconstructed from refraction-muted surface observations as a single-conversion primary reflected field, the interpretation of as a generalized reflectivity matrix is justified.

Now consider the local plane-wave unit polarization vectors , where is the local P-wave propagation direction, the S1 direction, and the S2 direction. The displacement vectors can be expressed in this same ray-centered coordinate system without loss of generality:

where u1 is the P-wave displacement amplitude, u2 is the S1 displacement amplitude, and u3 is the S2 displacement amplitude. In this local ray-coordinate frame, the elements of are associated with generalized non-specular elastic reflection coefficients:

 (2)

The generalized non-specular reflection coefficients are related to the plane-wave specular Zoeppritz coefficients as discussed by Frazer and Sen (1985), and will be examined in more detail later in this paper. It is apparent that the generalized reflection coefficients within can be isolated'' by the appropriate vector dot products. For example, the coefficient can be isolated as

 (3)

where is the local P-wave polarization vector of the incident displacement vector , evaluated at the subsurface point , and is the local P-wave polarization vector of the reflected displacement vector , evaluated at the subsurface point . Please refer to Figure to see the appropriate polarization vector geometry. Similar dot product relations can be stated for the other reflection coefficients of using the appropriate vector directions .For example, the coefficient can be isolated as

 (4)

I will define the reflected scalar function on the left of (4) as and the incident scalar function on the right of (4) as :

and
 (5)

geometry
Figure 1
The elastic polarization vector geometry. The source position is at , the receiver position is at and the subsurface reflection point is at . The polarization vectors are the local P, S1 and S2 plane-wave directions, and functions of . The polarization vectors for S2 waves point out of the plane of this page.

If I can forward model numerous source wavefields and I have numerous reconstructions of the reflected wavefield from multiple surface shot gather observations, then (5) (and all of its nine converted-wave counterparts) can be rearranged into an optimization problem to estimate the isolated reflection coefficient, hereafter called . The objective function J for this problem has the general lp form

 (6)

where Wd and Wm are arbitrary weighting functions in data and model space respectively. The weighting functions in this form are nonconvolutional, and therefore correspond to diagonal covariance functions in the usual least-squares theory sense. Note that adding the second term to (6) will add stability to the final least-squares solution, and will ensure that will be a minimum energy model in the lp sense, which is appropriate for a desired spiky reflectivity solution. Choosing the l2 norm and integrating over the implicit functional dependencies, one obtains:

 (7)

To extremize J and thus find an optimal'' solution for , I perform the following stationary point analysis. Perturb J by an arbitrary small amount :

 (8)

A stationary point of J with respect to occurs when

Neglecting terms of order ,

 (9)

Since is arbitrary, then the integrand kernel must vanish at the stationary point. This results in a least-squares reflectivity solution:

 (10)

Equation (10) is a weighted zero-lag correlation of the incident and reflected wavefield scalar products, normalized by the weighted minimum-threshold energy of the incident wavefield scalar product. Equation (10) is valid for all of the generalized elastic reflection coefficients of (2) by simply making the appropriate redefinitions of and as in (5).

Next: The Kirchhoff elastodynamic integral Up: THEORY Previous: THEORY
Stanford Exploration Project
11/17/1997


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Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835Article in journal (Refereed) Accepted
##### Abstract [en]

We consider parabolic operators of the form $$\partial_t+\mathcal{L},\ \mathcal{L}:=-\mbox{div}\, A(X,t)\nabla,$$ in$\mathbb R_+^{n+2}:=\{(X,t)=(x,x_{n+1},t)\in \mathbb R^{n}\times \mathbb R\times \mathbb R:\ x_{n+1}>0\}$, $n\geq 1$. We assume that $A$ is an $(n+1)\times (n+1)$-dimensional matrix which is bounded, measurable, uniformly elliptic and complex, and we assume, in addition, that the entries of A are independent of the spatial coordinate $x_{n+1}$ as well as of the time coordinate $t$. We prove that the boundedness of associated single layer potentials, with data in $L^2$, can be reduced to two crucial estimates (Theorem \ref{th0}), one being a square function estimate involving the single layer potential. By establishing a local parabolic Tb-theorem for square functions we are then able to verify the two  crucial estimates in the case of real, symmetric operators (Theorem \ref{th2}). Our results are crucial when addressing the solvability of the classical Dirichlet, Neumann and Regularity problems for the operator $\partial_t+\mathcal{L}$ in $\mathbb R_+^{n+2}$, with $L^2$-data on $\mathbb R^{n+1}=\partial\mathbb R_+^{n+2}$, and by way of layer potentials.

2016.
Mathematics
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## 数学代写|数值分析代写numerical analysis代考|MA1020

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## 数学代写|数值分析代写numerical analysis代考|Formulation of the Problem in the Particle Frame

In this section let us consider the geometry shown in Figure 1: a perfectly conducting angular slot $\mathbb{S}=\left{r=a,|\varphi| \leq \varphi_a, z\right}$ at distance $a$ from the axis and covering an angular sector of $2 \varphi_a$. A travelling charge $q$ moves parallel to the slots’s axis, placed at $\left(r_q, \varphi_q\right)$, at constant speed $v=\beta c, c$ being the speed of light in free space.

The problem is formulated in term of integral equations and its solution is reduced to the resolution of a linear system.

The electromagnetic interaction between the particle and the structure can be easily formulated and solved in the particle frame, being an electrostatic model adequate for such a problem. Once the electromagnetic quantities are computed, their values in the slot frame can be obtained by means of Lorentz transforms.
The electrostatic potential produced by the charge is
$$V_q^{\prime}=\frac{q}{4 \pi \varepsilon_0 \sqrt{r^{\prime 2}+r_q^2-2 r^{\prime} r_q \cos \left(\varphi^{\prime}-\varphi_q\right)+z^{\prime 2}}},$$
while the potential produced by the induced charge density $\sigma^{\prime}\left(\varphi^{\prime}, z^{\prime}\right)$ on the slot can be expressed as
$$V^{\prime}=\frac{a}{4 \pi \varepsilon_0} \int_{\mathbb{S}} \frac{\sigma^{\prime}\left(\varphi_0, z_0\right) d \varphi_0 d z_0}{\sqrt{r^{\prime 2}+a^2-2 r^{\prime} a \cos \left(\varphi^{\prime}-\varphi_0\right)+\left(z^{\prime}-z_0\right)^2}} .$$
Being a perfectly conducting slot, the boundary condition to be verified is that the tangential components of the electric field vanishes on the slot. This corresponds to impose that
$$V^{\prime}\left(r^{\prime}=a, \varphi^{\prime}, z\right)+V_q^{\prime}\left(r^{\prime}=a, \varphi^{\prime}, z\right)=0$$
for every $\left(\varphi^{\prime}, z^{\prime}\right) \in \mathbb{S}$.
Considering Equations (2) and (3), the boundary condition leads to
$$\int_{\mathrm{S}} \frac{\sigma^{\prime}\left(\varphi_0, z_0\right) d \varphi_0 d x_0}{\sqrt{2 a^2-2 a^2 \cos \left(\varphi^{\prime}-\varphi_0\right)+\left(z^{\prime}-z_0\right)^2}}-\frac{q / a}{\sqrt{a^2+r_q^2-2 a r_q \cos \left(\varphi^{\prime}-\varphi_q\right)+z^{\prime 2}}}$$

## 数学代写|数值分析代写numerical analysis代考|Electromagnetic Fields in the Slot Frame

In order to complete the problem formulation, it is proper to express the electromagnetic fields in the slot frame, too. This can be realized by applying the Lorentz transforms to the fields computed in the previous section in particle frame.

Let us consider at first the $z$ component of the electric field. The contribution provided by the traveling charge in the frequency domain is well known and is
$$E_{z, q}=\frac{j q \kappa \zeta_0}{2 \pi \beta \gamma} e^{-j z k / \beta} K_0\left(\kappa \sqrt{r^2+r_q^2-2 r r_q \cos (\varphi)}\right),$$
where $\gamma=1 / \sqrt{1-\beta^2}$ is the Lorentz factor, $\kappa=k /(\beta \gamma)$, and $\zeta_0=\sqrt{\mu_0 / \varepsilon_0}$ is the characteristic impedance of free space.

The contribution produced by the induced current density on the slot can be obtained with some manipulations as function of the representation coefficients $\sigma_n$.
In the particle frame, starting from Equation (3) it is possible to obtain
$$e_z^{\prime}\left(r^{\prime}, \varphi^{\prime}, z^{\prime}\right)=\frac{a}{4 \pi \varepsilon_0} \int_{\mathbb{S}} \frac{\sigma^{\prime}\left(\varphi_0, z_0\right)\left(z^{\prime}-z_0\right) d \varphi_0 d z_0}{\left[r^{\prime 2}+a^2-2 r^{\prime} a \cos \left(\varphi^{\prime}-\varphi_0\right)+\left(z^{\prime}-z_0\right)^2\right]^{3 / 2}} .$$
Lorentz transforms are now applied to obtain the electric field in the slot frame. In this specific case they are
$$e_z^{\prime}=e_z, \sigma^{\prime}=\sigma \gamma, r^{\prime}=r, \varphi^{\prime}=\varphi, z^{\prime}=\gamma(z-v t) .$$
Applying these transforms to Equation (19), it is found that
$$e_z(r, \varphi, z, t)=\frac{a \gamma}{4 \pi \varepsilon_0} \int_{\mathbb{S}} \frac{\sigma\left(\varphi_0, z_0\right)\left(\gamma(z-v t)-z_0\right) d \varphi_0 d z_0}{\left[r^2+a^2-2 r a \cos \left(\varphi-\varphi_0\right)+\left(\gamma(z-v t)-z_0\right)^2\right]^{3 / 2}} .$$
By means of Equation (8) and applying a spatial Fourier transform according to Equation (9), it is found that
$$e_z(r, \varphi, z, t)=\frac{j a \gamma}{2 \pi \varepsilon_0} \int_{-\varphi_a}^{+\varphi_a+\infty} \int_{-\infty} \tilde{\sigma}\left(\varphi_0, w\right) w e^{j w \gamma v t} K_0\left(w \sqrt{r^2+a^2-2 r a \cos \left(\varphi-\varphi_0\right)}\right) e^{-j w \gamma z} d \varphi_0 d w$$

# 数值分析代考

## 数学代写|数值分析代写numerical analysis代考|Formulation of the Problem in the Particle Frame

$$V_q^{\prime}=\frac{q}{4 \pi \varepsilon_0 \sqrt{r^{\prime 2}+r_q^2-2 r^{\prime} r_q \cos \left(\varphi^{\prime}-\varphi_q\right)+z^{\prime 2}}},$$

$$V^{\prime}=\frac{a}{4 \pi \varepsilon_0} \int_{\mathbb{S}} \frac{\sigma^{\prime}\left(\varphi_0, z_0\right) d \varphi_0 d z_0}{\sqrt{r^{\prime 2}+a^2-2 r^{\prime} a \cos \left(\varphi^{\prime}-\varphi_0\right)+\left(z^{\prime}-z_0\right)^2}} .$$

$$V^{\prime}\left(r^{\prime}=a, \varphi^{\prime}, z\right)+V_q^{\prime}\left(r^{\prime}=a, \varphi^{\prime}, z\right)=0$$

$$\int_{\mathrm{S}} \frac{\sigma^{\prime}\left(\varphi_0, z_0\right) d \varphi_0 d x_0}{\sqrt{2 a^2-2 a^2 \cos \left(\varphi^{\prime}-\varphi_0\right)+\left(z^{\prime}-z_0\right)^2}}-\frac{}{\sqrt{a^2+r_q^2-2 a}}$$

## 数学代写|数值分析代写numerical analysis代考|Electromagnetic Fields in the Slot Frame

$$E_{z, q}=\frac{j q \kappa \zeta_0}{2 \pi \beta \gamma} e^{-j z k / \beta} K_0\left(\kappa \sqrt{r^2+r_q^2-2 r r_q \cos (\varphi)}\right)$$

$$e_z^{\prime}\left(r^{\prime}, \varphi^{\prime}, z^{\prime}\right)=\frac{a}{4 \pi \varepsilon_0} \int_{\mathbb{S}} \frac{\sigma^{\prime}\left(\varphi_0, z_0\right)\left(z^{\prime}-z_0\right) d \varphi_0 d z_0}{\left[r^{\prime 2}+a^2-2 r^{\prime} a \cos \left(\varphi^{\prime}-\varphi_0\right)+\left(z^{\prime}\right.\right.}$$

$$e_z^{\prime}=e_z, \sigma^{\prime}=\sigma \gamma, r^{\prime}=r, \varphi^{\prime}=\varphi, z^{\prime}=\gamma(z-v t) .$$

$$e_z(r, \varphi, z, t)=\frac{a \gamma}{4 \pi \varepsilon_0} \int_{\mathbb{S}} \frac{\sigma\left(\varphi_0, z_0\right)\left(\gamma(z-v t)-z_0\right) d \varphi}{\left[r^2+a^2-2 r a \cos \left(\varphi-\varphi_0\right)+(\gamma(z-\right.}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。


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# Colouring the edges by weight in networkx (Matplotlib)

MatplotlibPythonData Visualization

To color the edges by weight in networkx, we can take the following steps −

• Set the figure size and adjust the padding between and around the subplots.
• Initialize a graph with edges, name, or graph attributes.
• Add nodes to the current graph.
• Add edges to the current graph's nodes.
• Iterate the given graph's edges and set some weight to them.
• Draw current graphs with weights for edge color.
• To display the figure, use show() method.

## Example

import random as rd
import matplotlib.pylab as plt
import networkx as nx

plt.rcParams["figure.figsize"] = [7.50, 3.50]
plt.rcParams["figure.autolayout"] = True

G = nx.DiGraph()
plt.show()


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HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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# Algebra of Continuous Functions

#### theorem

Suppose f and g be two real functions continuous at a real number c. Then
(1) f + g is continuous at x = c.
(2) f – g is continuous at x = c.
(3) f . g is continuous at x = c.
(4) (f/g) is continuous at x = c ,
(provided g(c) ≠ 0).

Proof:  We are investigating continuity of (f + g) at x = c.
Clearly it is defined at x = c. We have
lim_(x->c)(f + g)(x) = lim_(x->c)[f(x) + g(x)]
(by defination of f + g)
lim_(x->c)f(x) + lim_(x->c)g(x)
(by the theorem on limits)
= f(c) + g(c)  (as f and g are continuous)
=(f+g)(c)       (by defination of f + g)
Hence, f + g is continuous at x = c. Proofs for the remaining parts are similar and left as an exercise to the reader.

Remarks:
(i) As a special case of (3) above, if f is a constant function, i.e., f(x) = λ for some real number λ, then the function (λ . g) defined by (λ . g) (x) = λ . g(x) is also continuous. In particular if λ = – 1, the continuity of f implies continuity of – f.

(ii) As a special case of (4) above, if f is the constant function f(x) = λ, then the function lambda/g defined by lambda/g(x) = lambda/g(x) is also continuous wherever g(x) ≠ 0.

In particular, the continuity of g implies continuity of  1/g
The above theorem can be exploited to generate many continuous functions. They also aid in deciding if certain functions are continuous or not.

#### Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1

Series 2

Series 3

### Shaalaa.com

algebra of continuous function [00:36:17]
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series 3
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sparse-tensor-0.2: typesafe tensor algebra library

Copyright (c) 2019 Tobias Reinhart and Nils Alex MIT tobi.reinhart@fau.de, nils.alex@fau.de None Haskell2010

Math.Tensor.Examples.Gravity.SchwarzschildSymbolic

Description

This module provides the Schwarzschild metric as an example for a tensor with symbolic values as well as functions to calculate Christoffel symbols, Ricci tensors and Einstein tensors from metric tensors with symbolic values.

Synopsis

# Documentation

Schwarzschild metric $$g = (1-\frac{r_\text{s}}{r})\,\mathrm dt\otimes\mathrm dt - \frac{1}{1-\frac{r_\text{s}}{r}}\,\mathrm dr\otimes \mathrm dr - r^2\,\mathrm d\theta\otimes \mathrm d\theta - r^2\sin^2\theta\,\mathrm d\phi\otimes \mathrm d\phi$$.

Inverse Schwarzschild metric $$g = \frac{1}{1-\frac{r_\text{s}}{r}}\,\partial_t \otimes \partial_t - (1-\frac{r_\text{s}}{r})\,\partial_r \otimes \partial_r - \frac{1}{r^2}\,\partial_\theta \otimes \partial_\theta - \frac{1}{r^2\sin^2\theta}\,\partial_\phi \otimes \partial_\phi$$.

Christoffel symbols of any symbolic metric.

ricciS :: STTens 0 2 SSymbolic -> STTens 2 0 SSymbolic -> STTens 0 2 SSymbolic Source #

Ricci tensor of any symbolic metric.

Einstein tensor of any symbolic metric. The components evaluate to zero:

>>> let g  = schwarzschildS
>>> let g' = schwarzschildS'
>>> let e  = einsteinS g g'
>>> print e
ZeroTensor -- modulo symbolic simplification, which is not implemented yet.


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# What are the chances of funding cuts to science? (at the levels of the UK?)

by Simfish
Tags: chances, cuts, funding, levels, science
 PF Gold P: 828 I'm quite concerned about that...
 P: 1,123 Have you heard of any specific proposals for cuts?
 P: 3,390 The government are culling everything by the looks of it (aside from the things we really could cut - the olympics for one). Haven't seen any direct proposals, but they're slowly working through the lot. The only thing apparantely free of cuts so far is sports. In two years the university fees are going up to £9000 per year.
Emeritus
PF Gold
P: 11,154

## What are the chances of funding cuts to science? (at the levels of the UK?)

jared, Simfish is worried about cuts in the US.
P: 771
 Quote by WhoWee Have you heard of any specific proposals for cuts?
I heard about plans for a government hearing about the "scientific fraud" behind global warming. I know it's a banned topic here, but I think many of us can agree that the US Congress isn't in a position to determine scientific fraud, since so few of them are actually scientists.

http://www.theatlantic.com/politics/...-future/65477/

 According to Newsweek, the White House plans to aggressively enforce environmental regulations as they anticipate efforts from Republicans to strip authority from the EPA. Compromise on renewable energy standards is possible, but the posturing between Rep. Joe Barton, the chairman of the energy committee, and the administration, may make this terribly difficult. The GOP plans to hold high profile hearings examining the alleged "scientific fraud" behind global warming, a sleeper issue in this election that motivated the base quite a bit.
 P: 75 [QUOTE=Jack21222;2967838] but I think many of us can agree that the US Congress isn't in a position to determine scientific fraud, since so few of them are actually scientists. QUOTE] If there are so few of them able to determine if it is real science, or fraud, should they be able to pass laws based on said science, just because some scientists say it is so, or do they have a responsibility to weigh the facts, as they(and the public) see them? Imo, if the science is valid, bringing the facts into the light wont hurt.
 Sci Advisor P: 1,724 There were 3 actual scientists in the two houses, all physicists, all congressmen: http://www.nytimes.com/2008/06/10/science/10phys.html The one Republican, Vernon J. Ehlers, retired. Rush Holt won re-election yesterday, but Bill Foster was defeated. Given Energy Secretary Stephen Chu's questioning (on plate tectonics) at the hands of Joe Barton, any investigation that might be launched doesn't bode well from a purely scientific point of view. Although they might go more along the lines of a lack of fiduciary duty and/or financial fraud, instead (not saying there's anything there, but that sort of investigation would be more up their alley). EDIT: Looks like there're a few more with science backgrounds, including a chemist (John Olver) and an engineer with a Ph.D. in mathematics (Jerry McNerney): http://engineering.curiouscatblog.ne...s-in-congress/
 PF Gold P: 828 Looks like there's a good chance they'll cut science: http://www.nytimes.com/2010/11/04/bu...er=rss&emc=rss
P: 3,390
 Quote by Gokul43201 jared, Simfish is worried about cuts in the US.
P: 771
 Quote by Jasongreat If there are so few of them able to determine if it is real science, or fraud, should they be able to pass laws based on said science, just because some scientists say it is so, or do they have a responsibility to weigh the facts, as they(and the public) see them? Imo, if the science is valid, bringing the facts into the light wont hurt.
They don't generally pass laws on science. They pass laws to set up organizations like the NIH, NSF, DoE, NASA, NOAA and the like and those organizations govern the science in this country.

MATLABdude referenced this already. But here is the chairman of the energy committee grilling Nobel laureate and Energy Secretary Steven Chu about oil in Alaska:

Keep in mind this was posted by Joe Barton himself (or more likely, his staff) with the headline Energy Secretary Puzzled By Simple Question.

Is this the kind of thing you had in mind when you said they should "weigh the facts as they see them?"
 Mentor P: 14,243 Yes, Joe Barton is an idiot. So are most congresscritters. In the eyes of scientists, engineers, and mathematicians, congresscritters are useful idiots who fund quite a bit of lot the research that moves our fields forward. They are useful only to the extent that the funding pipeline remains open. Congressional tectonics appear to be poised to shift those funds elsewhere. The reverse is also true. Congresscritters view those of us who work in some technical endeavor as useful idiots. We remain useful so long as the truths we expose support their worldview and the knowledge we create puts money in their pockets or into the pockets of their voters. When we fail to be useful idiots are are just idiots whose funding can easily be shut off. That makes for strange bedfellows.
 Sci Advisor P: 1,724 ...What may be even more scary: Joe Barton is one of the Congressfolks with a science background (BS and MS in industrial engineering): http://en.wikipedia.org/wiki/Joe_Barton#Early_life AND has at least a short stint in the private sector in oil and gas.
Other Sci
 In the Republican platform, Pledge to America, the party vows to cut discretionary nonmilitary spending to 2008 levels. Under that plan, research and development at nonmilitary agencies — including those that sponsor science and health research — would fall 12.3 percent, to $57.8 billion, from the Mr. Obama’s request of$65.9 billion for fiscal year 2011. An analysis by the American Association for the Advancement of Science looked at what would happen if all of the agencies were cut to the 2008 amounts. The National Institutes of Health would lose $2.9 billion, or 9 percent, of its research money. The National Science Foundation would lose more than$1 billion, or almost 19 percent, of its budget, and the National Oceanic and Atmospheric Administration would lose \$324 million, or 34 percent.