text:
Author:
Subject:
Ratios and Proportions
Material Type:
Lesson Plan
Level:
Middle School
6
Provider:
Pearson
Tags:
6th Grade Mathematics, Multiplicative Structure, Value
Language:
English
Media Formats:

# Using Ratio Tables to Solve Problems

## Overview

Students focus on interpreting, creating, and using ratio tables to solve problems.

# Key Concepts

A ratio table shows pairs of corresponding values, with an equivalent ratio between each pair. Ratio tables have both an additive and a multiplicative structure:

# Goals and Learning Objectives

• Complete ratio tables.
• Use ratio tables to solve problems.

# Lesson Guide

Examine the ratio table with students, explaining what each column shows.

• Why do you think the table is called a ratio table?

ELL: Help students differentiate between comparing “within” pairs of values and “between” pairs of values. This is fundamental to conceptually understanding ratio tables. Provide students with plenty of time to make the distinction between terms and to internalize the new mathematical information.

# Introduction to Ratio Tables

Discuss:

• This ratio table shows the relationship between the number of students and the number of computers in a class that has 35 students and 28 computers.
• Column A shows the ratio of students to computers, which is 35:28.
• Column B shows that there are 1.25 students for every 1 computer.
• Column C shows that the simplest whole-number ratio is 5:4.
• Columns D through G show other ways to express the ratio of students to computers using whole numbers.

# Lesson Guide

Work through the problems with students and then answer the question as a class. If the class size grew to 40 students, then you would need 32 computers to maintain the same ratio.

$\frac{5}{4}=\frac{40}{32}$

SWD: Help students break down the problems into smaller parts and assist them in identifying relevant information.

# Mathematics

It is important that students understand the multiplicative nature of equivalent ratios. Explain that as one quantity changes or varies, the other quantity must change or vary in a similar way in order to maintain the same relationship between the quantities. To maintain the same relationship, you can multiply or divide both quantities in a ratio by the same number.

## Opening

If you multiply both quantities in a ratio by the same number, the resulting ratio will be equivalent to the original ratio. The calculations that follow illustrate how you can use this method to generate the ratio in column G by starting with the ratios in columns B or C.

$1.25:1=\frac{1.25}{1}=\frac{1.25\cdot 364}{1\cdot 364}=\frac{455}{364}=455:364$

$5:4=\frac{5}{4}=\frac{5\cdot 91}{4\cdot 91}=\frac{455}{364}=455:364$

Notice that the numbers in the ratio table are not arranged in order of size. The values in ratio tables in general do not have to follow any particular order.

• If the ratio of students to computers stays the same, how many computers would be needed if the class size grew to 40 students?

# Lesson Guide

Discuss the Math Mission. Students will use ratio tables to solve ratio problems.

## Opening

Use ratio tables to solve ratio problems.

# Lesson Guide

Have students work in pairs on the fruit punch problem.

SWD: Have students who easily understand the task demonstrate the patterns they observed to struggling students. This promotes cooperative learning and is beneficial to both the stronger student and the student who is struggling to learn the concept.

# Mathematical Practices

Mathematical Practice 4: Model with mathematics.

Students use a ratio table to represent the relationship between quantities in the ratio and to solve problems.

# Interventions

Student looks for relationship between values within a row.

• What do you notice about the relationship between values in each column?
• Focus on the ratio between values in each column, and then compare this ratio across the columns.
• Are the ratios between the two values in each column equivalent?

Student adds the same value to each quantity instead of multiplying (or dividing) the same value.

• Is this ratio equivalent to this ratio? Explain how you know.
• Can you use another model to check that these two ratios are equivalent?
• Try multiplying both quantities in the ratio by the same number to find an equivalent ratio.

• Solutions will vary. Possible solution: 16 + 64 = 80 cups of club soda; 24 + 96 = 120 cups of grape juice; If Carlos uses 80 cups of club soda, he will need 120 cups of grape juice.

# Fruit Punch

Carlos makes his own fruit punch using grape juice and club soda to serve at his parties. He makes different amounts of punch depending on the size of the party. He has found that using the ratio 2:3 for cups of club soda to cups of grape juice makes the tastiest fruit punch.

• Complete the ratio table.
• Use the table to determine how many cups of grape juice Carlos will need if he uses 80 cups of club soda. HANDOUT: Fruit Punch

How can you use the ratio 2 : 3 and the information in the ratio table to find an equivalent ratio that will enable you to determine the amount of punch needed for 80 cups of club soda?

# Lesson Guide

Have students work in pairs on the maple syrup problem.

# Mathematical Practices

Mathematical Practice 4: Model with mathematics.

Students use a ratio table to represent the relationship between quantities in the ratio and to solve problems.

Mathematical Practice 1: Make sense of problems and persevere in solving them.

Students need to understand the problem situation in order to set up the ratio table correctly. Look for students who may struggle, yet persevere, in finding a solution to the maple syrup problem.

# Interventions

Student looks for the relationship between values within a row.

• What do you notice about the relationship between values in each column?
• Focus on the ratio between values in each column, and then compare this ratio across the columns.
• Are the ratios between the two values in each column equivalent?

Student adds the same value to each quantity instead of multiplying (or dividing) the same value.

• Is this ratio equivalent to this ratio? Explain how you know.
• Can you use another model to check that these two ratios are equivalent?
• Try multiplying both quantities in the ratio by the same number to find an equivalent ratio.

Tables and solution methods will vary. Possible table and solution:

• The farmer would need 312 maple trees to get 144 gallons of maple syrup. 120 + 24 = 144 gallons of syrup; 260 + 52 = 312 trees

# Maple Syrup

A maple tree farmer can get 30 gallons of maple syrup from 65 maple trees.

Make a ratio table to help you solve this problem. The table should show the ratio of the number of trees to the number of gallons of maple syrup for various numbers of trees.

• How many maple trees would the farmer need to get 144 gallons of maple syrup?
• How many gallons of maple syrup can he get from other numbers of maple trees?

• How can you get from 30 gallons of maple syrup to 144 gallons of maple syrup?

HANDOUT: Maple Syrup

# Preparing for Ways of Thinking

Listen and look for the following student work to highlight during the Ways of Thinking discussion:

• Students who find the ratios in the table by multiplying (or dividing) both quantities in the ratio by the same value
• Students who use skip counting or repeated addition to fill in the missing numbers in the table
• Students who notice relationships between ratios to find other ratios.

# Challenge Problem

• Answers will vary. Possible answers: If you know the cost of one item, you could use a ratio table to find a predicted cost for x items. Then you could compare the offered price of x items to the predicted cost of x items. For example, if one item cost $5, it has a ratio of 1:5. You could set up a ratio table to find the cost for 50 items.  The equivalent ratio would be 50:250, with a cost of$250. You would know you are getting a good deal if the store offered the 50 items for a price lower than \$250. Or: No, a ratio table would not be useful for finding the price of discounted quantities. If you use the unit price to find the price of the larger quantity, the price will not reflect the discount the store is offering.

# Prepare a Presentation

• Explain the strategy you used for constructing a ratio table that helps you solve the problem of determing how many trees would be needed to make 144 gallons of maple syrup.
• Explain how you put other pairs of numbers representing equivalent ratios into the table.

# Challenge Problem

Would using a ratio table help you solve problems about calculating the costs of items in a store if the store offered special deals for buying large quantities of an item? Explain.

# Mathematics

Begin the discussion with presentations of at least two different ways to use the ratio table to solve the maple syrup problem. If no one addresses it, invite students to think about what can be added together in the table in order to solve the problem.

Sample methods:

### Method 1

Double 72 gallons equals 144 gallons of maple syrup, so double 156 trees would be 312 trees.

### Method 2

1 ⋅ 144 = 144

$2\frac{1}{6}\cdot 144=\frac{13}{6}\cdot 144=13\cdot 24=312$

### Method 3

144 ÷ 6 = 24

13 ⋅ 24 = 312

Close the discussion with a presentation from at least one pair of students who attempted the Challenge Problem.

SWD: One way to start the discussion is to ask students what questions arose during the maple syrup problem. Student-initiated inquiry promotes connection and engagement with the mathematics. Provide positive feedback, using gestures and prompting, to elicit deeper responses.

ELL: During class discussions, make sure you provide wait time for ELLs (5–10 seconds) and acknowledge student responses, both verbally and with gestures.

# Mathematical Practices

Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.

As students make their presentations, encourage other students to ask questions and critique the solution method. Presenters will need to articulate their reasoning in response.

# Ways of Thinking: Make Connections

Take notes about your classmates' strategies for using ratio tables to solve ratio problems.

• What were some of the challenges you encountered in making your ratio table?
• What does your ratio table show?

# A Possible Summary

Ratio tables show equivalent ratios between two quantities. You can create a ratio table by multiplying (or dividing) both quantities in the ratio by the same value to find an equivalent ratio. A ratio table can help you find equivalent ratios in order to solve problems.

# Summary of the Math: What I Learned about Ratio Tables

Write a summary about making and using ratio tables.

• Do you explain what a ratio table is?
• Do you explain how to make a ratio table?
• Do you describe how you can use a ratio table to solve ratio problems?

# Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections to find out how students think a ratio table is similar to or different from a double number line.

# Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful.

I think a ratio table is similar to a double number line because …

I think a ratio table is different from a double number line because …


text:
OpenKattis
Kattis Set 12

#### Start

2019-04-08 13:00 UTC

## Kattis Set 12

#### End

2019-04-15 09:29 UTC
The end is near!
Contest is over.
Not yet started.
Contest is starting in -218 days 23:06:41

164:29:59

0:00:00

# Problem BStained Carpet

The Algebraist Carpet Manufacturing (ACM) group likes to produce area carpets based upon various geometric figures. The 2014 ACM carpets are all equilateral triangles. Unfortunately, due to a manufacturing defect, some of the carpets are not as stain-resistant as intended. The ACM group is offering to replace each defective carpet that contains a stain.

The web form used to report the stained carpet requests the three distances that the stain is away from the corners of the rug. Based upon these three numbers, you need to compute the area of the rug that is to be sent to the customer, or indicate that the customer’s carpet doesn’t come from ACM.

## Input

Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will consist of a single line with three floating point numbers $a$, $b$ and $c$ ($0 < a,b,c \le 100$, at most $10$ digits after the decimal point) representing the distances from the stain to each of the three corners of the carpet. There will be a single space between $a$ and $b$, and between $b$ and $c$.

## Output

Output a single line with a single floating point number. If there is a carpet that satisfies the constraints, output the area of this carpet. If not, output -1. The output should have an absolute error of at most $10^{-3}$.

Sample Input 1 Sample Output 1
1 1 1.732050

1.732050808

Sample Input 2 Sample Output 2
1 1 3.0

-1

Sample Input 3 Sample Output 3
1.732051 1.732051 1.732051

3.897115183

format: plain


text:
# Door Rotation Matrix/Change of Basis Plus Translation

1. Jul 15, 2015

### Cora

I think I'm having a really big block over a really small hangup, so forgive me. I'm on an internship and this is my first time working with rotations/change of basis in a real world scenario.

I'm creating a calculator that gives torque in a door mechanism, after a given roll and pitch of the vehicle. It's for the torque in a door check mechanism, but the general torque at the axis of rotation (along door hinges) will suffice for this calculator. I am using rotation matrices to find the component of gravity into and out of the door, then multiplying that against the distance from the axis to the CG to find the torque created by gravity.

I'm setting up the matrices in Excel.

What I've got currently is Rx*Ry*Rz, where Rx is the roll transformation, Ry is the pitch and Rz is the yaw. That successive matrix is then multiplied against the gravity vector. The calculator gives accurate values for the gravity at the center of mass after the pitch and roll, but since I haven't accounted for the distance from the axis to the CG, the Rz matrix has no effect on the gravity.

I feel like I need to add a translation or inertia matrix in there somewhere. The door is being treated as a point mass at the center of gravity.

Rx*Ry*Rz
[1 0 0;0 cos(α) -sin(α);0 sin(α) cos(α)]*[cos(β) 0 sin(β);0 1 0;-sin(β) 0 cos(β)]*[cos(γ) -sin(γ) 0;sin(γ) cos(γ) 0; 0 0 1]
Gravity Vector
[0;0;W]
where α=roll angle, β=pitch angle, γ=yaw angle, W=weight

Thanks SO much with any direction anyone might be able to help with. I've spent hours staring by it at myself, but no one on my team has used linear algebra in decades...

2. Jul 15, 2015

### andrewkirk

It looks like your pitch, roll and yaw matrices are all expressed relative to a fixed basis. That makes the maths simple but are you sure that's what you want? If you do it that way then it's true that yaw has no effect on gravity.

An alternative way to do it, that seems more intuitive to me, is to specify an order for applying the transformations, transform the axes as well as the vector at each step, and then apply each transformation relative to a transformed set of axes.

Say the order of application you choose is pitch (rot around x axis) then roll (rot around y axis) then yaw (rot around z axis).
Say the vector that represents the centralised door hinge is v, which lies in the x-y plane.
Then when you apply pitch you rotate v, and the y and z axes around the x axis, to get v' and new y', z' axes.
Next apply roll: rotate v', and the x and z' axes around the y' axis, to get v'' and new x', z'' axes.
Finally apply yaw: rotate v'' around the z'' axis, to get v'''.

Because z'' is no longer vertical, the yaw transformation will affect the direction of gravity for the hinge.

The matrices you use for these transformations will be more complex. The pitch matrix is unchanged. The roll matrix will depend on both the angles of pitch and roll. The yaw matrix will depend on all three angles.

3. Jul 20, 2015

### Cora

I think I see what you're saying. I'm kicking myself for not saving my notebook from my dynamics class.

Originally I had aligned the y axis with the bottom edge of the door, the z axis with the hinge/front edge of the door. The origin being at the front bottom corner. My thought was that I would just translate the door's weight vector through the pitch, roll and yaw. I didn't take into consideration the position vector of the CG. So my yaw transformation doesn't affect the weight vector because I'm applying the transformation ABOUT the Z axis TO the z axis, rather than a vector positioned away from it. Does this seem like I've pinpointed the right problem?

#### Attached Files:

• ###### Snapshot.jpg
File size:
14 KB
Views:
71
4. Jul 20, 2015

### andrewkirk

From the diagrams, it looks like you've got the right idea Cora.
I find it helps to think about it from the point of view of an aeroplane pilot and what the controls of the aeroplane do. The aeroplane will usually have some nonzero pitch and roll relative to the Earth's up-down direction and some Yaw relative to say the East-West direction. But those coordinates are not relevant to the incremental impact of the controls of the attitude of the plane.

The important axes that determine the effect of the plane's controls are where x points from aft to fore, y points from one wingtip to the other and z is perpendicular to those two in the direction from wheels to roof. The elevators (tail flaps) control pitch by pulling back/pushing forward on the yoke ('steering stick'), the ailerons (small flaps on the wings) control roll by pushing the yoke to either side, and the rudder controls yaw via foot pedals.

All adjustments made to those control surfaces are relative to the aeroplane's transformed axes, not to the Earth-based axes. If you're flying upside down (eg in the middle of a barrel roll or a loop-the-loop) and you want to fly further from the ground, you need to pitch down relative to the plane's axes by pushing forward on the yoke.

To confuse things though, at least some of the plane's instruments give indicators of configuration relative to the Earth rather than to the plane's axes. I'm pretty sure the attitude indicator shows pitch relative to gravity, but I'm not sure about roll. It's just as well commercial airlines don't spend much time flying upside down!

5. Jul 20, 2015

### Hawkeye18

Hi Cora,

first you have to change the order of you matrices in the product, your rotation matrix $R$ has to be $R=R_z R_y R_x$ (first roll, then pitch, then yaw; the rightmost matrix corresponds to the first transformation, i.e. to the roll).

To compute the torque, you need 2 vectors: a vector $\mathbf a$ parallel to the axis of rotation of the door, and a vector $\mathbf r$ from the axis of rotation of the door to its center of mass. The to compute the torque about this axis you need to compute the cross product of $T\mathbf r$ and $m\mathbf g$ ($m$ is the mass of the door and $\mathbf g$ is the gravity vector), and then take the orthogonal projection of $m T\mathbf r \times \mathbf g$ onto the vector $T\mathbf a$.

And https://www.physicsforums.com/threads/door-rotation-matrix-change-of-basis-plus-translation.823423/members/andrewkirk.265790/ [Broken] is right, yaw does not change the magnitude of the torque.

Last edited by a moderator: May 7, 2017
6. Jul 21, 2015

### Cora

Thanks for talking that through. I figured I was missing at least one position vector. What is the variable T?

Last edited by a moderator: May 7, 2017
7. Jul 21, 2015

### Hawkeye18

Sorry, it was a typo, it should be $R$.


text:
This is an archived post. You won't be able to vote or comment.

[–] 4 points5 points  (5 children)

In that particular scenario, you'd really be wagering nothing but your turn because you only get the $1,000 if you choose not to flip it. Pat Sajak likes to include the "bribe money" (he always says "You'd be risking [current score +$x,000] for a 50/50 shot at $10,000), but you're really only risking what you already have. If another contestant has a large lead, it might be best to flip it and hope for the$10,000 so you can overtake them. This led to an interesting scenario on one episode about 2 years ago...

The current leader was Monica with a total score of $20,650. In second is Ben with a measly$3,000. In the Mystery Round, with one blank left, Ben hits a Mystery Wedge and calls that last letter. If he takes the $1,000, the round is his, but he'd still be behind by over$16,000. If he flips it and gets the Bankrupt, Monica, who would be next in control, would get to solve. Neither player had any money at that point, so if Monica solved, she would win the $1,000 minimum. If Ben got the$10,000, he would still be behind Monica, but it would be easier to beat her in future rounds. Ben got the Bankrupt, and told Pat he had to do it.

So, in my opinion, the best decision on whether to flip or not depends on your current standing in the game compared to the others, how many blanks are left in the puzzle (if it's early in the round, there's a slightly better chance of control getting back to you, though the more blanks there are, the more money opportunities there are for amassing through the regular cash wedges), and whether you know the puzzle or not. There a lot of good points to consider. For one, when you flip a wedge, you are also preventing your opponents from flipping one, since doing so takes the other wedge out of play, even if you flipped the Bankrupt one. On the other hand, the wedge's face value is $1,000. There is no other cash wedge on the Wheel higher than that expect for the round's top dollar value of$3,500.

[–][S] 0 points1 point  (4 children)

Is there a way to calculate the value of your turn then? In your example it was rather clearly in the player's best interest, contrary to what I said earlier.

[–] 1 point2 points  (3 children)

What do you mean by "calculate the value of your turn"?

[–][S] 0 points1 point  (2 children)

In figuring out whether or not to flip over the wedge, you need to figure out how bad it is to lose your turn.

Is there a way to put a monetary value to that to aid in figuring out whether or not to take the risk?

[–]Topology 1 point2 points  (0 children)

http://socrates.io/#WjJ0ueB

That's a quick analysis from a very short-sighted point of view: should I expect to have more money before my next spin if I go for it or not?

[–] 1 point2 points  (0 children)

Well, not an exact value, but you could always do a rough "worst case scenario" calculation. If I were in the lead, 3500 * the number of remaining consonants (assuming you know the puzzle, and if not, you can assume a little more than half of the blanks are consonants) would be the maximum my opponent could earn if I reveal the Bankrupt, plus any money or the value of any prizes they have now. Would that be enough to overtake me? If yes, I'd play it safe.

If I'm not in the lead, well, that's a different strategy which I'm having a hard time trying to explain in writing only. It's basically asking yourself, "If I take the money and keep spinning, are there enough letters left for me to earn enough on average by spinning to overtake the leader?" In this woman's case: http://www.youtube.com/watch?v=3UZWQ2kV3uk , she certainly could have amassed enough. Playing it safe would have given her $9,750, and on that episode, her opponent in the red podium was in the lead with$13,900. She only had $3,000 (this is concerning the total scores earned from solving puzzles). Earning another$1,200 at least and then solving would have given her the lead.


text:
# Using TrackMate from MATLAB

This page shows how to use and control TrackMate directly from within MATLAB. This is great and made possible thanks to the great Miji tool, that make the Fiji classes visible from MATLAB. Check this page first if you have not already. Note however that as 2016, Mark Hinerm and friends built a stronger replacement from Miji, ImageJ-MATLAB. This page still clings to using Miji, but moving to ImageJ-MATLAB should be painless.

All the following examples assume you have launched MATLAB, and properly initiated Miji, using for instance

Miji(false)

or

Miji(true)

if you want the Fiji window to be visible.

Apart from that, the collections of examples that follow just look like several scripts. Which is actually the case: We use the MATLAB interpreter as a scripting interface for TrackMate, as we did in the Scripting TrackMate page. We separated this page to highlight MATLAB specificities and to exploit its capabilities better.

## A simple tracking example

Here we open an image though Fiji (not though MATLAB) and track its content. The results are displayed in a Fiji window as well. MATLAB is used here only to control TrackMate and does not really plays a role in the process. This example is actually the same that in the first Scripting TrackMate example.

Note that we used the fully qualified name for TrackMate classes, e.g. fiji.plugin.trackmate.TrackMate instead of TrackMate. This is the first way to import classes in a MATLAB script. We will see another way later.

% Get currently selected image
% imp = ij.IJ.openImage('https://fiji.sc/samples/FakeTracks.tif')
imp = ij.ImagePlus('/Users/tinevez/Desktop/Data/FakeTracks.tif');
imp.show()

%----------------------------
% Create the model object now
%----------------------------

% Some of the parameters we configure below need to have
% a reference to the model at creation. So we create an
% empty model now.
model = fiji.plugin.trackmate.Model();

% Send all messages to ImageJ log window.
model.setLogger(fiji.plugin.trackmate.Logger.IJ_LOGGER)

%------------------------
% Prepare settings object
%------------------------

settings = fiji.plugin.trackmate.Settings();
settings.setFrom(imp)

% Configure detector - We use a java map
settings.detectorFactory = fiji.plugin.trackmate.detection.LogDetectorFactory();
map = java.util.HashMap();
map.put('DO_SUBPIXEL_LOCALIZATION', true);
map.put('TARGET_CHANNEL', 1);
map.put('THRESHOLD', 0);
map.put('DO_MEDIAN_FILTERING', false);
settings.detectorSettings = map;

% Configure spot filters - Classical filter on quality
filter1 = fiji.plugin.trackmate.features.FeatureFilter('QUALITY', 1.0, true);

% Configure tracker - We want to allow splits and fusions
settings.trackerFactory  = fiji.plugin.trackmate.tracking.sparselap.SparseLAPTrackerFactory();
settings.trackerSettings = fiji.plugin.trackmate.tracking.LAPUtils.getDefaultLAPSettingsMap(); % almost good enough
settings.trackerSettings.put('ALLOW_TRACK_SPLITTING', true);
settings.trackerSettings.put('ALLOW_TRACK_MERGING', true);

% Configure track analyzers - Later on we want to filter out tracks
% based on their displacement, so we need to state that we want
% track displacement to be calculated. By default, out of the GUI,
% not features are calculated.

% The displacement feature is provided by the TrackDurationAnalyzer.

% Configure track filters - We want to get rid of the two immobile spots at
% the bottom right of the image. Track displacement must be above 10 pixels.
filter2 = fiji.plugin.trackmate.features.FeatureFilter('TRACK_DISPLACEMENT', 10.0, true);

%-------------------
% Instantiate plugin
%-------------------

trackmate = fiji.plugin.trackmate.TrackMate(model, settings);

%--------
% Process
%--------

ok = trackmate.checkInput();
if ~ok
display(trackmate.getErrorMessage())
end

ok = trackmate.process();
if ~ok
display(trackmate.getErrorMessage())
end

%----------------
% Display results
%----------------

selectionModel = fiji.plugin.trackmate.SelectionModel(model);
displayer =  fiji.plugin.trackmate.visualization.hyperstack.HyperStackDisplayer(model, selectionModel, imp);
displayer.render()
displayer.refresh()

% Echo results
display(model.toString())

## Using imports in MATLAB

MATLAB lets you import java names into its workspace, using the import command. Check this. So we could rewrite the above script as follow:

%----------------------------------
% Import Fiji and TrackMate classes
%----------------------------------

import java.util.HashMap
import ij.*
import fiji.plugin.trackmate.*
import fiji.plugin.trackmate.detection.*
import fiji.plugin.trackmate.features.*
import fiji.plugin.trackmate.features.track.*
import fiji.plugin.trackmate.tracking.*
import fiji.plugin.trackmate.visualization.hyperstack.*

%--------------------
% Pick a source image
%--------------------

% Get currently selected image
% imp = IJ.openImage('https://fiji.sc/samples/FakeTracks.tif')
imp = ImagePlus('/Users/tinevez/Desktop/Data/FakeTracks.tif');
imp.show()

%----------------------------
% Create the model object now
%----------------------------

% Some of the parameters we configure below need to have
% a reference to the model at creation. So we create an
% empty model now.
model = Model();

% Send all messages to ImageJ log window.
model.setLogger(Logger.IJ_LOGGER)

%------------------------
% Prepare settings object
%------------------------

settings = Settings();
settings.setFrom(imp)

% Configure detector - We use a java map
settings.detectorFactory = LogDetectorFactory();
map = HashMap();
map.put('DO_SUBPIXEL_LOCALIZATION', true);
map.put('TARGET_CHANNEL', 1);
map.put('THRESHOLD', 0);
map.put('DO_MEDIAN_FILTERING', false);
settings.detectorSettings = map;

% Configure spot filters - Classical filter on quality
filter1 = FeatureFilter('QUALITY', 1.0, true);

% Configure tracker - We want to allow splits and fusions
settings.trackerFactory  = fiji.plugin.trackmate.tracking.sparselap.SparseLAPTrackerFactory();
settings.trackerSettings = LAPUtils.getDefaultLAPSettingsMap(); % almost good enough
settings.trackerSettings.put('ALLOW_TRACK_SPLITTING', true);
settings.trackerSettings.put('ALLOW_TRACK_MERGING', true);

% Configure track analyzers - Later on we want to filter out tracks
% based on their displacement, so we need to state that we want
% track displacement to be calculated. By default, out of the GUI,
% not features are calculated.

% The displacement feature is provided by the TrackDurationAnalyzer.

% Configure track filters - We want to get rid of the two immobile spots at
% the bottom right of the image. Track displacement must be above 10 pixels.
filter2 = FeatureFilter('TRACK_DISPLACEMENT', 10.0, true);

%-------------------
% Instantiate plugin
%-------------------

trackmate = TrackMate(model, settings);

%--------
% Process
%--------

ok = trackmate.checkInput();
if ~ok
display(trackmate.getErrorMessage())
end

ok = trackmate.process();
if ~ok
display(trackmate.getErrorMessage())
end

%----------------
% Display results
%----------------

selectionModel = SelectionModel(model);
displayer = HyperStackDisplayer(model, selectionModel, imp);
displayer.render()
displayer.refresh()

% Echo results
display(model.toString())

## Why is this greater than it seems?

Because your just ran a MATLAB script that uses and benefits from multithreading without relying on any toolbox! Here is how to tune the number of threads used by TrackMate:

% ... Do initialization before.

trackmate = TrackMate(model, settings);
trackmate.setNumThreads(3); % As many threads as you want.

JeanYvesTinevez (talk) 13:44, 17 January 2017 (CST)


text:
# Variance over two periods with known variances?

If period 1 has variance v1 and period 2 has variance v2, what is the variance over period 1 and period 2? (period 1 and period 2 are the same length)

I've done some manual calculations with random numbers, and I can't seem to figure out how to calculate the variance over period 1 and period 2 from v1 and v2.

-

Using the same set up as @ChrisTaylor, we can regard the data sets $A$ and $B$ as specifying the conditional probability mass functions of a random variable $X$, with $\mu_A, \mu_B$ the conditional means and $\sigma_A^2, \sigma_B^2$ as the conditional variances. Thus, as noted by Chris,
\begin{align*} E[X] = \mu &= E[X\mid A]P(A) + E[X\mid B]P(B)\\ &= \frac{n_A}{n_A+n_B}\mu_A + \frac{n_B}{n_A+n_B}\mu_B \end{align*} is the unconditional mean, while the unconditional variance is given by the sum of the mean of the conditional variances and the variance of the conditional means. Thus, \begin{align*} \text{var}(X) &= \left[\frac{n_A}{n_A+n_B}\text{var}(X\mid A) + \frac{n_B}{n_A+n_B} \text{var}(X\mid B)\right]\\ &\quad\quad\quad\quad\quad\quad\quad\quad+ \left[\frac{n_A}{n_A+n_B}(\mu_A - \mu)^2+\frac{n_B}{n_A+n_B}(\mu_B - \mu)^2\right] \\ &= \frac{n_A\sigma_A^2+n_B\sigma_B^2}{n_A + n_B} + \frac{n_An_B}{(n_A + n_B)^2}(\mu_A - \mu_B)^2 \end{align*} which is essentially the result that Chris Taylor obtained though I think that he made a minor error in his calculations and got the difference of the two terms above instead of the sum.

-
A clear explanation, easily generalizable to cases with more than two sets. – pharmine May 1 '13 at 2:57

If you only know the variances of your two sets, you can't compute the variance of the union of the two. However, if you know both the variances and the means of two sets, then there is a quick way to calculate the variance of their union.

Concretely, say you have two sets $A$ and $B$ for which you know the means $\mu_A$ and $\mu_B$ and variances $\sigma^2_A$ and $\sigma^2_B$, as well as the sizes of each set $n_A$ and $n_B$. You want to know the mean $\mu_X$ and variance $\sigma^2_X$ of the union $X=A\cup B$ of the two sets (assuming that the union is disjoint, i.e. that $A$ and $B$ don't have any elements in common).

With a little bit of scribbling and algebra, you can reveal that

$$\mu_X = \frac{n_A\mu_A + n_B\mu_B}{n_A+n_B}$$

and

$$\sigma^2_X = \frac{n_A\sigma^2_A + n_B\sigma^2_B}{n_A + n_B} - \frac{n_An_B}{(n_A+n_B)^2} (\mu_A - \mu_B)^2$$

As pointed out in the answer by tards, the formula for the variance of the combined set depends explicitly on the means of the sets $A$ and $B$, not just on their variances. Moreover, you can see that adding a constant to one of the sets doesn't change the first term (the variances remain the same) but it does change the second term, because one of the means changes.

The fact that the dependence on the means enters through a term of the form $\mu_A-\mu_B$ shows you that if you added the same constant to both sets, then the overall variance would not change (just as you'd expect) because although both the means change, the effect of this change cancels out. Magic!

-

There is no simple relationship between the variance of different periods and the variance for the entire time period.

As a simple example consider the following two data sets: {1, 2, 3} and {3, 4, 5}. The variance for these two sets of numbers is 1 whereas the overall variance is 2. Now if you were to add 1 to the second set of numbers which would result in the following set {4, 5, 6} its variance is still 1 whereas the overall variance has increased to 3.5. Thus, just knowing v1 and v2 will not be enough to compute the overall variance.

-


text:
# Why is momentum conserved when a ball hits a vertical wall?

Almost in every book on physics, there's an example of conservation of momentum when the ball that is moving horizontally in the air, hits some massive wall. They claim that the return speed of the ball when it bounces off is the same as it was before the hit. If there were no external forces acting on the system (or their net force was zero) that would be fine. But in this case, there is a gravitational force acting on the ball, and because there is no surface underneath it, there's no normal force and therefore it doesn't "cancel out" the gravitational force. So my question is, why they say that the momentum conserved? Do they neglect the gravitational force or what? I'm quite confused. Thanks!

-

The assumption in these problems is that the collision takes place instantaneously so that gravity has no time to change the momentum of the ball during the collision.

To see why this is makes sense, let $y$ denote the vertical direction, and notice that if the collision took some small amount of time $\delta t>0$ then the change in vertical momentum of the ball would be (by integrating both sides of Newton's second law) $$\delta p_y = \int_{t_0}^{t_0+\delta t}dt \,F(t) = F(t_0)\delta t + \mathcal O(\delta t^2)$$ so we see that as the collision time goes to zero, so does the change in momentum in the vertical direction.

-
Thank you very much sir. So basically it would never be the same velocity in real life. We just assume that everything happens very quick. I got it. –  brmch8 Mar 31 '13 at 16:07
@brmch8 Sure thing. I have a follow-up question (that I think will also strengthen your understanding ultimately): "Doesn't the vertical wall itself exert a force on the ball in the horizontal direction? In this case, why is the momentum in the $x$ direction conserved? There is an external force from the wall on the ball in that direction." –  joshphysics Mar 31 '13 at 16:20
there is a change in the momentum of the ball ($mv_f-mv_i=-2mv_i$), therefore there is an impulse acting on it. Impulse, by definition, is force that is acting on object during the time $\delta t$. It means that the wall itself got that amount of momentum ($2mv_i$), but because the mass of the wall is huge compared to the ball, the velocity it gets can be neglected. Am I correct? –  brmch8 Mar 31 '13 at 16:37
@brmch8 Yep! For this reason, I'd say it's actually misleading to say that momentum is conserved in the collision. It's true that its magnitude remains the same, but its direction reverses as you note. –  joshphysics Mar 31 '13 at 17:05
you said that the magnitude is the same but the direction is opposite - why then you say that it is misleading to say that the momentum is conserved (if we neglect the gravitation in that very short period of time of the collision)? As I know, conservation of momentum implies that the net momentum is conserved. If the wall got a momentum of $2mv_i$ after the collision (where $v_i$ is the initial velocity of the ball) then the momentum conservation equation would be right: $mv_i+0=-mv_i+2mv_i$. Isn't it? Wow, I feel I got confused again, sorry. –  brmch8 Mar 31 '13 at 17:15

The momentum conservation principle will be valid for horizontal direction. However, for the vertical direction gravity is the external force acting so it would not be valid

-


text:
# Line of sight

This topic is 1815 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I am currently working on a game in flash (with AS3), and I ran into a weird issue with the line of sight of the enemies. It's easier to explain with a picture. Blue = walls. Green = enemy. Red = area the enemy can't see the player.

This is the codes:

var playerVisible:Boolean = true;
var angleRadian = Math.atan2(_player.y - _enemy[i].y, _player.x - _enemy[i].x);
var angleDegree = angleRadian * 180 / Math.PI;

var enemyDistancex:Number = _player.x - _enemy[i].x;
var enemyDistancey:Number = _player.y - _enemy[i].y;
if(enemyDistancex < 0)
enemyDistancex *= -1;
if(enemyDistancey < 0)
enemyDistancey *= -1;
var enemyDistance:Number = Math.sqrt((enemyDistancex * enemyDistancex) + (enemyDistancey * enemyDistancey));

while(enemyDistance > 0 && playerVisible)
{
if(_walls.hitTestPoint(_enemy[i].x - (Math.sin(angleDegree * (Math.PI / 180)) * enemyDistance), _enemy[i].y - (Math.cos(angleDegree * (Math.PI / 180) * -1) * enemyDistance), true))
{
playerVisible = false;
}

enemyDistance--;
}

I tried a lot, but I can't seem to figure it out. Could someone help me out?

##### Share on other sites

I'm not quite understanding the picture. Is that the current behavior or the behavior you want to implement?

##### Share on other sites

That's the current behavior the code below the picture creates.

By the way, I use the same codes to calculate the enemy rotation for targeting the player and it works fine, but somehow it is buggy when I use it for the line of sight.

##### Share on other sites

Why aren't you using vectors? Calling atan2 and then calling sin, cos with the result is usually a sure sign you should be using 2d vectors instead of trigonometry for the problem.

Edited by Paradigm Shifter

##### Share on other sites

Using vectors how? Sorry I'm kind of a newbie when it comes to maths.

##### Share on other sites

Well you calculate the vector

player - enemy

and do a load of unnecessary trig stuff with it when that gives you the 2d direction vector from the enemy to the player directly...

I'd definitely recommend reading up on vectors, you rarely need to use trig and the stuff you do need/are using involving vectors is just the very basic stuff.

##### Share on other sites

I managed to fix it, thanks for the help :)

1. 1
Rutin
24
2. 2
3. 3
JoeJ
18
4. 4
5. 5

• 13
• 38
• 23
• 13
• 13
• ### Forum Statistics

• Total Topics
631714
• Total Posts
3001860
×


text:
Hypergeometric function

1. Jan 8, 2010

sara_87

1. The problem statement, all variables and given/known data

I have seen some hypergeometric function in the form:

2F1=(a,b;c;d),

Is there such thing as:
2F1=(a,b,c;d)

2. Relevant equations

3. The attempt at a solution

I dont understand why sometimes we have a comma and sometimes we have a semi-colon.

thank you

2. Jan 8, 2010

Staff: Mentor

This isn't anything that I know about, so I'll defer to Wikipedia: http://en.wikipedia.org/wiki/Hypergeometric_function
See especially the Notation section.

Based on my reading of that section, I don't think there is anything such as 2F1(a, b, c;d). I think you might have something like this: 3F1(a, b, c;d;e). Apparently the first number (the one before F) represents the number of parameters in the first position. The second number represents the number of parameters in the second section. The three sections are separated by semicolons, and the parameters within a section are separated by commas.

That's how it seems to me, FWIW.


text:
## Cryptology ePrint Archive: Report 2003/174

Relaxing Chosen-Ciphertext Security

Ran Canetti and Hugo Krawczyk and Jesper Nielsen

Abstract: Security against adaptive chosen ciphertext attacks (or, CCA security) has been accepted as the standard requirement from encryption schemes that need to withstand active attacks. In particular, it is regarded as the appropriate security notion for encryption schemes used as components within general protocols and applications. Indeed, CCA security was shown to suffice in a large variety of contexts. However, CCA security often appears to be somewhat {\em too strong:} there exist encryption schemes (some of which come up naturally in practice) that are not CCA secure, but seem sufficiently secure for most practical purposes.''

We propose a relaxed variant of CCA security, called {\sf Replayable CCA (RCCA)} security. RCCA security accepts as secure the non-CCA (yet arguably secure) schemes mentioned above; furthermore, it suffices for most existing applications of CCA security. We provide three formulations of RCCA security. The first one follows the spirit of semantic security and is formulated via an ideal functionality in the universally composable security framework. The other two are formulated following the indistinguishability and non-malleability approaches, respectively. We show that the three formulations are equivalent in most interesting cases.

Category / Keywords: public-key cryptography /

Publication Info: An extended abstract of thiswork appears in the proceedings of Crypto 2003.


text:
Book ChapterDOI

# Integrated CMOS sensor technologies for the CLIC tracker

27 Jun 2017-Vol. 213, pp 361-365

TL;DR: CMOS circuitry on a high resistivity epitaxial layer has been studied using the ALICE Investigator test-chip and a Technology Computer Aided Design based simulation chain has been developed to further explore the sensor technology.
Abstract: Integrated technologies are attractive candidates for an all silicon tracker at the proposed future multi-TeV linear $$\mathrm {e^{+} e^{-}}$$ collider CLIC. In this context CMOS circuitry on a high resistivity epitaxial layer has been studied using the ALICE Investigator test-chip. Test-beam campaigns have been performed to study the Investigator performance and a Technology Computer Aided Design based simulation chain has been developed to further explore the sensor technology.
Topics: CMOS sensor (53%)

Content maybe subject to copyright    Report

CLICdp-Conf-2017-011
27 June 2017
Integrated CMOS sensor technologies for the CLIC tracker
M. Munker
1)
On behalf of the CLICdp collaboration
CERN, Switzerland,
University of Bonn, Germany
Abstract
Integrated technologies are attractive candidates for an all silicon tracker at the proposed
future multi-TeV linear e
+
e
collider CLIC. In this context CMOS circuitry on a high res-
istivity epitaxial layer has been studied using the ALICE Investigator test-chip. Test-beam
campaigns have been performed to study the Investigator performance and a Technology
Computer Aided Design based simulation chain has been developed to further explore the
sensor technology.
Talk presented at International Conference on Technology and Instrumentation in Particle Physics 2017
(TIPP2017), Beijing, China, 22-26 May 2017
c
2017 CERN for the beneﬁt of the CLICdp Collaboration.
1
magdalena.munker@cern.ch

INTEGRATED CMOS SENSOR
TECHNOLOGIES FOR THE CLIC TRACKER
Magdalena Munker on behalf of the CLICdp collaboration
1
CERN magdalena.munker@cern.ch
2
University of Bonn
Abstract. Integrated technologies are attractive candidates for an all
silicon tracker at the proposed future multi-TeV linear e
+
e
collider
CLIC. In t h is context CMOS circuitry on a high resistivity epitaxial
layer has been studied using the ALICE Investigator test-chip. Test-beam
campaigns have been performed to stu d y the Investigator pe rform a n c e
and a Technology Computer Aided Design based simulation chain has
been developed to further explore the sensor technology.
1 Introduction
The Compact Linear Colli de r (CLIC) is an option for a future linear e
+
e
col-
lider at CERN in the post LHC era, reaching a centre of mass energy up to 3 TeV
[1, 2, 3, 4]. To perform highly precise physics measurements, a single point reso-
lution of 7 µm and a material budget of 1 2%X
0
per layer n ee d to be reached
in the large ar ea tracker detector. To suppress be am induced background par t i -
cles, a time stamping accuracy of 10 ns is required for the main tracker [2, 5].
A large surface ( 100 m
2
) all-silicon tracker is planned to address these require-
ments. Integrated technologies are promising candidates in view of large-scale
production and low material budget. Test beam campaigns to study the Investi-
gator High Resistivity (HR) CMOS test chip have been performed at the CERN
SPS with a 120 GeV pion beam. As a reference system, the CLICdp Timepix3
telescope has been used, providing an excellent tracking and timing resolution
on the Device Under Test (DUT) plane of 2 µm and 1 ns, respectively [6].
2 The Investigator chip
Within the ALICE ITS upgrade project, a fully monolithic chip, the ALPIDE
[7], has been developed in a 180 nm High Resistivity (HR) CMOS process (see
Figure 1). Using the same process, the Investigator test-chip has been developed
[8, 9]. Various pixel layouts are implemented in dierent mini-matrices with
8 8 pixels, to study the impact of the pixel layout on the performance. The
standard p r ocess h as been modiﬁed, inserting an additional n-layer (see Figure
2) to create a deep planar pn-ju nc ti on and achieve full lateral depletion of the
sensor. The output of the source foll ower of each individual pixel is connected
to a dedicated output buer with a rise time of 10 ns.

2
P
-
P
++
backside
Deep.P-well
N-well
P-MOS
N-MOS
Fig. 1. Investiga to r standard
process schematic cross section.
N
-
P
Deep'P-well
N-well
P-MOS
N-MOS
Fig. 2. Investigator modiﬁed
process schematic cross section.
The outpu t buers are read out by external ADCs, sampling the individual
pixel response with a f r eq ue nc y of 65 MHz [9]. The presented studies have been
performed for a mini -m at ri x with a pixel pitch of 28 µm and a bias voltage of
6 V, using chips with an epitaxial layer thickness of 18 µm for the standard, and
25 µm for the modiﬁed process.
3 Test beam data taking and reconstruction
If at least one pixel crosses a seed threshold, the ful l analogue waveform of all
8 8 pix el s is read out. In Figure 3, a typical waveform of a pixel with a particle
hit, as well as the ﬁt function to reconstruct the waveform, are p r ese nted.
Fig. 3. Single pixel waveform reconstructed by a ﬁt of the function f(t).
During the analysis, a threshold is applied on s in gl e pixel level. Since this t h re sh -
old is lower than the seed threshold during data taking, it is referred to as the
neighbour threshold. Adjacent pixe ls with a signal larger than the neighbour
threshold are combined to a clu st e r; and the position is reconstructed by linear
charge interpolati on and -correction. The distan ce be tween the predicted track
position on the Investigator and the reconstructed hit position is require d to be
within 100 µm. Moreove r, tracks passing through the outer half of the edge pixels
are discarded to avoid e.g. eects from the ﬁnite track prediction resolution .

3
4 Test-beam results
To explore the charge collection of the modiﬁed proc es s in detail, results are
projected onto the predic ted track position within individual pixel cells (in-pixel
presentation). A uniform eciency distribution c an be observed within the pixel
cell (see Figure 4). Fi gur e 5 shows the mean cluster size, deﬁned as the number of
pixels i n a cluster above threshold. As expected from geometrical considerations,
the lowest cluster size is obser ved in the pixel centre. The charge is shared most
likely to one n ei ghb ou r at the pixel edges, and to more than one neighbour at
the pixel corners. As shown in Figure 6, the impact of charge s hari n g is al so
reﬂected in the distribution of the high es t pixel signal (seed signal) in a cluster:
the more charge is share d between the pixels, the lower the se ed signal.
Fig. 4. Eciency within
the pixel cell.
Fig. 5. Mean cluster size
within the pixel cell.
Fig. 6. Mean seed signal
within the pixel cell.
A global eciency higher than 99 % and a spatial and timing resolution w it h
respect to the reference tracks of 6 µm and 5 ns, respectively, have been
measured. Even though the measur ed timing resolution is limited by the ADC
sampling frequency and the rise time of the output buer, the results are well
within the requirements for the CLIC tracker. In a next phase of R&D the results
on the Investigator test chip will be used to optimise the pixel layout for a fully
integrated chip for the CLIC tracker.
5 Simulation
A simulation chain using GEANT4 [11] to model the energy deposit in the sensor,
a 2-dimen si onal Technology Computer Aided Design (TCAD) [12] simulation to
model the devic e and perform a transient simulation of the charge collection,
and a parametric model to simulate energy ﬂuctuations and to perfor m the
position reconstruction has been developed [13]. The elect r ost at i c potential from
the TCAD simulation is shown in Fi gur e 7 and 8, respectively for the standard
and modiﬁed process. As indicated by the white lines, the depletion for the
standard process does extend over the full lateral size of the pixel, whereas the
expected full lateral depletion can be observed for the modiﬁed process. Results
are compared between simulation and data in Figure 9 - 11.

4
Fig. 7. Electrostatic potential from
Fig. 8. Electrostatic potential from
TCAD for the mo d i ed process.
A comparison of the mean cluster size in the X-direction within the pixel cell is
presented for t he standard process in Figure 9, showing a trend of larger cluster
sizes at the borders of the pixel at 0 and 1 in data, which is well de sc ri bed by
the simulation. For the modiﬁed process, an excellent agreement can be observed
between simulation and d at a in the residual distribution in Figur e 10, as well
as in the resolution, deﬁned as the Root Mean Square (RMS) of the residual
distribution, for dierent neighbour thresholds in Figure 11.
Fig. 9. Xclustersizewithin-
pixel cell standard process.
Fig. 10. Spatial residual
modiﬁed process.
Fig. 11. Spatial resid-
ual modiﬁed process.
6 Summary
The ALICE HR CMOS Investigator test chip has been explored in detail by
in-pixel t es t beam studies and a simulation based on GEANT4 and TCAD.
The simulation results reproduce the te st beam measurements, showing a good
understanding of the technology. An eciency of > 99 % and a spatial and
timing resolution of 6 µm and 5 ns, respectively, have been measured, using a
mini-matrix with a pitch of 28 µm and a bias voltage of 6 V. The measured
performance indic at es the suitability of the technology for the CLIC tracker and
the presented studies are used in a next R&D phase as input for the design of a
fully integrated chip for the CLIC tracker.

##### Citations
More filters

Book ChapterDOI
Andreas Nürnberg1Institutions (1)
28 Jun 2017
TL;DR: A detector concept meeting the requirements of the proposed future CLIC high-energy linear Open image in new window collider has been developed and an integrated R&D program addressing the challenges is progressing in the areas of ultra-thin sensors and readout ASICs, interconnect technology, mechanical integration and cooling.
Abstract: The physics aims at the proposed future CLIC high-energy linear Open image in new window collider pose challenging demands on the performance of the detector system. In particular the vertex and tracking detectors have to combine precision measurements with robustness against the expected high rates of beam-induced backgrounds. The requirements include ultra-low mass, facilitated by power pulsing and air cooling in the vertex-detector region, small cell sizes and precision hit timing at the few-ns level. A detector concept meeting these requirements has been developed and an integrated R&D program addressing the challenges is progressing in the areas of ultra-thin sensors and readout ASICs, interconnect technology, mechanical integration and cooling.

##### References
More filters

Journal ArticleDOI
S. Agostinelli1, John Allison2, K. Amako3, J. Apostolakis4  +123 moreInstitutions (34)
Abstract: G eant 4 is a toolkit for simulating the passage of particles through matter. It includes a complete range of functionality including tracking, geometry, physics models and hits. The physics processes offered cover a comprehensive range, including electromagnetic, hadronic and optical processes, a large set of long-lived particles, materials and elements, over a wide energy range starting, in some cases, from 250 eV and extending in others to the TeV energy range. It has been designed and constructed to expose the physics models utilised, to handle complex geometries, and to enable its easy adaptation for optimal use in different sets of applications. The toolkit is the result of a worldwide collaboration of physicists and software engineers. It has been created exploiting software engineering and object-oriented technology and implemented in the C++ programming language. It has been used in applications in particle physics, nuclear physics, accelerator design, space engineering and medical physics.

16,046 citations

Journal Article

6,559 citations

### "Integrated CMOS sensor technologies..." refers methods in this paper

• ...The ALICE HR CMOS Investigator test chip has been explored in detail by in-pixel test beam studies and a simulation based on GEANT4 and TCAD....

[...]

• ...A simulation chain using GEANT4 [11] to model the energy deposit in the sensor, a 2-dimensional Technology Computer Aided Design (TCAD) [12] simulation to model the device and perform a transient simulation of the charge collection, and a parametric model to simulate energy fluctuations and to perform the position reconstruction has been developed [13]....

[...]

DOI
01 Jan 2012
Abstract: This report describes the accelerator studies for a future multi-TeV e+e- collider based on the Compact Linear Collider (CLIC) technology. The CLIC concept as described in the report is based on high gradient normal-conducting accelerating structures where the RF power for the acceleration of the colliding beams is extracted from a high-current Drive Beam that runs parallel with the main linac. The focus of CLIC R&D over the last years has been on addressing a set of key feasibility issues that are essential for proving the fundamental validity of the CLIC concept. The status of these feasibility studies are described and summarized. The report also includes a technical description of the accelerator components and R&D to develop the most important parts and methods, as well as a description of the civil engineering and technical services associated with the installation. Several larger system tests have been performed to validate the two-beam scheme, and of particular importance are the results from the CLIC test facility at CERN (CTF3). Both the machine and detector/physics studies for CLIC have primarily focused on the 3 TeV implementation of CLIC as a benchmark for the CLIC feasibility. This report also includes specific studies for an initial 500 GeV machine, and some discussion of possible intermediate energy stages. The performance and operation issues related to operation at reduced energy compared to the nominal, and considerations of a staged construction program are included in the final part of the report. The CLIC accelerator study is organized as an international collaboration with 43 partners in 22 countries. An associated report describes the physics potential and experiments at CLIC and a shorter report in preparation will focus on the CLIC implementation strategy, together with a plan for the CLIC R&D studies 2012–2016. Critical and important implementation issues such as cost, power and schedule will be addressed there.

470 citations

### "Integrated CMOS sensor technologies..." refers background in this paper

• ...1 Introduction The Compact Linear Collider (CLIC) is an option for a future linear e+e collider at CERN in the post LHC era, reaching a centre of mass energy up to 3TeV [1, 2, 3, 4]....

[...]

Posted ContentDOI
Abstract: This report describes the physics potential and experiments at a future multi- TeV e+e collider based on the Compact Linear Collider (CLIC) technology The physics scenarios considered include precision measurements of known quantities as well as the discovery potential of physics beyond the Standard Model The report describes the detector performance required at CLIC, taking into account the interaction point environment and especially beaminduced backgrounds Two detector concepts, designed around highly granular calorimeters and based on concepts studied for the International Linear Collider (ILC), are described and used to study the physics reach and potential of such a collider Detector subsystems and the principal engineering challenges are illustrated The overall performance of these CLIC detector concepts is demonstrated by studies of the performance of individual subdetector systems as well as complete simulation studies of six benchmark physics processes These full detector simulation and reconstruction studies include beaminduced backgrounds and physics background processes After optimisation of the detector concepts and adopting the reconstruction algorithms the results show very efficient background rejection and clearly demonstrate the physics potential at CLIC in terms of precision mass and cross section measurements Finally, an overview of future plans of the CLIC detector and physics study is given and a list of key detector R&D topics needed for detectors at CLIC is presented

321 citations

### "Integrated CMOS sensor technologies..." refers background or methods in this paper

• ...1 Introduction The Compact Linear Collider (CLIC) is an option for a future linear e+e collider at CERN in the post LHC era, reaching a centre of mass energy up to 3TeV [1, 2, 3, 4]....

[...]

• ...To suppress beam induced background particles, a time stamping accuracy of ⇠ 10 ns is required for the main tracker [2, 5]....

[...]

DOI
12 Aug 2016
Abstract: The Compact Linear Collider (CLIC) is a multi-TeV high-luminosity linear e+e- collider under development. For an optimal exploitation of its physics potential, CLIC is foreseen to be built and operated in a staged approach with three centre-of-mass energy stages ranging from a few hundred GeV up to 3 TeV. The first stage will focus on precision Standard Model physics, in particular Higgs and top-quark measurements. Subsequent stages will focus on measurements of rare Higgs processes, as well as searches for new physics processes and precision measurements of new states, e.g. states previously discovered at LHC or at CLIC itself. In the 2012 CLIC Conceptual Design Report, a fully optimised 3 TeV collider was presented, while the proposed lower energy stages were not studied to the same level of detail. This report presents an updated baseline staging scenario for CLIC. The scenario is the result of a comprehensive study addressing the performance, cost and power of the CLIC accelerator complex as a function of centre-of-mass energy and it targets optimal physics output based on the current physics landscape. The optimised staging scenario foresees three main centre-of-mass energy stages at 380 GeV, 1.5 TeV and 3 TeV for a full CLIC programme spanning 22 years. For the first stage, an alternative to the CLIC drive beam scheme is presented in which the main linac power is produced using X-band klystrons.

156 citations

### "Integrated CMOS sensor technologies..." refers background in this paper

• ...1 Introduction The Compact Linear Collider (CLIC) is an option for a future linear e+e collider at CERN in the post LHC era, reaching a centre of mass energy up to 3TeV [1, 2, 3, 4]....

[...]

##### Network Information
###### Related Papers (5)
01 Nov 2002

Franck Larnaudie, Bruno Vignon +7 more

01 Jan 2003

Daniele Passeri, Pisana Placidi +5 more

Alessandro Marras, Daniele Passeri +6 more

04 Jun 2005

J.E. DeGroaf, D. Herman +4 more

Alessandro Gabrielli, G. De Robertis +3 more

##### Performance
###### Metrics
No. of citations received by the Paper in previous years
YearCitations
20171