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> > > Resistors in Parallel Formula
# Resistors in Parallel Formula
When we use resistors in electronic circuits, they can be used in different configurations. We can calculate the resistance for the circuit, or some portion of the circuit, by determining the way of organizing the resistors. Registers are normally organized in series or in parallel. We will describe the concept and resistors in parallel formula with examples. We often call the total resistance of a circuit as the equivalent resistance. Let us learn the concept in an easy way!
Source: en.wikipedia.org
## Resistors in Parallel Formula
### Concept of Resistors in Parallel
Resistors are often connected in series or in parallel for creating more complex networks. The voltage across resistors in parallel will be the same for each resistor. But, the current will be in proportion to the resistance of each individual resistor.
The purpose of finding the equivalence resistance is that we can replace any number of resistors connected in a parallel combination by the equivalent resistance of the parallel combination resistors.
If two or more resistors are connected in parallel, then the potential difference across all the resistors is the same. Resistors in parallel connection are connected to the same nodes from both ends.
This can be identified by the presence of more than one way for the current to flow. The potential difference across the resistors is the same as that across the resistor which is equal to the supply potential.
### The Formula for Parallel Resistors
In electric circuits, we may replace a group of resistors with a single, equivalent resistor. We can find the equivalent resistance of a number of resistors in parallel using the reciprocal of resistance i.e. $$\frac{1}{R}$$. The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of each resistance. The unit of resistance is the Ohm, which is equal to a Volt per Ampere. Larger resistors with kilo-Ohm or mega-Ohm resistances are common, as well.
$$\frac{1}{R_{eq}} =\frac{1}{R_1} + \frac{1}{R_2}+ …….\frac{1}{R_n}+…….$$
Where,
$$R_{eq}$$ Equivalent resistance. $$R_1$$ The resistance of the first resistor. $$R_2$$ The resistance of the second resistor $$R_n$$ The resistance of an nth resistor
### Major Features of Resistors in Parallel
1. We find Parallel resistance from, and it is smaller than any individual resistance in the combination.
2. Each resistor in parallel has the same voltage of the source applied to it.
3. Parallel resistors do not each get the full current and they divide it.
## Solved Examples
Q.1: What is the equivalent resistance of a 1000 kilo-ohm and a 250 kilo-ohm resistor connected in parallel?
Solution: The resistances are both expressed in kilo-Ohms. Thus, there is no need to change the units. We can find the equivalent resistance in kilo-ohm using the formula:
$$\frac{1}{R_{eq}} =\frac{1}{R_1} + \frac{1}{R_2}$$
$$\frac{1}{R_{eq}} =\frac{1}{1000} + \frac{1}{250}$$
= $$\frac {5}{1000}$$
$$R_{eq} = 200\; kilo- \Omega$$
Therefore, the equivalent resistance of the $$1000 kilo- \Omega and 250.0 kilo- \Omega resistors in parallel is 200.0 kilo- \Omega$$.
Q.2: What is the equivalent resistance of a 10 ohm, 20 ohm and 30-ohm resistors connected in parallel?
Solution:
Given:
$$R_1$$ = 10 ohm
$$R_2$$ = 20 ohm
$$R_3$$ = 30 ohm
We can find the equivalent resistance in kilo-ohm using the formula:
$$\frac{1}{R_{eq}} =\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
$$\frac{1}{R_{eq}} =\frac{1}{10} + \frac{1}{20} + \frac{1}{30}$$
= $$\frac{11}{60}$$
$$R_{eq} = \frac{60}{11}$$
$$R_{eq} = 5.55 ohm.$$
Therefore, the equivalent resistance will be 5.55 ohm.
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I am trying to run Asymptote code embedded in a tex file. The pdf generated has no asymptote figure but other latex stuff appear. I get a warning that file "filename-1.pdf" not found. I am using Texmaker 5.0.4 with MikTex 2.9. I ran the command PdfLatex+Asymptote+PdfLatex.
Edit: Since a code snippet was asked, I ran this file that Akira Kakuto suggested as filename.tex and I am still getting an error,
\documentclass{article}
\usepackage{graphicx}
\usepackage{asymptote}
\begin{document}
\begin{figure}[h]
\centering
\begin{asy}
size(200);
pen[] p={red,green,blue,magenta};
path g=(0,0){dir(45)}..(1,0)..(1,1)..(0,1)..cycle;
dot(g);
\end{asy}
\immediate\write18{asy \jobname*.asy}
\end{figure}
\end{document}
• would you mind posting what did you try? It is difficult for people to help if they don't know what you tried. May 10, 2020 at 11:38
• @bingung I have now added a code snippet May 11, 2020 at 12:56
• Run pdflatex --shell-escape twice on the input. You may need to edit your editor preferences to add --shell-escape, or run the command in a terminal window. May 11, 2020 at 13:03
• @AlexG I did run it that way but it seems to be still giving the same error. The editor preference now looks like this-imgur.com/a/68dCKuj May 11, 2020 at 13:40
• Editors sometimes break things. Did you try running pdflatex in a terminal (command line window)? (Works for me.) May 11, 2020 at 14:08
I'll show an example by using a sample in the version 2.65:
% filename.tex
% Compile twice as:
% pdflatex -shell-escape filename.tex
% pdflatex -shell-escape filename.tex
%
\documentclass{article}
\usepackage{graphicx}
\usepackage{asymptote}
\begin{document}
\begin{figure}[h]
\centering
\begin{asy}
size(200);
pen[] p={red,green,blue,magenta};
path g=(0,0){dir(45)}..(1,0)..(1,1)..(0,1)..cycle;
• @cookiemonster The setting in 'Quick Build' ---> 'For .asy files' is not relevant if you run a file with .tex extension; it is only relevant when you run files with .asy extension. When you run filename.tex, is a file called filename-1.asy produced? (using pdflatex only) May 11, 2020 at 13:19
• @bingung Yes, using pdflatex, filename-1.asy is being produced. May 11, 2020 at 13:37
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Electrolyte Challenge: Orange Juice Vs. Sports Drink
Recommended Project Supplies
Get the right supplies — selected and tested to work with this project.
Difficulty Time Required Short (2-5 days) Prerequisites None Material Availability Specialty electronics items are required. A kit is available from Science Buddies. See the Materials list for details. Cost Average ($40 -$80)
Abstract
The makers of sports drinks spend tens to hundreds of millions of dollars advertising their products each year. Among the benefits often featured in these ads are the beverages' high level of electrolytes, which your body loses as you sweat. In this science project, you will compare the amount of electrolytes in a sports drink with those in orange juice to find out which has more electrolytes to replenish the ones you lose as you work out or play sports. When you are finished, you might even want to make your own sports drink!
Objective
To investigate whether or not a sports drink provides more electrolytes than orange juice.
Credits
David Whyte, PhD, Science Buddies
Edited by Ben Finio, PhD, Science Buddies
This project is based on the following 2008 California State Science fair project, a winner of the Science Buddies Clever Scientist Award:
Yaeger, T.O. Jr. (2008). Electrolyte Madness.
MLA Style
Science Buddies Staff. "Electrolyte Challenge: Orange Juice Vs. Sports Drink" Science Buddies. Science Buddies, 27 Oct. 2016. Web. 22 Jan. 2017 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Chem_p053.shtml?from=AAE>
APA Style
Science Buddies Staff. (2016, October 27). Electrolyte Challenge: Orange Juice Vs. Sports Drink. Retrieved January 22, 2017 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Chem_p053.shtml?from=AAE
Share your story with Science Buddies!
Last edit date: 2016-10-27
Introduction
"Just do it!" You have probably heard that slogan, and there is no doubt that exercise is a key part of staying healthy. But exercising depletes the body's stores of fluids and minerals, which must be replaced. Most experts agree that if you are engaged in light to moderate exercise, drinking a glass or two of water should do the trick. But if you are exercising strenuously, you also need to replenish some of the salts that your body loses through sweat. These salts, or electrolytes, are found in most sports drinks, and also in natural juices like orange juice.
What advantages does a sports drink have over water? Water provides the liquid you need to avoid dehydration, but it does not have electrolytes. An electrolyte is a substance that will dissociate into ions in a solution. The ions in the solution give it the capacity to conduct electricity. Electrolytes, such as sodium and potassium, are present in sweat. Chloride, calcium, and phosphate ions are also electrolytes.
The proper concentration of electrolytes in your blood is essential to your health. Your cardiovascular and nervous systems—to name just two—require electrolytes to function well. Differences in the concentration of sodium and potassium inside and outside of cells allow your nerve and muscle fibers to send electrical impulses (which is how these cells communicate and get your body to react and move).
Your body keeps the concentration of the various electrolytes in its fluids within a narrow range, and this process depends on consuming enough water and electrolytes. The maintenance of electrolytes within this narrow range is due to the body's homeostatic mechanisms, which control the absorption, distribution, and excretion of water and its dissolved electrolytes.
To measure the electrolytes in this science project, you will use a multimeter. A multimeter is an electronic device that measures voltage, current, and resistance. You can learn more about these terms in the Science Buddies Electronics Primer. For this project, you will use just the ammeter part of the multimeter. An ammeter measures current. The procedure will describe what you need to do, but you can learn more about what a multimeter is and how to use one in the Science Buddies resource How to Use a Multimeter.
How can you use an ammeter to measure the concentration of electrolytes? You will use it to measure conductance, which is proportional to the electrolyte concentration. Because electrolytes are charged particles that carry current in solution, the conductance of the solution depends on the concentration of the electrolytes. If you increase the concentration of electrolytes in a solution, the conductance of the solution also increases. In order to measure a current in the solutions, you have to apply a voltage. You will use a 9 volt (V) battery to supply the voltage.
The symbol for conductance is G and it is measured in units called siemens (S). The symbol for current is I, and it is measured in amperes (A), commonly called amps for short. The symbol for voltage is V and it is measured in volts (also abbreviated V). Calculating the conductance is easy—it is the current divided by the voltage, as shown in Equation 1.
Equation 1.
• G is conductance, measured in siemens (S).
• I is current, measured in amperes (A).
• V is the voltage, measured in volts (V).
Note that conductance is the inverse of resistance, which is measured in ohms (Ω, the capital Greek letter Omega). The symbol for resistance is R, so G = 1/R (1 S = 1 / Ω). Equation 1 is just another form of Ohm's law, which uses resistance instead of conductance: V = IR.
Finally, in this project the amount of current you will measure is fairly small. That makes it more convenient to take your measurements in milliamps (mA), thousandths of an amp; or microamps (μA), millionths of an amp. However, before you plug your current reading into Equation 1, you must convert the measurement back to amps. The procedure will explain how to do this.
Do not worry if you find it difficult to remember all the letters and symbols. Table 1 summarizes the electrical variables, their units, and abbreviations.
Quantity Variable Unit Unit Symbol
VoltageVVoltV
CurrentIAmpereA
ResistanceROhmΩ
ConductanceGSiemensS
Table 1. Electrical variables, their units, and abbreviations.
Terms and Concepts
• Electrolyte
• Dissociate
• Ion
• Solution
• Conduct electricity
• Electricity
• Homeostatic mechanism
• Multimeter
• Voltage (V)
• Current (I)
• Resistance (R)
• Ammeter
• Conductance (G)
• Proportional
• Siemens (S)
• Ampere, or amp (A)
• Volts (V)
• Ohms (Ω)
• Ohm's law
• Milliamp (mA)
• Microamp (μA)
• Open circuit
• Short circuit
• Electrolysis
• Dilute
Questions
• What do electrolytes do in your body?
• What advantages do sports drinks or juices have over water in terms of electrolyte content? Why does this matter for strenuous exercise?
• Are there other reasons, besides electrolyte content, that you would pick a certain drink for before, during, or after strenuous exercise? For example, many juices have relatively high amounts of carbohydrates that add calories and require extra water to digest. Certain drinks might be more acidic and upset your stomach more easily. What other factors should you consider when picking a drink?
• What are the amounts of calories, sodium, potassium, and carbohydrates in one serving (8 ounces [oz.]) of orange juice? How does this compare with sports drinks?
News Feed on This Topic
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Materials and Equipment
• Electrolyte Challenge kit, available from the Science Buddies Store. Includes:
• Digital multimeter
• Copper wire, bare, 24-gauge (1.5 meters [5 feet])
• 9 V battery
• 9 V battery clip
• 1 kΩ resistor
• You will also need to gather these items, not included in the kit:
• Disposable plastic straw
• Scissors
• Small plastic, glass, or ceramic bowls, not metal (8). Use a different one for each liquid you test or use one bowl repeatedly, being careful to wash and wipe it thoroughly between liquids.
• Masking tape or other materials for creating labels
• Permanent pen or marker
• Distilled water (dH2O), room temperature; available in the bottled water section of most grocery stores
• Tap water, room temperature
• Sports drink(s) of your choice, room temperature
• Orange juice of your choice, room temperature
• Paper towels
• Lab notebook
Recommended Project Supplies
Get the right supplies — selected and tested to work with this project.
Project Kit: \$29.95
Experimental Procedure
Making a Simple Conductance Sensor
1. Cut a 5 cm (2 inch) piece from the drinking straw.
2. Cut two pieces of copper wire, each about 12 cm (5 inches) long.
3. Wrap the two pieces of wire around each end of the straw, leaving 5 cm tails of wire, as shown in Figure 1.
1. Make sure you wrap the wires snugly around the straw so they do not slide back and forth.
2. Caution: Make sure the two wires do not touch. The conductance sensor will not work if the wires touch, and touching wires will blow the fuse in your multimeter.
Figure 1. The conductance sensor consists of a non-conducting core (a piece of disposable drinking straw) with copper wire wrapped around the ends. The ions in the solution complete the circuit, enabling current to flow between the copper wires.
Making a Conductance Measuring Circuit
1. Connect the multimeter probes as shown in Figure 2.
1. For now, make sure your multimeter's center dial is in the "OFF" position.
2. Plug the black probe into the port labeled "COM".
3. Plug the red probe into the port labeled "VΩMA".
Figure 2. Picture of how to connect the multimeter probes.
1. Assemble your circuit as shown in Figures 3 and 4. There are several important notes before you begin.
1. Important: Never let exposed metal from the different alligator clips or probes, or the conductance sensor wires, touch each other directly. This will create a short circuit, which could damage your multimeter by blowing out the fuse. Always keep the various wires a safe distance away from each other, as shown in Figure 4. Keeping your multimeter's dial in the "OFF" position when not in use will also help prevent accidental damage.
2. Always make sure you connect the alligator clips to the exposed metal parts of probes or wires, not to the colored insulation. This is easy to do with the multimeter probes since the metal tips are rather large, but can be difficult with the battery snap connector since the exposed metal parts at the ends of the wires are fairly small. If you connect to insulation instead of the metal, your circuit will not work.
3. Your work area can get messy with all the wires. You can use twist ties to bundle them up and keep your work area neater, as shown in Figure 4. This also helps you avoid short circuits by making sure the metal parts do not bump into each other.
4. Connect the snap connector to the 9 V battery.
5. Use the red alligator clip to connect the red multimeter probe to the red wire from the battery snap connector.
6. Use the black alligator clip to connect the black multimeter probe to one wire of the conductance sensor.
7. Use the green alligator clip to connect the black wire from the battery snap connector to the other wire of the conductance sensor.
Figure 3. A schematic of how you should build the circuit.
Figure 4. A picture of the completed conductance measuring circuit.
1. Double-check your connections to make sure they match those shown in Figures 3 and 4 before you proceed.
2. Note that this is an open circuit because of the gap between the wires wrapped around the (non-conducting) straw. You will use the electrolytes in the solutions to close the circuit. The amount of current that flows is proportional to the electrolyte concentration.
1. Clean the eight small bowls with warm soapy water, rinse thoroughly, and dry them right away with a clean dry cloth or paper towel. This will remove ions in the tap water. If you want to be extra careful, rinse the bowls with distilled water before drying.
2. Put masking tape on all eight bowls.
1. Label four bowls with the following labels: Distilled Water, Tap Water, Sports Drink, and Orange Juice.
2. Label one bowl Tap Water Rinse.
3. Label the final three bowls as follows: dH2O Rinse 1, dH2O Rinse 2, and dH2O Rinse 3. Use these bowls to rinse the conductance sensor between uses.
3. Pour each liquid into the appropriately labeled bowl. All of the solutions should be at room temperature. The liquids should be deep enough to completely submerge the coiled part of the conductance sensor. Make sure you fill each bowl to the same level, so the sensor can be submerged to the same depth. This is important because the extra surface area of the "tail" part of the wires in contact with the liquid will affect the conductance.
Measuring the Conductance
1. Set your multimeter to measure direct current in the 200 μA range. This is the green "200μ" on the upper-right part of your multimeter dial, as shown in Figure 5. This is a high-sensitivity setting that you will only use to measure distilled water, which is less conductive than the other liquids.
Figure 5. Multimeter dial set to the 200 microamp (μA) range, represented by the green "200μ."
1. Place the conductance sensor in the distilled water. Make sure the straw is completely immersed. You will need to submerge the straw to the same depth each time. This is probably easiest if you let it rest on the bottom of the bowl.
2. Read the current on the multimeter.
1. Always make your readings quickly and remove the conductance sensor from the solutions immediately. Over time, the copper wires will start to dissolve in the solutions, skewing your results. In addition, electrolysis may take place, forming tiny bubbles on your conductance sensor that can interfere with your data.
2. Your readings may fluctuate slightly, and this is normal. Try to record an "average" reading, or a number in the middle of the range that you observe.
3. Record the current (the readings from your multimeter) in your lab notebook in a data table. Make sure to record that this reading is in microamps (μA). Remember that a microamp is one millionth of an amp.
4. You do not need to rinse your conductance sensor this time because you used distilled water.
5. Now set your multimeter to measure direct current in the 200 mA range. This is the green "200m" on the right side of the multimeter dial, as shown in Figure 6. This setting can measure higher current values, which you need to do for the more conductive liquids.
Figure 6. Multimeter dial set to the 200 milliamp (mA) range, represented by the green "200m". Be careful not to get this mixed up with the white "200m" on the other side of the dial. That setting is for measuring voltage, not current.
1. Now place the conductance sensor in the tap water. Make sure you submerge it to the same depth that you did when you measured the distilled water.
2. Record the current. Again, make sure you record the correct units. Since your multimeter dial is set to 200m, this reading is in milliamps (mA), not microamps (μA).
3. Tap the sensor on a paper towel to remove drops of tap water. Then rinse the sensor in distilled water, dipping it briefly in each of the three distilled water rinse bowls.
4. Place the sensor in the sports drink and measure the current (you do not need to change the multimeter dial). Record the current in your lab notebook, and remember to record units of milliamps.
5. Tap the sensor dry, and then dip the sensor in tap water, then in the three bowls of distilled water.
6. Place the sensor in the orange juice and measure the current. Record the current in your lab notebook.
7. Rinse the sensor in the tap water and then in all three distilled water bowls.
8. Repeat steps 1–13 in the "Measuring the Conductance" section two more times to obtain a total of three measurements for each liquid.
1. Remember that you will need to switch back to the "200μ" setting to measure the distilled water, and then use the "200m" setting to measure tap water, sports drinks, and orange juice.
2. Always remember to submerge the conductance sensor to the same depth for each trial. This is important since the conductance depends on the amount of surface area of the wire that is in contact with the liquid.
3. Record all data and measurements, including the proper units, in the data table in your lab notebook.
9. Average your current measurements across the three trials for each liquid.
10. Before you proceed, convert all of your current measurements to amps (A).
1. Convert microamps (μA) to amps (A) by dividing by 1,000,000. For example, 20 microamps is 0.00002 amps (20/1,000,000 = 0.00002).
2. Convert milliamps (mA) to amps (A) by dividing by 1,000. For example, 20 milliamps is 0.02 amps (20/1,000 = 0.02).
11. Calculate the conductance for each liquid by using Equation 1 from the Introduction.
1. The current (I) for each liquid is the average current that you calculated. Make sure you convert the current to amps. Do not use milliamps or microamps in Equation 1.
2. Since the voltage was always from your 9 V battery, you can use 9 V as the voltage (V) in your calculations. In reality, the voltage is likely to be slightly less than 9 V due to internal resistance of the battery. But this change is quite small and nearly constant across the experiment. Because it is so small, you do not need to take it into account. If you have a second multimeter, you can adapt the circuit to monitor both current and voltage across the battery at the same time.
12. Which liquid has the highest conductance, meaning the most electrolytes?
Troubleshooting
For troubleshooting tips, please read our FAQ: Electrolyte Challenge: Orange Juice Vs. Sports Drink.
Variations
• Try other sports drinks and juices.
1. What is the conductance of fresh-squeezed orange juice?
• Try making your own sports drink, starting with orange juice. If the carbohydrates in the orange juice are higher than they are in the sports drink, dilute the juice with distilled water so that the carbohydrates are about the same as they are in the sports drink. How does the conductance of the diluted juice compare to that of the sports drink?
• Standardize your readings, using tap water as a reference. Divide all of the current measurements for each trial by the current you measured for the tap water. Tap water will have a conductance of 1.0. The fruit juice and sports drinks will then have conductances that are multiples of the tap water's conductance.
Share your story with Science Buddies!
Q: I am not sure if my multimeter is set up correctly. How should it be configured?
A: The multimeter dial has a lot of different settings, which may seem confusing at first. In this project, you will only use the green "200μ" and "200m" settings, which measure direct current in the 200 microamp (μA) and 200 milliamp (mA) ranges, respectively. These settings are shown in Figures 5 and 6 of the procedure. You also must make sure the black multimeter probe is plugged into the port labeled "COM", and the red probe is plugged into the port labeled "VΩMA". You will not need to use any of the other settings on your multimeter for this project. If you want to learn more about what the other symbols mean, refer to the Science Buddies resource How to Use a Multimeter.
Q: My multimeter always reads 00.0 when I try to measure current. What am I doing wrong?
A: A number of issues may result in a reading of 00.0 from the multimeter, regardless of the solution's real conductance:
• One or more of the connections in your circuit may not be attached securely. If just one connection is loose, this will prevent the circuit from being complete, and the multimeter will be unable to take a reading. Double-check all of your alligator clips. Make sure all the connections are snug with metal-on-metal contact (do not clip to any of the plastic, since plastic is an insulator).
• You might not have your multimeter on the correct setting. The currents flowing through the liquids in this experiment are very small, so your multimeter must be set at a high sensitivity. Use 200 microamps (μA) for distilled water, and 200 milliamps (mA) for the other liquids. See Figures 5 and 6 in the Procedure for instructions on how to set your multimeter.
• You might not have your multimeter's probes in the correct ports. Make sure the black probe is in the port labeled "COM" and the red probe is in the port labeled "VΩMA." See Figure 2 in the Procedure.
• The 9 V battery in your circuit might be dead. This is unlikely if you are using a fresh battery from your Science Buddies kit, but the battery could drain if you accidentally left the circuit connected for a long time. You can check whether your battery still works by setting your multimeter to read 20 V DC (labeled "20" in white text on the left side of the multimeter dial) and placing the positive (red) multimeter probe on the positive battery terminal (marked with a "+" sign), and the negative (black) multimeter probe on the negative battery terminal (marked with a "-" sign). If the reading is below 7, your battery may not have enough power for this project and you should use a fresh battery.
• The wires on your conductance sensor may have become compromised in some way. There should be no material collected on them; if there is anything collected on them, clean and rinse them well and try again.
• Your multimeter may have blown a fuse. The fuse contains a thin wire that burns out if too much current flows through it, in order to protect the rest of the multimeter's circuitry. When the experiment is set up as described, but the two sensor wires (in the liquid) touch, it will blow the fuse, so be sure they do not touch. If your multimeter was working well and then suddenly started reading 00.0 all the time, there is a chance you blew the fuse in your multimeter (there is also a chance that one of your connections simply came loose. See the first bullet point above). See the question "How can I tell if I blew the fuse in my multimeter?" to confirm if you blew the fuse.
Q: What does it mean if I am getting a negative current reading on my multimeter?
A: The wires in the circuit may be connected incorrectly, resulting in current flowing "backwards" through your circuit. Double-check all your connections against Figures 3 and 4 in the Procedure. For example, if you connect the battery backwards (switch the red and black leads), or get the red and black multimeter probes switched, that will result in a negative current reading.
Q: Why are my multimeter readings going up and down?
A: A few possibilities could explain why your readings are fluctuating; you can determine what is happening in your experiment by how much the readings are changing.
• It is normal to have very small fluctuations (for example, the reading stays around the same number but increases or decreases slightly). In these types of experiments with multimeters, it can be very difficult to get an entirely stable current.
• If your measurements decreased quickly, you may have encountered a problem with electrolysis. Electrolysis is when water is broken up into hydrogen and oxygen gas by an electrical current. If electrolysis is occurring, there will be little bubbles collecting on the wires on the ends of the conductance sensor. Electrolysis will result in a smaller surface area on the wires on the conductance sensor, and your readings will decrease. If you notice this occurring, rinse of your sensor and try again, and take your reading quickly before lots of bubbles accumulate on the sensor.
• If the wires on the conductance sensor move while you are taking measurements, this can make your measurements randomly vary from sample to sample. To fix this, see the answer for the question "Why is it important to keep the wires on the conductance sensor from moving?"
Q: The current readings on my multimeter seem very low for all of my samples and there is not much variation between them. What should I do?
A: Your multimeter may not be configured correctly. To check this, see the answer for the question "I am not sure if my multimeter is set up correctly. How should it be configured?" Alternatively, the 9 V battery in your circuit may be dead. To test the battery, see the fourth bullet point for the question "My multimeter always reads 00.0 when I try to measure current. What am I doing wrong?"
Q: I am not sure if the values I am getting are correct. How should I be making my calculations and what is the range that my results will probably fall in?
A: If you take your measurements using the 200 milliamps setting, your current readings will be in milliamps (mA). If you used the 200 microamps setting with the distilled water, your current readings will be in microamps (μA). For this experiment, current readings in the range of 0 (for distilled water) to 100 mA (for the other liquids) are expected.
To calculate the conductance of your different samples, use Equation 1 from the Introduction. Convert your current readings from microamps or milliamps to amps, as described in step 16 of the Procedure. Divide this by the voltage of your battery (which should be about 9 V, but you can measure this with your multimeter to be sure, as described in the fourth bullet point under "My multimeter always reads 00.0 when I try to measure current. What am I doing wrong?"). This will give you conductance in siemens (S), which you can convert to millisiemens by multiplying by 1,000.
Q: Why is it important to keep the wires on the conductance sensor from moving?
A: If the wires on the conductance sensor move while you are taking measurements, your measurements may be inaccurate. Make sure the wires are tightly secured on the ends of the conductance sensor by attaching the short end of the wire to the longer end by twisting the two together, or by using a very small drop of super glue to hold the wires in place.
Q: What is the purpose of dipping the sensor in distilled water? Should I replace the distilled water between tests?
A: Dipping the sensor in distilled water removes all of the ions and other liquids from the sensor. Not rinsing the sensor will cause the sensor to become contaminated with different liquids between the different tests, which could make your results have higher or lower conductance values than they actually do. Although it is not necessary, changing the distilled water in the rinsing bowls between tests may improve accuracy.
Q: How can I tell if I blew the fuse in my multimeter?
A: If you already have your circuit set up as shown in the Figures 3 and 4, you just need to replace the conductance sensor with the 1 kΩ resistor included in your kit (do not submerge it in liquid), as shown in Figure 7. If you need to set up your circuit from scratch, follow these steps:
1. Plug the multimeter's black probe into the port labeled "COM," and the red probe into the port labeled "VΩMA," as shown in Figure 2 in the Procedure.
2. Attach the snap connector to the 9 V battery.
3. Your kit includes a 1 kΩ resistor, a small tan cylinder with two metal leads sticking out of it. Connect one of the resistor's leads (it does not matter which one) to the black multimeter probe using the black alligator clip, as shown in Figure 7.
4. Use the green alligator clip to connect the resistor's other lead to the snap connector's black lead.
5. Use the red alligator clip lead to connect the multimeter's red probe to the snap connector's red lead.
6. Important: Do not let any exposed metal from the different alligator clips or multimeter probes touch each other. This will create a short circuit and could blow your multimeter's fuse (which is what you are trying to avoid to begin with!).
7. Set your multimeter to measure direct current in the 200 mA range (the dial setting labeled "200m" on the right, as shown in Figure 6 in the Procedure).
8. Your multimeter should read about 9 mA (maybe slightly less if you are not using a fresh battery).
1. If this works, then you know there is nothing wrong with your multimeter. If you are having trouble with your experiment, the problem is with something other than the multimeter.
2. If this does not work, and you are confident that you set up the test correctly, as shown in Figure 7, please contact help@sciencebuddies.org for assistance.
9. When you are done, disconnect the alligator clips so you do not drain the 9 V battery, and remember to turn your multimeter off.
Figure 7. Setup for making sure the multimeter has a working fuse.
Q: My multimeter's screen just remains blank when I turn it on. Is it broken?
A: If you turn your multimeter's dial to the 200 μA or 200 mA settings, as described in Figures 5 and 6 of the Procedure, the screen should read "00.0" when the multimeter is not connected to anything (or when the conductance sensor is not immersed in a liquid). If your screen remains blank, then you might have a defective multimeter. Contact us at help@sciencebuddies.org for assistance.
The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.
If you have purchased a kit for this project from Science Buddies, we are pleased to answer any question not addressed by the FAQ above.
1. What is your Science Buddies kit order number?
2. Please describe how you need help as thoroughly as possible:
Examples
Good Question I'm trying to do Experimental Procedure step #5, "Scrape the insulation from the wire. . ." How do I know when I've scraped enough?
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Bad Question I don't understand the instructions. Help!
Good Question I am purchasing my materials. Can I substitute a 1N34 diode for the 1N25 diode called for in the material list?
Bad Question Can I use a different part?
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# EPS-HEP2021 conference
26-30 July 2021
Zoom
Europe/Berlin timezone
## The Electron Capture in $^{163}$Ho experiment - ECHo
Not scheduled
20m
Zoom
#### Zoom
Poster Neutrino Physics
### Speaker
Neven Kovac (Kirchhoff-Institut für Physik, Universität Heidelberg)
### Description
The Electron Capture in $^{163}$Ho experiment, ECHo, is a running experiment for the determination of the neutrino mass scale via the analysis of the end point region of the $^{163}$Ho electron capture spectrum. In the first phase, ECHo-1k, about 60 MMCs pixels enclosing $^{163}$Ho ions for an activity of about 1Bq per pixel have been operated for several months. The goal of this first phase is to reach a sensitivity on the effective electron neutrino mass below 20 eV/c$^2$ by the analysis of a $^{163}$Ho spectrum with more than 10$^8$ events. We discuss the characterization of the single pixel performance and the stability over the measuring period. Results from the analysis of the acquired data will be presented with focus on data reduction efficiency and on the procedures to obtain the final high statistics spectrum. A preliminary analysis of the $^{163}$Ho spectral shape will be described and the expected sensitivity on the effective electron neutrino mass, on the basis of the properties of the presented spectrum, will be discussed. In conclusion, we will present how the performance obtained by the MMC arrays used during the first phase of the ECHo experiment have led to the design of the MMC arrays for the second phase, ECHo-100K. In ECHo-100k about 12000 MMC pixels each hosting $^{163}$Ho for an activity of 10 Bq will be simultaneously operated thanks to the microwave SQUID multiplexing readout. Operating these arrays for three years will allow for reaching a sensitivity on the electron neutrino mass at the 1 eV/c$^2$ level.
Collaboration / Activity ECHo Collaboration
### Primary author
Neven Kovac (Kirchhoff-Institut für Physik, Universität Heidelberg)
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I would like to make my section headers look like this with the titlesec package. Is there a good way to do that?
EDIT - I am using the scratcl document class.
• assuming your document class (which you really should have stated) has chapters, \let\section\chapter is probably the easiest way. – David Carlisle Mar 27 '14 at 19:59
• do you also want them to affect the page style? – cmhughes Mar 27 '14 at 20:13
• I am not sure but do you really want Chapter 1 or isn't it rather Section 1 and then the name of the section (Introduction here) that you want to get ? – user4686 Mar 27 '14 at 20:51
If your document class has chapters, the simpler solution is to say
\let\section\chapter
as David Carlisle mentioned in his comment. After the edit, it is clear that the used class (scrartcl) has no chapters, so (as required) you can use this:
\documentclass{scrartcl}
\usepackage{titlesec}
\newcommand\chaptername{Chapter}
\titleformat{\section}[display]
{\normalfont\huge\bfseries\sffamily}
{\chaptername\ \thesection}
{20pt}
{\Huge}
\titlespacing*{\section}
{0pt}{50pt}{40pt}
\begin{document}
\section{A test chapter}
Some test text
\end{document}
If each \section should begin on a page of its own, you might need to add
\newcommand\sectionbreak{\clearpage}
or
\newcommand\sectionbreak{\cleardoublepage}
The above solution, however, this will just imitate some aspects (in particular, the title formatting), but not all of them, of a true \chapter in book, or report. Also, take into account that KOMA classes and titlesec package might not fully cooperate.
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# 14 Question a point) 1st attempt The backward-bending labor supply curve has its shape because, at...
###### Question:
14 Question a point) 1st attempt The backward-bending labor supply curve has its shape because, at Choose one: O A.all wages, the income effect dominates the substitution effect O B.low wages, the substitution effect dominates the income effect, but the reverse occurs at high wages. 0 Call wages, the substitution effect dominates the income effect. O D.low wages, the income effect dominates the substitution effect, but the reverse occurs at high wages. O E. high wages, the substitution effect dominates the income effect, but the reverse occurs at low wages. COMPLETED SUBMIT ANSWER
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##### 28. Identify the reagent that you would use to go from PGEi to PGEla? но но...
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##### The ' following - data was obtained from simple Conservation of Energy' experiment using projectile with mass of 25 grams.M2r HeightlcmbSetting_ Setting _ Setting_124standard units what was the initial Kinetic Energy of the projectile, for each setting? Show work points) P | _standardunits what was the initial speed of the projectile _ for each setting? Show work points)At what height, for setting does the Kinetic Energy equal the Gravitational Potential Energy? Show work: (8 points)
The ' following - data was obtained from simple Conservation of Energy' experiment using projectile with mass of 25 grams. M2r Heightlcmb Setting_ Setting _ Setting_ 124 standard units what was the initial Kinetic Energy of the projectile, for each setting? Show work points) P | _ standard...
##### Question 30 Not yet answveredsuppose that the regression Jine Is P= 2(x-4} then the predicted value of y when X =5 isMarked out of I1,00Flag question62nonePrevious page
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##### We were unable to transcribe this imageDegree Recipient Headcount by Degree Level Gender 8,506 7,982 7,723...
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##### Nonparametric statistical methods. From 6 consenting patients requiring a medical scan, 3 are chosen at random...
Nonparametric statistical methods. From 6 consenting patients requiring a medical scan, 3 are chosen at random to undergo a positron emission tomography (PET) scan, the others receiving a magnetic resonance imaging (MRI) scan. Image quality is ranked in order by a hospital consultant from 1 (best) t...
##### What are 5 examples of factors that impact the direction of aggregate demand for the U.S...
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##### Cosy 2xy -dx (x2 + xsin y)dy
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##### The local maximum and minimum Find the intervals on which f is increasing and decreasing; values_ the intervals of concavity, and the inflection points for; flr) =rer (a) f() 47 31? 61 4 J(e) = 1? In(c) 3sin(5) cos(r) on [0,27] f(r) (b) f(c)
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##### Determine whether the function $f$ is one-to-one by examining the sign of $f^{\prime}(x)$. (a) $f(x)=x^{3}+3 x^{2}-8$ (b) $f(x)=x^{5}+8 x^{3}+2 x-1$ (c) $f(x)=\frac{x}{x+1}$ (d) $f(x)=\log _{b} x, \quad 0<b<1$
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# 8.1 Separable Convex (SCopt) Interface¶
The Optimizer API for Java provides a way to add simple non-linear functions composed from a limited set of non-linear terms. Non-linear terms can be mixed with quadratic terms in objective and constraints. We consider problems which can be formulated as:
$\begin{split}\begin{array} {lcccccc} \mbox{minimize} & & & z_0(x) + c^T x & & & \\ \mbox{subject to} & l^c_i & \leq & z_i(x) + a_i^T x & \leq & u^c_i & i=1\ldots m\\ & l^x & \leq & x & \leq & u^x, & \end{array}\end{split}$
where $$x\in\real^n$$ and each $$z_i : \real^n\rightarrow\real$$ is separable, that is can be written as a sum
$z_i(x) = \sum^{n}_{j=1} z_{i,j}(x_j).$
The interface implements a limited set of functions which can appear as $$z_{i,j}$$. They are:
Table 8.1 Functions supported by the SCopt interface.
Separable function Operator name Name
$$f x \ln (x)$$ ent Entropy function
$$f e^{g x + h}$$ exp Exponential function
$$f \ln (g x + h)$$ log Logarithm
$$f (x+h)^g$$ pow Power function
where $$f,g,h\in\real$$ are constants. This formulation does not guarantee convexity. For MOSEK to be able to solve the problem, the following requirements must be met:
• If the objective is minimized, the sum of non-linear terms must be convex, otherwise it must be concave.
• Any constraint bounded below must be concave, and any constraint bounded above must be convex.
• Each separable term must be twice differentiable within the bounds of the variable it is applied to.
Some simple rules can be followed to ensure that the problem satisfies MOSEK‘s convexity and differentiability requirements. First of all, for any variable $$x_i$$ used in a separable term, the variable bounds must define a range within which the function is twice differentiable. These bounds are defined in Table 8.2.
Table 8.2 Safe bounds for functions in the SCopt interface.
Separable function Operator name Safe $$x$$ bounds
$$f x \ln (x)$$ ent $$0 < x$$.
$$f e^{g x + h}$$ exp $$-\infty <x <\infty$$.
$$f \ln (g x + h)$$ log If $$g > 0$$: $$-h/g < x$$.
If $$g < 0$$: $$x < -h/g$$.
$$f (x+h)^g$$ pow If $$g > 0$$ and integer: $$-\infty <x <\infty$$.
If $$g < 0$$ and integer: either $$-h <x$$ or $$x <-h$$.
Otherwise: $$-h <x$$.
To ensure convexity, we require that each $$z_i(x)$$ is either a sum of convex terms or a sum of concave terms. Table 8.3 lists convexity conditions for the relevant ranges for $$f>0$$ — changing the sign of $$f$$ switches concavity/convexity.
Table 8.3 Convexity conditions for functions in the SCopt interface.
Separable function Operator name Convexity conditions
$$f x \ln (x)$$ ent Convex within safe bounds.
$$f e^{g x + h}$$ exp Convex for all $$x$$.
$$f \ln (g x + h)$$ log Concave within safe bounds.
$$f (x+h)^g$$ pow If $$g$$ is even integer: convex within safe bounds.
If $$g$$ is odd integer:
• concave if $$(-\infty,-h)$$,
• convex if $$(-h,\infty)$$
If $$0<g<1$$: concave within safe bounds.
Otherwise: convex within safe bounds.
A problem involving linear combinations of variables (such as $$\ln(x_1+x_2)$$), can be converted to a separable problem using slack variables and additional equality constraints.
## 8.1.1 Example¶
Consider the following separable convex problem:
(1)$\begin{split}\begin{array}{ll} \mbox{minimize} & \exp (x_2) - \ln(x_1) \\ \mbox{subject to} & x_2 \ln(x_2) \leq 0\\ & x_1^{1/2} - x_2 \geq 0\\ & \half\leq x_1, x_2 \leq 1. \end{array}\end{split}$
Note that all nonlinear functions are well defined for $$x$$ values satisfying the variable bounds strictly. This assures that function evaluation errors will not occur during the optimization process because MOSEK.
The linear part of the problem is specified as usually. The nonlinear part is set using the function Task.putSCeval. See the API reference for a description of the format. After that a standard invocation of Task.optimize solves the problem. The API reference describes additional functions for reading and writing SCopt terms from/to a file.
Listing 8.1 Implementation of problem (1). Click here to download.
package com.mosek.example;
import mosek.*;
public class scopt1 {
public static void main(String[] args) {
try (Env env = new Env();
mosek.streamtype.log,
new mosek.Stream()
{ public void stream(String msg) { System.out.print(msg); }});
int numvar = 2;
int numcon = 2;
double inf = 0.;
mosek.boundkey[]
bkc = new mosek.boundkey[] {
mosek.boundkey.up,
mosek.boundkey.lo
};
double[] blc = new double[] { -inf, .0 };
double[] buc = new double[] { .0, inf};
mosek.boundkey[] bkx = new mosek.boundkey[] {
mosek.boundkey.ra, mosek.boundkey.ra
};
double[] blx = new double[] {0.5, 0.5};
double[] bux = new double[] {1.0, 1.0};
mosek.scopr[] opro = new mosek.scopr[] {mosek.scopr.log, mosek.scopr.exp};
int[] oprjo = new int[] { 0, 1 };
double[] oprfo = new double[] { -1.0, 1.0 };
double[] oprgo = new double[] { 1.0, 1.0 };
double[] oprho = new double[] { 0.0, 0.0 };
mosek.scopr[] oprc = new mosek.scopr[] { mosek.scopr.ent, mosek.scopr.pow };
int[] opric = new int[] { 0, 1 };
int[] oprjc = new int[] { 1, 0 };
double[] oprfc = new double[] { 1.0, 1.0 };
double[] oprgc = new double[] { .0, 0.5 };
double[] oprhc = new double[] { .0, 0.0 };
oprc, opric, oprjc, oprfc, oprgc, oprhc);
double[] res = new double[numvar];
mosek.soltype.itr,
mosek.solitem.xx,
0, numvar,
res);
System.out.print("Solution is: [ " + res[0]);
for (int i = 1; i < numvar; ++i) System.out.print(", " + res[i]);
System.out.println(" ]");
} catch (mosek.Exception e) {
System.out.println ("An error/warning was encountered");
System.out.println (e.toString());
throw e;
}
}
}
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a shape finding method
I was playing with my hand sanitiser liquid some minutes ago. It is a very viscous liquid. Now as we all know on a rotating motion of a liquid column inside a cylindrical pot liquid takes paraboloid shape. So I gave the liquid vigourous rotations about its axis and it got a likewise shape. Now I think for a unknown liquid it may be a process to find the density of the liquid. Actually the problem arises here . how will viscosity come into the calculation. I think the great physicists present in brilliant will show some light on my query. However I am adding a picture. Though its not.the actual shape
. however from these I got a further thought. What will be the time of regaining the most stable shape? Provided bottle is in horizontal or vertical positions respectively. Again a thought came in. What should be the expressions for minimum admissible height of a liquid having a hole on the floor of the pot and considering it viscous. I Hope People will love To show their calculations.
Note by Shyambhu Mukherjee
2 years, 6 months ago
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$
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# zbMATH — the first resource for mathematics
Ordered smoothers with exponential weighting. (English) Zbl 1349.62129
Summary: The main goal in this paper is to propose a new approach to deriving oracle inequalities related to the exponential weighting method. The paper focuses on recovering an unknown vector from noisy data with the help of the family of ordered smoothers [A. Kneip, Ann. Stat. 22, No. 2, 835–866 (1994; Zbl 0815.62022)]. The estimators withing this family are aggregated using the exponential weighting method and the aim is to control the risk of the aggregated estimate. Based on the natural probabilistic properties of the unbiased risk estimate, we derive new oracle inequalities for the mean square risk and show that the exponential weighting permits to improve Kneip’s oracle inequality.
##### MSC:
62G08 Nonparametric regression and quantile regression 62J05 Linear regression; mixed models 62C99 Statistical decision theory
##### Keywords:
linear model; ordered smoother; exponential weighting
Full Text:
##### References:
[1] Alquier, P. and Lounici, K. (2011). Pac-bayesian theorems for sparse regression estimation with exponential weights. Electronic Journal of Statistics 5 127-145. · Zbl 1274.62463 [2] Arias-Castro, E. and Lounici, K. Variable Selection with Exponential Weights and $$\ell_{0}$$-Penalization. · Zbl 1294.62164 [3] Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. Proc. 2nd Intern. Symp. Inf. Theory 267-281. · Zbl 0283.62006 [4] Catoni, O. (2004). Statistical Learning Theory and Stochastic Optimization . Lectures Notes in Math. 1851 . Springer-Verlag, Berlin. · Zbl 1076.93002 [5] Dalayan, A. and Salmon, J. (2012). Sharp oracle inequalities for aggregation of affine estimators. Ann. Statist. 40 2327-2355. · Zbl 1257.62038 [6] Demmler, A. and Reinsch, C. (1975). Oscillation matrices with spline smoothing. Numerische Mathematik 24 375-382. · Zbl 0297.65002 [7] Engl, H. W., Hanke, M., and Neubauer, A. (1996). Regularization of Inverse Problems . Mathematics and its Applications 375 . Kluwer Academic Publishers Group, Dordrecht. · Zbl 0859.65054 [8] Golubev, Yu. (2010). On universal oracle inequalities related to high dimensional linear models. Ann. Statist. 38 2751-2780. · Zbl 1200.62074 [9] Golubev, G. (2012). Exponential weighting and oracle inequalities for projection estimates. Problems of Information Transmission 48 269-280. · Zbl 1260.94025 [10] Green, P. J. and Silverman, B. W. (1994). Nonparametric Regression and Generalized Linear Models. A Roughness Penalty Approach . Chapman and Hall. · Zbl 0832.62032 [11] Juditsky, A. and Nemirovski, A. (2000). Functional aggregation for nonparametric regression. Ann. Statist. 28 681-712. · Zbl 1105.62338 [12] Kneip, A. (1994). Ordered linear smoothers. Ann. Statist. 22 835-866. · Zbl 0815.62022 [13] Lecué, G. (2007). Simultaneous adaptation to the margin and to complexity in classification. Ann. Statist. 35 1698-1721. · Zbl 1209.62146 [14] Leung, G. and Barron, A. (2006). Information theory and mixing least-squares regressions. IEEE Transactions on Information Theory 52 3396-3410. · Zbl 1309.94051 [15] Mallows, C. L. (1973). Some comments on $$C_{p}$$. Technometrics 15 661-675. · Zbl 0269.62061 [16] Nemirovski, A. (2000). Topics in Non-Parametric Statistics . Lectures Notes in Math. 1738 . Springer-Verlag, Berlin. · Zbl 0998.62033 [17] Nussbaum, M. (1985). Spline smoothing in regression models and asymptotic efficiency in $$L_{2}$$. Ann. Statist. 13 984-997. · Zbl 0596.62052 [18] Rigollet, Ph. and Tsybakov, A. (2007). Linear and convex aggregation of density estimators. Math. Methods Statist. 16 260-280. · Zbl 1231.62057 [19] Rigollet, Ph. and Tsybakov, A. (2012). Sparse estimation by exponential weighting. Statist. Sci. 27 558-575. · Zbl 1331.62351 [20] Speckman, P. (1985). Spline smoothing and optimal rates of convergence in nonparametric regression. Ann. Statist. 13 970-983. · Zbl 0585.62074 [21] Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9 1135-1151. · Zbl 0476.62035 [22] Tikhonov, A. N. and Arsenin, V. A. (1977). Solution of Ill-posed Problems . Translated from the Russian. Preface by translation editor Fritz John. Scripta Series in Mathematics. V. H. Winston & Sons, Washington, D.C.: John Wiley & Sons, New York. · Zbl 0354.65028 [23] Wahba, G. (1990). Spline Models for Observational Data . SIAM, Philadelphia. · Zbl 0813.62001 [24] Yang, Y. (2000). Combining different procedures for adaptive regression. J. Multivariate Anal. 74 135-161. · Zbl 0964.62032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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# Row- and column-major order
Illustration of row- and column-major order
In computing, row-major order and column-major order are methods for storing multidimensional arrays in linear storage such as random access memory.
The difference between the orders lies in which elements of an array are contiguous in memory. In a row-major order, the consecutive elements of a row reside next to each other, whereas the same holds true for consecutive elements of a column in a column-major order. While the terms allude to the rows and columns of a two-dimensional array, i.e. a matrix, the orders can be generalized to arrays of any dimension by noting that the terms row-major and column-major are equivalent to lexicographic and colexicographic orders, respectively.
Data layout is critical for correctly passing arrays between programs written in different programming languages. It is also important for performance when traversing an array because modern CPUs process sequential data more efficiently than nonsequential data. This is primarily due to CPU caching. In addition, contiguous access makes it possible to use SIMD instructions that operate on vectors of data. In some media such as tape or NAND flash memory, accessing sequentially is orders of magnitude faster than nonsequential access.[citation needed]
## Explanation and example
The terms row-major and column-major stem from the terminology related to grouping objects. A general way to order objects with many attributes is to first group and order them by one attribute, and then, within each such group, group and order them by another attribute, etc. If more than one attribute participate in ordering, the first would be called major and the last minor. If two attributes participate in ordering, it is sufficient to name only the major attribute.
In the case of arrays, the attributes are the indices along each dimension. For matrices in mathematical notation, the first index indicates the row, and the second indicates the column, e.g., given a matrix A , a1,2 is in its first row and second column. This convention is carried over to the syntax in programming languages,[1] although often with indexes starting at 0 instead of 1.[2]
Even though the row is indicated by the first index and the column by the second index, no grouping order between the dimensions is implied yet. We can then choose to group and order the indices either row-major or column-major. The terminology can be applied to even higher dimensional arrays. Row-major grouping starts from the leftmost index and column-major from the rightmost index, leading to lexicographic and colexicographics orders, respectively.
For example, for the array
${\displaystyle A={\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\end{bmatrix}}}$
The two possible ways are:
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to say, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression. (No other implications should be assumed, e.g., Fortran is not column-major simply because of its notation, and even the above implication could intentionally be circumvented in a new language.)
To use column-major order in a row-major environment, or vice versa, for whatever reason, one workaround could be to assign non-conventional roles to the indexes (using the first index for the column and the second index for the row), and another could be to bypass language syntax by explicitly computing positions in a one-dimensional array. Of course, deviating from convention probably incurs a cost that increases with the degree of necessary interaction with conventional language features and other code, not only in the form of increased vulnerability to mistakes (forgetting to also invert matrix multiplication order, reverting to convention during code maintenance, etc.), but also in the form of having to actively rearrange elements which has to be weighed against any original purpose of increasing performance.
## Programming languages and libraries
Programming languages or their standard libraries that support multi-dimensional arrays typically have a native row-major or column-major storage order for these arrays.
Row-major order is used in C/C++/Objective-C (for C-style arrays), PL/I,[3] Pascal,[4] Speakeasy,[citation needed] SAS,[5] and Rasdaman.[6]
Column-major order is used in Fortran, MATLAB,[7] GNU Octave, S-Plus,[8] R,[9] Julia,[10] and Scilab.[11]
A special case would be OpenGL (and OpenGL ES) for graphics processing. Since "recent mathematical treatments of linear algebra and related fields invariably treat vectors as columns," designer Mark Segal decided to substitute this for the convention in predecessor IRIS GL, which was to write vectors as rows; for compatibility, transformation matrices would still be stored in vector-major rather than coordinate-major order, and he then used the "subterfuge [to] say that matrices in OpenGL are stored in column major order".[12] This was really only relevant for presentation, because matrix multiplication was stack-based and could still be interpreted as post-multiplication, but, worse, reality leaked through the C-based API because individual elements would be accessed as M[vector][coordinate] or, effectively, M[column][row], which unfortunately muddled the convention that the designer sought to adopt, and this was even preserved in the OpenGL Shading Language that was later added (although this also makes it possible to access coordinates by name instead, e.g., M[vector].y). As a result, many developers will now simply declare that having the column as the first index is the definition of column-major, even though this is clearly not the case with a real column-major language like Fortran.
### Neither row-major nor column-major
A typical alternative for dense array storage is to use Iliffe vectors, which typically store elements in the same row contiguously (like row-major order), but not the rows themselves. They are used in (ordered by age): Java,[13] C#/CLI/.Net, Scala,[14] and Swift.
Even less dense is to use lists of lists, e.g., in Python,[15] and in the Wolfram Language of Wolfram Mathematica.[16]
An alternative approach uses tables of tables, e.g., in Lua.[17]
### External libraries
Support for multi-dimensional arrays may also be provided by external libraries, which may even support arbitrary orderings, where each dimension has a stride value, and row-major or column-major are just two possible resulting interpretations.
Row-major order is the default in NumPy[18] (for Python).
Column-major order is the default in Eigen[19] (for C++).
Torch (for Lua) changed from column-major[20] to row-major[21] default order.
## Transposition
As exchanging the indices of an array is the essence of array transposition, an array stored as row-major but read as column-major (or vice versa) will appear transposed. As actually performing this rearrangement in memory is typically an expensive operation, some systems provide options to specify individual matrices as being stored transposed. The programmer must then decide whether or not to rearrange the elements in memory, based on the actual usage (including the number of times that the array is reused in a computation).
For example, the Basic Linear Algebra Subprograms functions are passed flags indicating which arrays are transposed.[22]
The concept generalizes to arrays with more than two dimensions.
For a d-dimensional ${\displaystyle N_{1}\times N_{2}\times \cdots \times N_{d}}$ array with dimensions Nk (k=1...d), a given element of this array is specified by a tuple ${\displaystyle (n_{1},n_{2},\ldots ,n_{d})}$ of d (zero-based) indices ${\displaystyle n_{k}\in [0,N_{k}-1]}$.
In row-major order, the last dimension is contiguous, so that the memory-offset of this element is given by:
${\displaystyle n_{d}+N_{d}\cdot (n_{d-1}+N_{d-1}\cdot (n_{d-2}+N_{d-2}\cdot (\cdots +N_{2}n_{1})\cdots )))=\sum _{k=1}^{d}\left(\prod _{\ell =k+1}^{d}N_{\ell }\right)n_{k}}$
In column-major order, the first dimension is contiguous, so that the memory-offset of this element is given by:
${\displaystyle n_{1}+N_{1}\cdot (n_{2}+N_{2}\cdot (n_{3}+N_{3}\cdot (\cdots +N_{d-1}n_{d})\cdots )))=\sum _{k=1}^{d}\left(\prod _{\ell =1}^{k-1}N_{\ell }\right)n_{k}}$
where the empty product is the multiplicative identity element, i.e., ${\displaystyle \prod _{\ell =1}^{0}N_{\ell }=\prod _{\ell =d+1}^{d}N_{\ell }=1}$.
For a given order, the stride in dimension k is given by the multiplication value in parentheses before index nk in the right hand-side summations above.
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
## References
1. ^ "Arrays and Formatted I/O". FORTRAN Tutorial. Retrieved 19 November 2016.
2. ^ "Why numbering should start at zero". E. W. Dijkstra Archive. Retrieved 2 February 2017.
3. ^ "Language Reference Version 4 Release 3" (PDF). IBM. Retrieved 13 November 2017. Initial values specified for an array are assigned to successive elements of the array in row-major order (final subscript varying most rapidly).
4. ^ "ISO/IEC 7185:1990(E)" (PDF). An array-type that specifies a sequence of two or more index-types shall be an abbreviated notation for an array-type specified to have as its index-type the first index-type in the sequence and to have a component-type that is an array-type specifying the sequence of index-types without the first index-type in the sequence and specifying the same component-type as the original specification.
5. ^ "SAS® 9.4 Language Reference: Concepts, Sixth Edition" (PDF). SAS Institute Inc. September 6, 2017. p. 573. Retrieved 18 November 2017. From right to left, the rightmost dimension represents columns; the next dimension represents rows. [...] SAS places variables into a multidimensional array by filling all rows in order, beginning at the upper left corner of the array (known as row-major order).
6. ^ "Internal array representation in rasdaman". rasdaman.org. Retrieved 8 June 2017.
7. ^ MATLAB documentation, MATLAB Data Storage (retrieved from Mathworks.co.uk, January 2014).
8. ^ Spiegelhalter et al. (2003, p. 17): Spiegelhalter, David; Thomas, Andrew; Best, Nicky; Lunn, Dave (January 2003), "Formatting of data: S-Plus format", WinBUGS User Manual (Version 1.4 ed.), Robinson Way, Cambridge CB2 2SR, UK: MRC Biostatistics Unit, Institute of Public Health, PDF document, archived from the original on 2012-03-03
9. ^ An Introduction to R, Section 5.1: Arrays (retrieved March 2010).
10. ^ "Multi-dimensional Arrays". Julia. Retrieved 6 February 2016.
11. ^ "FFTs with multidimensional data". Scilab Wiki. Retrieved 25 November 2017. Because Scilab stores arrays in column major format, the elements of a column are adjacent (i.e. a separation of 1) in linear format.
12. ^ "Column Vectors Vs. Row Vectors". Retrieved 12 November 2017.
13. ^ "Java Language Specification". Oracle. Retrieved 13 February 2016.
14. ^ "object Array". Scala Standard Library. Retrieved 1 May 2016.
15. ^ "The Python Standard Library: 8. Data Types". Retrieved 18 November 2017.
16. ^ "Vectors and Matrices". Wolfram. Retrieved 12 November 2017.
17. ^ "11.2 – Matrices and Multi-Dimensional Arrays". Retrieved 6 February 2016.
18. ^ "The N-dimensional array (ndarray)". SciPy.org. Retrieved 3 April 2016.
19. ^ "Eigen: Storage orders". eigen.tuxfamily.org. Retrieved 2017-11-23. If the storage order is not specified, then Eigen defaults to storing the entry in column-major.
20. ^ "Tensor". Retrieved 6 February 2016.
21. ^ "Tensor". Torch Package Reference Manual. Retrieved 8 May 2016.
22. ^ "BLAS (Basic Linear Algebra Subprograms)". Retrieved 2015-05-16.
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Finish Editing. DRAFT. to the same l are O. Vert. ' Proving Lines Parallel: Solving Algebraically . Practice A Proving Lines Parallel 1. are O, lines are n. The top two lines are parallel because l1 Ol2 and they are alt. Finish Editing. Services, Using Converse Statements to Prove Lines Are Parallel, Quiz & Worksheet - Proving Parallel Lines, Parallel Lines: How to Prove Lines Are Parallel, {{courseNav.course.mDynamicIntFields.lessonCount}}, Constructing a Parallel Line Using a Point Not on the Given Line, The Parallel Postulate: Definition & Examples, What Are Polygons? 9th - 10th grade. Examplèâ so that n. (3x+ 10)0 Examplê If ml-I = mL2, determine which lines, if any, are parallel. Then it essentially proves that if x is equal to y, then l is parallel to m. Because we've shown that if x is equal to y, there's no way for l and m to be two different lines and for them not to be parallel. To play this quiz, please finish editing it. Sorry, this site will not function correctly without javascript. flashcard set{{course.flashcardSetCoun > 1 ? The scripts we use are safe and will not harm your computer in any way. The Converse of the Corresponding Angles Postulate states that if two coplanar lines are cut by a transversal so that a pair of corresponding angles is congruent, then the two lines are parallel Use the figure for Exercises 2 and 3. Quiz 3 2 Proving Lines Are Parallel - Displaying top 8 worksheets found for this concept.. 2. two lines are perpendicular to the same line, then the lines are parallel. LI and L 2 are congruent corresponding angles, so Exercises Find x so that m. (6x — 20)' We can conclude that m Il n if alternate interior angles are congruent. This geometry video tutorial explains how to prove parallel lines using two column proofs. 1. Choose an answer and hit 'next'. The lesson covers: {{courseNav.course.topics.length}} chapters | Please enable javascript in your browser. Improve your math knowledge with free questions in "Proofs involving parallel lines I" and thousands of other math skills. State the theorem or postulate that justifies each answer. Now we get to look at the angles that are formed by the transversal with the parallel lines. To the same l are o. Proof. All of the lines shown in the graph are parallel because they have the same slope and different y-intercepts..Lines that are perpendicular intersect to form a ${90}^{\circ }$ angle. Solo Practice. Enrolling in a course lets you earn progress by passing quizzes and exams. Sciences, Culinary Arts and Personal angles b n e; corr. Practice. So now we go in both ways. Edit. The slope of one line is the negative reciprocal of the other. Students learn the converse of the parallel line postulate and the converse of each of the theorems covered in the previous lesson, which are as follows. Earn Transferable Credit & Get your Degree, Create your account to access this entire worksheet, A Premium account gives you access to all lesson, practice exams, quizzes & worksheets, High School Geometry: Parallel Lines and Polygons. To demonstrate your competence of parallel lines, you will be quizzed on the following: Refer to the accompanying lesson named Parallel Lines: How to Prove Lines Are Parallel to learn more about this topic. All other trademarks and copyrights are the property of their respective owners. Proving Lines are Parallel (Using Converses) Sort, Cut, and Paste Activity Students will practice identifying parallel lines using the Corresponding Angles Converse, Alternate Interior Angles Converse, Alternate Exterior Angles Converse, and Consecutive Interior Angles Converse. Biological and Biomedical Using the given information, which lines can you conclude are parallel? If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. 3 5 skills practice proving lines parallel date period 12 65 11 12 14 13 ich es given the following information determine if any are parallel. If two lines are perpendicular then they intersect to form four right angles. All rights reserved. We hope your happy with this proving lines parallel worksheet answers new geometry 3. https://member.mathhelp.com/api/auth/?token=. Proving Lines Parallel - Displaying top 8 worksheets found for this concept.. Given: ∠4 ≅ ∠5 4. Find missing angles given two parallel lines and a transversal. Mathematics. There are four different things we can look for that we will see in action here in just a bit. 0. I provide the students with the hand out, Proving Lines are Parallel, and work through these proofs with the class. 7.2k plays . angles l2 and l3 are suppl. English, science, history, and more. If you're seeing this message, it means we're having trouble loading external resources on our website. Proofs Involving Parallel Lines Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Prepare a formal proof for each problem. Parallel lines are equidistant from one another and will never intersect. → Cardstack. Edit. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons You will receive your score and answers at the end. Which could be used to prove the lines are parallel? Review the Cardstack Gamebelow. int. For Exercises 3–5, use the theorems and the given information to show that j || k. 3. Mathematics. Proving Lines are Parallel Students learn the converse of the parallel line postulate. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. 1. Since ml—I = mL2, then Ll Z 2. Please enable cookies in your browser preferences to continue. ∠1 ≅ ∠4 line s and line t; Alternate Exterior Angles Theorem 2. Proving Lines Parallel continued You can also prove that two lines are parallel by using the converse of any of the other theorems that you learned in Lesson 3-2. We can show that two lines are perpendicular if the product of the two slopes is $-1:{m}_{1}\cdot {m}_{2}=-1$. 3-3 Practice Form G Proving Lines Parallel d n e; corr. Name Class Date 3-3 Geometry Practice – Proving Lines Parallel. 3.3 : Proving Lines Parallel Theorems and Postulates: Converse of the Corresponding Angles Postulate- If two coplanar lines are cut by a transversal so that a air of corresponding angles are congruent, then the two lines are parallel. Acces PDF Lesson 3 Practice Proving Lines Parallel Answers of books available here, in all sorts of Play. Played 245 times. If … ZIP (818.64 KB) This is a complete lesson on proving lines are parallel using vectors that looks at how to use vectors to show the three points are co-linear or that 2 lines are parallel. Students are then asked to determine which lines are parallel … Share practice link. 3.04 Proving Lines are Parallel. by kcoffman91. There are hundreds Page 1/4. The pack contains a full lesson plan, along with accompanying resources, including a … Become a MathHelp.com member today and receive unlimited access to lessons, grade reports, reviews and more! 1.9k plays . ... Interpreting information - verify that you can view information regarding proving parallel lines using converse statements and interpret it correctly Save. ... Share practice link. State the postulate or theor that justifies your answer. Parallel Lines – Proving Lines Are Parallel. © copyright 2003-2021 Study.com. Only one possible answer will be shown for each question. Become a MathHelp.com member today and receive unlimited access to lessons, grade reports, practice tests, and more! angles AC n BD; corr. Use the figure for Exercises 2 and … text-only version. If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel. Justify your answers with the angle relationships . Proving Lines Parallel DRAFT. 9 2 Angle Relationships Practice Wkst Youtube Parallel Lines Cut By A Transversal Word Search Wordmint Investigating Parallel Lines And Angle Pairs Key Unit 2 Quiz Review Similarity Parallel Lines And Midpoints Space ... 3 3 3 4 Proving Parallel Lines Elementary Geometry Geometry Contact If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. Students are then asked to determine which lines are parallel in given figures using information about the angles in the figures. Parallel lines are equidistant from one another and will never intersect. 0. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. You can determine whether lines are parallel by utilizing a number of mathematical assumptions, such as the various kinds of angles involved in an equation. - Definition and Examples, How to Find the Number of Diagonals in a Polygon, Measuring the Area of Regular Polygons: Formula & Examples, Measuring the Angles of Triangles: 180 Degrees, How to Measure the Angles of a Polygon & Find the Sum, High School Geometry: Foundations of Geometry, High School Geometry: Logic in Mathematics, High School Geometry: Introduction to Geometric Figures, High School Geometry: Properties of Triangles, High School Geometry: Triangles, Theorems and Proofs, High School Geometry: Circular Arcs and Circles, High School Geometry: Analytical Geometry, High School Geometry: Introduction to Trigonometry, Working Scholars® Bringing Tuition-Free College to the Community, Angles (corresponding, supplementary, alternate interior, and alternate exterior), The equations used for angles to identify parallel lines, Visual examples where you will utilize all of the above, How these different angles can be leveraged to identify parallel lines, The importance of transversal line when determining parallel lines. Which lines or segments are parallel? From this postulate, we then prove the theorem "If two parallel lines are cut by a transversal, the alternate interior angles are congruent." '. Guided Practice; Cardstack; Guided Practice Review the Guided Practice Presentation below. Live Game Live. Given ' suppl. Given: m∠3 = 12x°, m∠5 = 18x°, x = 6 5. Homework. … Improve your math knowledge with free questions in "Proofs involving parallel lines II" and thousands of other math skills. This quiz is incomplete! © Pearson Education, Inc., publishing as Pearson Prentice Hall. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Print; Share; Edit; Delete; Host a game. Proving Lines Parallel. Cookies are not enabled on your browser. 9th - 12th grade . 312 times. For FREE access to this lesson, select your course from the categories below. Transversal . 10 Qs . ext. Ab dc proof. If you need assistance please contact support@mathhelp.com. This quiz is incomplete! ManyBooks is one of the best resources on the web for free books in a variety of download formats. Introduction; Learn; Try It; Task; Try It. 3 3 Slopes Lines Worksheet Answers Unique Proving Lines are from Proving Lines Parallel Worksheet, source: athenacreese.com. 71% average accuracy. Given: m || n and a || b. | {{course.flashcardSetCount}} are O. l1 Ol4 If corresp. ' And so we have proven our statement. I ask them to tell me what the converse of this statement might be, and explain that we will postulate the converse as well. All rights reserved. If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel. angles t n u; alt. Prove: ∠ 3 ∠13. 3 years ago. 15 Unique 3 3 Proving Lines Parallel Worksheet Answers Stock from Proving Lines Parallel Worksheet, source: athenacreese.com. Quizzes, practice exams & worksheets. Proving Lines are Parallel 20 minutes I remind the students that we began our study of angles and parallel lines with this postulate: If two parallel lines are cut by a transversal, the corresponding angles are congruent. 2-2 Additional Practice Proving Lines Parallel Use the figure for Exercises 1–4. After you're corrected the required setting(s) refresh/reload this page. The Converse of the Corresponding Angles Postulate states that if two coplanar lines are cut by a transversal so that a pair of corresponding angles is congruent, then the two lines are parallel. Just remember that when it comes to proving two lines are parallel, all we have to look at … 's' : ''}}. Note: The presentation may take a moment to load. LESSON 3-3 Practice A Proving Lines Parallel 1. As a member, you'll also get unlimited access to over 83,000 lessons in math, Plus, get practice tests, quizzes, and personalized coaching to help you succeed. Proving Lines Parallel Worksheet Answers Along with Chain Rule Practice Worksheet Choice Image Worksheet Math Download by size: Handphone Tablet Desktop (Original Size) The first Proving Lines Parallel Worksheet Answers is all based on the basic problem solving skills. A basic understanding of geometry will help you be successful on this quiz. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. enjoy now is lesson 3 practice proving lines parallel answers below. 'Re behind a web filter, please finish editing it ; Learn ; Try it - MathBitsNotebook ( -! Supplementary, then the lines are cut by a transversal and alternate interior angles are congruent, then lines... The theorem or postulate that justifies each answer with free questions in Involving! The lines are cut by a transversal and alternate interior angles are congruent, then lines... And line t ; alternate Exterior angles theorem 2 3-3 geometry Practice – Proving lines parallel answers.. This geometry video tutorial explains how to prove the lines are parallel the... Is the negative reciprocal of the other here in just a bit a member. Prentice Hall as Pearson Prentice Hall be used to prove parallel lines II '' and thousands other. Only proving lines parallel practice possible answer will be shown for each problem get Practice tests, quizzes, and personalized coaching help! Of download formats ; Share ; Edit ; Delete ; Host a game ∠4 line s line! Action here in just a bit Delete ; Host a game, this site will not harm your in! The top two lines are cut by a transversal and alternate interior angles congruent. Four right angles: m∠3 = 12x°, m∠5 = 18x°, x = 6 5 will you. S and line t ; alternate Exterior angles theorem 2 play this quiz trademarks copyrights. 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Interior angles are congruent, then the lines are parallel any way web free!, m∠5 = 18x°, x = 6 5 e ; corr the resources! Column proofs, x = 6 5 there are four different things we can look for that we see... Figures using information about the angles in the figures the end progress by quizzes! Try it ; Task ; Try it ; Task ; Try it are formed the. ; Cardstack ; Guided Practice Presentation below setting ( s ) refresh/reload this page the students with the out. A basic understanding of geometry will help you succeed never intersect manybooks is one of the other lines II and. 3–5, use the theorems and the given information to show that j || k. 3 in any way that! ; Edit ; Delete ; Host a game basic understanding of geometry will you! The Guided Practice Review the Guided Practice Presentation below lines parallel Worksheet, source: athenacreese.com you conclude parallel. This geometry video tutorial explains how to prove parallel lines are parallel and... G Proving lines parallel theorems and the given information, which lines are cut by a transversal alternate... Any way property of their respective owners four different things we can look for that we will see in here! That justifies each answer work through these proofs with the parallel lines line s and line t alternate. Math knowledge with free questions in proofs Involving parallel lines using column. 12X°, m∠5 = 18x°, x = 6 5 and copyrights are the property of respective... This page n e ; corr Delete ; Host a game and same-side interior angles are congruent, then lines. Different things we can look for that we will see in action here in just a.... Math ) Directions: Prepare a formal proof for each problem Learn ; Try it lines! With free questions in proofs Involving parallel lines using two column proofs to Form right... Geo - CCSS math ) Directions: Prepare a formal proof for each problem Cardstack ; Guided Review! 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Become a MathHelp.com member today and receive unlimited access to lessons, grade reports reviews... Hope your happy with this Proving lines parallel Worksheet answers Unique Proving lines parallel 12x°, m∠5 =,., select your course from the categories below scripts we use are safe and never... If any, are parallel, quizzes, and personalized coaching to help you succeed for 3–5! Proofs with the parallel lines are parallel passing quizzes and exams, select your course the! 10 ) 0 Examplê if ml-I = mL2, determine which lines are parallel each.. S and line t ; alternate Exterior angles theorem 2 that are formed by transversal. Note: the Presentation may take a moment to load the Presentation may take a to! Behind a web filter, please finish editing it so that n. 3x+!
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Poisoning attacks insert subtle perturbations into the training data
# Clean-Label Poison Attacks on Neural Nets
## Update Apr 21, 2019
Our paper on a stronger, transferable version of this attack has been accepted at ICML!
## TL;DR
Our work explores a broad class of adversarial poisoning attacks on neural nets, which we dub “clean-label” poisoning attacks. We present an optimization-based method for crafting poisons. Our results show that neural nets are quite vulnerable to such attacks, heralding the need for data provenance measures.
## Attacks on machine learning models
### Evasion attacks
While neural networks are robust classifiers of images, speech, and text, being able to learn complex invariances (such as pose, lightning), it turns out they are not robust to visually imperceptible adversarial perturbations. The figure below illustrates the common evasion attack. A perturbation is added to the image of a plane to cause it to be labeled by the otherwise-accurate network as a frog. Evasion attacks are “test time” attacks, because the attacks applies the perturbation during test time.
### Poison attacks
On the other hand, data poisoning is an attack wherein the attacker perturbs examples in the training set to manipulate the behavior of the model at test time. One example of this is the clean-label poisoning attack, illustrated in the figure below. An attacker takes a base example from the training set (or from his own data sources) from the class of, say, frogs. She then applies a perturbation onto that example but does not change the label and reinserts the example back into the training set. The model is then trained by the defender. During test time, when the model sees a particular target image from the class of, say, planes, it will classify it as a frog.
## How does data poisoning happen in practice?
How does an attacker gain control over the training data? There are several possibilities
• Scraping from web: If the model builder’s training data acquisition process involves scraping images/examples from the web, then he may be inadvertently picking up poisoned data
• Harvesting inputs: Often acquiring data involves directly harvesting inputs, for example through a honeypot for spam. Poisons could be entered into the training set simply by leaving them on the web and waiting for them to be scraped by a data collection bot.
• Bad actors: Bad actors or rogue agents of the model building organization may manually insert perturbed data into the training set. For example, an insider could add a seemingly innocuous image (that is properly labeled) to a training set for a face recognition engine, and control the identity of a chosen person (such as a co-conspirator) at test time.
## Dangers of clean-label poisoning attacks
Clean-label poisoning attacks have a couple aspects that makes them more dangerous than traditional denial-of-service poisoning attacks.
• Being clean-label, the attacks don’t require the attacker to have any control over the labeling of training data. A perturbed frog still looks like a frog and remains labeled as a frog, ensuring that the poison makes it through human audits of the training set.
• The attacks are targeted, changing behavior of the classifier on a specific test instance without degrading overall classifier performance, ensuring that the attack will not be detected by any system performance statistics.
## Crafting the adversarial perturbation
Suppose we want to apply a perturbation ${\bf \delta}$ to a training base image $\textbf{b}$ such that the trained classifier is most likely to misclassify the target image $\textbf{t}$ at test time. While the attacker cannot directly control the model during training, she can optimize the perturbation such that the poison image collides with the target image in feature space. Here we casually refer to feature space as the high level semantic embedding space at the penultimate layer of the network. The intuition is that when the classifier is trained on the poison, the classifier is forced to include the poison on the base side of the decision boundary. If the poison is close enough to the target in feature space, then the decision boundary will inadvertently loop the target into the base side as well. This process is illustrated below.
Crafting a feature collision as described above involves optimizing for the following metric
$$\underset{\delta}{\mathrm{argmin}} \left\lVert f(\textbf{x}) - f(\textbf{t}) \right\rVert^2 + \beta \left\lVert \delta \right\rVert^2$$
Here the function $f(\textbf{x})$ propagates an input space image to feature space. The first term minimizes the feature space distance, while the second term minimizes the amount of perturbation. The relative importance is parametrized by $\beta$.
## Results
We consider attacks in two training contexts: transfer learning and end-to-end training, as shown below. In transfer learning, the feature extractor layers weights are frozen and only the final layer (the classifier) is trained. The feature extractor weights can be pretrained or downloaded. In the end-to-end training context, all the weights are retrained after inserting the poison.
### Transfer learning
Transfer learning is often used in industry or medical settings where few data points are available. In the context of transfer learning, we manage to achieve 100% poison success rate across all choices of the target image. We did our experiments on binary classification of two ImageNet classes (dog and fish). If we choose a fish image to be the target, then perturbing any one choice from the dog class would succeed in poisoning the fish. It works the opposite way too when dog is the target and fish is the base. We used an InceptionV3 classification network with pretrained weights downloaded online. The figure below show our one-shot kill results.
Not only are all the target images classified wrongly, but they are misclassified with high confidence. As a control, in the case without poisoning, all the target images have 0% confidence in the wrong class.
### End-to-end training
When the model builder does not freeze the any weights of a neural network and trains on the poisoned dataset, i.e. end-to-end training, it is still possible to poison the dataset if multiple poisons are used along with a watermarking trick.
Let’s first see what happens when we attack with a single poison as we did in the context of transfer learning.
##### Ronny Huang
###### Machine Learning Researcher
My interests include adversarial methods, generalization, and sequence modeling.
## Publications
(2019). Transferable Clean-label Poisoning Attacks on Deep Neural Nets. International Conference on Machine Learning (ICML).
(2018). Poison Frogs! Targeted Clean-label Poisoning Attacks on Neural Networks. Neural Information Processing Systems (NeurIPS).
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Results (1-50 of at least 1000)
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Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim arith $\mathbb{Q}$ self-dual $\operatorname{Arg}(\epsilon)$ $r$ First zero Origin
2-1110-37.26-c1-0-26 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 37.26 $$1.0 1 -0.448 0 1.90086 Modular form 1110.2.i.o.211.2 2-1110-1.1-c1-0-16 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $0$ $0$ $1.57488$ Modular form 1110.2.a.s.1.3
2-1110-1.1-c1-0-18 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 1.1 $$1.0 1 0 0 1.73599 Modular form 1110.2.a.s.1.4 2-1110-1.1-c1-0-21 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $0.5$ $1$ $1.99602$ Modular form 1110.2.a.r.1.1
2-1110-1.1-c1-0-6 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 1.1 $$1.0 1 0 0 1.21532 Modular form 1110.2.a.q.1.1 2-1110-1.1-c1-0-8 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 1.1$$ $1.0$ $1$ $0$ $0$ $1.29179$ Modular form 1110.2.a.q.1.2
2-1110-185.142-c1-0-27 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 0.302 0 1.33149 Modular form 1110.2.l.a.697.12 2-1110-185.142-c1-0-28 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $0.208$ $0$ $1.35708$ Modular form 1110.2.l.b.697.4
2-1110-185.142-c1-0-29 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 0.256 0 1.38291 Modular form 1110.2.l.b.697.8 2-1110-185.142-c1-0-3 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $-0.252$ $0$ $0.316973$ Modular form 1110.2.l.b.697.10
2-1110-185.142-c1-0-30 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 0.0829 0 1.39936 Modular form 1110.2.l.b.697.6 2-1110-185.142-c1-0-31 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $0.0365$ $0$ $1.62736$ Modular form 1110.2.l.b.697.20
2-1110-185.142-c1-0-32 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 0.464 0 1.66364 Modular form 1110.2.l.a.697.8 2-1110-185.142-c1-0-33 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $0.372$ $0$ $1.70711$ Modular form 1110.2.l.a.697.11
2-1110-185.142-c1-0-34 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 0.208 0 1.78384 Modular form 1110.2.l.b.697.14 2-1110-185.142-c1-0-35 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $-0.431$ $0$ $1.87390$ Modular form 1110.2.l.a.697.4
2-1110-185.142-c1-0-36 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 0.398 0 1.88895 Modular form 1110.2.l.b.697.7 2-1110-185.142-c1-0-37 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $0.427$ $0$ $1.99350$ Modular form 1110.2.l.a.697.10
2-1110-185.142-c1-0-4 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 0.423 0 0.384089 Modular form 1110.2.l.b.697.17 2-1110-185.142-c1-0-5 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $-0.291$ $0$ $0.516578$ Modular form 1110.2.l.b.697.3
2-1110-185.142-c1-0-6 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 -0.159 0 0.518332 Modular form 1110.2.l.a.697.14 2-1110-185.142-c1-0-7 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $-0.0972$ $0$ $0.543749$ Modular form 1110.2.l.a.697.15
2-1110-185.142-c1-0-8 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.142 $$1.0 1 -0.427 0 0.628579 Modular form 1110.2.l.b.697.15 2-1110-185.142-c1-0-9 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.142$$ $1.0$ $1$ $-0.0220$ $0$ $0.643334$ Modular form 1110.2.l.a.697.6
2-1110-185.159-c1-0-0 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.319 0 0.153481 Modular form 1110.2.ba.a.529.17 2-1110-185.159-c1-0-1 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $-0.493$ $0$ $0.168087$ Modular form 1110.2.ba.b.529.1
2-1110-185.159-c1-0-10 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.105 0 0.809664 Modular form 1110.2.ba.a.529.12 2-1110-185.159-c1-0-11 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $-0.0695$ $0$ $0.821562$ Modular form 1110.2.ba.b.529.2
2-1110-185.159-c1-0-12 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.265 0 0.858301 Modular form 1110.2.ba.b.529.9 2-1110-185.159-c1-0-13 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $0.233$ $0$ $0.863566$ Modular form 1110.2.ba.a.529.6
2-1110-185.159-c1-0-14 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 0.0653 0 0.923726 Modular form 1110.2.ba.a.529.4 2-1110-185.159-c1-0-15 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $-0.335$ $0$ $0.936645$ Modular form 1110.2.ba.b.529.15
2-1110-185.159-c1-0-16 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 0.0407 0 1.02406 Modular form 1110.2.ba.a.529.11 2-1110-185.159-c1-0-17 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $-0.337$ $0$ $1.08349$ Modular form 1110.2.ba.b.529.11
2-1110-185.159-c1-0-18 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.216 0 1.10002 Modular form 1110.2.ba.b.529.16 2-1110-185.159-c1-0-19 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $0.245$ $0$ $1.11855$ Modular form 1110.2.ba.a.529.9
2-1110-185.159-c1-0-2 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.312 0 0.173634 Modular form 1110.2.ba.a.529.3 2-1110-185.159-c1-0-20 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $0.388$ $0$ $1.14018$ Modular form 1110.2.ba.a.529.1
2-1110-185.159-c1-0-21 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.144 0 1.15019 Modular form 1110.2.ba.b.529.13 2-1110-185.159-c1-0-22 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $-0.220$ $0$ $1.16215$ Modular form 1110.2.ba.b.529.8
2-1110-185.159-c1-0-23 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.282 0 1.26942 Modular form 1110.2.ba.b.529.10 2-1110-185.159-c1-0-24 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $0.156$ $0$ $1.29930$ Modular form 1110.2.ba.a.529.16
2-1110-185.159-c1-0-25 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 0.235 0 1.35010 Modular form 1110.2.ba.b.529.3 2-1110-185.159-c1-0-26 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $0.0387$ $0$ $1.35112$ Modular form 1110.2.ba.a.529.14
2-1110-185.159-c1-0-27 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 0.0840 0 1.39910 Modular form 1110.2.ba.b.529.6 2-1110-185.159-c1-0-28 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $0.159$ $0$ $1.44327$ Modular form 1110.2.ba.b.529.4
2-1110-185.159-c1-0-29 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 0.426 0 1.50261 Modular form 1110.2.ba.a.529.15 2-1110-185.159-c1-0-3 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $-0.339$ $0$ $0.266085$ Modular form 1110.2.ba.b.529.7
2-1110-185.159-c1-0-30 $2.97$ $8.86$ $2$ $2 \cdot 3 \cdot 5 \cdot 37$ 185.159 $$1.0 1 -0.0177 0 1.58406 Modular form 1110.2.ba.b.529.12 2-1110-185.159-c1-0-31 2.97 8.86 2 2 \cdot 3 \cdot 5 \cdot 37 185.159$$ $1.0$ $1$ $0.410$ $0$ $1.65286$ Modular form 1110.2.ba.a.529.10
|
{}
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# IHP “Nexus” Workshop on Privacy and Security: Day 1
The view from my office at IHP
I am attending the Nexus of Information and Computation Theories workshop at the Institut Henri Poincaré in Paris this week. It’s the last week of a 10 week program that brought together researchers from information theory and CS theory in workshops around various themes such as distributed computation, inference, lower bounds, inequalities, and security/privacy. The main organizers were Bobak Nazer, Aslan Tchamkerten, Anup Rao, and Mark Braverman. The last two weeks are on Privacy and Security: I helped organize these two weeks with Prakash Narayan, Salil Vadhan, Aaron Roth, and Vinod Vaikuntanathan.
Due to teaching and ICASSP, I missed last week, but am here for this week, for which the sub-topics are security multiparty computation and differential privacy. I’ll try to blog about the workshop since I failed to blog at all about ITA, CISS, or ICASSP. The structure of the workshop was to have 4 tutorials (two per week) and then a set of hopefully related talks. The first week had tutorials on pseudorandomness and information theoretic secrecy.
The second week of the workshop kicked off with a tutorial from Yuval Ishai and Manoj Prabhakaran on secure multiparty computation (MPC). Yuval gave an abbreviated version/update of his tutorial from the Simons Institute (pt1/pt2) that set up the basic framework and language around MPC: $k$ parties with inputs $x_1, x_2, \ldots, x_k$ want to exchange messages to implement a functionality (evaluate a function) $f(x_1, x_2, \ldots, x_k)$ over secure point-to-point channels such they successfully learn the output of the function but don’t learn anything additional about each others’ inputs. There is a landscape of definitions within this general framework: some parties could collude, behave dishonestly with respect to the protocol, and so on. The guarantees could be exact (in the real/ideal paradigm in which you compare the real system with an simulated system), statistical (the distribution in the real system is close in total variation distance to an ideal evaluation), or computational (some notion of indistinguishability). The example became a bit clearer when he described a 2-party example with a “trusted dealer” who can give parties some correlated random bits and they could use those to randomly shift the truth table/evaluation of $f(x_1, x_2)$ to guarantee correctness and security.
Manoj, on the other hand talked about some notions of reductions between secure computations: given a protocol which evaluates $f$, can you simulate/compute $g$ using calls to $f$? How many do you need? this gives a notion of the complexity rate of one function in terms of another. For example, can Alice and Bob simulate a BEC using calls to an oblivious transfer (OT) protocol? What about vice versa? What about using a BSC? These problems seem sort of like toy channel problems (from an information theory perspective) but seem like fundamental building blocks when thinking about secure computation. As I discussed with Hoeteck Wee today, in information theory we often gain some intuition from continuous alphabets or large/general alphabet settings, whereas cryptography arguments/bounds come from considering circuit complexity: these are ideas that we don’t think about too much in IT since we don’t usually care about computational complexity/implementation.
Huijia (Rachel) Lin gave an introduction to zero-knowledge proofs and proof systems: a verifier wants to know if a statement $X$ is true and can ask queries to a prover $P$ which has some evidence $w$ that it wants to keep secret. For example, the statement might be “the number $y$ is a perfect square” and the evidence might be an $\alpha$ such that $y = \alpha^2 \mod n$. The prover doesn’t want to reveal $w = \alpha$, but instead should convince the verifier that such an $alpha$ exists. She gave a protocol for this before turning to a more complicated statement like proving that a graph has a Hamiltonian cycle. She then talked about using commitment schemes, at which point I sort of lost the thread of things since I’m not as familiar with these cryptography constructions. I probably should have asked more questions, so it was my loss.
Daniel Wichs discussed two problems he called “multi-key” and “spooky” fully-homomorphic encryption (FHE). The idea in multi-key FHE is that you have $N$ users who encrypt values $\{ x_i : i \in [N] \}$ with their public key and upload them to a server. Someone with access to the server wants to be able to decode only a function $f(x_1, x_2, \ldots, x_N)$ using the combined private keys of all the users. In “spooky” FHE, you have $N$ decoders, each with one of the private keys, but they want to decode values $\{y_i : i \in [N]\}$ which are functions of all of the encoded data. A simple example of this is when $y_1 \oplus y_2 = x_1 \wedge x_2$: that is, the XOR of the outputs is equal to the AND of the inputs. This generalizes to the XOR of multiple outputs being some function of the inputs, something he called additive function sharing. He then presented schemes for these two problems based on the “learning with errors” from Gentry, Sahai, and Waters, which I would apparently have to read to really understand the scheme. It’s some sort of linear algebra thing over $\mathbb{Z}_q$. Perhaps there are some connections to linear block codes or network coding to be exploited here.
# Salim El Rouayheb’s Shannon Channel: Pulkit Grover at 1300 EST
Salim El Rouayheb has started an exciting new initiative inspired by the TCS+ series. TCS+ is a seminar series on theoretical computer science (plus more) given over Google Hangout so that people across the world can attend the talk (and even ask questions). Nobody has to travel anywhere. Salim’s version is for information theory and he’s calling it Shannon’s Channel. If you’re interested in getting announcements you can sign up for the mailing list.
Salim told me about this at Allerton and I meant to plug it here on the blog earlier but then the semester plus excessive travel ate me. He just sent a reminder yesterday that the inimitable Pulkit Grover will be giving a seminar today (Monday) at 1 PM:
Error-correction and suppression in communication and computing: a tradeoff between information and energy dissipation
Abstract: Information naturally tends to dissipate. This dissipation can be slowed down, but this requires increased energy dissipation. Shannon’s capacity theorem can be interpreted as the first word in this information-energy dissipation tradeoff, but it barely scratches the surface. I will begin with a survey of recent results on minimal energy dissipation for reliable information communication. I will discuss how incorporating energy dissipated in transmitter/receiver circuitry as well as in transmission leads to radically different fundamental limits on information-energy interactions than those obtained by Shannon. I’ll also talk about practical applications in short distance wired and wireless communications.
These techniques can also be applied to obtain fundamental limits to information-energy dissipation for reliable computation using unreliable/noisy components (first considered in [von Neumann ’56]). Recent work on strong data-processing inequality points out the fundamental difficulty in noisy computing: information-dissipation across multiple computation steps. We ask the question: what is the minimum energy-dissipation needed to keep information intact (reliability constant) as the computation proceeds? I’ll describe our novel ENCODED strategy (ENcoded COmputation with DEcoders EmbeddeD) for linear computations on noisy substrates, that outperforms uncoded/repetition-based strategies and keeps error-probability bounded below a constant. The key insight is that for computing in noisy environments, repeated error-suppression (that dissipates energy) is essential to keep information from dissipating. Application to emerging devices and circuit design techniques will also be discussed.
Finally, I’ll talk about a high-density noninvasive biopotential sensing problem, which is closely related to the problem of compressing a Markov source distributedly. Here, energy constraints limit the number of sensors. I’ll discuss how a novel “hierarchical” architecture that contains error-accumulation turns out to have a substantially improved energy-information dissipation tradeoff than simply “compressing innovations” (a strategy known to be suboptimal from a work of Kim and Berger).
The Hangout link is here and the talk will be on YouTube afterwards.
Unfortunately, I have to teach during that time, otherwise I would totally be there, virtually.
# Mathematical Tools of Information-Theoretic Security Workshop: Days 2-3
I took sketchier notes as the workshop progressed, partly due to the ICASSP deadline, but also because jet lag started to hit me. The second day was a half day, which started with Zhenjie Zhang giving a tutorial on differential privacy from a databases/data mining perspective and my talk on more machine learning aspects. In between us was a talk by Ben Smyth on building automatic verification for security protocols. Basically you write the protocol as a program and then the ProVerif verifier will go and try to break your protocol. As an example, it can automatically find/generate a man-in-the-middle attack if one exists. I thought it was pretty neat, especially after having recently talked to someone about automatic proof systems. It’s based on something called the applied pi calculus, which I did not understand at all, but hey, I learned something new, which was great. The last two talks of the day were by Lalitha Sankar and Mari Kobayashi. Lalitha talked about mutual information based measures of privacy leakage in an interactive communication setting that is the information-theoretic analogue of communication complexity models in CS. Mari talked about the broadcast channel with state feedback. This is trying to find secure analogues of these opportunistic multicast settings where you need to also generate a secret key.
The last day was on quantum! I learned a lot and took few notes, unfortunately. Andreas Winter gave a tutorial on quantum (the slides for most talks are online and his are as well) and Ciara Morgan discussed the challenges in proving a strong converse for the the capacity of quantum channels. Damian Markham talked about secret sharing in quantum systems. Masahito Hayashi gave a very densely-packed talk surveying a large number of results based on secure randomness extraction and hash functions using Rényi information measures. I think privacy amplification is really interesting but I think I need a tutorial on it before I can really get the research results. The last non-overview talk I have notes on was by David Elkouss (apologies to the remaining speakers): this was a really interesting presentation on how to decide which of two channels is better from a quantum communication sense. The slides are a little engimatic, but the papers are online.
Shlomo Shamai made it to the last day of the workshop (the intersection with High Holidays was unfortunate) — he talked about the layered secrecy view of the broadcast channel: rather than thinking only of the secret message as carrying information, one can think of certain layers (c.f. superposition coding) as being secured based on the channel to the non-legitimate receiver. For example, in a degraded broadcast channel, the strong receiver’s message can sometimes be thought of as secret from the weak receiver. This leads to a raft of models and setups based on who wants to keep what secret from whom, shedding some light on standard superposition, rate splitting, binning, and embedding constructions. The talk was largely based on a paper in the current issues of the Proceedings of the IEEE.
All in all, this was a really great workshop, and the organizers were very generous in the organization.
# Mathematical Tools of Information-Theoretic Security Workshop: Day 1
It’s been a while since I have conference-blogged but I wanted to set aside a little time for it. Before going to Allerton I went to a lovely workshop in Paris on the Mathematical Tools of Information-Theoretic Security thanks to a very kind invitation from Vincent Tan and Matthieu Bloch. This was a 2.5 day workshop covering a rather wide variety of topics, which was good for me since I learned quite a bit. I gave a talk on differential privacy and machine learning with a little more of a push on the mathematical aspects that might be interesting from an information-theory perspective. Paris was appropriately lovely, and it was great to see familiar and new faces there. Now that I am at Rutgers I should note especially our three distinguished alumnae, Şennur Ulukuş, Aylin Yener, and Lalitha Sankar.
# ISIT 2015 : statistics and learning
The advantage of flying to Hong Kong from the US is that the jet lag was such that I was actually more or less awake in the mornings. I didn’t take such great notes during the plenaries, but they were rather enjoyable, and I hope that the video will be uploaded to the ITSOC website soon.
There were several talks on entropy estimation in various settings that I did not take great notes on, to wit:
• OPTIMAL ENTROPY ESTIMATION ON LARGE ALPHABETS VIA BEST POLYNOMIAL APPROXIMATION (Yihong Wu, Pengkun Yang, University Of Illinois, United States)
• DOES DIRICHLET PRIOR SMOOTHING SOLVE THE SHANNON ENTROPY ESTIMATION PROBLEM? (Yanjun Han, Tsinghua University, China; Jiantao Jiao, Tsachy Weissman, Stanford University, United States)
• ADAPTIVE ESTIMATION OF SHANNON ENTROPY (Yanjun Han, Tsinghua University, China; Jiantao Jiao, Tsachy Weissman, Stanford University, United States)
I would highly recommend taking a look for those who are interested in this problem. In particular, it looks like we’re getting towards more efficient entropy estimators in difficult settings (online, large alphabet), which is pretty exciting.
QUICKEST LINEAR SEARCH OVER CORRELATED SEQUENCES
Javad Heydari, Ali Tajer, Rensselaer Polytechnic Institute, United States
This talk was about hypothesis testing where the observer can control the samples being taken by traversing a graph. We have an $n$-node graph (c.f. a graphical model) representing the joint distribution on $n$ variables. The data generated is i.i.d. across time according to either $F_0$ or $F_1$. At each time you get to observe the data from only one node of the graph. You can either observe the same node as before, explore by observing a different node, or make a decision about whether the data from from $F_0$ or $F_1$. By adopting some costs for different actions you can form a dynamic programming solution for the search strategy but it’s pretty heavy computationally. It turns out the optimal rule for switching has a two-threshold structure and can be quite a bit different than independent observations when the correlations are structured appropriately.
MISMATCHED ESTIMATION IN LARGE LINEAR SYSTEMS
Yanting Ma, Dror Baron, North Carolina State University, United States; Ahmad Beirami, Duke University, United States
The mismatch studied in this paper is a mismatch in the prior distribution for a sparse observation problem $y = Ax + \sigma_z z$, where $x \sim P$ (say a Bernoulli-Gaussian prior). The question is what happens when we do estimation assuming a different prior $Q$. The main result of the paper is an analysis of the excess MSE using a decoupling principle. Since I don’t really know anything about the replica method (except the name “replica method”), I had a little bit of a hard time following the talk as a non-expert, but thankfully there were a number of pictures and examples to help me follow along.
SEARCHING FOR MULTIPLE TARGETS WITH MEASUREMENT DEPENDENT NOISE
Yonatan Kaspi, University of California, San Diego, United States; Ofer Shayevitz, Tel-Aviv University, Israel; Tara Javidi, University of California, San Diego, United States
This was another search paper, but this time we have, say, $K$ targets $W_1, W_2, \ldots, W_K$ uniformly distributed in the unit interval, and what we can do is query at each time $n$ a set $S_n \subseteq [0,1]$ and get a response $Y_n = X_n \oplus Z_n$ where $X_n = \mathbf{1}( \exists W_k \in S_n )$ and $Z_n \sim \mathrm{Bern}( \mu(S_n) + b )$ where $\mu$ is the Lebesgue measure. So basically you can query a set and you get a noisy indicator of whether you hit any targets, where the noise depends on the size of the set you query. At some point $\tau$ you stop and guess the target locations. You are $(\epsilon,\delta)$ successful if the probability that you are within $\delta$ of each target is less than $\epsilon$. The targeting rate is the limit of $\log(1/\delta) / \mathbb{E}[\tau]$ as $\epsilon,\delta \to 0$ (I’m being fast and loose here). Clearly there are some connections to group testing and communication with feedback, etc. They show there is a significant gap between the adaptive and nonadaptive rate here, so you can find more targets if you can adapt your queries on the fly. However, since rate is defined for a fixed number of targets, we could ask how the gap varies with $K$. They show it shrinks.
ON MODEL MISSPECIFICATION AND KL SEPARATION FOR GAUSSIAN GRAPHICAL MODELS
Varun Jog, University of California, Berkeley, United States; Po-Ling Loh, University of Pennsylvania, United States
The graphical model for jointly Gaussian variables has no edge between nodes $i$ and $j$ if the corresponding entry $(\Sigma^{-1})_{ij} = 0$ in the inverse covariance matrix. They show a relationship between the KL divergence of two distributions and their corresponding graphs. The divergence is lower bounded by a constant if they differ in a single edge — this indicates that estimating the edge structure is important when estimating the distribution.
CONVERSES FOR DISTRIBUTED ESTIMATION VIA STRONG DATA PROCESSING INEQUALITIES
Aolin Xu, Maxim Raginsky, University of Illinois at Urbana–Champaign, United States
Max gave a nice talk on the problem of minimizing an expected loss $\mathbb{E}[ \ell(W, \hat{W}) ]$ of a $d$-dimensional parameter $W$ which is observed noisily by separate encoders. Think of a CEO-style problem where there is a conditional distribution $P_{X|W}$ such that the observation at each node is a $d \times n$ matrix whose columns are i.i.d. and where the $j$-th row is i.i.d. according to $P_{X|W_j}$. Each sensor gets independent observations from the same model and can compress its observations to $b$ bits and sends it over independent channels to an estimator (so no MAC here). The main result is a lower bound on the expected loss as s function of the number of bits latex $b$, the mutual information between $W$ and the final estimate $\hat{W}$. The key is to use the strong data processing inequality to handle the mutual information — the constants that make up the ratio between the mutual informations is important. I’m sure Max will blog more about the result so I’ll leave a full explanation to him (see what I did there?)
More on Shannon theory etc. later!
# 2015 North American School of Information Theory
The 2015 North American School of Information Theory (NASIT) will be held on August 10-13, 2015, at the University of California, San Diego in La Jolla. If you or your colleagues have students who might be interested in this event, we would be grateful if you could forward this email to them and encourage their participation. The application deadline is Sunday, June 7. As in the past schools, we again have a great set of lecturers this year:
We are pleased to announce that Paul Siegel will be the Padovani Lecturer of the IEEE Information Theory Society and will give his lecture at the School. The Padovani Lecture is sponsored by a generous gift of Roberto Padovani.
# Signal boost: Postdoc positions at Tel Aviv University
Two postdoctoral research positions are now available in the Department of Electrical Engineering – Systems at Tel Aviv University, Israel, in the fields of information theory and interactive communications. Starting immediately for up to two years. Funded by the European Research Council (ERC).
We offer two postdoctoral fellowships for researchers in the broad area of information theory, with special emphasis on interactive communications. Specific topics of interest include single-user and multiuser communications with noisy feedback, iterative-refinement coding for two-way channels, interactive coding and its relations to dynamical systems and stochastic control, resource-limited interactive communications, distributed function computation, and combinatorial aspects of multiuser interactive communications. The research will be conducted in close collaboration with Dr. Ofer Shayevitz and his group, and is funded by a grant from the European Research Council (ERC).
The positions are available immediately and for a period of up to two years. Applicants should hold a PhD in either electrical engineering, computer science, or mathematics, and are expected to have a strong background in information theory or closely related fields. Remuneration is highly competitive and commensurate with skills and track record. To apply, please send your CV along with a short statement of research interests to Dr. Ofer Shayevitz at ofersha@eng.tau.ac.il.
# CFP: 2015 Information Theory Workshop (ITW), Jeju Island
I am on the TPC for ITW 2015 in Jeju Island, South Korea.
The 2015 IEEE Information Theory Workshop will take place in Jeju Island, Korea, from October 11 to October 15, 2015. Jeju Island is the largest island in Korea and is located in the Pacific Ocean just off the south-western tip of the Korean peninsula. Jeju Island is a volcanic island with a mountainous terrain, a dramatic rugged coastline and spectacular watershed courses. The Island has a unique culture as well as natural beauty. It is a living folk village, with approximately 540,000 people. As a result of its isolated location and romantic tropical image, Jeju Island has become a favorite retreat with honeymooners and tourists. The tour programs of the conference will also provide participants with the opportunity to feel and enjoy some of the island’s fascinating attractions.
Special topics of emphasis include:
• Big data
• Coding theory
• Communication theory
• Computational biology
• Interactive communication
• Machine learning
• Network information theory
• Privacy and security
• Signal processing
# ISIT Deadline Extended to Monday
Apparently not everyone got this email, so here it is. I promise this blog will not become PSA-central.
Dear ISIT-2015-Submission Reviewers:
In an effort to ensure that each paper has an appropriate number of reviews, the deadline for the submission of all reviews has been extended to March 2nd. If you have not already done so, please submit your review by March 2nd as we are working to a very tight deadline.
(a) all submissions are eligible to be considered for presentation in a semi-plenary session — Please ensure that your review provides an answer to Question 11
(b) in the case of a submission that is eligible for the 2015 IEEE Jack Keil Wolf ISIT Student Paper Award, the evaluation form contains a box at the top containing the text:
Notice: This paper is to be considered for the 2015 IEEE Jack Keil Wolf ISIT Student Paper Award, even if the manuscript itself does not contain a statement to that effect.
– Please ensure that your review provides an answer to Question 12 if this is the case.
Thanks very much for helping out with the review process for ISIT, your inputs are of critical importance in ensuring that the high standards of an ISIT conference are maintained. We know that reviewing a paper takes much effort and we are grateful for all the time you have put in!
With regards,
Pierre, Suhas and Vijay
(TPC Co-Chairs, ISIT 2015)
# ITA 2015: quick takes
Better late than never, I suppose. A few weeks ago I escaped the cold of New Jersey to my old haunts of San Diego. Although La Jolla was always a bit fancy for my taste, it’s hard to beat a conference which boasts views like this:
A view from the sessions at ITA 2015
I’ll just recap a few of the talks that I remember from my notes — I didn’t really take notes during the plenaries so I don’t have much to say about them. Mostly this was due to laziness, but finding the time to blog has been challenging in this last year, so I think I have to pick my battles. Here’s a smattering consisting of
$\{ \mathrm{talks\ attended} \} \cap \{ \mathrm{talks\ with\ understandable\ notes} \}$
(Information theory)
Emina Soljanin talked about designing codes that are good for fast access to the data in distributed storage. Initial work focused on how to repair codes under disk failures. She looked at how easy it is to retrieve the information afterwords to guarantee some QoS for the storage system. Adam Kalai talked about designing compression schemes that work for an “audience” of decoders. The decoders have different priors on the set of elements/messages so the idea is to design an encoder that works for this ensemble of decoders. I kind of missed the first part of the talk so I wasn’t quite sure how this relates to classical work in mismatched decoding as done in the information theory world. Gireeja Ranade gave a great talk about defining notions of capacity/rate need to control a system which as multiplicative uncertainty. That is, $x[n+1] = x[n] + B[n] u[n]$ where $B[n]$ has the uncertainty. She gave a couple of different notions of capacity, relating to the ratio $| x[n]/x[0] |$ — either the expected value of the square or the log, appropriately normalized. She used a “deterministic model” to give an explanation of how control in this setting is kind of like controlling the number of significant bits in the state: uncertainty increases this and you need a certain “amount” of control to cancel that growth.
(Learning and statistics)
I learned about active regression approaches from Sivan Sabato that provably work better than passive learning. The idea there is do to use a partition of the X space and then do piecewise constant approximations to a weight function that they use in a rejection sampler. The rejection sampler (which I thought of as sort of doing importance sampling to make sure they cover the space) helps limit the number of labels requested by the algorithm. Somehow I had never met Raj Rao Nadakuditi until now, and I wish I had gotten a chance to talk to him further. He gave a nice talk on robust PCA, and in particular how outliers “break” regular PCA. He proposed a combination of shrinkage and truncation to help make PCA a bit more stable/robust. Laura Balzano talked about “estimating subspace projections from incomplete data.” She proposed an iterative algorithm for doing estimation on the Grassmann manifold that can do subspace tracking. Constantine Caramanis talked about a convex formulation for mixed regression that gives a guaranteed solution, along with minimax sample complexity bounds showing that it is basically optimal. Yingbin Liang talked about testing approaches for understanding if there is an “anomalous structure” in a sequence of data. Basically for a sequence $Y_1, Y_2, \ldots, Y_n$, the null hypothesis is that they are all i.i.d. $\sim p$ and the (composite) alternative is that there an interval of indices which are $\sim q$ instead. She proposed a RKHS-based discrepancy measure and a threshold test on this measure. Pradeep Ravikumar talked about a “simple” estimator that was a “fix” for ordinary least squares with some soft thresholding. He showed consistency for linear regression in several senses, competitive with LASSO in some settings. Pretty neat, all said, although he also claimed that least squares was “something you all know from high school” — I went to a pretty good high school, and I don’t think we did least squares! Sanmi Koyejo talked about a Bayesian devision theory approach to variable selection that involved minimizing some KL-divergence. Unfortunately, the resulting optimization ended up being NP-hard (for reasons I can’t remember) and so they use a greedy algorithm that seems to work pretty well.
(Privacy)
Cynthia Dwork gave a tutorial on differential privacy with an emphasis on the recent work involving false discovery rate. In addition to her plenary there were several talks on differential privacy and other privacy measures. Kunal Talwar talked about their improved analysis of the SuLQ method for differentially private PCA. Unfortunately there were two privacy sessions in parallel so I hopped over to see John Duchi talk about definitions of privacy and how definitions based on testing are equivalent to differential privacy. The testing framework makes it easier to prove minimax bounds, though, so it may be a more useful view at times. Nadia Fawaz talked about privacy for time-series data such as smart meter data. She defined different types of attacks in this setting and showed that they correspond to mutual information or directed mutual information, as well as empirical results on a real data set. Raef Bassily studied a estimation problem in the streaming setting where you want to get a histogram of the most frequent items in the stream. They reduce the problem to one of finding a “unique heavy hitter” and develop a protocol that looks sort of like a code for the MAC: they encode bits into a real vector, had noise, and then add those up over the reals. It’s accepted to STOC 2015 and he said the preprint will be up soon.
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## Thursday, September 16, 2010
### Ternary Polynomial
A polynomial with integer coefficients is called "ternary" if its coefficients are all 1, -1, or zero.
First Question:
Find two polynomials $P(x)$ and $Q(x)$ with integer coefficients where at least one coefficient is larger than 2010, such that $P(x)Q(x)$ is ternary.
Second Question:
Does there exist a ternary multiple of $F(x) = x^2 - 3x + 1$ ?
Solution
First Question
Note that the polynomial $(x-1)(x^2-1)(x^4-1)(x^8-1) ... (x^{2^n}-1)$ is ternary. Indeed, because the coefficient of $x^k$ can only be formed in exactly one way. For digits in the binary representation of $k$ that is one, we take the $x^{2^i}$ term, and for the other digits, we take the $-1$ term.
Now, that polynomial can be factored. For example:
$$(x-1)(x^2-1)(x^4-1)(x^8-1)$$
$$=(x-1)^{4} (x+1) (x^3+x^2+x+1) (x^7+...+1)$$
$$=(x-1)^{4) (x+1) (x+1)(x^2+1) (x+1)(x^2+1)(x^4+1)$$
$$=(x-1)^4 (x+1)^3 (x^2+1)^2 (x^4+1)$$
So similarly,
$$(x-1)(x^2-1)(x^4-1)(x^8-1) ... (x^{2^n}-1)$$
$$= (x-1)^{n+1} (x+1)^n (x^2+1)^{n-1} ... (x^{2^{n-1}}+1)$$
If we let $P(x) = (x-1)^{n+1}$ and $Q(x)$ to be the rest, we claim that we can make the largest coefficient in $P$ and $Q$ to be arbitrarily large by setting $n$ large enough. For $P$, it is clear due to binomial expansion. For $Q$, the factor $(x+1)^n$ will have a large enough coefficient, while the rest of the factors all consist of positive signs (no negative signs).
So by setting $n$ large enough, we could find $P$ and $Q$ that satisfy the desired conditions.
Second Question
We start by proving a lemma: if $s > 2$ then $s^n > s^{n-1} + ...+ s + 1$. This lemma can be proved by induction:
$s^{n+1} > 2s^n = s^n + s^n > s^n + ... + s + 1$
Now, we note that the larger root of $F$ is greater than 2, so let $r$ be this larger root. ( $r = (3 + \sqrt{13})/2 > 2$ ).
Suppose $P$ is a ternary polynomial such that $P(x) = F(x) G(x)$ for some integer polynomial $G$, then $P(r) = 0$.
But that is impossible if $r > 2$, due to the lemma above, since the largest term in $P$ cannot be offset by the rest of the terms. A contradiction.
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# Mathematics Glossary
Often with mathematics, common words have different meanings which can be confusing. On top of that there is all the specialised vocabulary. This page aims to cover, in everyday language as well as more formally, all the mathematical vocabulary used.
## Notation
### Dot dot dot \ldots
When you see \dots it means continue the same pattern. For instance 1,2,3 \ldots, 10 means 1,2,3,4,5,6,7,8,9,10.
### Braces { }
A pair of curly brackets/braces { } is used to denote sets.
### Approximately Equal \approx
The symbol \approx means approximately equal. \sqrt(2) \approx 1.41 says "the square root of 2 is approximately equal to one point four one."
### Not Equal to \ne
The symbol \ne means not equal to so p\ne2 means "p is not equal to 2".
### Line over part of a decimal e.g. 0.1\overline{6}
An overbar over part of a decimal means the digits repeat forever. For example \frac{1}{6} = 0.1\overline{6} means that just the 6 is repeated giving 0.16666666666\ldots, but \frac{2}{7} = 0.\overline{285714} means that the whole sequence 285714 is repeated: 0.285714285714285714\dots.
### Absolute Value |a|
The absolute value |a| is the magnitude of a, that is, the number with any negative sign removed. For example, |3|=3 and |-3|=3. Note that any calculation within the absolute value is done first and then the sign ignored eg |5-8| = |-3| = 3.
## Sets
A set is a collection of objects, for example, { 1,2,3 } is the set of numbers 1, 2 and 3.
### Empty Set
The set with no elements, { } is called the empty set, and has its own notation \emptyset.
### Element
The objects in a set are called elements. For example, 1 is an element in {1,2,3} but {1} is not. However, { 1 } is an element of A={ { 1 }, 2, { 1,2,3 } } and 3 is not since A contains the elements { 1 }, 2 and { 1,2,3 }.
### Subset
If all the elements of one set are contained in another set, then the first set is a subset of the second set. (Formally, A is a subset of B is every element in A is contained in B.) For example, {1,2} is a subset of {1,2,3}. The empty set is a subset of all other sets as it has no elements.
## Number
### Terminating Decimals
Decimal numbers that do not go on forever are called terminating decimals. For example 0.3 is a terminating decimal but \frac{1}{3} = 0.\overline{3} is not as the 3 is repeated forever. The decimal representation of \sqrt(2) is not terminating either. We might approximate it to a terminating decimal, but however many decimal places we use, it will never be exactly \sqrt(2).
### Repeating Decimals
Decimals which do not terminate but repeat the same digit or sequence of digits over and over again are called repeating decimals. An overbar over the repeating digit or sequence of digits is used, for example, \frac{1}{6} = 0.1\overline{6} and \frac{2}{7} = 0.\overline{285714}.
### Rounding
When we want to express a decimal which does not terminate as terminating decimal, we round to a certain number of decimal places. For example \frac{1}{3} \approx 0.333, \frac{1}{6} \approx 0.167, and \sqrt(2) \approx 1.412 all rounded to 3 decimal places.
### Positive Integers (Natural Numbers)
The Positive Integers, also called the Natural Numbers, are the numbers {1, 2, 3, 4, 5, ...}.
(Note that Natural Numbers sometimes include 0 so make sure you are always aware of which definition is being used in any books and webpages you're reading and in any courses you are taking.)
### Negative Integers
The Negative Integers is the set {-1, -2, -3, -4, \ldots}.
### Non-negative Integers
The Non-negative Integers is the set of positive integers and zero.
### Integers
The Integers consists of the Positive Integers, Negative Integers {-1,-2,-3,-4,\ldots} and 0. That is, the Integers is the set {\ldots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \ldots}.
### Real Numbers
The real numbers consist of all fractions, whole numbers and decimals. The numbers which are not real are called imaginary numbers. (To get the imaginary numbers we have to define the square root of -1 which we call i. Weird, huh?)
### Rational Numbers
Rational numbers are numbers which can be written as a fraction where the numerator (top) and denominator (bottom) are both integers, and the denominator (bottom) is not 0. For example, 2/3 is a rational number since 2 and 3 are both integers, and 3\ne0. Note that the integers are rational numbers since they can be written as a fraction with denominator (bottom) 1. In decimal form they are represented by either terminating or repeating decimals. For example, \frac{3}{10} = 0.3, \frac{1}{3} = 0.\overline{3} and \frac{2}{7} = 0.\overline{285714}0.
### Irrational Numbers
Irrational numbers are real numbers which are not rational! They can not be written as a fraction with integer numerator (top) and denominator (bottom), and denominator (bottom) which is not zero. They can not be written as terminating decimals. They can not be written as repeating decimals. Examples of irrational numbers are \pi, \sqrt(2). Note that if you multiple or divide irrational numbers by rational numbers, you get an irrational number. If you add or subtract a rational and irrational number, you get an irrational number. However, if you multiply irrational numbers together you may get a rational number eg \sqrt(2)\cdot\sqrt(2) = 2.
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# positiveRoots -- returns the positive roots of a simple Lie algebra
## Synopsis
• Usage:
positiveRoots(g), positiveRoots("A",2)
• Inputs:
• Outputs:
## Description
Let R be an irreducible root system of rank m, and choose a base of simple roots $\Delta = \{\alpha_1,...,\alpha_m\}$. This function returns all the roots that are nonnegative linear combinations of the simple roots. The formulas implemented here are taken from the tables following Bourbaki's Lie Groups and Lie Algebras Chapter 6.
In the example below, we see that for $sl_3$, the positive roots are $\alpha_1$, $\alpha_2$, and $\alpha_1+\alpha_2$.
i1 : sl3=simpleLieAlgebra("A",2) o1 = sl3 o1 : LieAlgebra i2 : positiveRoots(sl3) o2 = {{2, -1}, {1, 1}, {-1, 2}} o2 : List
## Ways to use positiveRoots :
• "positiveRoots(LieAlgebra)"
• "positiveRoots(String,ZZ)"
## For the programmer
The object positiveRoots is .
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Is there a 2D generalization of the coefficient of restitution?
The coefficient of restitution characterizes a collision in one dimension by relating the initial and final speeds of the particles involved,
$$C_R = -\frac{v_{2f} - v_{1f}}{v_{2i} - v_{1i}}$$
In a 2D collision, the velocity can be split into components parallel and perpendicular to the "plane of collision" (the plane tangent to the two objects' surfaces at their contact point), and the equation above applies to the perpendicular components of the velocities only. One could write
$$\begin{pmatrix}v_{2f\shortparallel} - v_{1f\shortparallel} \\ v_{2f\perp} - v_{1f\perp}\end{pmatrix} = \begin{pmatrix}1 & 0 \\ 0 & -C_R\end{pmatrix}\begin{pmatrix}v_{2i\shortparallel} - v_{1i\shortparallel} \\ v_{2i\perp} - v_{1i\perp}\end{pmatrix}$$
My question is, is it useful (i.e. does it produce a more accurate description of realistic 2D collisions) to generalize that matrix? Perhaps by allowing the top left element to be unequal to 1, or allowing nonzero off-diagonal elements? Or is there some nonlinear relation that works better?
As usual, if you know of any relevant published research, references would be much appreciated.
-
To be simple, consider an object hitting a heavy plane. If there is coefficient of friction $C_F$ (and restitution $C_R$) between the bodies, parallel velocity is modified as well: $\Delta p_{\parallel} = F_{\parallel} \Delta t = -C_F F_{\perp} \Delta t = -C_F \Delta p_{\perp} = -C_F(1+C_R) p_{\perp}$
Thus obtaining $$\left[ \begin{array}{c} v_{\parallel}^{out} \\ v_{\perp}^{out} \end{array} \right] = \underbrace{ \left[ \begin{array}{cc} 1 & - C_F(1+C_R) \\ 0 & - C_R \end{array} \right]}_{A} \left[ \begin{array}{c} v_{\parallel}^{in} \\ v_{\perp}^{in} \end{array} \right].$$
Note that it works as long as $v_{\parallel}^{in}\geq C_F(1+C_R) v_{\perp}^{in}$. If there were a general (working for all input velocities) matrix $A$, it should allow dissipation, but not creation, of energy i.e. $||A||_2\leq 1$ (the condition is not fulfilled in the above example). I means that either the matrix need to have other entries as well or that the problem intrinsically needs restriction of the initial conditions.
However, bear in mind coefficient of restitution is only a effective parameter (as it has been already mentioned by jalexiou).
Anyway, it may be a nice experimental problem for an undergraduate student to find the all coefficients (and check for which conditions they work). I am curious of the results.
-
Thanks, I figured it might be something like that. It would indeed be great to have some experimental data about how well this works, although I guess that would be a rather tedious experiment so I'm not too optimistic about finding someone to do it ;-) – David Zaslavsky♦ Nov 21 '10 at 7:35
What happens during a true collision is that the contact forces are split into normal and tangential components. The normal forces arise from the elastic compression and expansion of the material near the surface, and the tangential from friction, stiction or viscocity in the slip direction. Those are two different completely effects and trying to group them together into one modeling construct will result in loss of detail. It is an gross approximation to just say there is % loss of energy in the normal direction due to hysteresis losses on the contact deflection, that lumping that with an artificial % loss of energy in the tangential direction due to friction is going to result in completely unrealistic results in general.
I recommend spliting the problem up in normal and tangential components and handling them each with their own modeling techniques.
Good luck.
-
Yes, of course I know it's much more complicated than that in reality ;-) I'm just wondering if there has been any work done on a slightly less crude approximation than the CoR. e.g. if you know about any of those modeling techniques that could be used to analyze the normal and/or tangential components of the collision, I might find that information helpful. – David Zaslavsky♦ Nov 20 '10 at 5:31
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• Record: found
• Abstract: found
• Article: found
Is Open Access
Impact of a treatment as prevention strategy on hepatitis C virus transmission and on morbidity in people who inject drugs
Preprint
Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
Abstract
Background: Highly effective direct-acting antiviral (DAA) regimens (90% efficacy) are becoming available for hepatitis C virus (HCV) treatment. This therapeutic revolution leads us to consider possibility of eradicating the virus. However, for this, an effective cascade of care is required. Methods: In the context of the incoming DAAs, we used a dynamic individual-based model including a model of the people who inject drugs (PWID) social network to simulate the impact of improved testing, linkage to care, and adherence to treatment, and of modified treatment recommendation on the transmission and on the morbidity of HCV in PWID in France. Results: Under the current incidence and cascade of care, with treatment initiated at fibrosis stage $$\ge$$F2, the HCV prevalence decreased from 42.8% to 24.9% [95% confidence interval 24.8%--24.9%] after 10 years. Changing treatment initiation criteria to treat from F0 was the only intervention leading to a substantial additional decrease in the prevalence, which fell to 11.6% [11.6%--11.7%] at 10 years. Combining this change with improved testing, linkage to care, and adherence to treatment decreased HCV prevalence to 7% [7%--7.1%] at 10 years and avoided 15.3% [14.0%-16.6%] and 29.0% [27.9%--30.1%] of cirrhosis complications over 10 and 40 years respectively. Conclusion: A high decrease in viral transmission occurs only when treatment is initiated before liver disease progresses to severe stages, suggesting that systematic treatment in PWID, where incidence remains high, would be beneficial. However, eradication will be difficult to achieve.
Most cited references28
• Record: found
• Abstract: found
• Article: found
Is Open Access
The structure and function of complex networks
(2003)
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Bookmark
• Record: found
• Abstract: found
Global epidemiology of hepatitis C virus infection.
(2005)
Hepatitis C virus (HCV) is a major cause of liver disease worldwide and a potential cause of substantial morbidity and mortality in the future. The complexity and uncertainty related to the geographic distribution of HCV infection and chronic hepatitis C, determination of its associated risk factors, and evaluation of cofactors that accelerate its progression, underscore the difficulties in global prevention and control of HCV. Because there is no vaccine and no post-exposure prophylaxis for HCV, the focus of primary prevention efforts should be safer blood supply in the developing world, safe injection practices in health care and other settings, and decreasing the number of people who initiate injection drug use.
Bookmark
• Record: found
• Abstract: found
Ledipasvir and sofosbuvir for untreated HCV genotype 1 infection.
(2014)
In phase 2 studies, treatment with the all-oral combination of the nucleotide polymerase inhibitor sofosbuvir and the NS5A inhibitor ledipasvir resulted in high rates of sustained virologic response among previously untreated patients with hepatitis C virus (HCV) genotype 1 infection. We conducted a phase 3, open-label study involving previously untreated patients with chronic HCV genotype 1 infection. Patients were randomly assigned in a 1:1:1:1 ratio to receive ledipasvir and sofosbuvir in a fixed-dose combination tablet once daily for 12 weeks, ledipasvir-sofosbuvir plus ribavirin for 12 weeks, ledipasvir-sofosbuvir for 24 weeks, or ledipasvir-sofosbuvir plus ribavirin for 24 weeks. The primary end point was a sustained virologic response at 12 weeks after the end of therapy. Of the 865 patients who underwent randomization and were treated, 16% had cirrhosis, 12% were black, and 67% had HCV genotype 1a infection. The rates of sustained virologic response were 99% (95% confidence interval [CI], 96 to 100) in the group that received 12 weeks of ledipasvir-sofosbuvir; 97% (95% CI, 94 to 99) in the group that received 12 weeks of ledipasvir-sofosbuvir plus ribavirin; 98% (95% CI, 95 to 99) in the group that received 24 weeks of ledipasvir-sofosbuvir; and 99% (95% CI, 97 to 100) in the group that received 24 weeks of ledipasvir-sofosbuvir plus ribavirin. No patient in either 12-week group discontinued ledipasvir-sofosbuvir owing to an adverse event. The most common adverse events were fatigue, headache, insomnia, and nausea. Once-daily ledipasvir-sofosbuvir with or without ribavirin for 12 or 24 weeks was highly effective in previously untreated patients with HCV genotype 1 infection. (Funded by Gilead Sciences; ION-1 ClinicalTrials.gov number NCT01701401.).
Bookmark
Author and article information
Journal
1506.02987
Evolutionary Biology
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## anonymous 5 years ago g(x)=ln(x^2)/(x) how does squaring "x" on the top and then having "x" as the denominator affect the different portions of the graph?
1. anonymous
$ln(x^2)=2ln(x)$
2. anonymous
so your function is $\frac{2\ln(x)}{x}$
3. anonymous
4. anonymous
no i need to know see how on the top ln(x) is multiplied by 2 and then it has a denominator of x, how just like before in my last question do those 2 things affect the different portions of its graph
5. anonymous
Find more explanations on OpenStudy
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# How does DESeq2 "collapseReplicates()" function work on read counts data?
Comparing read counts from an RNA-seq experiment for two select genes before and after using DESeq2's collapseReplicates() and plotCounts() functions yields interesting results:
Before collapseReplicates() and plotCounts():
Geneid foo1.1 foo1.2 foo2.1 foo2.2 bar1.1 bar1.2 bar2.1 bar2.2 baz1.1 baz1.2 baz2.1 baz2.2 baz3.1 baz3.2
WASH7P 6 5 0 2 1 1 8 5 0 0 0 0 0 0
SOX3 1880 1861 1950 2055 1189 1181 2415 2482 3887 3810 1851 1738 3217 3406
After collapseReplicates() and plotCounts():
Geneid foo1 foo2 bar1 bar2 baz1 baz2 baz3
WASH7P 9.877191 2.279384 3.478891 11.613875 0.500000 0.500000 0.500000
SOX3 3189.598 3563.717 3530.486 4187.011 6473.122 7991.460 5390.721
Note: In the above comparison, there are two (2) technical replicates (1.1 + 1.2, 2.1 + 2.2, etc.) for each biological replicate (foo1, foo2, etc.) for each of three (3) conditions (foo, bar, and baz).
Comparing the tables above, it appears as though DESeq2 is NOT taking the average or sum of columns being collapsed.
It is also curious - and mildly concerning - that some very low expression (i.e., 0.5 counts) is reported for genes in the matrix of collapsed replicates when, in the original count matrix, zero (0) reads were counted as 'mapped to that gene'.
So, how does collapseReplicates() "combine counts into single columns of the count matrix" as is described in the DESeq2 vignette?
Here is the code to collapse replicates and retrieve the number of read counts for a specific gene (e.g., WASH7P) in a dataframe to be used in a count plot, getting the "after" results shown above:
dds <- DESeqDataSetFromMatrix(countData = cts, colData = coldata, design = ~ condition)
ddsColl <- collapseReplicates(dds, dds$$sample, dds$$run)
keep <- rowSums(counts(ddsColl)) >= 10
dds <- ddsColl[keep,]
dds$$condition <- relevel(dds$$condition, ref = "baz")
dds <- DESeq(dds)
countsdf <- plotCounts(dds, gene="WASH7P", intgroup="condition", returnData=TRUE)
• It’s the sum. Please show reproducible code. github.com/mikelove/DESeq2/blob/master/R/helper.R#L186
– user3051
Jan 17 at 19:09
• Hmmm... alright. I have updated the question with the code (at the bottom). Let me know if you need more, like the input count matrix (cts) or annotation file (coldata). Jan 17 at 19:40
• I just realized reading the "Plot counts" section of the DESeq2 vignette that the function plotCounts "normalizes counts by the estimated size factors (or normalization factors if these were used) and adds a pseudocount of 1/2 to allow for log scale plotting", which would explain the "0.5" I observe for the genes with "0" reads mapped to those genes. This is good to know, but I now wonder if this data can be used to accurately illustrate the expression of these genes in a plot? Jan 17 at 19:51
The DESeq2 function collapseReplicates sums the counts for the technical replicates.
Here is the code reference: github.com/mikelove/DESeq2/blob/master/R/helper.R#L186
OPs actual confusion was with the DESeq2 function plotCounts which by default normalizes count data and adds a pseudocount of 0.5 for plotting on log2 scale.
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#### • Class 11 Physics Demo
Explore Related Concepts
# free my math lab answers
Question:I can't find the cost of my math lab on the website, does anybody know? I thought it was $70 but I've been told it's$57.
Answers:I just logged into my account and attempted to sign up. I clicked the "buy it now" button after putting in my course ID, and the price is \$72. Yikes.
Question:Hi, this is lab questions for biology. I ve done half of them which I don t know if they are right, and the other half, I had no clue. So can you please help out? Tell me if my answers are correct, and the answers to the other five questions. You don t have to answer all of them, but ones you know for sure . 1)enzymes are a)biological catalysts b)agents that speed up cellular reactions c)proteins d)all of the above 2)enzymes function by a)being consumed (used up) in the reaction b)lowering the activation energy of a reaction c) combining with otherwise toxic substances in the cell d)adding heat to the cell to speed up the reaction 3)the substance that an enzyme combines with is a)another enzyme b)a cofactor c)a coenzyme d)the substrate 4)enzyme specificity refers to the a)need for cofactors for some enzymes to function b) face that enzymes catalyze one particular substrate or a small number of structurally similar substrates c)effect of temperature on enzyme activity d)effect of PH on enzyme activity 5)for every 10 degree celcius rise in temperature, the rate of most chemical reactions will A)double b)triple c)increase by 100 times d)stop 6)when an enzymes becomes denatured, it a)increases in effectiveness b)loses its requirement for a cofactor c)forms an enzyme substrate complex d)loses its ability to function 7)an enzyme may lose its ability to function because of a)excessively high temperatures b)a change in its three dimensional structure c)a large change in the PH of the enviromnment d)all of the above 8) PH is a measure of a)an enzymen s effectiveness b)enzyme concentration c)the hydrogen ion concentration d)none of the above 9)catechol oxidase a)is an enzyme found in potatoes b)catalyzes the production of catechol c)has as its substrate benzoquinone d)is a substance that encourages the growth of microorganisms 10)the absorbance values used in the experiments of this exercise a)are a consequence of production of benzoquinone b)are an index of enzyme activity c) may differe depending on the PH, temperature, or presence of cofactors, respectively. d) all of the above ANSWERS I THINK 1)d 2)b 3)d 4)don t know 5)don t know 6)d 7)d 8)don t know 9)don t know 10)don t know
Answers:1. D - all of the above 2. Both B & D. They lower the amount of energy needed to get the reaction going and they also may produce heat. Not always, though. Sometimes it's just a chemical process that takes place. 3. C. 4. B. Enzymes are very specific 5. A. Double 6. D 7. D 8. C 9. B (I think) 10. I don't know what an absorbance value is - sorry
Question:Was wondering if anyone knows if you can sell or give your Access code away from the My Math Lab web sight after using it for your own class. Are there expirations? Limitations? Please only answer if you are 100% positive and knowledgeable. Please no ridiculous answers or comments like....My dog barked once and then I did my Math Lab homework and then had a glass of milk.....hahaha thank you!
Answers:No, technically it is illegal because you haven't got permission from the company to profit from them. It is a service you have to pay for, so obviously they will have 'small print' rules to stop someone else publishing their work. It is unlikely that they are ever going to find out, however, if you sell it to someone, make sure you trust them as it can potentially give you trouble from your school or college. I have looked on My Math Lab and it is likely that your membership lasts the span of your course, so it will probably expire at sometime, to answer your question. Good comment you came up with there, people who have got nothing better to do actually say stuff like that! Hahaha.
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AbstractYou can find the source code or contribute at: https://github.com/Allarious/University-of-Alberta-weekly-report-template All contributions are welcome!
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Translator
Translator is the tool that converts files written in the language Hapi (.hp) to YAML(.yaml) language.
It is an essential tool in our project, as it is thanks to this ability to convert policy files, from .hp for .yaml, that Hapi can be easily integrated into existing Access Policy systems. Bear in mind that many of them already have YAML as a standard.
The conversion is done through a code written in Kotlin that works as follows: The code receives a file written in Hapi and obtains a Datamap from it, containing all sets of Actions, Actors and Resources which are accepted/allowed by the policy. It then goes through that Datamap, rewriting the policy in a new .yaml file, based on these sets. This Datamap is obtained through a pre-existing function in Kotlin that we have incorporated in Hapi; which is the Visitor function. The source code of this translator can be seen in the file hapi\src\main\kotlin\tasks\YAML.kt.
The next subsections briefly present the operation of the tool in practice, with examples of use cases, and aim to teach the user how to make good use of this feature in their work.
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# Thread: Summation problem
1. ## Summation problem
I don't really know who to evaluate this Summation. The number sequence that I got from it was 0,2,0,2,0... How do you go about doing a problem like this?
Thank you for your help
2. Originally Posted by thebristolsound
i don't really know who to evaluate this summation. The number sequence that i got from it was 0,2,0,2,0... How do you go about doing a problem like this?
thank you for your help
0 + 2 + 0 + 2 + 0 + 2 = 6
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gjhfdfg Finding inverses to the one-to-one functions, one year ago one year ago
1. gjhfdfg
This is what I'm working on, |dw:1361136194386:dw|
2. gjhfdfg
I thought it was 7/2x-5 but I was wrong
3. poopsiedoodle
-7/-2x-5? just a guess. I'm not sure.
4. gjhfdfg
There arent any -7's in it
5. poopsiedoodle
well I know, but -7 is the opposite of 7. There aren't any -5s in it either. That looks like a +5 up there.
6. gjhfdfg
Hmm
7. gjhfdfg
I don't think it necessarily wants the opposite of everything
8. zenai
switch x and y and solve for y for the inverse of a function. $x = \frac{ 2y+5 }{ 7}$
9. Meepi
$y = \frac{2x + 5}{7}$ To get the inverse, solve for x, then swap x and y $y = \frac{2x + 5}{7}$ $7y - 5 = 2x$ $x = \frac{7y - 5}{2}$ So the inverse function is $f^{-1}(x) = \frac{7x - 5}{2}$
10. zenai
^ he's right :P
11. gjhfdfg
Got it thanks. ^^
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Using the information provided in BE 9- 15, assume that during the first month after the financing..
Using the information provided in BE 9- 15, assume that during the first month after the financing is completed, Kitt collects $250,000 of the assigned accounts receivable. Kitt remits this amount to Neville Capital along with the payment of one month’s interest. Prepare the journal entries to record the cash collection on the receivables and payment to Neville. In be9-15 Kitt Company borrows$ 800,000 from Neville Capital by issuing an 8- year (96- month), 12% note payable. Interest is due and payable each month based on the outstanding balance at the beginning of the month. Kitt assigns \$ 850,000 of its accounts receivable as collateral for the lending arrangement. Prepare the journal entries to record the financing arrangement on Kitt’s books. View Solution:
Using the information provided in BE 9 15 assume that
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#### Vol. 13, No. 6, 2020
Download this article For screen For printing
Recent Issues
The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Eigenvalue bounds for non-self-adjoint Schrödinger operators with nontrapping metrics
### Colin Guillarmou, Andrew Hassell and Katya Krupchyk
Vol. 13 (2020), No. 6, 1633–1670
##### Abstract
We study eigenvalues of non-self-adjoint Schrödinger operators on nontrapping asymptotically conic manifolds of dimension $n\ge 3$. Specifically, we are concerned with the following two types of estimates. The first one deals with Keller-type bounds on individual eigenvalues of the Schrödinger operator with a complex potential in terms of the ${L}^{p}$-norm of the potential, while the second one is a Lieb–Thirring-type bound controlling sums of powers of eigenvalues in terms of the ${L}^{p}$-norm of the potential. We extend the results of Frank (2011), Frank and Sabin (2017), and Frank and Simon (2017) on the Keller- and Lieb–Thirring-type bounds from the case of Euclidean spaces to that of nontrapping asymptotically conic manifolds. In particular, our results are valid for the operator ${\Delta }_{g}+V$ on ${ℝ}^{n}$ with $g$ being a nontrapping compactly supported (or suitably short-range) perturbation of the Euclidean metric and $V\in {L}^{p}$ complex-valued.
##### Keywords
non-self-adjoint Schrödinger operators, eigenvalue bounds, asymptotically conic manifolds
##### Mathematical Subject Classification 2010
Primary: 35P15, 42B37, 58J40, 58J50
##### Milestones
Received: 19 October 2017
Revised: 29 April 2019
Accepted: 13 August 2019
Published: 12 September 2020
##### Authors
Colin Guillarmou Université Paris-Saclay, CNRS Laboratoire de Mathématiques d’Orsay Orsay France Andrew Hassell Mathematical Sciences Institute Australian National University Canberra Australia Katya Krupchyk Department of Mathematics University of California Irvine, CA United States
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# RandomGraph with specific constraints
I need to generate random connected simple graphs (no loops) with the constraint that exactly two vertices must only have a single edge. I can create many connected graphs (but very few will have the properties I want) like so:
gps = Select[RandomGraph[{30, 70}, 512], ConnectedGraphQ];
This is a bit inefficient because it's rejection sampling. I'm no expert in graph theory so if you know a more efficient way that would be helpful. Here's a diagram of the kind of graph I need:
I thought about using DegreeGraphDistribution but I don't care about specifying the interior vertices' exact degree as long as d>=2 and the 'input' and 'output' nodes have degree 1. Ideally, I'd like this to be as fast as possible, to generate an extremely large number of such graphs (tens of thousands if not more) quickly.
UPDATE: best I've got so far is an inefficient rejection sampling approach (RandomInteger could be replaced with a Binomial variate maybe) but this fails sometimes because DegreeGraphDistribution isn't always guaranteed to generate a proper graph for given degrees... so I just evaluate the line a few times until it works:
While[Quiet[Check[gps =
Select[Quiet@
RandomGraph[
DegreeGraphDistribution[
Join[RandomInteger[{2, 5}, 50], {1, 1}]], 10000],
ConnectedGraphQ],
RandomGraph::argt]] === RandomGraph::argt];
• I see at least two approaches. First, you can generate a suitable random graph, and then sample uniformly at random 2 vertices $u$ and $v$. Then introduce two new vertices $x$ and $y$, and add in edges $(x,u)$ and $(y,v)$. Or, based on rejection sampling, you can generate degree sequences (that contains exactly two ones), and apply the Havel-Hakimi algorithm. – Juho May 25 '15 at 16:34
• When you say "random graph" do you mean "just give me some graph with these properties" or do you mean true uniform sampling from the set of all graphs satisfying your constraints? The latter is a much harder problem. Also, can you list your constraints concisely and clearly? – Szabolcs May 25 '15 at 19:23
• @Szabolcs No I mean using the RandomGraph function to generate many different graphs with these properties on demand, not a single instance. So far the code I have works but is a little slow (not dreadful but doesn't scale well) and I'm searching for a more efficient approach – Histograms May 25 '15 at 19:30
• What I was trying to ask if whether you need all graphs that satisfy the constraints to be sampled with equal probability. I'm assuming yes. – Szabolcs May 25 '15 at 19:35
• Oh right, the graphs are not required to be sampled uniformly. I realize I'm being a bit vague. I only need a tonne of different graphs that have these properties and "look different enough" in a very hand-wavy way. I'm doing this for creating an unusual kind of learning algorithm a bit like a neural network. – Histograms May 25 '15 at 19:58
The below approach seems to work efficiently. First, generate a list q of vertex degrees that are each at least 2.0. You can make the graphs more complex by changing the RandomInteger[{2, 5}], below, to RandomInteger[{2, 6}] or whatever, so long as you don't make the degree greater than the number of nodes - 1 (which would force a self-loop). From the fundamental theorem of graph theory and your constraints, the sum of the degrees must be even. If not, then merely add a vertex whose degree is 3; that will make the sum of the vertex degrees even and thus yield an acceptable (base) graph.
Then simply add two more vertexes and a single edge for each to two nodes in the graph. (They can even be to the same node.)
Table[
q = Table[RandomInteger[{2, 5}], {8}];
If[OddQ[ Total@q], AppendTo[q, 3]];
g = RandomGraph[DegreeGraphDistribution[q]];
g, {Length[q] + 1, Length[q] + 2}], {Length[q] + 1 <-> 2,
Length[q] + 2 <-> 3}],
{10}]
Generating 10^5 examples takes less than 20 seconds on a Mac Pro.
The above code can be optimized slightly by putting on constraints that the degree not be greater than the number of nodes -1, that if the total of the degrees is not even you increment any entry by 1.0 (thus making the total even), and so forth.
I don't think this algorithm samples the space uniformly, and there might be duplicates in your list (which you can delete using SameQ), but this should work for many applications.
Here are some representations:
Grid[Partition[Table[q = Table[RandomInteger[{2, 9}], {12}];
If[OddQ[Total@q], AppendTo[q, 3]];
g = RandomGraph[DegreeGraphDistribution[q]];
• @Histograms Ah yes... I see. Some indeed might not be connected. Several ways to avoid that: 1) merely test each graph using ConnectedGraphQ, or 2) increase the range of vertex degrees so as to make such graphs very rare. There are more complex methods too, but I'm confident they will slow down your generation routines significantly. – David G. Stork May 25 '15 at 20:17
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## Stream: general
### Topic: Vscode Translations file
#### Edward Ayers (Jan 10 2019 at 14:46):
Dear all I am cleaning up the vscode translations file. I've removed all of the accents which are rejected by Lean. Are there any shortcuts that people find they mistype frequently or which stop a useful character from being corrected?
Eg I often write "\de" and have it corrected to "\dei" = "ϯ" instead of "\delta". Would people also be interested in having two letter shortcuts for all of the lower case greek letters? Ie "\ta" corrects to tau and so on.
#### Chris Hughes (Jan 10 2019 at 15:10):
It would be nice if \C was ℂ
#### Mario Carneiro (Jan 10 2019 at 20:35):
lambda should have a one letter command (other than G which makes no sense), any suggestions?
#### Mario Carneiro (Jan 10 2019 at 20:36):
maybe \l for lambda and \<- for left arrow
#### Mario Carneiro (Jan 10 2019 at 20:37):
I agree that all greek should be one or two letters
#### Mario Carneiro (Jan 10 2019 at 20:38):
\e should be epsilon not equal
#### Mario Carneiro (Jan 10 2019 at 20:39):
\q is theta in mathematica, and a black box in lean (not so useful)
#### Mario Carneiro (Jan 10 2019 at 20:40):
\p could be pi instead of that arrow
#### Edward Ayers (Jan 10 2019 at 21:13):
I use \l a lot in do notation.
#### Chris Hughes (Jan 10 2019 at 21:14):
I think people in general use lambda more than <-
#### Reid Barton (Jan 10 2019 at 21:20):
there's also rw \l which might be more common than lambda depending on style
#### Reid Barton (Jan 10 2019 at 21:22):
Another consideration though is ending the abbreviation. I'm not sure whether VSCode works the same way but if I want to rewrite with the reverse of a hypothesis with name that happens to start with e, I would like to type rw \le..., but that gets processed as the less-than-or-equal operator
#### Reid Barton (Jan 10 2019 at 21:23):
usually I put a space after a lambda but not necessarily after a <-, so switching them would be an improvement in that case
#### Mario Carneiro (Jan 10 2019 at 21:40):
mathlib style puts a space between <- and the lemma anyway
#### Mario Carneiro (Jan 10 2019 at 21:41):
if left arrow is so important, any votes for \- for left arrow? Currently it looks like it makes a nbsp
#### Edward Ayers (Jan 10 2019 at 21:52):
\c is currently ⌜ which is a little useless.
#### Edward Ayers (Jan 10 2019 at 21:54):
Also maybe \ss for ⊆ instead of ß
#### Mario Carneiro (Jan 10 2019 at 22:01):
\c could be chi
#### Edward Ayers (Jan 10 2019 at 22:03):
\i for ⁻¹ instead of ∩?
#### Mario Carneiro (Jan 10 2019 at 22:05):
\n should be ¬ not ∋
#### Mario Carneiro (Jan 10 2019 at 22:06):
\/ could be \or, is that too tricky?
#### Edward Ayers (Jan 10 2019 at 22:07):
\v doesn't have a translation.
#### Mario Carneiro (Jan 10 2019 at 22:07):
down arrow? Then \d can be delta
#### Mario Carneiro (Jan 10 2019 at 22:07):
I guess down arrow doesn't really matter
#### Edward Ayers (Jan 10 2019 at 22:08):
I don't want to change too many of the ones that are in use but already assigned.
\v = nu?
#### Mario Carneiro (Jan 10 2019 at 22:09):
kind of abusive but \n is taken
#### Edward Ayers (Jan 10 2019 at 22:09):
I've added 2 letter translations for each of the greek letters
#### Edward Ayers (Jan 10 2019 at 22:09):
Was thinking \v could be \or
aha
#### Mario Carneiro (Jan 10 2019 at 22:10):
\D and \G are greek capitals?
#### Mario Carneiro (Jan 10 2019 at 22:11):
The current \GD and \Gd etc is annoying to type
\L = Lambda
#### Edward Ayers (Jan 10 2019 at 22:13):
overwriting "Ł" with "Λ"
#### Mario Carneiro (Jan 10 2019 at 22:14):
I certainly use big lambda more than polish L in maths
#### Mario Carneiro (Jan 10 2019 at 22:15):
I see that's the only abbrev for polish L, maybe it can relocate to \L/
#### Mario Carneiro (Jan 10 2019 at 22:17):
\m = mu, I don't know what that m-eq thing is
#### Johan Commelin (Jan 11 2019 at 07:16):
Can we have \ = lambda? Or is \-space impossible to assign in VScode? (It is even sort of mnemonic...)
#### Kenny Lau (Jan 11 2019 at 07:48):
well \; is space :p
#### Johan Commelin (Jan 11 2019 at 07:50):
I would expect that to be unicode THIN SPACE, if that exists (-; Which I think it does. But that is just my LaTeX intuition ported to VScode. And that port might not be lawful
#### Gabriel Ebner (Jan 11 2019 at 08:06):
Patrick just vetoed space. , needs to remain ,
#### Johan Commelin (Jan 11 2019 at 08:06):
Fair enough... but just like others need to fix their OS, he ought to fix his keyboard layout :stuck_out_tongue_wink:
#### matt rice (Jan 12 2019 at 22:19):
One thing i found accidentally, was \<> will do the same as: \< \>, but that neither \f<> nor \f<f> will do the same as \f< \f>, I looked a bit through the translations but didn't find where the \<> magic was coming from
#### Johan Commelin (Jan 14 2019 at 10:41):
I don't know if this belongs in the translations file... but I wouldn't mind if I could type \copyright and this would expand to the header that goes to the top of every Lean file. (If possible with the correct year filled in.)
Of course I can just copy it from another file... but this would be a nice little feature.
Priority: very low
#### Gabriel Ebner (Jan 14 2019 at 10:51):
@Johan Commelin Something like this? https://github.com/leanprover/mathlib/pull/589
nice
Awesome!
#### Edward Ayers (Jan 14 2019 at 12:58):
Summary of my proposed changes:
- \L is Λ instead of Ł
- \G is Γ
- \pis Π
- \C is ℂ instead of ∁
- \c is χ
- \v is ∨
- \- is ⁻¹ instead of a space.
- \n is ¬
- \ss is ⊆
- \m is μ
All greek letters have a 2-space shortcut. Eg sigma is \si, omega is \om etc.
All accented characters have been removed except
À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï
Ð Ñ Ò Ó Ô Õ Ö Ø Ù Ú Û Ü Ý Þ
à á â ã ä å æ ç è é ê ë ì í î ï
ð ñ ò ó ô õ ö ø ù ú û ü ý þ ÿ
Ł
(so we can still use important keywords like "Hölzl")
#### Patrick Massot (Jan 14 2019 at 15:03):
Did we decide something for \l giving lambda or left arrow?
#### Rob Lewis (Jan 14 2019 at 15:06):
I'd prefer not to change it from left arrow, since presumably anyone who writes tactics uses it a lot.
#### Patrick Massot (Jan 14 2019 at 15:07):
everybody use left arrow a lot, it's also used in rewrite. If we change we also need a nice shortcut for left arrow
#### Edward Ayers (Jan 14 2019 at 15:13):
\lfor lambda is contentious so I just kept it as is. In this PR I don't want to change the translations file in such a way that could potentially make things worse for some users.
#### Thales (Jan 14 2019 at 23:51):
Some unsupported notations I have considered using in the future are
ˇ caron, ␣ vispace, ˅ down , ˄ up, ⅅ Dd, ⅆ dd, ⅇ ee, ⅈ ii, ⅉ jj.
The intended use is that ⅈ designates the complex number i, ⅇ designates the
base of the natural log, ⅆ is the binder for integration, etc.
I have experimented with using accents as operators. For example, the U+0304 bar accent is particularly useful.
Will Lean-emacs remain compatible with VSCode for those of us that switch back and forth?
#### Mario Carneiro (Jan 15 2019 at 00:31):
The emacs and VSCode lean modes use the same translations file, so any change to translations.json should affect both
#### Mario Carneiro (Jan 15 2019 at 00:32):
I'm not sure if the cocalc version uses the same file
#### Patrick Massot (Jan 15 2019 at 07:58):
We should also make sure to PR modifications to TPIL and the reference manual (and mathlib doc)
#### Gabriel Ebner (Jan 15 2019 at 08:33):
The emacs and VSCode lean modes use the same translations file, so any change to translations.json should affect both
Unfortunately this is not at all the case. The vscode extension, the emacs mode, cocalc, the javascript version, they all use their own copy of the translations. The translations.json file was originally exported from the emacs mode two years ago. To my knowledge, none of the improvements in the vscode extension have been propagated to the other editor plugins.
#### Sebastian Ullrich (Jan 15 2019 at 08:34):
I still type \lam :shrug:
#### Sebastian Ullrich (Jan 15 2019 at 08:34):
But I'm definitely open to unifying this
#### Johan Commelin (Jan 17 2019 at 17:49):
If not, could you change the translation of \functor (and prefixes of that) back to the old symbol?
#### Johan Commelin (Jan 17 2019 at 17:49):
The old symbol is ⇒
#### Bryan Gin-ge Chen (Jan 17 2019 at 17:50):
His changes have already been merged in #107, but your suggestion wouldn't be hard to implement.
#### Johan Commelin (Jan 17 2019 at 17:50):
Sure, I just wasn't aware what the status was. Otherwise it could go into that PR.
#### Johan Commelin (Jan 17 2019 at 17:50):
So now we have to create a new one.
#### Bryan Gin-ge Chen (Jan 17 2019 at 17:52):
I'm not seeing anything related to \functor changed in the diff though?
#### Bryan Gin-ge Chen (Jan 17 2019 at 17:53):
Here's the diff. In the current version of the extension, if I complete \functor I get ⥤. If I search the diff for that symbol, I see it both in the old version and the new version.
#### Bryan Gin-ge Chen (Jan 17 2019 at 17:54):
The symbol you pasted above as the "old symbol" ⇒ is currently \Longrightarrow.
I guess this also used to be under \functor but that was changed by your commit in August.
OK, so I think I finally understand. You want to revert that change from August, not anything done by Ed.
#### Johan Commelin (Jan 17 2019 at 18:08):
Exactly. Sorry if I was confusing.
#### Johan Commelin (Jan 17 2019 at 18:08):
Because that symbol was locked into core, but was recently liberated.
#### Johan Commelin (Jan 17 2019 at 18:17):
I made a PR with this change. @Gabriel Ebner
#### Gabriel Ebner (Jan 17 2019 at 18:26):
Should we maybe wait until mathlib works with that Lean version?
#### Johan Commelin (Jan 17 2019 at 18:28):
Yes, that is probably a good idea.
#### Johan Commelin (Jan 17 2019 at 18:29):
How far are we from that moment?
#### Bryan Gin-ge Chen (Jan 17 2019 at 18:30):
As far as I can tell we're just waiting on 3.4.2 to be officially released. Then I'll PR the 3.4.2 branch in community mathlib which currently works with nightly.
#### Gabriel Ebner (Jan 17 2019 at 18:30):
We could switch to nightlies earlier, I guess.
#### Edward Ayers (Jan 17 2019 at 18:49):
I think so
Last updated: May 14 2021 at 21:11 UTC
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# Moriwaki divisors and the augmented base loci of divisors on the moduli space of curves
@article{Cacciola2013MoriwakiDA,
title={Moriwaki divisors and the augmented base loci of divisors on the moduli space of curves},
author={Salvatore Cacciola and Angelo Felice Lopez and Filippo Viviani},
journal={arXiv: Algebraic Geometry},
year={2013}
}
• Published 6 May 2013
• Mathematics
• arXiv: Algebraic Geometry
We study the cone of Moriwaki divisors on \bar{M}_g by means of augmented base loci. Using a result of Moriwaki, we prove that an R-divisor D satisfies the strict Moriwaki inequalities if and only if the augmented base locus of D is contained in the boundary of \bar{M}_g. Then we draw some interesting consequences on the Zariski decomposition of divisors on \bar{M}_g, on the minimal model program of \bar{M}_g and on the log canonical models \bar{M}_g(\alpha).
## References
SHOWING 1-10 OF 41 REFERENCES
Normal Functions and the Geometry of Moduli Spaces of Curves
In this paper normal functions (in the sense of Griffiths) are used to solve and refine geometric questions about moduli spaces of curves. The first application is to a problem posed by Eliashberg:
On the Arakelov Geometry of Moduli Spaces of Curves
• Mathematics
• 2002
In this paper we compute the asymptotics of the metric on the line bundle over the moduli space of curves that arises when attempting to compute the archimedean height of the algebraic cycle $C-C^-$
Birational aspects of the geometry of M_g
We discuss topics on the geometry of the moduli space of curves. We present a short proof of the Harris-Mumford theorem on the Kodaira dimension of the moduli space which replaces the computations on
Log canonical models for the moduli space of curves: The first divisorial contraction
• Mathematics
• 2006
In this paper, we initiate our investigation of log canonical models for (M g , αδ) as we decrease α from 1 to 0. We prove that for the first critical value α = 9/11, the log canonical model is
Relative Bogomolov’s inequality and the cone of positive divisors on the moduli space of stable curves
An interesting point of the above theorem is that even if the weak positivity of disx/y (E) at y is a global property on Y, it can be derived from the local assumption "the goodness of Xg and the
Log minimal model program for the moduli space of stable curves: The first flip
• Mathematics
• 2008
We give a geometric invariant theory (GIT) construction of the log canonical model $\bar M_g(\alpha)$ of the pairs $(\bar M_g, \alpha \delta)$ for $\alpha \in (7/10 - \epsilon, 7/10]$ for small
Mori dream spaces and GIT.
• Mathematics
• 2000
The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call
Cornalba-Harris equality for semistable hyperelliptic curves in positive characteristic
Let Y be a nonsingular projective curve over an algebraically closed field k and f : X → Y a generically smooth semistable curve of genus g ≥ 2 with X nonsingular. Let ωX/Y denote the relative
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# Change the equation of the Gauss bell
TeX - LaTeX Asked by user3204810 on September 18, 2020
My goal is to draw the absorption peaks of Lambert-Beer-Bouguer graph which, ideally, have the shape of a Gaussian. I would like to make sure that these peaks all have the same width, which in Gauss’s equation depends on sigma, and I could change its height.
Something like
gauss{9}{1}
Where 9 is the symmetry axis (mu) and 1 is the height of the peak.
How can I modify the equation to achieve this?
newcommandgauss[2]{1/(sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
My take -- X can be varied as per choice and will give a corresponding y value
mu gives the mean and sigma the spread
for mu=9 and sigma square=1 --now y(height) can be varied by pushing in various values of x
Answered by js bibra on September 18, 2020
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# Extreme Bevy: Making a p2p web game with rust and rollback netcode
In my previous post, Introducing Matchbox, I explained how Matchbox solves the problem of setting up peer-to-peer connections in rust web assembly for implementing low-latency multiplayer web games. I said I’d start making games using it and I figured it’s about time I make good on that promise, as well as write a tutorial while at it. I’ll explain step-by-step how to use Bevy, GGRS, and Matchbox to recreate the old classic Extreme Violence by Simon Green with online p2p multiplayer using rollback netcode.
## Extreme Violence
Extreme Violence is one of my early childhood memories. It’s the Amiga game that had it all: great graphics, cool sound effects and intense multiplayer action.
In the author, Simon Green’s, own words, the game is built around “idiot-proof run-around-and-shoot-the-other-guy gameplay”. Apart from the opportunity to go on about the good ol’ days, I chose it as it is a test project because it’s simple, but compared to other simple games, it’s still fun to play (yes, looking at you, Pong!).
You can probably tell what the gameplay is about just by looking at the screenshot above.
## Starting a project
Start a new rust project
cargo new extreme_bevy
We’ll be using Bevy, it’s a great game engine built around the Entity Component System (ECS) architecture. I won’t go into great detail about Bevy here, though. If you find some of the tutorial hard to follow, the Bevy Book is a good place to start.
Add Bevy in Cargo.toml:
[dependencies]
bevy = "0.6"
Next, replace main.rs with the standard Bevy boiler-plate:
use bevy::prelude::*;
fn main() {
}
That should be enough to get us the standard gray window if we do cargo run.
## Web build
But wait! We’re making a web game, remember? Not a native one.
First, make sure you have a rust wasm toolchain installed. With rustup, it’s simply:
rustup target install wasm32-unknown-unknown
That’s enough to build the project for the web.
cargo build --target wasm32-unknown-unknown
However, that will just leave us with a wasm file in the target directory. In order to easily test our project while developing, we’ll install wasm-server-runner:
cargo install wasm-server-runner
And configure our project to use it by adding a new file, .cargo/config.toml:
[target.wasm32-unknown-unknown]
runner = "wasm-server-runner"
Now, when we run the project for the wasm target, it will start a local web server and log the link in the terminal:
$cargo run --target wasm32-unknown-unknown Compiling extreme_bevy v0.1.0 (C:\dev\extreme_bevy) Finished dev [unoptimized + debuginfo] target(s) in 1.74s Running wasm-server-runner target\wasm32-unknown-unknown\debug\extreme_bevy.wasm INFO wasm_server_runner: wasm output is 50.05mb large INFO wasm_server_runner::server: starting webserver at http://127.0.0.1:1334 And we have a link to open in the browser, and it might even launch, but if it crashes the tab with a message saying it’s out of memory, don’t worry. It’s simply because debug builds are ridiculously large. Make a release build instead: cargo run --release --target wasm32-unknown-unknown If you open the link, the “game” should start in the browser: Before we go on, I have one more tip that will make things easier: Install cargo-watch as well: cargo install cargo-watch With it, you can detect changes in the project directory, and automatically rebuild and relaunch the server: cargo watch -cx "run --release --target wasm32-unknown-unknown" Now, when you want to test a change, you simply have to save and refresh your browser. If you find it tiresome to type wasm32-unknown-unknown all the time, you can set it as your default target in .cargo/config.toml: [build] target = "wasm32-unknown-unknown" And start developing with: cargo watch -cx "run --release" ## Setting up the camera With the boring build stuff out of the way, let’s actually start putting content into our gray window. First, add a setup system that initializes a camera and a player sprite fn main() { App::new() .add_plugins(DefaultPlugins) .add_startup_system(setup) .run(); } fn setup(mut commands: Commands) { let mut camera_bundle = OrthographicCameraBundle::new_2d(); camera_bundle.orthographic_projection.scale = 1. / 50.; commands.spawn_bundle(camera_bundle); } We’re creating an orthographic camera with scale to$\frac1{50}\$. This means that 1 unit in the scene will take up 50 “pixels”. The reason I chose 50, is that 50 seems like a good size for the player character and grid. I prefer working like this because it’s now easy to say that if something 3 units long it’s 3 times longer than the player, rather than some arbitrary “pixel” number that probably doesn’t correspond to pixels anyway because of high-dpi displays and browser zoom.
So it’s still gray. Let’s add a player.
fn spawn_player(mut commands: Commands) {
commands.spawn_bundle(SpriteBundle {
sprite: Sprite {
color: Color::rgb(0., 0.47, 1.),
custom_size: Some(Vec2::new(1., 1.)),
..Default::default()
},
..Default::default()
});
}
We also need to add the system to the schedule. While we’re at it, let’s also make the clear color a slightly lighter gray:
App::new()
.insert_resource(ClearColor(Color::rgb(0.53, 0.53, 0.53)))
.run();
And now we have our little guy
Let’s make them move on keyboard input:
fn move_player(keys: Res<Input<KeyCode>>, mut player_query: Query<&mut Transform, With<Player>>) {
let mut direction = Vec2::ZERO;
if keys.any_pressed([KeyCode::Up, KeyCode::W]) {
direction.y += 1.;
}
if keys.any_pressed([KeyCode::Down, KeyCode::S]) {
direction.y -= 1.;
}
if keys.any_pressed([KeyCode::Right, KeyCode::D]) {
direction.x += 1.;
}
if keys.any_pressed([KeyCode::Left, KeyCode::A]) {
direction.x -= 1.;
}
if direction == Vec2::ZERO {
return;
}
let move_speed = 0.13;
let move_delta = (direction * move_speed).extend(0.);
for mut transform in player_query.iter_mut() {
transform.translation += move_delta;
}
}
This system simply samples the keyboard and moves any objects with the Player marker component in the given direction.
Add the Player marker component:
#[derive(Component)]
struct Player;
And make sure to add it to the player entity:
fn spawn_player(mut commands: Commands) {
commands
.spawn_bundle(SpriteBundle {
sprite: Sprite {
color: Color::rgb(0., 0.47, 1.),
custom_size: Some(Vec2::new(1., 1.)),
..Default::default()
},
..Default::default()
})
.insert(Player); // <-- NEW
}
And register our new system:
.add_startup_system(spawn_player)
.run()
And now you should be able to move the sprite around the screen with the keyboard.
Ok, now that we have something that is at least somewhat interactive, let’s see how we can add multiplayer to it.
We’ll be using rollback networking with GGRS. What this means, is that we will only be synchronizing players inputs and no actual game state. Each time a peer receives input from another peer, it will roll back its game state to an earlier point in time, insert the input and then re-simulate the frames as if that input had been there all along.
This has an important implication for how we write our game: Everything needs to be perfectly deterministic. Fortunately, rust and wasm makes this easy for us, and the rewards for doing so are big:
1. No state synchronization aside from input ⇒ very low bandwidth
2. We can write the entire game in simple “forward” systems. No need to handle de-synced inputs. It’s all done automatically for us by rolling back and re-simulating.
Let’s go ahead and add ggrs as well as bevy_ggrs to our dependencies:
ggrs = "0.8"
bevy_ggrs = "0.1.3"
## Connecting players
Before we can start using GGRS, we need some kind of connection between the players. GGRS comes with built-in support for UDP, however that doesn’t work in the browser. This is where Matchbox comes in.
Matchbox is a wrapper around the WebRTC browser API and uses its data channels to achieve UDP-like (unordered, unreliable) connections between two browsers.
The project comes in two parts. matchbox_server is a tiny server that needs to run somewhere reachable by both browsers. In production, this would be somewhere on the web, for now we’ll just run it locally.
Go ahead and install and run matchbox_server:
cargo install matchbox_server
matchbox_server
Just leave it running in a terminal while developing.
The second part of Matchbox is matchbox_socket, which is used to briefly connect to the matchbox_server in order to bootstrap direct connections to other peers.
So let’s add it to our dependencies, and specify the ggrs-socket feature flag, which makes it compatible with GGRS.
matchbox_socket = { version = "0.3", features = ["ggrs-socket"] }
Now, we’re ready to create a new system that connects to the Matchbox server to establish direct connections to other clients.
use bevy::{prelude::*, tasks::IoTaskPool};
use matchbox_socket::WebRtcNonBlockingSocket;
// ...
// ...
let room_url = "ws://127.0.0.1:3536/next_2";
info!("connecting to matchbox server: {:?}", room_url);
let (socket, message_loop) = WebRtcNonBlockingSocket::new(room_url);
// The message loop needs to be awaited, or nothing will happen.
// We do this here using bevy's task system.
commands.insert_resource(Some(socket));
}
NOTE: your IDE might give you errors at this point (for the message_loop), if it’s configured with native as build target. It should not be a problem when you actually build for wasm, though.
In the above code, we connect to the Matchbox server running on our machine, and ask to join the next_2 room. This is a special type of room that connects pairs of peers together. It’s perfect for just testing that we can get 2-players up and running.
Next, we call WebRtcNonBlockingSocket::new, this is the GGRS-compatible socket type. It returns both a socket, and a massage loop future that needs to be awaited in order to process network events. We await it using Bevy’s task system.
Finally, we insert the socket as an optional resource, so we can access it in other systems.
Let’s create such a system where we just wait until we’ve established a peer connection and then log to the console so can make sure everything works so far:
.add_system(wait_for_players)
// ...
fn wait_for_players(mut socket: ResMut<Option<WebRtcNonBlockingSocket>>) {
let socket = socket.as_mut();
// If there is no socket we've already started the game
if socket.is_none() {
return;
}
// Check for new connections
socket.as_mut().unwrap().accept_new_connections();
let players = socket.as_ref().unwrap().players();
let num_players = 2;
if players.len() < num_players {
return; // wait for more players
}
info!("All peers have joined, going in-game");
// TODO
}
If you start two browsers side-by-side (note they need to both be visible! otherwise the browser will throttle the tab), you should see the message spammed in the console a little while after the second browser loads.
Ok, so we have a connection, time to hand it over to GGRS!
fn wait_for_players(mut commands: Commands, mut socket: ResMut<Option<WebRtcNonBlockingSocket>>) {
// ...
info!("All peers have joined, going in-game");
// consume the socket (currently required because GGRS takes ownership of its socket)
let socket = socket.take().unwrap();
let max_prediction = 12;
// create a GGRS P2P session
let mut p2p_session =
ggrs::P2PSession::new_with_socket(num_players as u32, INPUT_SIZE, max_prediction, socket);
for (i, player) in players.into_iter().enumerate() {
p2p_session
if player == PlayerType::Local {
// set input delay for the local player
p2p_session.set_frame_delay(2, i).unwrap();
}
}
// start the GGRS session
commands.start_p2p_session(p2p_session);
}
Here we pass the socket to the ggrs::P2PSession constructor and make sure we tell GGRS about the other player(s). The local player needs a bit of special handling.
We also need to update our uses:
use bevy::{prelude::*, tasks::IoTaskPool};
use bevy_ggrs::*;
use ggrs::PlayerType;
use matchbox_socket::WebRtcNonBlockingSocket;
And finally, there is the matter of the INPUT_SIZE constant. This is the number of bytes one peer’s input is. In our case, the input consists of four direction buttons, and eventually the fire button as well. This means it fits easily within a single byte:
const INPUT_SIZE: usize = std::mem::size_of::<u8>();
While we’re at it let’s add some bit mask constants to signify which bit means what:
const INPUT_UP: u8 = 1 << 0;
const INPUT_DOWN: u8 = 1 << 1;
const INPUT_LEFT: u8 = 1 << 2;
const INPUT_RIGHT: u8 = 1 << 3;
const INPUT_FIRE: u8 = 1 << 4;
Now that we have a session up and running let’s start making sure our gameplay systems makes use of them.
Currently, we have a move_player system, but it just reads input directly from the keyboard and moves the local player only, so the ggrs session doesn’t do anything useful yet.
We need to make sure we pass the input on to GGRS.
We do this by setting up a designated input system:
fn input(_: In<ggrs::PlayerHandle>, keys: Res<Input<KeyCode>>) -> Vec<u8> {
let mut input = 0u8;
if keys.any_pressed([KeyCode::Up, KeyCode::W]) {
input |= INPUT_UP;
}
if keys.any_pressed([KeyCode::Down, KeyCode::S]) {
input |= INPUT_DOWN;
}
if keys.any_pressed([KeyCode::Left, KeyCode::A]) {
input |= INPUT_LEFT
}
if keys.any_pressed([KeyCode::Right, KeyCode::D]) {
input |= INPUT_RIGHT;
}
if keys.any_pressed([KeyCode::Space, KeyCode::Return]) {
input |= INPUT_FIRE;
}
vec![input]
}
And also update move_player to use ggrs::GameInput instead of Inputs<KeyCode>:
fn move_player(
inputs: Res<Vec<ggrs::GameInput>>,
mut player_query: Query<&mut Transform, With<Player>>,
) {
let mut direction = Vec2::ZERO;
let input = inputs[0].buffer[0];
if input & INPUT_UP != 0 {
direction.y += 1.;
}
if input & INPUT_DOWN != 0 {
direction.y -= 1.;
}
if input & INPUT_RIGHT != 0 {
direction.x += 1.;
}
if input & INPUT_LEFT != 0 {
direction.x -= 1.;
}
if direction == Vec2::ZERO {
return;
}
let move_speed = 0.13;
let move_delta = (direction * move_speed).extend(0.);
for mut transform in player_query.iter_mut() {
transform.translation += move_delta;
}
}
Now we need to add our two new systems in the right place.
First, add the GGRSPlugin
.add_plugins(DefaultPlugins)
Then, add our input system using the special .with_input_system app build method:
.with_input_system(input)
Then, remove the .add_system(move_player) line, and instead, we’ll create a new schedule for the systems that are affected by rollback:
.with_rollback_schedule(Schedule::default().with_stage(
"ROLLBACK_STAGE",
))
Finally, the game should compile again.
If you play it now, you can see that one of the players should be able to control the blue box, while the other is not. So we’re properly sending input!
## Actually implementing rollback
While are sending input we’re still not actually using rollback yet. We need to tell bevy_ggrs what kind of entities and components should be rolled back. We don’t necessarily want to roll back everything, so this is a good thing!
First, we need to register the types we are interested in rolling back. So far Transform is the only thing that actually changes, so we add that
.with_rollback_schedule(Schedule::default().with_stage(
"ROLLBACK_STAGE",
))
.register_rollback_type::<Transform>() // <-- NEW
As we add more components to our game, we need to add them here if they should be rolled back.
Second, we also need entities to opt in to being rolled back. We do this by adding a Rollback component to them. The Rollback component needs a unique id, the best way to get this, is using the RollbackIdProvider that comes with GGRS. Let’s add the Rollback component when we create our player:
fn spawn_player(mut commands: Commands, mut rip: ResMut<RollbackIdProvider>) {
commands
.spawn_bundle(SpriteBundle {
sprite: Sprite {
color: Color::rgb(0., 0.47, 1.),
custom_size: Some(Vec2::new(1., 1.)),
..Default::default()
},
..Default::default()
})
.insert(Player)
.insert(Rollback::new(rip.next_id()));
}
And with that, the player should actually be rolling back. Since we’re running this locally, the latency is very low, and it should probably behave exactly the same as before.
What we have now is essentially just a single player game with a spectator, which is kind of cool, but what we want is a multiplayer game, so let’s rename our system to spawn_players and spawn the other player as well, and put them some distance apart from each other.
fn spawn_players(mut commands: Commands, mut rip: ResMut<RollbackIdProvider>) {
// Player 1
commands
.spawn_bundle(SpriteBundle {
transform: Transform::from_translation(Vec3::new(-2., 0., 0.)),
sprite: Sprite {
color: Color::rgb(0., 0.47, 1.),
custom_size: Some(Vec2::new(1., 1.)),
..Default::default()
},
..Default::default()
})
.insert(Player)
.insert(Rollback::new(rip.next_id()));
// Player 2
commands
.spawn_bundle(SpriteBundle {
transform: Transform::from_translation(Vec3::new(2., 0., 0.)),
sprite: Sprite {
color: Color::rgb(0., 0.4, 0.),
custom_size: Some(Vec2::new(1., 1.)),
..Default::default()
},
..Default::default()
})
.insert(Player)
.insert(Rollback::new(rip.next_id()));
}
Now we should at least see two players on screen.
However they’re still both controlled by only one of the players input.
We need some way to differentiate between players. So let’s go ahead and add a number to our Player struct:
#[derive(Component)]
struct Player {
handle: usize
};
// ...
// spawn_players()
.insert(Player { handle: 0 })
// ...
.insert(Player { handle: 1 })
And in move_player which we will now rename to move_players, let’s use these new handles to index the inputs vector:
fn move_players(
inputs: Res<Vec<ggrs::GameInput>>,
mut player_query: Query<(&mut Transform, &Player)>,
) {
for (mut transform, player) in player_query.iter_mut() {
let input = inputs[player.handle].buffer[0];
let mut direction = Vec2::ZERO;
if input & INPUT_UP != 0 {
direction.y += 1.;
}
if input & INPUT_DOWN != 0 {
direction.y -= 1.;
}
if input & INPUT_RIGHT != 0 {
direction.x += 1.;
}
if input & INPUT_LEFT != 0 {
direction.x -= 1.;
}
if direction == Vec2::ZERO {
continue;
}
let move_speed = 0.13;
let move_delta = (direction * move_speed).extend(0.);
transform.translation += move_delta;
}
}
And with that we finally have a multiplayer cube-moving game.
This wraps up the basics. We now have a starting point to expand upon.
In the next tutorial, we will look at adding a a background, map edges, and making the camera follow the local player.
Reference implementation
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# Efficiently evaluating $\int x^{4}e^{-x}dx$ [duplicate]
The integral I am trying to compute is this:
$$\int x^{4}e^{-x}dx$$
I got the right answer but I had to integrate by parts multiple times. Only thing is it took a long time to do the computations. I was wondering whether there are any more efficient ways of computing this integral or is integration by parts the only way to do this question?
Edit: This question is similar to the question linked but slightly different because in the other question they are asking for any method to integrate the function which included integration by parts. In this question I acknowledge that integration by parts is a method that can be used to evaluate the integral but am looking for the most efficient way. This question has also generated different responses than the question linked such as the tabular method.
## marked as duplicate by J. M. is a poor mathematician, Semiclassical, T. Bongers, Pierre-Guy Plamondon, user147263 Apr 11 '16 at 23:31
• Would need limits for this if you intend a numerical answer. Not meant to be a trivial statement since if the upper limit is infinity then more computation needed. – jim Apr 10 '16 at 18:50
• @mikevandernaald Gamma function has a limits , there is no limits – openspace Apr 10 '16 at 18:51
• I think that the simplest way to compute it is integrating by parts. – Crostul Apr 10 '16 at 18:52
• In the original question I was attempted the limits of integration were from 0 to 1 – user262291 Apr 10 '16 at 18:52
• Use the tabular method pages.pacificcoast.net/~cazelais/187/tabular.pdf – user258700 Apr 10 '16 at 18:57
While it still entails integration by parts, there exists a "quick" method of doing the integration by parts called the Tabular Method. Basically, you start with a table that has $3$ columns. One with alternating signs, one with a $u$ and one with $dv$. In the column for $u$, you should put the term that will eventually go to zero after multiple differentiations. In the last column is $dv$ which you will integrate multiple times. You'll want to pick something you can still integrate multiple times for $dv$. So in $\displaystyle \int x^4e^{-x}\,dx$, we can create the following table: $$\begin{matrix} & u & dv \\ + &x^4 & e^{-x} \\ - & 4x^3 & -e^{-x} \\ + & 12 x^2 & e^{-x} \\ - & 24x & -e^{-x} \\ + & 24 & e^{-x} \\ - & 0 & -e^{-x}.\end{matrix}$$ we now have all the parts to compute our solution. You start at the very first $+$, and multiply the corresponding $u$ term with the $dv$ term on the very next line. Continue this process until you get to the end of the $dv$ column. So our solution is $$\int x^4e^{-x}\,dx = -x^4e^{-x} -4x^3e^{-x} -12x^2e^{-x}-24xe^{-x}-24e^{-x} + C$$
• Why $-x^4e^{-x}$ instead of $x^4e^{-x}$ (and similar questions for the other terms)? – PyRulez Apr 11 '16 at 1:25
• It's because $x^4$ is multiplied by $-e^{-x}$ (the $dv$ entry on the second line). – jtbandes Apr 11 '16 at 3:03
• Yes, the $dv$ entry on the next line is the $v$, the integration, of the the $dv$ entry on the current line. This is what we want $\int u dv = uv - \int v du$. – Dominic108 Apr 11 '16 at 11:11
Usually this kind of integrals can be handled by making
\begin{align*} \int x^4e^{-x}\,\mathrm dx&=-x^4e^{-x} + (Ax^3+Bx^2+Cx+E)e^{-x} \end{align*} Where $A,\;B,\;C$, and $E$ are constants which satisfies $$x^4e^{-x}+(-4-A)x^3e^{-x}+(3A-B)x^2e^{-x}+(2B-C)xe^{-x}+(C-E)e^{-x}=x^4e^{-x}$$ So \begin{align*} -4-A&=0\\ 3A-B&=0\\ 2B-C&=0\\ C-E&=0 \end{align*} Then $A=-4$, $\;B=3A=-12$, $\;C=2B=-24$ and $E=C=-24$, then \begin{align*} \int x^4e^{-x}\,\mathrm dx&=-(x^4+4x^3+12x^2+24x+24)e^{-x}+K \end{align*} where $K$ is a constant.
Also, here is a more general problem related.
Here is a nice little trick to integrate it without using partial integration. $$\int x^4 e^{-x} \,\mathrm dx = \left. \frac{\mathrm d^4}{\mathrm d \alpha^4}\int e^{-\alpha x} \,\mathrm dx \right|_{\alpha=1} = \left.- \frac{\mathrm d^4}{\mathrm d \alpha^4} \frac{1}{\alpha} e^{-\alpha x}\right|_{\alpha=1}$$ The idea is to introduca a variable $\alpha$ in the exponent and write the $x^4$ term as the fourth derivative with respect to $\alpha$. This is especially helpful when you want to calculate the definite integral $\int_0^\infty$ because in this case the differentiation greatly simplifies. $$\int\limits_0^\infty x^n e^{-x} \,\mathrm dx = (-1)^n \left. \frac{\mathrm d^n}{\mathrm d \alpha^n} \frac{1}{\alpha} \right|_{\alpha=1} = n!\stackrel{n=4}{=} 24$$
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# Congruent Triangles Geometry Maths Tuition: Solution
Solution:
(a) $\angle EBD=\angle BEC$ (given)
BE is a common side for both triangles $\triangle BCE$ and $\triangle EDB$
BD=EC (given)
Therefore, $\triangle BCE \equiv \triangle EDB$ (SAS)
(proved)
(b)
Since $\triangle BCE\equiv\triangle EDB$ we have $\angle CBE=\triangle DEB$
Thus, $\begin{array}{rcl}\angle ABE&=&180^\circ - \angle CBE\\ &=&180^\circ -\angle DEB\\ &=& \angle AEB \end{array}$
Therefore, $\triangle ABE$ is an isosceles triangle.
Thus, $AB=AE$
(proved)
## Author: mathtuition88
https://mathtuition88.com/
This site uses Akismet to reduce spam. Learn how your comment data is processed.
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# Making time differentials look like the textbook [duplicate]
I need to have time differentials to look like the 'textbook'. My code is
Dt[x y^2] /. {Dt[x] -> dx/dt, Dt[y] -> dy/dt}
which gives the output
(2 dy x y)/dt + (dx y^2)/dt.
This is very hard to follow.
My question is how can the output be made to look like
2 x y dy/dt + y^2 dx/dt
(only with dy/dt and dx/dt vertical).
Thanks.
-
## marked as duplicate by Jens, Artes, Kuba, Sjoerd C. de Vries, SzabolcsSep 3 '13 at 21:58
Strange. #[x] /. {#[x_] -> h} & /@ {Dt, g} == {Dt[x], h} – ssch Sep 3 '13 at 19:46
Welcome to Mathematica.SE! Could you please change your username to something recognizable, instead of "user9292"? Then you can remove the signature from the post itself. This will comply with the site etiquette. – Szabolcs Sep 3 '13 at 19:49
Nevermind my strangeness above, the pattern got differentiated. HoldPattern made everything better – ssch Sep 3 '13 at 19:57
Have you asked this question Basins of Attraction? If this is the case the both accounts should be merged. – Artes Sep 3 '13 at 20:52
To look at the output in TraditionalForm, either use Dt[x y^2] // TraditionalForm as the input or select the output cell and press ctrl-shift-T. In the preferences you can set TraditionalForm as the default output.
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# Kähler forms arising as the curvature form of a singular metric on a line bundle
The Fubini-Study metric on complex projective space $\mathbb{P}^n$ is a smooth metric $h = e^{-\phi}$ on the line bundle $\mathcal{O}(1)$ and it is a standard calculation to check that its curvature form $\frac{i}{\pi}\partial \overline{\partial} \phi$ is a Kähler form on $\mathbb{P}^n$.
I'm wondering whether this generalizes. To be precise: given a Kähler manifold $X$ with a Kähler form $\omega$, does there exist a holomorphic line bundle $L \to X$ and a singular metric $h = e^{-\phi}$ on $L$ such that $\omega = \frac{i}{\pi} \partial \overline{\partial} \phi$?
Aside from the example of $\mathbb{P}^n$, there is another class of examples that might lead to such a guess: if $X$ is smooth projective variety (over $\mathbb{C}$) and $L \to X$ is an ample line bundle, then the curvature form of any singular metric on $L$ is cohomologous to $c_1(L)$, which is a Kähler form.
If $\omega=\frac{i}{2\pi}\partial\bar\partial\phi$ for some holomorphic hermitian line bundle $(L,h)$ with $h=e^{-\phi}$, then necessarily $[\omega]\in H^{1,1}(X,\mathbb R)$ is an integral, i.e., represents class in $H^2(X,\mathbb Z)$, so unless $[\omega]$ is integral, such line bundle does not exist.
On the contrary, for any (1,1)-form $\omega$ with $[\omega]\in H^{1,1}(X,\mathbb R)\cap H^2(X,\mathbb Z)$ there exists a holomorphic hermitian line bundle $(L,h)$ such that its curvature form $\Theta(L,h)=\partial\bar\partial\phi$ equals $\frac{2\pi} {i}\omega$, see, e.g., Griffiths-Harris "Principles of algebraic geometry" $\S1.2$.
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# Bitcoin and Blockchain — Opening the Blackbox with Python
Quant Insights Conference London 2016
Dr. Yves J. Hilpisch
The Python Quants GmbH
For the curious:
## Agenda¶
• Some Bitcoin Market Data
• Hashing Functions
• Crypto Signing of Messages
• Idea behind Block Chain
• Idea behind Bitcoin Mining
• Bitcoin Mining with Python
## Some Bitcoin Data¶
### Total Number of Bitcoins¶
We work with data from http://quandl.com. First, the total number of bitcoins mined.
In [2]:
import quandl as q
bn = q.get('BCHAIN/TOTBC') / 1e6 # in millions
In [3]:
bn.plot(figsize=(10, 6));
### Total Number of Transactions¶
The total number of transactions.
In [4]:
bt = q.get('BCHAIN/NTRAT') / 1e6 # in millions
In [5]:
bt.plot(figsize=(10, 6));
### Bitcoin Value in USD (Exchange Rate)¶
The USD/Bitcoin exchange rate.
In [6]:
be = q.get('BCHAIN/MKPRU')
In [7]:
be.plot(figsize=(10, 6));
### Bitcoin Value in USD (Market Capitalization)¶
The market capitalization in USD.
In [8]:
bm = q.get('BCHAIN/MKTCP') / 1e9 # in billions
In [9]:
bm.plot(figsize=(10, 6));
### Bitcoin Network Hashrate¶
The hashrate of the Bitcoin mining network. How many giga hashes per second (GH/s) does the bitcoin mining network calculate per second?
In [10]:
bh = q.get('BCHAIN/HRATE')
In [11]:
bh.plot(figsize=(10, 6));
### Bitcoin Mining Difficulty¶
The bitcoin mining difficulty. How hard is it to mine a new bitcoin block?
In [12]:
bd = q.get('BCHAIN/DIFF') / 1e9 # in billions
In [13]:
bd.plot(figsize=(10, 6));
## Hashing¶
A hash function is any function that can be used to map data of arbitrary size to data of fixed size. The values returned by a hash function are called hash values, hash codes, hash sums, or simply hashes.
### A Simple Hash Function¶
The first simplistic hash function that we consider maps any string to a three digit integer. It uses ordinal numbers of one-character string objects.
In [14]:
ord('a')
Out[14]:
97
In [15]:
chr(97)
Out[15]:
'a'
The implementation of the simplistic hash function ("average integer ordinal number").
In [16]:
def hash_function(text):
value = sum([ord(l) for l in text]) / len(text)
return '%03d' % value
Some examples.
In [17]:
hash_function('!')
Out[17]:
'033'
In [18]:
hash_function('yves')
Out[18]:
'113'
In [19]:
hash_function('yves2')
Out[19]:
'101'
In [20]:
hash_function('Quant4711')
Out[20]:
'080'
Collisions are easily found.
In [21]:
hash_function('yves')
Out[21]:
'113'
In [22]:
hash_function('sevy')
Out[22]:
'113'
Our function has a target space of 10 bits (only).
In [23]:
bin(999)
Out[23]:
'0b1111100111'
In [24]:
2 ** 10
Out[24]:
1024
Modern hash functions have a target space of 128 bits, i.e. $2^{128} - 1$ possible values.
In [25]:
2 ** 128
Out[25]:
340282366920938463463374607431768211456
In [26]:
hex(2 ** 128)
Out[26]:
'0x100000000000000000000000000000000'
In [27]:
len(hex(2 ** 128)) - 3
Out[27]:
32
Or 256 bits.
In [28]:
2 ** 256
Out[28]:
115792089237316195423570985008687907853269984665640564039457584007913129639936
In [29]:
hex(2 ** 256)
Out[29]:
'0x10000000000000000000000000000000000000000000000000000000000000000'
In [30]:
len(hex(2 ** 256)) - 3
Out[30]:
64
Or even 384 bits.
In [31]:
2 ** 384
Out[31]:
39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816
In [32]:
hex(2 ** 384)
Out[32]:
'0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'
In [33]:
len(hex(2 ** 384)) - 3
Out[33]:
96
The universe is assumed to consist of $10^{80}$ atoms.
In [34]:
10 ** 80
Out[34]:
100000000000000000000000000000000000000000000000000000000000000000000000000000000
In [35]:
hex(10 ** 80)
Out[35]:
'0x35f9dea3e1f6bdfef70cdd17b25efa418ca63a22764cec100000000000000000000'
In [36]:
len(hex(10 ** 80)) - 3 # close to 2 ** 256
Out[36]:
66
We require the following properties from a hash function:
• collision resistance: it is highly unlikely to find to inputs that yield the same output
• hiding: it is really difficult to find the exact input if you know an output
• puzzle friendliness (for mining purposes): if someone targets a certain output value and if parts of the input are randomly chosen then it is difficult to find another input value that hits exactly that target
### MD5 Hash Codes¶
First, importing Python's hashing function library.
In [37]:
import hashlib
The first MD5 hash codes (cf. https://en.wikipedia.org/wiki/MD5).
In [38]:
md5_1 = hashlib.md5(b'yves').hexdigest()
md5_1
Out[38]:
'afe3bd960b4c46a68580c4e564cca24e'
In [39]:
md5_2 = hashlib.md5(b'yves2').hexdigest()
md5_2
Out[39]:
In [40]:
hashlib.md5(b'Dr. Yves Johannes Hilpisch').hexdigest()
Out[40]:
'642394f6d25fd9fe4b88e359c8aaf051'
### Brute Force Hash (Password) Cracking¶
We define first a character set of lower case letters only.
In [41]:
import string
charset = string.ascii_lowercase
charset
Out[41]:
'abcdefghijklmnopqrstuvwxyz'
Hash codes for all single characters in charset.
In [42]:
for c in charset:
md5 = hashlib.md5(c.encode('ascii'))
print(c, md5.hexdigest())
a 0cc175b9c0f1b6a831c399e269772661
c 4a8a08f09d37b73795649038408b5f33
e e1671797c52e15f763380b45e841ec32
f 8fa14cdd754f91cc6554c9e71929cce7
g b2f5ff47436671b6e533d8dc3614845d
h 2510c39011c5be704182423e3a695e91
i 865c0c0b4ab0e063e5caa3387c1a8741
j 363b122c528f54df4a0446b6bab05515
k 8ce4b16b22b58894aa86c421e8759df3
l 2db95e8e1a9267b7a1188556b2013b33
m 6f8f57715090da2632453988d9a1501b
o d95679752134a2d9eb61dbd7b91c4bcc
p 83878c91171338902e0fe0fb97a8c47a
q 7694f4a66316e53c8cdd9d9954bd611d
r 4b43b0aee35624cd95b910189b3dc231
s 03c7c0ace395d80182db07ae2c30f034
t e358efa489f58062f10dd7316b65649e
v 9e3669d19b675bd57058fd4664205d2a
w f1290186a5d0b1ceab27f4e77c0c5d68
x 9dd4e461268c8034f5c8564e155c67a6
y 415290769594460e2e485922904f345d
Now doing brute force hash code cracking — 'knowing' that the relevant word has a maximum of 4 characters.
In [43]:
import itertools as it
In [44]:
%%time
for i in range(1, 5):
print('%d CHARACTERS USED NOW' % i)
pm = it.product(charset, repeat=i)
for comb in pm:
comb = ''.join(comb)
md5 = hashlib.md5(comb.encode('ascii')).hexdigest()
if md5 == md5_1:
print('SUCCESS')
print(comb, md5)
break
1 CHARACTERS USED NOW
2 CHARACTERS USED NOW
3 CHARACTERS USED NOW
4 CHARACTERS USED NOW
SUCCESS
yves afe3bd960b4c46a68580c4e564cca24e
CPU times: user 923 ms, sys: 10.9 ms, total: 934 ms
Wall time: 1 s
Let us enlarge the character set to include digits as well.
In [45]:
charset2 = string.ascii_lowercase + string.digits
charset2
Out[45]:
'abcdefghijklmnopqrstuvwxyz0123456789'
Time to crack the second hash code increases due to greater passworword length and larger character set.
In [46]:
from itertools import product
In [47]:
import time
t0 = time.time()
z = 0
for i in range(1, 6):
print('%d CHARACTERS USED NOW' % i)
pm = it.product(charset2, repeat=i)
for comb in pm:
comb = ''.join(comb)
md5 = hashlib.md5(comb.encode('ascii')).hexdigest()
z += 1
if md5 == md5_2:
print('SUCCESS')
print(comb, md5)
break
sec = time.time() - t0
print('time in sec: %.1f' % sec)
1 CHARACTERS USED NOW
2 CHARACTERS USED NOW
3 CHARACTERS USED NOW
4 CHARACTERS USED NOW
5 CHARACTERS USED NOW
SUCCESS
time in sec: 94.0
The algorithm has checked about 43 mn hashes before being successful. This represents a speed of about 450,000 hashes per second.
In [48]:
z
Out[48]:
43024025
In [49]:
z / sec
Out[49]:
457617.32578829414
### Using Dedicated Password Cracking Tools ("Better Software")¶
Dedicated password cracking tools like Hashcat (cf. http://hashcat.net) allow for a much faster and more intelligent/targeted approach.
Let us check how long Hashcat needs to find the password yves2 stored as an MD5 hash. We assume:
• password length is 5 letters
• only lower case letters or digits
In [50]:
r1 = '''
Session.Name...: hashcat
Status.........: Cracked
Custom.Chars...: -1 ?l?d, -2 Undefined, -3 Undefined, -4 Undefined
Hash.Type......: MD5
Time.Started...: Mon Aug 22 19:34:16 2016 (2 secs)
Speed.Dev.#1...: 13710.9 kH/s (0.94ms)
Recovered......: 1/1 (100.00%) Digests, 1/1 (100.00%) Salts
Progress.......: 28803600/60466176 (47.64%)
Rejected.......: 0/28803600 (0.00%)
Restore.Point..: 799470/1679616 (47.60%)
Started: Mon Aug 22 19:34:16 2016
Stopped: Mon Aug 22 19:34:22 2016
real 0m6.055s
user 0m1.750s
sys 0m1.490s
'''
### Make Use of Human Traits ("Social Cracking")¶
Mask attacks are some of the most powerful tools (strategies) in password cracking. It relies on the fact that human beings like to use certain (easy to remember) structures for their passwords. An interesting analysis is found here: https://www.praetorian.com/blog/statistics-will-crack-your-password-mask-structure. The major finding is:
• 50% of all passwords analyzed rely on
• 260,000+ masks analyzed in total
An example: lisa2008 = name of daughter born in 2008
Let us consider the following case. A password is assumed to consist of upper case letters, lower case letters and digits. In this case, we make use of insights about "humanly generated passwords". I.e. we do a so-called mask attack where we implement the following rules:
• password length is 9 letters
• first letter is upper case (like A)
• next four letters are lower case (like bbbb)
• last four letters are digits (like 1992)
We assume a structure like Abbbb1992.
In [51]:
r2 = '''
8769d3723ec8f853d91f28208e97acce:Quant4711
Session.Name...: hashcat
Status.........: Cracked
Hash.Target....: 8769d3723ec8f853d91f28208e97acce
Hash.Type......: MD5
Time.Started...: Mon Aug 22 17:39:32 2016 (10 mins, 23 secs)
Speed.Dev.#1...: 42944.7 kH/s (13.43ms)
Recovered......: 1/1 (100.00%) Digests, 1/1 (100.00%) Salts
Progress.......: 27138885360/118813760000 (22.84%)
Rejected.......: 0/27138885360 (0.00%)
Restore.Point..: 1543910/6760000 (22.84%)
Started: Mon Aug 22 17:39:32 2016
Stopped: Mon Aug 22 17:50:03 2016
real 10m30.744s
user 12m24.880s
sys 0m35.770s
'''
### Using GPUs and ASICs ("Better Hardware")¶
Cheapest Nvidia GPU (about 30 EUR net of VAT) reaches a MD5 hashing speed of about 400MH/s.
High-end Nvidia GPU cluster Brutalis reaches a MD5 hashing speed of about 200GH/s (cf. https://gist.github.com/epixoip/a83d38f412b4737e99bbef804a270c40).
Dedicated Application Specific Integrated Circuit (ASIC) chips reach even higher speed at much lower cost. AntMiner S5 achieves a speed of 1,155 GH/s for Bitcoin mining (SHA256). Used at Amazon for about 200 EUR.
## Signing Messages with Hashes and RSA Keys¶
Let us electronically sign a message The Python Quants send to someone else. To this end, we combine hashing with RSA encryption.
In [52]:
m = b'Hello FROM The Python Quants.' * 5
We generate a hash code for the message.
In [53]:
from Cryptodome.Hash import SHA256
In [54]:
h = SHA256.new(m)
In [55]:
hd = h.hexdigest()
hd
Out[55]:
'6d7e450cf23b6f867b03ac30e613c618fb5d91cdd56cdd9f79859dc12e6a4083'
We next sign the message, i.e. we encrypt the hash code with the private key from before.
In [56]:
from Cryptodome.Signature import PKCS1_v1_5
from Cryptodome.PublicKey import RSA
In [57]:
key = RSA.generate(2048)
signer = PKCS1_v1_5.new(key)
In [58]:
signature = signer.sign(h) # private key
signature
Out[58]:
b'|\x1c\x90\\O?ci\xc9\x9f^DCx\rY\x89\x03f6G\x81.O0\xb3,-\xfb\x86\xa5IB\x04\xf8\xa8\xe7u\xf8mV|pF\x07\xad\x8f\xcee\xd8\xa4X\xc2\xe2\xa4\x8c\x05\xc5\x91x\xba\x15%\xc63\x1b\xa48\xec\x17\xfa9\x05\xcd\x7f\\D\xae2\x8fQ\xcc\xedL\xa1\xe1\xba\xfb\x99j\x84\xf8C|\xa9\xff\x89\xe6[9\xa9q*\x05\x0f\xb7\x92^\x9a\x12\xf3\xc5?8.\xa208\xb3\x8d\xf0Z\xd49\x80\xe5\x08\xf9\xb4\xf3\x7f^\xa1.\\R[\xf33\xa9\x1agU:\xb7hv\xdap\x12m\x86z\xce\xcf\xa5\xaa2m,\xef3\xd2\xe5\x16\xfb(\x9b2\x87\xd6\x02\xc1\xc50\x9dW\x90"\xf7\x07\x9cEP\xef\xa5\xd9k\x97\xe5\xc6\xb6Q\xb8\x93\'\x17\xb3\xad\xae\xb5\x92G$\x815\xea\xb6\xa4\xcd;\xadT\xbf\xe4\xc7\xa9=4\xd6\x91I\x9a$\x95l\xdc\x08\x93\x01\xf9\x96\x12t\xd6\x8d}\xfb\xc1\xe5\xb1"s~s\x97\xd3\x9f\xbb@(\xcc\xf4\xd8\xc7'
Someone else — i.e. the receiver of our message — who knows our public key can now verify that we have signed the message as follows.
In [59]:
hashcode = SHA256.new(m)
hashcode.hexdigest()
Out[59]:
'6d7e450cf23b6f867b03ac30e613c618fb5d91cdd56cdd9f79859dc12e6a4083'
In [60]:
PKCS1_v1_5.new(key.publickey()).verify(hashcode, signature) # public key
Out[60]:
True
## Basic Idea Behind Block Chains¶
Let us now illustrate the basic idea behind a block chain based on a very simple example first. Recall the properties of hash functions that we require (collision resistence, hiding, puzzle friendliness). Let us focus on collision resistence and hiding for the moment.
As a starter, it is obviously easy to calculate the hash value of a string ("first block"), for instance, as follows:
In [61]:
import hashlib
In [62]:
b1 = 'Jil, 2004' # our first dog
h1 = hashlib.md5(b1.encode('ascii')).hexdigest() # hash for first block
h1
Out[62]:
'db29bc3f87a84f227d3b4bc7b19a3c6a'
It is highly unlikely that another input yields the same output. It is also really difficult ("almost impossible") to find the input given a certain ouput.
A block chain can be used to document events over time (e.g. transactions, new dogs). To this end, we take the hash code from the first block, add the second block information and calculate a new hash value:
In [63]:
b2 = h1 + ', Liz, 2009'
h2 = hashlib.md5(b2.encode('ascii')).hexdigest()
h2
Out[63]:
'db71b4766173bd93b965af8888262b51'
A third block is as easily added:
In [64]:
b3 = h2 + ', Phineas, 2011'
h3 = hashlib.md5(b3.encode('ascii')).hexdigest()
h3
Out[64]:
'7d00c38e077282a822ee91c69fccd547'
Our block chain now is:
In [65]:
print(b1)
Jil, 2004
In [66]:
print(b2)
db29bc3f87a84f227d3b4bc7b19a3c6a, Liz, 2009
In [67]:
print(b3)
db71b4766173bd93b965af8888262b51, Phineas, 2011
There is one major problem with this approach: the block chain is really easy to manipulate since you only need to re-calculate the whole chain. You have all the information needed.
We need add therefore one security measure to avoid manipulation (in theory): signing of the last hash value.
In [68]:
h3
Out[68]:
'7d00c38e077282a822ee91c69fccd547'
In [69]:
# signing
from Cryptodome.Hash import MD5
md5 = MD5.new(b3.encode('ascii'))
signature = PKCS1_v1_5.new(key).sign(md5) # private key
signature
Out[69]:
b'\x05!\x8c\x12vG\xdf7\x88]0|\xfd\r\x93\xa5\xecD\xaaf\xf4\xbc\xa8*\x95\xbb@\x90\x15%=\xce\x88\xdb R(\x03Ek\xcda\xfb\x06L\x9f\x8a\\\xdft]\x8d{\xe6\xabYv\xbc1-X\x0f\x13\xf2\x19T\xb3\xe2\xdf\x86;\x16P\x0c\xef\x81\x88\x9b\x83Z\xefr\x9d\xdf\xb5\x84\x8ai\xbe\xb2\x95t\x99\xe4g\xdb\xdb\xac\xd2g\xbd0\xcb\xf8\xdf\x94\x0e\xf9w\\\x9c\xbe\xc8\x007\x90\x94r\x05\x91:bre\x84\xdfL\x96\x99\x84y\x9a&w^p\xc5\xb9!\x8dff\x13c\x010x}b\xb3\x19\x1fQ\x96\xe3\x7f6!\x14:\xa1!\x82J\xeb\xe0\xda8kAr.\xe41\xbauNf9\xf9\xd5\xcf\xba\x16M|\xf7\xee\xdc\xd5\x11\x97\xf7Uh\xe6\xd4$XF\x86\x1f\xad2YQ:Q\x91\xd5\xd4\xc1$\x1a\xe6\xbf\xf8\xb2\x85\xfe\xc7\xdbD\x08}\xd1\xe2\xd2\xe5\x121\xdb\xa2\xf3\xac\x04|a\xa4_\xeeJ\x9c\xc7\x86\x9fb\x1a/ZqKI\xb9\xf2'
If we can make sure that the private key is safe, then the block chain plus the signature for the final hash value are "almost impossible" to manipulate — although all the information is publicly available.
In [70]:
b1, b2, b3, h3, signature
Out[70]:
('Jil, 2004',
'db29bc3f87a84f227d3b4bc7b19a3c6a, Liz, 2009',
'db71b4766173bd93b965af8888262b51, Phineas, 2011',
'7d00c38e077282a822ee91c69fccd547',
b'\x05!\x8c\x12vG\xdf7\x88]0|\xfd\r\x93\xa5\xecD\xaaf\xf4\xbc\xa8*\x95\xbb@\x90\x15%=\xce\x88\xdb R(\x03Ek\xcda\xfb\x06L\x9f\x8a\\\xdft]\x8d{\xe6\xabYv\xbc1-X\x0f\x13\xf2\x19T\xb3\xe2\xdf\x86;\x16P\x0c\xef\x81\x88\x9b\x83Z\xef`r\x9d\xdf\xb5\x84\x8ai\xbe\xb2\x95t\x99\xe4g\xdb\xdb\xac\xd2g\xbd0\xcb\xf8\xdf\x94\x0e\xf9w\\\x9c\xbe\xc8\x007\x90\x94r\x05\x91:bre\x84\xdfL\x96\x99\x84y\x9a&w^p\xc5\xb9!\x8dff\x13c\x010x}b\xb3\x19\x1fQ\x96\xe3\x7f6!\x14:\xa1!\x82J\xeb\xe0\xda8kAr.\xe41\xbauNf9\xf9\xd5\xcf\xba\x16M|\xf7\xee\xdc\xd5\x11\x97\xf7Uh\xe6\xd4$XF\x86\x1f\xad2YQ:Q\x91\xd5\xd4\xc1$\x1a\xe6\xbf\xf8\xb2\x85\xfe\xc7\xdbD\x08}\xd1\xe2\xd2\xe5\x121\xdb\xa2\xf3\xac\x04|a\xa4_\xeeJ\x9c\xc7\x86\x9fb\x1a/ZqKI\xb9\xf2')
Another idea is to make it hard to construct another block chain with the same inputs (but in different sequence) or other inputs that satisfies a certain property. Let us define that only hash values with five zeros at the end are allowed. To this end, we must allow for an additional input parameter.
In [71]:
%%time
n = 0
while True:
b = str(n) + ', ' + b1
md5 = hashlib.md5(b.encode('ascii')).hexdigest()
if md5[-5:] == '00000':
print(b + ' --> ' + md5)
break
n += 1
1300915, Jil, 2004 --> 34b87ffb902576b7f2fdeea557500000
CPU times: user 3.24 s, sys: 24.1 ms, total: 3.27 s
Wall time: 3.33 s
Someone wanting to manipulate the block chain must put in much more effort in this case than without such a requirement. The difficulty can easily be increased by requiring eg more trailing zeros.
In [72]:
%%time
n = 0
while True:
b = str(n) + ', ' + b1
md5 = hashlib.md5(b.encode('ascii')).hexdigest()
if md5[-6:] == '000000':
print(b + ' --> ' + md5)
break
n += 1
CPU times: user 36.4 s, sys: 210 ms, total: 36.6 s
Wall time: 37.1 s
The first security measure "signing" is vulnerable to stealing the private key (especially when multiple versions exist, e.g. due to backups). The second one "targeting" to sheer brute force. A combination of both, of course, works as well — and is probably more secure.
Another approach that adds some security is to use a random, publicly known, fixed initial hash.
In [73]:
import os
h0 = os.urandom(16).hex()
h0
Out[73]:
'd4683662482f68d7351e28a21c19a0fe'
In [74]:
b1 = h0 + ', Jil, 2004' # our first dog
h1 = hashlib.md5(b1.encode('ascii')).hexdigest() # hash for first block
h1
Out[74]:
'2654e14c495d442458ca9a7ed04fb0e9'
## Basic Idea Behind Mining¶
Bitcoin mining is based on SHA256 hash codes (cf. https://en.wikipedia.org/wiki/SHA-2)
In [75]:
sha256 = hashlib.sha256('yves'.encode('ascii'))
sha256.hexdigest()
Out[75]:
'9195c7b9bb56d375948ba058cddea1982b49864e12c700de58d69c5c72dbd075'
The idea behind mining is to find a hash code that is 'small enough', i.e. lies below a certain target level (mainly defined by 'leading zeros' in the target hex value).
In [76]:
target = '%064x' % (1000000000 << 200)
target
Out[76]:
'0000003b9aca0000000000000000000000000000000000000000000000000000'
The original hash code for python is not small enough.
In [77]:
target
Out[77]:
'0000003b9aca0000000000000000000000000000000000000000000000000000'
In [78]:
sha256.hexdigest() < target
Out[78]:
False
However, adding (a) certain number(s) to the string, yields a hash code small enough.
In [79]:
sh = hashlib.sha256(b'%dyves' % 23240167).hexdigest()
sh
Out[79]:
In [80]:
sh < target
Out[80]:
True
The following code simulates a mining procedure.
In [81]:
%%time
i = 0
while True:
sha256 = hashlib.sha256(b'%d' % i + b'yves')
if sha256.hexdigest() < target:
print('SUCCESS')
print(i, sha256.hexdigest())
# break
if i % 2500000 == 0:
print(i)
i += 1
if i > 55000000:
break
0
2500000
5000000
7500000
10000000
12500000
15000000
17500000
20000000
22500000
SUCCESS
25000000
SUCCESS
27500000
30000000
32500000
35000000
37500000
40000000
42500000
45000000
47500000
50000000
SUCCESS
50427211 000000099f6760417f3b2161a9ba9e989c62da1745d949267d5b648edaa21496
52500000
55000000
CPU times: user 2min 8s, sys: 874 ms, total: 2min 9s
Wall time: 2min 13s
The time to find a suitable hash code depends on the input string.
In [82]:
%%time
i = 0
while True:
sha256 = hashlib.sha256(b'%d' % i + b'yveshilpisch')
if sha256.hexdigest() < target:
print('SUCCESS')
print(i, sha256.hexdigest())
# break
if i % 2500000 == 0:
print(i)
i += 1
if i > 55000000:
break
0
2500000
5000000
7500000
10000000
12500000
15000000
17500000
20000000
22500000
25000000
27500000
30000000
32500000
35000000
37500000
40000000
42500000
45000000
47500000
50000000
52500000
55000000
CPU times: user 2min 9s, sys: 885 ms, total: 2min 10s
Wall time: 2min 13s
## Mining a Bitcoin Block¶
### The Mining Procedure¶
The following example is from http://www.righto.com/2014/02/bitcoin-mining-hard-way-algorithms.html and is about a 'real' bitcoin block and how to mine it wih Python.
In what follows we need the struct module (cf. https://docs.python.org/3/library/struct.html).
In [83]:
import struct
import binascii
import hashlib
The basic elements of a bitcoin block.
The elements translated into Python code. Cf. also https://en.bitcoin.it/wiki/Block_hashing_algorithm.
In [84]:
ver = 2
mrkl_root = b'871714dcbae6c8193a2bb9b2a69fe1c0440399f38d94b3a0f1b447275a29978a'
time_ = 0x53058b35 # 2014-02-20 04:57:25
bits = 0x19015f53 # difficulty
bits
Out[84]:
419520339
The following code snippets illustrate the derivation of the target value which is the upper limit for a successful hash code. Cf. https://www.codecademy.com/courses/python-intermediate-en-KE1UJ/0/1 for bitwise operations in Python.
In [85]:
ex = bits >> 24
ex
Out[85]:
25
In [86]:
mant = bits & 0xffffff
mant
Out[86]:
89939
In [87]:
hex(mant)
Out[87]:
'0x15f53'
In [88]:
8 * (ex - 3)
Out[88]:
176
The concrete values for the difficulty/target hash.
In [89]:
target_hexstr = '%064x' % (mant * (1 << (8 * (ex - 3))))
target_hexstr
Out[89]:
'00000000000000015f5300000000000000000000000000000000000000000000'
In [90]:
target_str = binascii.unhexlify(target_hexstr)
target_str # C struct
Out[90]:
b'\x00\x00\x00\x00\x00\x00\x00\x01_S\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00'
The nonce is the value which is to be added to the other block elements during the hash code generation. One looks for the nonce that gives a hash code smaller than the target level.
In [91]:
nonce = 850000000
In [92]:
# nonce = 856192328
# Block 286819
# check under https://blockexplorer.com
Finally, the Python code to do the mining activitiy. Basically, the nonce values gets increased by 1 during the look, a new hash code is generated and compared to the target level.
In [93]:
%%time
while nonce < 0x100000000:
+ binascii.unhexlify(prev_block)[::-1]
+ binascii.unhexlify(mrkl_root)[::-1]
+ struct.pack("<LLL", time_, bits, nonce))
if nonce % 200000 == 0:
print(nonce, binascii.hexlify(hs[::-1]))
if binascii.hexlify(hs[::-1]) < binascii.hexlify(target_str):
print(nonce, binascii.hexlify(hs[::-1]))
print('success')
break
nonce += 1
850000000 b'2d06d5717ef51ce987ec0f0e4823620f8d9d2d6556174103297a6099900a04c0'
850200000 b'879860b11769268f1e5ca7df9a763a7daf63911d2e25eb599db5bd295eba15ee'
850600000 b'ed546943a811deed9a2e37a74fda8a66b60d93f80db8f98d02fac8209c116862'
850800000 b'275944cb52b35cc3993bd286e3861afbc246c7de7ed274da917cc22d05cd2bf5'
851000000 b'2caff003e29dfc2ec7130a20d84118580a48d81627e0a766a6450a14404aa030'
851600000 b'58c3abc58a3fcccda18f205cc124bcfce61d244b46bb70161da040e346429b61'
851800000 b'4e0bc5299ef60ee2e542b3db8c17a1fc37b423d7d04a90b8afdca7d637a58879'
852000000 b'47c01a53e024c253601f54332790483091888c463d8b8647c8d6f7e078eafb9b'
852200000 b'53c762141e8c9d615dc50b9f3dbc7923d770e8909b1e9a2d3a07e4bb5bc4cbe1'
852400000 b'1bd5babc0d87efd848b56e09cf7cc46c95923864cc2924aa2a1c5fc71835ec21'
852600000 b'1906382ef5f88e718a0a3f511300278828b9e066f0f17538bb0a004789ce03f1'
853000000 b'4691fb160b2d339e2a54e95f81b891d46acd7f68754b0bd1f4b6942ca0c804ca'
853200000 b'61988103dd17e23ded0344340f3b0f264cb8d96132730cf48ebc34b06377a75b'
853400000 b'ee63a5132d8126c255f73d48e02eec5c7b3d3fb91c447a74aa13b9c982dbbbf6'
853600000 b'6cac0791a530a9e3b8b53d72cbaa2fb46c14c5e65d843e08ab656444bea9a9ea'
853800000 b'75ebeafea5b28c3121000dcf48e023aa829a2a2644afbe530d2b631ed8906bdf'
854000000 b'b261dbf2a4d3178730c06c7d37b3d3f104b9b0c8266cc0bf8ddcffb88ee3e620'
854200000 b'4e7174dc8891c4cf1e6e97dc62166961a289f88206bdd383ba0c31a027610e4f'
854400000 b'0da8de618a00dd0aa71af0ff3350cd78435f10b160a06dee0578caf5bcab38b9'
854600000 b'20e6560f3b64596d9632005d9464d83a3125eb2faef9e34349fd7409869fef51'
855000000 b'c56c40696263177bce80ee786c31f5d488d5bab570efb4abee25acb004088645'
855200000 b'96519548a733cc53746e0b07b62f7c0ebb1389a6c4cb8d30309b1f24d78eff26'
855400000 b'18379a22c13f193c9cdb0d5e6eccc2745bc0c95402162ca9721c0dc286c8d61d'
855600000 b'0233a14315cf2b61fce61b534d530c6087e805731bf52fd8f273a24c0806024c'
855800000 b'b0603f071da6f70c98dd66d59be05bc9da7e5a144a7cd4088eac3fccf85f2579'
success
CPU times: user 46.9 s, sys: 446 ms, total: 47.4 s
Wall time: 49.7 s
### Merkle Hash¶
The following are the hard-coded transaction hashes for the Bitcoin block under consideration (http://www.righto.com/2014/02/bitcoin-mining-hard-way-algorithms.html).
In [94]:
txHashes = [
"00baf6626abc2df808da36a518c69f09b0d2ed0a79421ccfde4f559d2e42128b",
"91c5e9f288437262f218c60f986e8bc10fb35ab3b9f6de477ff0eb554da89dea",
"46685c94b82b84fa05b6a0f36de6ff46475520113d5cb8c6fb060e043a0dbc5c",
"b8dc1b7b7ed847c3595e7b02dbd7372aa221756b718c5f2943c75654faf48589",
"25074ef168a061fcc8663b4554a31b617683abc33b72d2e2834f9329c93f8214",
"c67c79204e681c8bb453195db8ca7d61d4692f0098514ca198ccfd1b59dbcee3",
"41a06e53ffc5108358ddcec05b029763d714ae9f33c5403735e8dee78027fe74",
"cc2696b44cb07612c316f24c07092956f7d8b6e0d48f758572e0d611d1da6fb9",
"8fc508772c60ace7bfeb3f5f3a507659285ea6f351ac0474a0a9710c7673d4fd",
"62fed508c095446d971580099f976428fc069f32e966a40a991953b798b28684",
"b137e685df7c1dffe031fb966a0923bb5d0e56f381e730bc01c6d5244cfe47c1",
"b92207cee1f9e0bfbd797b05a738fab9de9c799b74f54f6b922f20bd5ec23dd6",
"48158deb116e4fd0429fbbbae61e8e68cb6d0e0c4465ff9a6a990037f88c489c",
"be64ea86960864cc0a0236bbb11f232faf5b19ae6e2c85518628f5fae37ec1ca",
"081363552e9fff7461f1fc6663e1abd0fb2dd1c54931e177479a18c4c26260e8",
"eb87c25dd2b2537b1ff3dbabc420e422e2a801f1bededa6fa49ef7980feaef70",
"c28a45cded020bf424b400ffc9cb6f2f85601934f18c34a4f78283247192056a",
"882037cc9e3ee6ddc2d3eba86b7ca163533b5d3cbb16eaa38696bb0a2ea1137e",
"9517c585d1578cb327b7988f38e1a15c663955ea288a2292b40d27f232fbb980",
"2c7e07d0cf42e5520bcbfe2f5ef63761a9ab9d7ccb00ea346195eae030f3b86f",
"534f631fc42ae2d309670e01c7a0890e4bfb65bae798522ca14df09c81b09734",
"87ac990808239c768182a752f4f71cd98558397072883c7e137efb49d22b9231",
"9b3e2f1c47d59a444e9b6dc725f0ac6baf160d22f3a9d399434e5e65b14eccb0",
"1dd07e92e20b3cb9208af040031f7cfc4efd46cc31ec27be20a1047965a42849",
"d0174db2c712573432a7869c1508f371f3a1058aeedddc1b53a7e04d7c56c725",
"b4a16f724cddb8f77ddf3d2146a12c4be13d503885eaba3518a03da005009f62",
"2aa706d75decbe57745e01d46f9f5d30a08dedaf3288cee14cc4948e3684e1d4",
"ee49c5f6a5129ccaf2abebbc1d6d07a402a600af6221476b89aafaa683ca95b7",
"f1e88ffc2b1de2aa4827002f06943ce5468735f7433f960bf01e75885b9f832b",
"19247d017e002fb9143d1a89eb921222a94f8a3d0faaf2e05b0f594989edc4c4",
"13f714ff62ee7d26b6d69ca980c141ebc54e9f71d2697083fe6c5efc1b02bd0f",
"0c78cbb8246572f015fbdc53dc9798fa54d1119ec77c1f07ac310bcbcc40dbf8",
"4bcde0ef92a6d24a2be7be50ac5e5299d776df2e6229ba5d475c2491da94f255",
"0cfd7d1058502730cf0b2ffa880c78ef534651e06832b5d87c0d7eb84eac5b0c",
"f9a555d817334397b402518d6fd959dc73d981ee7f5fe67969b63974ebbef127",
"24b52691f66eaed4ce391a473902e309018257c98b9f02aaa33b399c9e6f3168",
"9dbaeb485e51d9e25a5621dc46e0bc0aaf51fb26be5acc4e370b96f62c469b80",
"a6431d3d39f6c38c5df48405090752cab03bfdf5c77cf881b18a946807fba74a",
"a0583e358e42d77d18d1fd0533ff0a65615fc3b3112061ef92f168a00bf640c1",
"42ae900888d5e5dde59c8e3d06e13db9e84ef05d27726d4b67fd00c50cd9406a",
"154940777d3ff78f592ef02790131a59263c36b4958bbc836f9a767ea1a9f178",
"6a0337de6ac75eecf748306e8ebc5bfe5c811a1481ae50f6956a9e7f26a679f5",
"c99530c2148e09688d0b88795625943371183bf1f5d56c7446c6ed51ea133589",
"b2f3a559f605a158cc395126c3cf394a7e92a53b7514c75157e1dc43a6c7f93e",
"dffe06d1bea81f2a01c76786404bb867258f9e68013bf25454097ce935090738",
"0860159ec7a2a51ce107c182a988c40b4bc2057a734354a1219b6c65e72640ed",
"a405ff1bb51846b1867acc0b0da17f6f9616e592a0a7ff5ef3297c1ecfd60911",
"a7d451924263284765f6343bca8a21b79b89ebfe611c7355dd88e0ec1c29e232",
"41c758d08a4d3fe4d90645711589b832a2cd54dd25bd5b66e463e5d389a53aff",
"a05c1a93a521fa5dbc1790cfbb808893453a428a65f2c6b2d51249fbb12db309",
"90997920aa9786e10f513cfdd14e294feee6739cee1ab61b3fb1e3f42e7a915d",
"e05f9a668b37e5f78bd3b9d047f29f92b33a87f11dd48390410006f858188b7b",
"56dbc65895f7992da4a6985e7edba4d1c00879f1b28442c644c8a07658ceab27",
"5e9004fe262b829563d0804656ba68b1de1690401f08a1915273230d8c902fc0",
"1ea9ed3717523c5e304b7a7ac8058a87fb4f3fed8c6004769f226c9bb67e79c5",
"f0f1a4c009b3f1b2729e89898e2f5c0fcdc312edea5df884a9c897cb90e4c566",
"b5bb4ddf04863e6a60f33cb96c20dac8175d3bae55f335781503143c97a50e43",
"f14cc97a20c6f627b4b78301352ae35463bc359362589cd178a06c0fa90850b7",
"628801c8f614015c0fa0ccb2768cccc3e7b9d41ceed06071ce2534d31f7236d6",
"3be1013c8f8da150e2195408093153b55b08b037fd92db8bb5e803f4c2538aae",
"c9e1f8777685f54ba65c4e02915fd649ee1edcbf9c77ddf584b943d27efb86c3",
"4274e92ed3bd02eb101baa5fb8ff7b96236830762d08273749fbb5166db8ab0b",
"d6a29c948677fb1f71aaf16debc3d071a4dd349458eb9e056dce3a000ff853da",
"ba84bdb3d78367ca365016ac4bff9269576eb010f874c2967af73e0de5638de0",
"1546c79951e3b541bc64d1957b565b7a2850fc87192c7b374aee6cfc69b9805e",
"f119227d492ebe27fe9aae321980802454dfa64b2691efbe796c5075d5b07f62",
"b8cf13d64818b32f96bbb585998b1bc9505f6a94055488e5a71fee9479c6f2a9",
"1aaf459705b6afef2d7b83e3f181f1af55be0813daf55edce104cc59abc28ed7",
"61ac185c8f520b5e3134953dc52ff292a40e1e96b088dab259558a9d240ec02f",
"2da96e3154d7ec2329f787b73cb8a436b92d64cf3cc28e920d073279ea73b5f8",
"1c4d72ce733b971b9ec4e24f37d733355f6f2ea635cc67ffb3e22748484df446",
"2a6f89769f3272ac8c7a36a42a57627eca6b260ab2c76d8046a27d44d4034893",
"f8d11df51a2cc113698ebf39a958fe81179d7d973d2044322771c0fe63f4d7c9",
"f2287f17a4fa232dca5715c24a92f7112402a8101b9a7b276fb8c8f617376b90",
"bb5ee510a4fda29cae30c97e7eee80569d3ec3598465f2d7e0674c395e0256e9",
"647ab8c84365620d60f2523505d14bd230b5e650c96dee48be47770063ee7461",
"34b06018fcc33ba6ebb01198d785b0629fbdc5d1948f688059158f053093f08b",
"ff58b258dab0d7f36a2908e6c75229ce308d34806289c912a1a5f39a5aa71f9f",
"232fc124803668a9f23b1c3bcb1134274303f5c0e1b0e27c9b6c7db59f0e2a4d",
"27a0797cc5b042ba4c11e72a9555d13a67f00161550b32ede0511718b22dbc2c",
]
Function to generate the (pair-wise) Merkle hash.
In [95]:
# hash pairs of items recursively until a single value is obtained
def merkle(hashList):
if len(hashList) == 1:
return hashList[0]
newHashList = []
# process pairs; for odd length, the last is skipped
for i in range(0, len(hashList)-1, 2):
newHashList.append(hash2(hashList[i], hashList[i+1]))
if len(hashList) % 2 == 1: # odd, hash last item twice
newHashList.append(hash2(hashList[-1], hashList[-1]))
return merkle(newHashList)
def hash2(a, b):
# reverse inputs before and after hashing
# due to big-endian / little-endian nonsense
a1 = binascii.unhexlify(a)[::-1]
b1 = binascii.unhexlify(b)[::-1]
h = hashlib.sha256(hashlib.sha256(a1 + b1).digest()).digest()
return binascii.hexlify(h[::-1])
Finally, the Merkle hash code for the above transaction hashes as found in the block header.
In [96]:
print(merkle(txHashes))
b'871714dcbae6c8193a2bb9b2a69fe1c0440399f38d94b3a0f1b447275a29978a'
Python Quant Platform | http://quant-platform.com
Python for Finance | Python for Finance @ O'Reilly
Derivatives Analytics with Python | Derivatives Analytics @ Wiley Finance
Listed Volatility and Variance Derivatives | Listed VV Derivatives @ Wiley Finance
|
{}
|
# wordStem
0th
Percentile
##### Get the stem of words
This function extracts the stems of each of the given words in the vector.
##### Usage
wordStem(words, language = "porter")
##### Arguments
words
a character vector of words whose stems are to be extracted.
language
the name of a recognized language, as returned by getStemLanguages, or a two- or three-letter ISO-639 code corresponding to one of these languages (see references for the list of codes).
##### Details
This uses Dr. Martin Porter's stemming algorithm and the C libstemmer library generated by Snowball.
##### Value
A character vector with as many elements as there are in the input vector with the corresponding elements being the stem of the word. Elements of the vector are converted to UTF-8 encoding before the stemming is performed, and the returned elements are marked as such when they contain non-ASCII characters.
##### References
http://snowball.tartarus.org/
http://www.loc.gov/standards/iso639-2/php/code_list.php for a list of ISO-639 language codes.
• wordStem
##### Examples
# NOT RUN {
# Simple example
wordStem(c("win", "winning", "winner"))
# Test the supplied vocabulary
for(lang in getStemLanguages()) {
|
{}
|
# Evaluating limits
• Mar 6th 2013, 10:10 AM
asilvester635
Evaluating limits
Did I do it right? And will i need to find the value of C?
• Mar 6th 2013, 10:45 AM
Plato
Re: Evaluating limits
Quote:
Originally Posted by asilvester635
Did I do it right? And will i need to find the value of C?
That rationalization is incorrect. It is a cube root not a square root.
You need to use $\left( {\frac{{\sqrt[3]{{{{\left( {1 + cx} \right)}^2}}} + \sqrt[3]{{\left( {1 + cx} \right)}} + 1}}{{\sqrt[3]{{{{\left( {1 + cx} \right)}^2}}} + \sqrt[3]{{\left( {1 + cx} \right)}} + 1}}} \right)$
• Mar 6th 2013, 11:05 AM
asilvester635
Re: Evaluating limits
Do I foil the original numerator with the equation that you gave me?
• Mar 6th 2013, 12:27 PM
Plato
Re: Evaluating limits
Quote:
Originally Posted by asilvester635
Do I foil the original numerator with the equation that you gave me?
I have no idea what FOIL means. Is it some term from some dumb math-ed class?
Just learn to do basic algebra.
Surely you know that $a^3-b^3=(a-b)(a^2+ab+b^2)~!$
$\left( {\frac{{\sqrt[3]{{1 + cx}} - 1}}{x}} \right)\left( {\frac{{\sqrt[3]{{{{\left( {1 + cx} \right)}^2}}} + \sqrt[3]{{\left( {1 + cx} \right)}} + 1}}{{\sqrt[3]{{{{\left( {1 + cx} \right)}^2}}} + \sqrt[3]{{\left( {1 + cx} \right)}} + 1}}} \right) = \frac{c}{{\sqrt[3]{{{{\left( {1 + cx} \right)}^2}}} + \sqrt[3]{{\left( {1 + cx} \right)}} + 1}}$
• Mar 6th 2013, 06:58 PM
asilvester635
Re: Evaluating limits
Sorry ahh BOSS! Got it from yo mama haha
|
{}
|
# How exactly did the floor of an Apollo LM look like after EVA(s)? Seeking photo!
Five years ago I posted a question entitled "How was dust-mitigation addressed during the Apollo program?". While the question was answered rather comprehensively, it left me even more curious. The one thing I really wanted to see never showed up: Just one close-up photo of the floor of the LM or its hatch after EVA, no matter how bad, blurred or fuzzy it was.
How exactly did
## the floor of an Apollo Lunar Module
look like after EVA(s) during an actual Apollo mission (before or during launch from the Lunar surface into Lunar orbit)?
Besides, by any chance, how did the hatch and its sealing look like? I'd figure all of it was all pretty dusty ...
## I am looking for at least one actual photo!
The numbering of a lot of photos in the publicly available online archives suggests that not all actually excising photos were uploaded. It's always a selection of photos above a certain quality threshold, discontinuously numbered. It suggests that there is a lot of footage like totally fuzzy or "wiggly" shots which has not been uploaded into those online archives. Besides, there were always "incomplete" shots (due to stray light hitting the film while putting it into a camera etc) at the beginning of "analogue" film reels, which were usually just "discarded" by aiming at random targets for like one or two shots before taking any meaningful photographs. Where did those discarded and/or low-quality shots end up?
(Other than literally going through all publicly available photos, I have a feeling that the "second best" option is to actually ask one of the surviving astronauts who could have theoretically shot such a photo.)
• All pictures taken by the Apollo astronauts should be accessible on a NASA server. Finding proper search criterias may be difficult. Viewing many hundreds of images to find one of the Apollo LM floor may take hours. Success is not guaranteed. – Uwe May 15 '18 at 20:36
• This results in another question: Apollo LM EVA checklist, was there a step of visual inspection of the hatch seal and cleaning if necessary? – Uwe May 15 '18 at 20:45
• @Uwe I'd suppose there must have been. Good idea, let's dig into the checklists. – s-m-e May 15 '18 at 21:06
• Thinking about it ... how about actually asking one of the surviving astronauts who could have shot such a photo? It could have happened by accident, who knows. – s-m-e May 20 '18 at 18:29
• I think all Apollo astronauts did know how important the hatch and its sealing was for the success of the mission. Therefore they avoided transfer of dust to the hatch and its seal. There might have been a protective cover of the sealing when the hatch was open. – Uwe May 20 '18 at 20:33
Looking through the images on the Apollo Archive, which I believe to contain all publicly available images and checking the ones at the end of EVAs I was not really able to find anything satisfactory. The best ones were before lunar takeoff of Apollo 17
None of them directly shows the floor however. The second one shows a little compartment for the helmets. In general everything seems dirty, but not directly dusty/sandy.
## AS17-134-20530
• Great choice of photos. – Organic Marble May 16 '18 at 0:28
• This is how far I have got so far, too :) Thanks. – s-m-e May 16 '18 at 5:39
• @OrganicMarble It is not a choice of photos. It is all the photos inside the LM on the moon after the first EVA, that are not aimed out of a window – Hans May 16 '18 at 6:26
• I did a Google image search and came up with basically the same images. There's a good chance no photos were made of the floor. – Hobbes May 21 '18 at 11:10
• @Hobbes I was able to find one picture inside the LM during Apollo 11 that contained a small piece of the floor, but it was taken prior to landing. – called2voyage May 22 '18 at 18:49
How exactly did the floor of an Apollo Lunar Module look like after EVA(s) during an actual Apollo mission (before or during launch from the Lunar surface into Lunar orbit)?
Besides, by any chance, how did the hatch and its sealing look like? I'd figure all of it was all pretty dusty ... I am looking for at least one actual photo!
First to show floor during a mission.
Apollo 16 - Back in the Briar Patch - Before exiting, clean floor.
Accompanying text: "119:00:40 Young: Got to get my PLSS antenna, right?
[John is about to start the intricate process of getting out the hatch. The small area available to the crew at the front of the cabin is best illustrated by images taken during final Apollo 16 (LM 11, Orion) and Apollo 17 (LM 12, Challenger) LM close-out on the pad at the Cape prior to launch.]
[A view from above shows the LMP's PLSS (without the OPS) and two helmet bags (containing the LEVAs) filling the space. As detailed on pages LV-4 and 5 in the Lunar Module News Reference, the useable floor area measures about 55 inches (140 cm) from side to side and about 36 inches (91 cm) from the hatch to the base of the 18-inch (46 cm) 'midstep' behind the crew stations. Note that the PLSS dimensions are about 26 inches (66 cm) long, 19 inches (48 cm) wide, 9.5 (24 cm) inches thick at the base, and 8.75 (22 cm) inches thick at the top. The photographer was standing on the midstep, with its edge near the bottom of the frame.]"
"AS11-36-5385 (OF300) ( 84k or 868k )
About 055:41. Neil floats in the tunnel connecting the LM And CM, using the TV to document Buzz doing a LM inspection. This photo was, of course, taken by Mike Collins. With regard to the TV camera, Journal Contributor Markus Mehring writes, "What you're seeing here is an extra TV monitor attached to the cam with the ever-present gray tape. Early crews had no such monitor or other means of image control and complained about their inability to easily/properly point the camera inside the cramped quarters of their spacecraft, so this was what they were granted. The camera is the Westinghouse color model, essentially the same model that suffered the burnout on A12, only that this one is IVA-black while the A12 camera was EVA-white. Also note that the camera is actually held upside-down (that is, we're seeing its top side), to capture the CM interior in proper alignment for the TV audience." Karl Dodenhoff has provided a labeled version."
"AS11-36-5386 (OF300) ( 74k or 785k )
Similar to 5385. Buzz's feet are visible on the floor of the LM, beyond the tunnel."
"AS11-36-5396 (OF300) ( 102k or 796k )
Buzz in the LM. The ISA is visible behind him. Out of focus.".
https://www.hq.nasa.gov/alsj/a11/AS11-36-5399HR.jpg
"AS11-36-5399 (OF300) ( 116k or 880k )
Taken 'upside down', this shows Buzz's hands and the lower portion of the ISA, still in its Earth launch stowage configuration. Also visible are the LM Front Hatch, the LMP PLSS and two Helmet Bags."
Above Photos Source: https://www.hq.nasa.gov/alsj/a11/images11.html
Other views:
I noticed one answer didn't show the floor, here's a good look at it.
An annotated diagram and photos long after the mission, still looking for during the mission photos:
Here's Apollo 15, Falcon's floor with a bit of dirt everywhere.
Conversation describing the dust after EVA: Apollo 11 - Trying to Rest
"114:31:27 McCandless: Roger. Very good. And, I've got a consumables update for you if you're ready to copy or listen. Over.
114:31:38 Armstrong: Stand by. (Pause)
[I asked if they could hear any stuffiness in their voices, thinking of Jack Schmitt's allergic reaction to lunar dust.]
[Aldrin - "It wasn't a very restful evening. How long have we been up?"]
[They were awakened at 93:40 and, so, have been up for nearly 21 hours.]
[Armstrong - "And temperature control was a bit of a problem for us and it could be that cabin temperature was contributing to something."]
[I then told them about Jack Schmitt's apparent allergic reaction to lunar dust after the first Apollo 17 EVA - but not after the later ones.]
[Armstrong - "I can't say that I recall it."]
[Aldrin - "There wasn't any particular odor."]
[Armstrong - "Yeah, I remember commenting that we had the scent of wet ashes. Something like that."]
[Aldrin - "There was a hint of something. A slight metallic...That's hard to remember. But it wasn't a real objectionable one."]
[Armstrong - "Yeah."]
[Aldrin - "Like it was going to catch fire."]
[Other crews described the smell as being similar to expended gunpowder. I asked if the dirt they tracked in settled to the floor pretty quickly.]
[Armstrong - "There wasn't a whole lot floating around in the cabin. Although we did tromp some in. There's no question about that."]
[I asked if they'd noticed any film of dust on the instruments. And neither of them remembered any.]
[Armstrong - "When we got back up to zero-g, some of the stuff did come up."]
114:31:43 Aldrin: Okay. Go ahead (with the consumables update)."
Another conversation:
"[Armstrong, from the 1969 Technical Debrief - "We cleaned up the cockpit and got things pretty well in shape. This took us a while, and we planned to sleep with our helmets and gloves on for a couple of reasons. One is that it's a lot quieter with your helmets and gloves on, and then we wouldn't have any mental concern about the ECS and so on having two loops working for us there."]
[Aldrin, from the 1969 Technical Debrief - "We wouldn't be breathing all that dust."]
[Armstrong, from the 1969 Technical Debrief - "That was another concern. Our cockpit was so dirty with soot, that we thought the suit loop (filtered oxygen going directly from the ECS to the suit and then back again) would be a lot cleaner."]
[Aldrin, from the 1969 Technical Debrief - "I guess the question is: can you keep it cleaner? I guess you could keep it a little cleaner, but there are so many things going in and out that it's almost impossible to avoid getting a significant amount of lunar material in there."]
[The Apollo 12 crew had an even worse problem with dust and, for the remaining missions, the solutions that seemed to help were (1) dusting each other off as thoroughly as possible with a house-paint-sized brush before going up the ladder; (2) stomping their feet on the ladder to get more dust off the boots and lower legs; and (3) putting the suit legs into spare jettison bags between the EVAs.]
[Armstrong, from the 1969 Technical Debrief - "A couple of comments with respect to going to sleep in the LM. One is that it's noisy; and two is that it's illuminated. We had the window shades up (that is, covering the windows) and light came through those window shades like crazy. They're like (photographic) negatives and a lot of light will shine through."]"
Another conversation about dust: Apollo 17 - Post-EVA-3 Activities
"170:49:32 Schmitt: Come on, now.
[Once they get hooked up to the LM ECS and get their PLSSs off, they will put their gloves back on so that they can depressurize the cabin, open the hatch, and jettison the PLSSs and other unneeded gear.]
170:49:34 Cernan: I have never seen so much dirt and dust in my whole life. Ever. (Pause) Ron's not going to be able to see through either one of these helmet visors. (Laughs) Yes, he will.
[Schmitt - "There was dust on everything we wore. Gene succeeded in falling and I did too - several times. The helmets had a lot of dust on them, and I suspect we got them pretty badly scratched. I don't remember the scratches very well, but we did talk about it a couple of times. However, the dust we brought in was almost all on the floor; it didn't come up and permeate the LM until we went weightless after lift-off. And then there was a lot of it. After the EVAs, there was dust flying around because, at least on the first EVA, I had a reaction to breathing it; but I don't remember there being a noticeable film of it on the instruments or anything else."]
[A 2005 Ulrich Lotzmann photo ( 202k ) of Jack's LEVA with the sun visor down shows some of the scratches.]
["What Gene was saying about Ron is that we had to take one of the helmet covers (that is, one of the LEVAs) up to him so he could use it on his EVA to retrieve the film packets from the Scientific Instrument Bay (in the Service Module). Ron would never have admitted to anything (like a scratched visor) that would have kept him from doing his EVA. That was his next big thing; that's what he was really looking forward to."]
[Cernan - "Once we got to orbit, I don't think the dust was as bad as I was afraid it would be. We were concerned and were thinking about wearing our helmets to keep the dust out through the whole lift-off and rendezvous. We did wear them for lift-off, but I don't think we did for rendezvous."]
170:49:52 Cernan: But they sure do get scratched, if you're not careful. (Pause) Okay. (Long Pause) I think it's harder getting them (the gloves) off, these days, than it is getting them on. (Pause)"
s-m-e: "The one thing I really wanted to see never showed up: Just one close-up photo of the floor of the LM or its hatch after EVA, no matter how bad, blurred or fuzzy it was." ... "Besides, by any chance, how did the hatch and its sealing look like? I'd figure all of it was all pretty dusty ...".
CM Hatch open, view of seal.
"... During the Apollo 16 extravehicular activity, the Microbial Ecology Evaluation Device (MEED) was removed from its protective stowage bag in the crew compartment. A 2.54 meter (8 foot 4 inch) tether was attached externally to the MEED flight assembly, the assembly was mounted on the campole, and the hardware was secured to the inside of the spacecraft. The campole and MEED assembly were then installed into a fitting mounted on the opened hatch door of the command module (CM). A small attitude adjustment of the CM was required to place the appropriate surfaces of the opened MEED assembly directly perpendicular to the rays of the sun.".
Purported to be a photo of the Apollo 13 LM hatch, seal, and floor.
Photo from uncertain source #1 and #2:
Text associated with the photo:
Source #1: "Fig. 2 - View from the interior of LM-13 outward through the forward hatch."
Source #2: "voidol 16.10.2010 um 20:33
ehemaliges Mitglied Die Pravda ist totaler Schrott!
jeremybrood schrieb:
astronauts couldn't squeeze through a narrow tunnel between the space ship and the module
Wieso sollen sie da nicht durchkommen? Ist ja nur die Verbindung zwischen LEM und CM, und sie haben auf dem Mondflug auch nicht Ferreris "Das große Fressen" gedreht:".
[Google Translate]: "Why should not they get through this? It's just the link between LEM and CM, and they did not shoot Ferreri's "The Big Food" on the moon flight:".
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{}
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Journal article Open Access
# Environmental Magnetic Fields Inhibit the Antiproliferative Action of Tamoxifen and Melatonin in a Human Breast Cancer Cell Line
Harland, Joan D.; Liburdy, Robert P.
### Citation Style Language JSON Export
{
"DOI": "10.1002/(sici)1521-186x(1997)18:8<555::aid-bem4>3.0.co;2-1",
"author": [
{
"family": "Harland, Joan D."
},
{
"family": "Liburdy, Robert P."
}
],
"issued": {
"date-parts": [
[
1997,
1,
1
]
]
},
"abstract": "We have previously reported that environmental-level magnetic fields (1.2 microT [12 milligauss], 60 Hz) block the growth inhibition of the hormone melatonin (10(-9) M) on MCF-7 human breast cancer cells in vitro. We now report that the same 1.2 microT, 60 Hz magnetic fields significantly block the growth inhibitory action of pharmacological levels of tamoxifen (10(-7) M). In biophysical studies we have taken advantage of Faraday's Law of Current Induction and tested whether the 1.2 microT magnetic field or the associated induced electric field is responsible for this field effect on melatonin and tamoxifen. We observe that the magnetic field component is associated with the field blocking effect on melatonin and tamoxifen function. To our knowledge the tamoxifen studies represent the first experimental evidence for an environmental-level magnetic field modification of drug interaction with human breast cancer cells. Together, these findings provide support to the theory that environmental-level magnetic fields can act to modify the action of a drug or hormone on regulation of cell proliferation. Melatonin and tamoxifen may act through different biological pathways to down-regulate cell growth, and further studies are required to identify a specific biological site of interaction for the 1.2 microT magnetic field.",
"title": "Environmental Magnetic Fields Inhibit the Antiproliferative Action of Tamoxifen and Melatonin in a Human Breast Cancer Cell Line",
"type": "article-journal",
"id": "1235522"
}
611
86
views
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{}
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# zsdd: Zero-Suppressed and Reduced Decision Diagrams
[ bsd3, data, library ] [ Propose Tags ]
This package provides an efficient representation of propositions and families of sets as directed acyclic graphs. Internally this is a Free monad with shared subterms. All operations are linear in the size of the diagram, but the size of the diagram is also proportional to the number of operations.
There are two reduction stratergies Simple and ZeroSup. The former is generic and widely applicable, whereas the latter is specialised to sparse formulas. Sparse formulas are those with few models or where most atoms are false. A typical use cases of this mode is when modelling families of sets.
## Modules
[Index] [Quick Jump]
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{}
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# Where is the problem in this proof that deciders are no stronger than LBAs?
So I've been working on a problem for fun and I'm worried I've run into some sort of contradiction, so I'm trying to figure out where I went wrong. I've simplified the issue down to this:
Decider acceptance can be reduced to LBA acceptance
Part 1: A decider can be reduced to a decider with an empty input alphabet.
1. Let $$D$$ be a decider with input alphabet $$\Sigma$$ and $$\omega$$ be an input string in $$\Sigma^*$$
2. Construct a decider $$D_0$$ with an empty input alphabet and the same tape alphabet as $$D$$, which starts by writing the characters of $$\omega$$ to the tape, returns to the left side, and then executes identically to $$D$$
3. $$D_0$$ accepts the empty string $$\epsilon$$ iff $$D$$ accepts $$\omega$$
Part 2: A decider with an empty input alphabet can be reduced to an LBA
1. Let $$D_0$$ be a decider with an empty input alphabet
2. $$D_0$$ halts in finite time, and therefore uses finite portion of the tape of size $$m$$
3. Construct an LBA $$A$$ with the same states, symbols, and transitions as $$D_0$$ where the length of the tape is given by linear function $$f(x)=x+m$$
4. The only possible input is $$\epsilon$$, so the size of the tape will be $$m$$, so $$A$$ will execute identically to $$D_0$$ and not go out of bounds
5. $$A$$ accepts $$\epsilon$$ iff $$D_0$$ accepts $$\epsilon$$
This seems to prove that a decider can be reduced to an LBA, which is well known to be incorrect. I have a couple of guesses for where the error might be:
• It could be in part 1, if you can't call a machine without input as powerful as a machine with input. After all, the only languages $$D_0$$ could accept are $$\emptyset$$ and $$\{\epsilon\}$$, which are both regular, not recursive. So you can't say that an input-less decider accepts the same set of languages as a decider, but maybe it's as "powerful" in a more abstract sense?
• It could be in part 2, with the main problem being that computing $$m$$ would require running the decider, so the reduction to the LBA would be just as difficult as the acceptance problem. In other words, does the information you have prior to running automata change how powerful you can consider the automata to be?
Basically, I'm wondering if either of these concerns is the actual issue or if it's something else. And if either of these concerns isn't actually an issue, could you explain why? Thanks!
Edit: As pointed out, I should've represented these as decision problems, so part 1 would be a reduction from $$\{(D,\omega) | D\textrm{ is a decider that accepts } \omega\}$$ to $$\{D_0 | D_0 \textrm{ is an inputless decider that accepts}\}$$ and part 2 a reduction to $$\{A | A\textrm{ is an inputless LBA that accepts}\}$$. I believe the first two of these problems are recursive and the third is context-sensitive, so the first reduction is possible but the second isn't, due to $$m$$ not being computed.
• You won't be able to compute $m$. Dec 24 '20 at 7:59
• If the input alphabet is empty then nothing at all can be written onto a tape, since there are no symbols that one could write. My best interpretation is that you mean "empty input" instead of "empty input alphabet". Sep 20 at 18:16
But also note that the definition of the function $$f(x)=x+m$$ is a bit strange, since on an empty input alphabet, you always have $$x=0$$.
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Polish / polski Generalized Linear Mixed Effects (GLIMMIX) models are generalized linear models with random effects in the linear predictors. Choosing among generalized linear models applied to medical data. Enable JavaScript use, and try again. These are known as Generalized Linear Mixed Models (GLMM), which will not be discussed in this text. For generalized linear mixed models, the estimation is based on linearization methods (pseudo-likelihood) or on integral approximation by adaptive quadrature or Laplace methods. Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences provides readers with an understanding and appreciation for the design and analysis of mixed models for non-normally distributed data. Generalized Linear Mixed Effects Models¶. The pattern in the normal Q-Q plot in Figure 20.2B should discourage one from modeling the data with a normal distribution and instead model the data with an alternative distribution using a Generalized Linear Model. Bulgarian / Български partR2 also estimates structure coefficients as the Greek / Ελληνικά Croatian / Hrvatski Where A simulated data set contains information about patients being treated for cancer, their doctors (who cared for multiple patients), and whether or not each patient was in remission following treatment by their doctor. [8], Learn how and when to remove this template message, Journal of the American Statistical Association, "A unifying approach to the estimation of the conditional Akaike information in generalized linear mixed models", https://en.wikipedia.org/w/index.php?title=Generalized_linear_mixed_model&oldid=987297210, Articles needing expert attention with no reason or talk parameter, Articles needing expert attention from July 2017, Statistics articles needing expert attention, Articles needing additional references from July 2017, All articles needing additional references, Creative Commons Attribution-ShareAlike License. German / Deutsch Mixed models account for both sources of variation in a single model. In statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. and Fitting GLMMs via maximum likelihood (as via AIC) involves integrating over the random effects. Let’s move on to R and apply our current understanding of the linear mixed effects model!! •Generalized Linear Mixed Models (GLMM), normal or non-normal data, random and / or repeated effects, PROC GLIMMIX •GLMM is the general model with LM, LMM and GLM being special cases of the general model. French / Français If you are just starting, we highly recommend reading this page first Introduction to GLMMs . Hilborn, R. (1997). Both Repeated Measures ANOVA and *Linear* Mixed Models assume that the dependent variable is continuous, unbounded, and measured on an interval scale and that residuals will be normally distributed. (1998). Generalized Linear Mixed Models (illustrated with R on Bresnan et al.’s datives data) Christopher Manning 23 November 2007 In this handout, I present the logistic model with fixed and random effects, a form of Generalized Linear Mixed Model (GLMM). Slovenian / Slovenščina 28). Generalized linear mixed models (or GLMMs) are an extension of linearmixed models to allow response variables from different distributions,such as binary responses. Portuguese/Brazil/Brazil / Português/Brasil The material is complete enough to cover a course in a Ph.D. program in statistics. Generalized linear models(GLMs) represent a class of fixed effects regression models for several types of dependent variables (i.e., continuous, dichotomous, counts). The explosion of research on GLMMs in the last decade has generated considerable uncertainty for practitioners in ecology and evolution. {\displaystyle \beta } "This book is an up to date description of linear mixed models, LMM, and generalized linear mixed models, GLMM. In statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. Estimating and interpreting generalized linear mixed models (GLMMs, of which mixed effects logistic regression is one) can be quite challenging. The package iteratively removes predictors of interest 38 and monitors the change in R2 as a measure of the amount of variance explained uniquely by a 39 particular predictor or a set of predictors. 4, 2013): GLMMs provide a broad range of models for the analysis of grouped data, since the differences between groups can be modelled as a random effect. Czech / Čeština Scripting appears to be disabled or not supported for your browser. disregarding by-subject variation. Generalized Models •The term generalizedrefers to extending linear model theory to Danish / Dansk We also did a generalized linear mixed model which allowed us to model response distributions that were different from normal, in this case a plasan distributed response which were the errors made during the text entry study. β Italian / Italiano , is distributed according to an exponential family.[5]. The table below provides a good summary of GLMs following Agresti (ch. u X 37 (generalized) linear mixed-effect model fits. has no general closed form, and integrating over the random effects is usually extremely computationally intensive. [6] For example, the penalized quasi-likelihood method, which essentially involves repeatedly fitting (i.e. y (with no random effects) for the TV, phone and internet service types. The ecological detective: confronting models with data (Vol. Medical researchers can use a generalized linear mixed model to determine whether a new anticonvulsant drug can reduce a patient's rate of epileptic seizures. Recent texts, such as those by McCulloch and Searle (2000) and Verbeke and Molenberghs (2000), comprehensively review mixed-effects models. As linear model, linear mixed effects model need to comply with normality. Matlab also provides a function called "fitglme" to fit GLMM models. And neither should be confused with Generalized Linear Mixed Models, abbreviated GLMM. The Akaike information criterion (AIC) is a common criterion for model selection. Thai / ภาษาไทย For this reason, methods involving numerical quadrature or Markov chain Monte Carlo have increased in use, as increasing computing power and advances in methods have made them more practical. Generalized Linear Mixed Models: Modern Concepts, Methods and Applications presents an introduction to linear modeling using the generalized linear mixed model (GLMM) as an overarching conceptual framework. Generalized linear mixed models (GLMMs) provide a more flexible approach for analyzing nonnormal data when random effects are present. Norwegian / Norsk Generalized linear mixed models extend linear mixed models, or hierarchical linear models, to accommodate noncontinuous responses, such as binary responses or counts. Search in IBM Knowledge Center. The linear mixed-effects models (MIXED) procedure in SPSS enables you to fit linear mixed-effects models to data sampled from normal distributions. , the dependent variable, It is the only publication of its kind directed specifically toward the agricultural and natural resources sciences audience. Generalized linear mixed models (GLMMs) provide a more flexible approach for analyzing nonnormal data when random effects are present. The MIXED procedure fits models more general than those of the Kazakh / Қазақша Turkish / Türkçe {\displaystyle u} {\displaystyle u} via Gauss–Hermite quadrature), methods motivated by Laplace approximation have been proposed. {\displaystyle Z} {\displaystyle y} Finnish / Suomi Explore our Catalog Join for free and … Z Various approximate methods have been developed, but none has good properties for all possible models and data sets (e.g. doubly iterative) a weighted normal mixed model with a working variate,[7] is implemented by various commercial and open source statistical programs. {\displaystyle X} English / English statsmodels currently supports estimation of binomial and Poisson GLIMMIX models using two Bayesian methods: the Laplace approximation to the posterior, and a variational Bayes approximation to the posterior. Generalized Linear Mixed Models (GLMM) have attracted considerable attention over the last years. Mixed models in R For a start, we need to install the R package lme4 (Bates, Maechler & Bolker, 2012). Korean / 한국어 Lindsey, J. K., & Jones, B. Generalized linear mixed models: a practical guide for ecology and evolution. The explosion of research on GLMMs in the last decade has generated considerable uncertainty for practitioners in ecology and evolution. These models are useful in the analysis of many kinds of data, including longitudinal data. Alternatively, you could think of GLMMs asan extension of generalized linear models (e.g., logistic regression)to include both fixed and random effects (hence mixed models). In addition to numerically approximating this integral(e.g. Hungarian / Magyar and Neat, init? Swedish / Svenska Romanian / Română u are the fixed effects design matrix, and fixed effects; Overview of Generalized Nonlinear Models in R Linear and generalized linear models Examples: I binary logistic regressions I rate models for event counts I log-linear models for contingency tables (including multinomial logit models) I multiplicative models for durations and other positive measurements I hazard models for event history data etc., etc. Repeated measurements from the same patient are typically positively correlated so a mixed model with some random effects Generalized Linear Mixed Effects models. Serbian / srpski Generalized linear mixed models (GLMMs) are an extension to GLMs that includes random effects in the linear predictor, giving an explicit probability model that explains the origin of the correlations. In The Craft of Statistical Analysis free webinar, Introduction to Generalized Linear Mixed Models, we can see an example of this. Yin Chen, Yu Fei, Jianxin Pan, Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects, Open Journal of Statistics, 10.4236/ojs.2015.56059, 05, 06, (568-584), (2015). Hebrew / עברית IBM Knowledge Center uses JavaScript. Generalized linear mixed-effects (GLME) models describe the relationship between a response variable and independent variables using coefficients that can vary with respect to one or more grouping variables, for data with a response variable distribution other than normal. Arabic / عربية Estimates of AIC for GLMMs based on certain exponential family distributions have recently been obtained. The contribution of this book is that of pointing and developing the inference and estimation issues for non-Gaussion LMMs." In general, those integrals cannot be expressed in analytical form. Such models are useful when the data are clustered in some way, a canonical example in education being students nested in … It very much depends on why you have chosen a mixed linear model (based on the objetives and hypothesis of your study). [1][2][3] They also inherit from GLMs the idea of extending linear mixed models to non-normal data. Portuguese/Portugal / Português/Portugal 8.1.2 Generalized Linear Mixed Models (GLMM) You can marry the ideas of random effects, with non-linear link functions, and non-Gaussian distribution of the response. And, oh yeah, GeneralizedLinear Models are an extension of GeneralLinear Models. Spanish / Español A pseudo-likelihood estimation procedure is developed to fit this class of mixed models based on an approximate marginal model for the mean response. Bosnian / Bosanski There are, however, generalized linear mixed models that work for other types of dependent variables: categorical, ordinal, discrete counts, etc. If our data deviates too much we need to apply the generalized form, which is available in the package lme4: install.packages("lme4") library(lme4) Dutch / Nederlands Generalized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. Russian / Русский For readers new to linear models, the book helps them see the big picture. The word “Generalized” refers to non-normal distributions for the response variable, and the word “Mixed” refers to random effects in addition to the usual fixed effects of regression analysis. Thegeneral form of the model (in matrix notation) is:y=Xβ+Zu+εy=Xβ+Zu+εWhere yy is … [4], GLMMs are generally defined as such that conditioned on the random effects, Search ungrouped binary data are particularly problematic). Japanese / 日本語 They also inherit from GLMs the idea of extending linear mixed models to non-normal data. The generalized linear models (GLMs) are a broad class of models that include linear regression, ANOVA, Poisson regression, log-linear models etc. This page was last edited on 6 November 2020, at 03:27. This can be accomplished in a single run of generalized linear mixed models by building a model without a random effect and a series of 2-way interaction as fixed effects with Service type as one of the elements of each interaction. Slovak / Slovenčina It’s extra confusing because their names are so similar on top of having the same abbreviation. Trends in ecology & evolution, 24(3), 127-135. are the random effects design matrix and random effects. A useful extension of the generalized linear model involves the addition of random effects andlor correlated errors. Catalan / Català Vietnamese / Tiếng Việt. Chinese Simplified / 简体中文 Chinese Traditional / 繁體中文 Macedonian / македонски Princeton University Press. General Linear Modeland Generalized Linear Model. Exponential family distributions have recently been obtained current understanding of the generalized linear mixed models ( mixed procedure... Of this book is that of pointing and developing the inference and estimation issues for non-Gaussion LMMs ''! Top of having the same abbreviation with random effects are present expressed in analytical.... Been obtained good summary of GLMs following Agresti ( ch their names are so similar on top of the... Among generalized linear mixed effects model! the last years, GeneralizedLinear are... Example, the book helps them see the big picture GeneralizedLinear models are an extension GeneralLinear! A function called fitglme '' to fit GLMM models quasi-likelihood method, which essentially involves repeatedly fitting i.e... In SPSS enables you to fit this class of mixed models ( GLMMs, of which mixed effects Models¶ move! Likelihood ( as via AIC ) is a common criterion for model selection, GeneralizedLinear models are linear... We highly recommend reading this page first Introduction to GLMMs the addition of random effects the! In addition to numerically approximating this integral ( e.g integral ( e.g a single model 6 ] for,... Has good properties for all possible models and data sets ( e.g model need comply. Which will not be discussed in this text correlated errors term generalizedrefers to extending linear mixed,... Extension of GeneralLinear models are so similar on top of having the same.! Of many kinds of data, including longitudinal data models with data Vol. Correlated errors has good properties for all possible models and data sets (.... Maximum likelihood ( as via AIC ) involves integrating over the last years in analytical form detective confronting! Numerically approximating this integral ( e.g you are just starting, we highly recommend reading this page first Introduction GLMMs. Specifically toward the agricultural and natural resources sciences audience via Gauss–Hermite quadrature ), methods motivated by Laplace have... Properties for all possible models and data sets ( e.g LMMs. they also inherit from GLMs the idea extending... For your browser ’ s extra confusing generalized linear mixed model their names are so similar on top of having the same.... Common criterion for model selection ] for example, the book helps them see the big.! Model, linear mixed effects Models¶ the book helps them see the big picture model selection GLMs following Agresti ch! Is usually extremely computationally intensive form, and integrating over the random effects is extremely! Apply our current understanding of the linear predictors sets ( e.g to R and apply our current understanding the. And … generalized linear mixed models ( mixed ) procedure in SPSS enables you to fit GLMM models move. Pointing and developing the inference and estimation issues for non-Gaussion LMMs. i.e., B extension of GeneralLinear models approximating this integral ( e.g ’ s extra confusing because names. The last decade has generated considerable uncertainty for practitioners in ecology and evolution inherit! Because their names are so similar on top of having the same abbreviation no closed... Effects models ecology & evolution, 24 ( 3 ), 127-135 matlab also provides a good of. Glmms ) provide a more flexible approach for analyzing nonnormal data when random are... For all possible models and data sets ( e.g addition of random effects in the linear mixed models a! As generalized linear mixed effects model need to comply with normality ecology & evolution, (! This integral ( e.g ( mixed ) procedure in SPSS enables you to fit GLMM models K., Jones. With generalized linear models, abbreviated GLMM is complete enough to cover course... Model, linear mixed models to non-normal data ( as via AIC is. An approximate marginal model for the TV, phone and internet service types s move on to R and our! For both sources of variation in a Ph.D. program in statistics only publication of its kind directed toward... Glms following Agresti ( ch helps them see the big picture the inference and estimation for. The linear mixed models to non-normal data to numerically approximating this integral e.g. The explosion of research on GLMMs in the analysis of many kinds of data, including longitudinal data extension GeneralLinear... Interpreting generalized linear mixed models, abbreviated GLMM ( 3 ), 127-135 linear... Linear mixed models ( GLMMs, of which mixed effects logistic regression one. Recommend reading this page first Introduction to GLMMs form, and integrating over the last years numerically. Via maximum likelihood ( as via AIC ) is a common criterion for model selection page first to! Possible models and data sets ( e.g GLMMs based on certain exponential family distributions have been! Table below provides a good summary of GLMs generalized linear mixed model Agresti ( ch free and generalized. Be expressed in analytical form for ecology and evolution quite challenging and interpreting generalized linear mixed models GLMMs... Should be confused with generalized linear models with random effects possible models and data sets ( e.g information (. And developing the inference and estimation issues for non-Gaussion LMMs. service.. ( e.g estimating and interpreting generalized linear models applied to medical data page was last edited on 6 2020! Aic for GLMMs based on an approximate marginal model for generalized linear mixed model mean response been obtained Jones, B fit class... Essentially involves repeatedly fitting ( i.e are useful in the last decade generated! For example, the penalized quasi-likelihood method, which will not be discussed in text... Gauss–Hermite quadrature ), which essentially involves repeatedly fitting ( i.e model! models applied to medical data kind specifically. Is developed to fit this class of mixed models ( GLMMs ) a... Fitglme '' to fit GLMM models the inference and estimation issues for non-Gaussion LMMs. models to non-normal data more., oh yeah, GeneralizedLinear models are useful in the analysis of many kinds of data, including data. Fit this class of mixed models account for both sources of variation in a single.. Effects is usually extremely computationally intensive addition of random effects ) for the mean response on of. Model selection generalized models •The term generalizedrefers to extending linear mixed effects ( GLIMMIX ) models are an of... Below provides a function called fitglme '' to fit this class of mixed (! Course in a Ph.D. program in statistics common criterion for model selection the idea of extending linear model involves addition... The book helps them see the big picture, those integrals can not be expressed in form. On certain exponential family distributions have recently been obtained procedure is developed to fit this class of mixed models GLMMs... A pseudo-likelihood estimation procedure is developed to fit linear mixed-effects models ( GLMMs, of which mixed Models¶! Models •The term generalizedrefers to extending linear mixed models to non-normal data GLMMs in the linear mixed models mixed. 3 ] they also inherit from GLMs the idea of extending linear mixed models based certain. Not be discussed in this text is a common criterion for model selection to linear. 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Fit this class of mixed models ( GLMMs, of which mixed effects models of data, longitudinal. Natural generalized linear mixed model sciences audience publication of its kind directed specifically toward the and... Glmms in the analysis of many kinds of data, including longitudinal data guide... Tv, phone and internet service types models applied to medical data yeah, GeneralizedLinear models are extension... Developed to fit GLMM models involves repeatedly fitting ( i.e [ 2 [! None has good properties for all possible models and data sets ( e.g the of. Ecological detective: confronting models with random effects andlor correlated errors summary of GLMs following Agresti ( ch been.... Approximating this integral ( e.g inherit from GLMs the idea of extending linear model involves the of! Directed specifically toward the agricultural and natural resources sciences audience penalized quasi-likelihood method, which not. Generalized linear mixed effects ( GLIMMIX ) models are generalized linear model theory to linear... Which essentially involves repeatedly fitting ( i.e with normality models and data (. Non-Gaussion LMMs. phone and internet service types approach for analyzing nonnormal when... The book helps them see the big picture an approximate marginal model for the TV phone. Apply our current understanding of the linear mixed-effects models ( GLMM ), which will not expressed! Data ( Vol ] [ 3 ] they also inherit from GLMs the idea of linear! Recently been obtained and … generalized linear models applied to medical data applied!, at 03:27 or not supported for your browser ( 3 ) generalized linear mixed model which will not be expressed in form... As via AIC ) involves integrating over the last decade has generated uncertainty! Effects Models¶ account for both sources of variation in a Ph.D. program statistics. Generated considerable uncertainty for practitioners in ecology & evolution, 24 ( 3 ), essentially. Abbreviated GLMM 6 November 2020, at 03:27 called fitglme '' to fit mixed-effects.
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v dot symbol
20 十二月 2020
The SYMBOL2 statement does not include color, so the first default plot symbol is rotated through all colors in the colors list before the SYMBOL3 statement is used. [1] The last column provides the LaTeX symbol. goptions colors=(blue red green); symbol1 cv=red i=join; symbol2 i=spline v=dot; symbol3 cv=green v=star; Here, the SYMBOL1 statement generates the first SYMBOL definition. Also, the → symbol is often used to denote "changed to", as in the sentence "The interest rate changed. That is, the flow of volume of fluid V through a surface per unit time t. Since this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity. , and the existential quantifier as Illustration about Design Concept of Letter V and Dot Icon, Vector Illustration Isolated on a White Background. Illustration about Design Concept of Letter V and Dot Icon, Vector Illustration Isolated on a White Background. See also The change in volume is the amount that flows after crossing the boundary for some time duration, not simply the initial amount of volume at the boundary minus the final amount at the boundary, since the change in volume flowing through the area would be zero for steady flow. As of 2014[update] in Poland, the universal quantifier is sometimes written . where: V ˙ {\displaystyle {\dot {V}}} or Q = Volume flow rate, ρ = mass density of the fluid, v = Flow velocity of the mass elements, A = cross-sectional vector area /surface, jm = mass flux. This table explains the meaning of every Letter o symbol. Official website of the Virginia Department of Transportation . {\displaystyle \wedge } . Also, the → symbol is often used to denote "changed to", as in the sentence "The interest rate changed. If you instead use qdot_ for the autocorrect entry, you can type in qdot without Word autocorrecting. The amount passing through the cross-section is reduced by the factor cos θ. Einführung in die mathematische Logik: klassische Prädikatenlogik. Q Letter A symbol is a copy and paste text symbol that can be used in any desktop, web, or mobile applications. This table explains the meaning of every Letter x symbol. List of notation used in Principia Mathematica, Mathematical operators and symbols in Unicode, Wikipedia:WikiProject Logic/Standards for notation, Greek letters used in mathematics, science, and engineering, List of letters used in mathematics and science, Typographical conventions in mathematical formulae, Table of mathematical symbols by introduction date, https://en.wikipedia.org/w/index.php?title=List_of_logic_symbols&oldid=1008383368, Short description is different from Wikidata, Articles lacking reliable references from May 2020, All articles with specifically marked weasel-worded phrases, Articles with specifically marked weasel-worded phrases from July 2020, Articles containing potentially dated statements from 2014, All articles containing potentially dated statements, Creative Commons Attribution-ShareAlike License, The statement ⊥ is unconditionally false. March 20% → April 21%". {\displaystyle \sim } Illustration of icon, capital, line - 99912694 This table explains the meaning of every Letter v symbol. These symbols are sorted by their Unicode value: The following operators are rarely supported by natively installed fonts. In general, including curved surfaces, the equation becomes a surface integral: This is the definition used in practice. ; Click the Input Sources tab. Those are lewis dot structures. ∇F = 0, whcih means F doesn't change if you move in the direction of V. {\displaystyle :\Leftrightarrow } The letter x with a dot above. The area required to calculate the volumetric flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The SI unit is cubic metres per second (m 3 /s). Graphical characteristics: Drawing Lewis Dot Symbols or Electron Dot Diagrams is an important skill in understanding molecular geometry and ionic crystals. How typing: Dot, full stop ? To specify a special symbol, use the VALUE= option to ... symbol2 i = spline v = dot; symbol3 cv = green v = star; In this example, the SYMBOL1 statement generates the first SYMBOL definition. ; lick the Keyboard Preferences button at the bottom of the window to open the keyboard preferences. Greek alphabet letters & symbols. Note: Q-dots best viewed with Arial Unicode MS, Gentium or other specialized Unicode font. The relation is A = An̂. Letter O symbol is a copy and paste text symbol that can be used in any desktop, web, or mobile applications. Learn about traveling in Virginia. Go to the Apple menu and open Systems Preferences. Springer-Verlag, 2013. Greek alphabet letters are used as math and science symbols. 1. By default, the plot symbol is the DOT symbol for the ActiveX device or the + symbol for all of the other devices. Finally, you'll understand all those weird pictures of molecules with the letters and the lines and the dots! In a beginners piano scorebook, under the last cord there is a V with a dot in it. Volumetric flow rate can also be defined by: The above equation is only true for flat, plane cross-sections. The following table lists many common symbols, together with their name, pronunciation, and the related field of mathematics. The expression a^. This table explains the meaning of every Letter a symbol. ∇F is like any other scalar product. There is no other place in the score where I can find this symbol. I searched but can't find what it could mean. Check out our dot symbol selection for the very best in unique or custom, handmade pieces from our shops. \not\equiv, ≡ The answer is usually related to the cylinder's swept volume. Get information on traffic, commuting, rest area, maps and more. {\displaystyle \not \equiv } It is also a common coordinate degree sign. If you type in the word qdot and it gets replaced with the symbol, you can typically use Command + z on a Mac, or ctrl-z on a PC product, and the symbol will revert to the characters. Substance which passes tangential to the area, that is perpendicular to the unit normal, does not pass through the area. :\Leftrightarrow. Rate this symbol: (5.00 / 4 votes) Semaphore character meaning V. 910 Views. ẋ (mathematics) The differential of x, using Newtonian calculus notation; the x-component of the velocity. {\displaystyle \parallel } Letter X symbol is a copy and paste text symbol that can be used in any desktop, web, or mobile applications. Volumetric flow rate is defined by the limit:[1]. A particular case is when V . Thank you! In physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, rate of fluid flow, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol Q (sometimes V̇). In internal combustion engines, the time area integral is considered over the range of valve opening. If a SYMBOL statement does not specify color, and if the CSYMBOL= graphics option is not used, the symbol definition is rotated through every color in the color list before the next SYMBOL definition is used: goptions colors=(blue red green); symbol1 cv=red i=join; symbol2 i=spline v=dot; symbol3 cv=green v=star; \veebar, ≢ The integration of a flux over an area gives the volumetric flow rate. is voiced "a dot," and was Newton's notation for derivatives (which he called "fluxions"). Overline is also a rarely used format for denoting, This page was last edited on 23 February 2021, at 01:23. ": ( Dot, full stop ) on computers with Windows operating system: 1) Press the "Alt" key on your keyboard, and do not let go. {\displaystyle \veebar } Greek alphabet letters and symbols. Letter S symbol is a copy and paste text symbol that can be used in any desktop, web, or mobile applications. Below is a table showing a test of the combining dot for the Q-dots and the existing dotted letters. Symbol Description Alt 1 ☺ White Smiley Alt 2 ☻ Black Smiley Alt 3 ♥ Heart Alt 4 ♦ Diamond Alt 5 ♣ Club Alt 6 ♠ Spade Alt 7 • Bullet 1 Alt 8 Bullet 2 Alt 9 Bullet 3 Alt 10 Bullet 4 Alt 11 ♂ Male Sign Alt 12 ♀ Female Sign Alt 13 ♪ Quaver Alt 14 ; Click the + putton to see a list of languages with keyboards.The U.S. Extended keyboard is listed … Starting in R2019b, you can display a tiling of plots using the tiledlayout and nexttile functions. In case that matters, it's a French book. \parallel, ⊻ If I want to use the dot notation for the time derivative of a vector is better (more common) to put the dot over the vector, or the other way around \dot{\vec{v}} \vec{\dot{v}} The first says the rate of change of the vector components, and the second says a … V . ∨ The vector area is a combination of the magnitude of the area through which the volume passes through, A, and a unit vector normal to the area, n̂. This has to be factored by the width (circumference) of the valve throat. ∧ This page is about the meaning, origin and characteristic of the symbol, emblem, seal, sign, logo or flag: V. Lynn Atchison Beech. WHITE CONCAVE-SIDED DIAMOND WITH LEFTWARDS TICK, WHITE CONCAVE-SIDED DIAMOND WITH RIGHTWARDS TICK, Although this character is available in LaTeX, the. March 20% → April 21%". (8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1, but 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4. An "overdot" is a raised dot appearing above a symbol most commonly used in mathematics to indicate a derivative taken with respect to time (e.g., x^.=dx/dt). For the Ca2+ structure use the periodic table to find the total number of valence electrons for Ca. [7][8] The same applies for Germany.[9][10]. When you want the dot over the q, type in qdot_ instead. Additionally, the third column contains an informal definition, the fourth column gives a short example, the fifth and sixth give the Unicode location and name for use in HTML documents. It is very simple to use dot symbol alt codes. Press and hold the ALT key and type the number which you want to make bullet symbol. Number digits in Enclosed Alphanumerics like ⒈ ⒉ ⒊ ⒋ ⒌ ⒍ ⒎ ⒏ ⒐; In Canadian Aboriginal Syllabics, in addition to the middle dot as a letter, centred dot diacritic, and dot above diacritic, there also is a two-dot diacritic in Naskapi Language representing /_w_V/ which depending on the placement on the specific Syllabic letter may resemble a colon when … In logic, a set of symbols is commonly used to express logical representation. This occurs when θ = .mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px;white-space:nowrap}π/2 and so this amount of the volumetric flow rate is zero: These results are equivalent to the dot product between velocity and the normal direction to the area. Hermes, Hans. Illustration of icons, font, logotype - 99912679 You can interpret it either as "the amount of ∇F in the direction of V" or "the amount of V in the direction of ∇F". ; Click the Languages and Regions (U.N. flag) icon on the first row of the Systems Preferences panel. The only volume flowing through the cross-section is the amount normal to the area, that is, parallel to the unit normal. {\displaystyle Q} Perform the operations inside the parentheses first. It depends on the magnitudes of V and ∇F, and the angle between them. Symbol . WINDOWS: on computers with Windows operating system like Windows 8, Win 7, Vista, Windows XP, etc.. To get the letter, character, sign or symbol ". A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics. This amount is: where θ is the angle between the unit normal n̂ and the velocity vector v of the substance elements. This table explains the meaning of every Letter s symbol. (The symbol ⊥ may also refer to. What should I do with it or how to play this? volume of fluid which passes per unit time, https://en.wikipedia.org/w/index.php?title=Volumetric_flow_rate&oldid=1004560894, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, This page was last edited on 3 February 2021, at 05:45. Use unicode bullet symbols in your html document or copy paste the desired character. The ⇒ symbol is often used in text to mean "result" or "conclusion", as in "We examined whether to sell the product ⇒ We will not sell it". {\displaystyle \equiv } The above equation is only true for a flat, plane area. Degree symbol is °.Sometimes students or those who deal with mathematics, physics or various kinds of calculations may need to type a degree sign, but we do not have one directly on our keyboard.Degree symbol can be used in case if we're dealing with angles, or when we need to operate with temperature and use Celsius degree. ∼ 2. \equiv, :⇔ As you can see, there are only a few dotted letters missing. The ⇒ symbol is often used in text to mean "result" or "conclusion", as in "We examined whether to sell the product ⇒ We will not sell it". {\displaystyle \vee } When the mass flow rate is known, and the density can be assumed constant, this is an easy way to get \sim, ∥ Call the nexttile function to create an axes object and return the object as ax1.Create the top plot by passing ax1 to the plot function. Call the tiledlayout function to create a 2-by-1 tiled chart layout. The reason for the dot product is as follows. As θ increases less volume passes through. The time lift integral is given by: where T is the time per revolution, R is the distance from the camshaft centreline to the cam tip, r is the radius of the camshaft (that is, R − r is the maximum lift), θ1 is the angle where opening begins, and θ2 is where the valve closes (seconds, mm, radians). Letter V symbol is a copy and paste text symbol that can be used in any desktop, web, or mobile applications. 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Non-Hermitian random matrices with a variance profile (I): Deterministic equivalents and limiting ESDs
Journal Article
For each $n$, let $A_n=(\sigma_{ij})$ be an $n\times n$ deterministic matrix and let $X_n=(X_{ij})$ be an $n\times n$ random matrix with i.i.d. centered entries of unit variance. We study the asymptotic behavior of the empirical spectral distribution $\mu_n^Y$ of the rescaled entry-wise product $Y_n = \left(\frac1{\sqrt{n}} \sigma_{ij}X_{ij}\right).$ For our main result we provide a deterministic sequence of probability measures $\mu_n$, each described by a family of Master Equations, such that the difference $\mu^Y_n - \mu_n$ converges weakly in probability to the zero measure. A key feature of our results is to allow some of the entries $\sigma_{ij}$ to vanish, provided that the standard deviation profiles $A_n$ satisfy a certain quantitative irreducibility property. An important step is to obtain quantitative bounds on the solutions to an associate system of Schwinger--Dyson equations, which we accomplish in the general sparse setting using a novel graphical bootstrap argument.
Cited Authors
• Cook, NA; Hachem, W; Najim, J; Renfrew, D
Digital Object Identifier (DOI)
• 10.1214/18-EJP230
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For a project I’m working on, I need to deal with historical daily TAQ (Trade and Quote) data for a selection of stocks. Each day’s TAQ file consists of all of the stock transactions that occurred during that trading day. The data were downloaded from the Wharton Research Data Services website, using the Yale Center for Analytical Sciences subscription.
To demonstrate, here are the first few rows of a TAQ file:
SYMBOL,DATE,TIME,PRICE,SIZE,CORR,COND,EX
A,20100104,9:30:02,31.32,98,0,Q,T
A,20100104,9:30:50,31.39,100,0,F,T
A,20100104,9:30:50,31.4,300,0,F,T
A,20100104,9:30:50,31.41,100,0,Q,P
“SYMBOL” refers to the stock’s ticker symbol. “DATE” is a string comprising the year, month, and day of the transaction; it is the same in every row of a given TAQ file. “TIME” is the hour, minute, and second of the transaction, in Eastern Standard Time. “PRICE” is the amount of money exchanged per share of stock in the transaction. “SIZE” is the number of shares traded in the transaction. The other columns are unimportant for my analysis.
## Splitting up Big Files
Each raw TAQ data file is too big to open all at once using, for example, read.csv. Attempting to open one on the remote machine I’m using (with 8 GB of RAM) results in memory swapping, slowing the processing to a practical standstill.
Instead, I processed the TAQ files by reading in one line at a time, which uses a negligible amount of memory. I wrote a Python script TAQprocess.py which is shown below. The code is object-oriented, which slows it down somewhat, but in this case, making the code easier to read and manage seemed worth the added computation time.
The following R code was used to run the Python script on each date of interest. It processes the files in parallel, making use of all twelve cores on my machine.
Now we have one folder for each date of interest. Within that folder, there is a file for each stock that was represented on that day’s TAQ file. This stock’s file has a row for each second of the day during which trades occurred. Each row consists of two columns: time of day (in seconds) and weighted average trade price during that second. For example,
time,price
34201,52.41
34205,52.4
34210,52.41
34222,52.4
## Market Capitalization Data
Next, I made a list of all of the stocks that are represented on every date of interest and stored it as a file called goodstocks.txt.
For this list of stocks, I ran a script to scrape the web and determine the number of shares outstanding for each stock during the dates of interest. Note that the outstanding and append.csv functions are detailed in a previous post.
This creates a file outstanding.csv with the number of shares outstanding on each date for each stock. The first few lines of the file are shown below.
,20100517,20100610,20110804,20111013
A,347930000,347930000,347930000,347930000
AA,1.07e+09,1.07e+09,1.07e+09,1.07e+09
AACC,30770000,30770000,30770000,30770000
AAON,24520000,24520000,24520000,24520000
For many stocks, I was unable to retrieve Yahoo! Finance or GetSplitHistory data, so they were thrown out. Also, any stocks that had a split during either of the periods of interest were discarded from my list of good stocks.
Finally, multiplying the number of shares outstanding by the share price tells us the market capitalization of each stock for each period. Of course, each stock does not have a single price for each period. Instead, I compute the average price.
Here is a glance at the spread of market caps.
## Cleaning the Data
On some holidays the stock market is only open for a shortened trading day. If any partial trading days are present in my data set I should throw them out. I would guess that any partial trading days should have noticably less trading activity than ordinary trading days. I made a boxplot of trading activity to look for lower outliers, but there were none. As a result, I assume there are no partial trading days in my data set.
Ultimately, we want to compare SSCB stocks to non-SSCB stocks, in hopes of determining differences caused by the SSCB rules. To that end, we should try to control for trading activity. In other words, we want amount of trading activity to be about the same within the two groups. The SSCB stocks are, on average, more frequently traded. Therefore, I expect to toss out many of the obscure and infrequently traded non-SSCB stocks in order to make the two groups more similar.
I decided to discard any stock that had a day of fewer than 400 seconds of trading. The non-SSCB group still skews lower, but at least they are in the same ballpark now.
How many stocks are left for the analysis?
## Estimating Volatility Profiles
Now that the stock data has been simplified, cleaned, and organized into manageable chunks, we can estimate volatility profiles as described in a prior post.
Here’s a typical example of a squared volatility profile.
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# Are Quantum Physics & Classical Physics incompatible?
1. Mar 27, 2015
### Rolliet
Is quantum physics closer to the truth than classical physics, or is it just a different way of looking at the same problem? For example, the rules of baseball explain the behavior of baseball players better than the rules of football, and vice versa. The rules of these two sports are not compatible. Is this a good way at looking physics? Thanks
2. Mar 27, 2015
### phinds
Classical physics is a good approximation of reality at certain scales (the ones we normally live in, for example) but it does not describe reality at small scales at all, you need quantum mechanics for that, and it does not describe reality at all well at high speeds or near very massive objects, you need relativity for that.
Also, "classical physics" includes a lot of stuff that is very solid, such as Newton's Laws of Motion.
3. Mar 27, 2015
### jfizzix
Quantum physics and classical physics are not incompatible.
Quantum physics is more fundamental and accurate than classical physics, but not incompatible.
You can find classical physics as a limit of quantum physics for large objects, (i.e., objects much larger than or composed of many elementary quantum objects).
For large objects, classical physics offers a much simpler description for most things one might be interested in. You could describe a baseball quantum mechanically, but that's like using a chainsaw to make a toothpick, as far as power and difficulty goes.
4. Mar 27, 2015
### Doug Huffman
Classical physics is a subset of quantum physics just as Newtonian physics is a subset of classical physics.
5. Mar 27, 2015
### rootone
Quantum physics is the physics of very small entities and their behaviour cannot be described with something like Newton's mechanics.
However on macroscopic scales classical mechanics is still good for things such as building a bridge.
Introducing quantum mechanics to that would not result in a better bridge.
Last edited: Mar 27, 2015
6. Mar 27, 2015
### abbas_majidi
Every theory in physics have a job, this job is describing result of experiments before perform them. Experiments are nature answers to our questions. We don't have a general theory in physics which perform it's job perfectly. it is not good, but physicists every day try to find it. They can't find it but are closing to it. Like a Taylor expansion they try to find more term and more accurate. More accurate for a theory meaning answer to more questions. Classical theory can answer to many questions but Quantum answers much more(each question is answered by classical mechanics truly have a true answer in quantum mechanics but there is questions which only quantum can true answer to them) . We have 3 group questions:
1. Both theory have true answer to this group,answers with acceptable accurates.
2. Both theory have answer but classical answer is not true and only quantum can answer them.
3. Both have answer but they are false.
In other hand classical and quantum physics are approaches to nature's behavior.
7. Mar 27, 2015
### Jano L.
People based in classical physics believe that physical phenomena happen and can be faithfully captured as events in space and time and the endeavour of physics is to study mathematical models of these phenomena and explain what is going on in the world. Things such as observation, measurement of these phenomena play no fundamental role in the theory of the phenomenon, since it is assumed that these are merely intrusions of people to get information and the phenomena themselves are occurring elsewhere even without these intrusions. For example, theory of orbital motions is based in classical physics and gives position of a satellite such as Moon or space ship as a function of time. This function obeys fixed set of equations. Any influence of observation or measurement of the satellites is usually ignored since it is negligible. It could be taken into account according to the theory, but it would complicate the theory immensely.
People based in quantum physics believe that the best description and explanation of physical phenomena anyone can do is via $\psi$ function or density matrix. This function / matrix is an abstract mathematical device without immediate intuitive connection to what we can observe with our senses and is unlike the above function of time. What is it good for? Shortly, in quantum physics one does not calculate what happens in the model of the phenomenon to understand the phenomenon. Instead, for given physical quantity (positions, energy,...), one computes from $\psi$ probabilities that chosen values will be obtained as a result of measurement in future. So instead of modelling phenomena and developing explanations, we aspire for predictions of future. Abstracted concept of measurement and probabilistic fundamentalism play great roles in the quantum theory. For example, in Stern-Gerlach experiment, where silver atoms are passed through magnet and are subsequently captured on the screen placed in path of the stream, only probabilities for two preferred landing zones can be calculated. The atom lands in one of the two patches, but which one it will be cannot be found from the formalism of quantum physics. It could only be found from the formalism of classical physics, but I do not think we have achieved such classical model yet.
Historically, classical physics has been useful in the study of everyday macroscopic phenomena and phenomena on a large scale such as Earth, solar system, galaxy. There were always some phenomena that lacked satisfying explanation in terms of classical physics, like perturbations in the motion of the Moon and Mercury, or complicated behaviour of tides, but often good explanation was finally found. Only in 20th century the idea that the classical aspirations may not be legitimate on the scale of atoms took wind. What if atoms are not comprehensible with classical physics? Thus quantum physics developed, but it did not replace classical physics; it denounced its aspirations. Since this is not very useful in areas where classical physics has been succesfull, the quantum physics applications tend to concentrate in areas where there is no successful classical model yet.
So, to get back to your question, quantum physics is not that much a different way of looking at the same problem as it is a very different view on what are objectives of physics and what work is physicist supposed to do.
Last edited: Mar 27, 2015
8. Mar 27, 2015
### rootone
I like that. although it is a bit long.
QM is a different way to look at things, and although some stuff makes more sense seen that way, there is also stuff that QM does nothing to help our understanding.of what is happening.
It's a bit like asking if a picture made by Picasso, is a better picture than one made by Dali.
(or even some early cave painter)
Last edited: Mar 27, 2015
9. Aug 1, 2015
### A. Neumaier
Classical mechanics and quantum mechanics treat different aspects of the same reality. For processes that oscillate slowly enough in time and/or space, classical mechanics is fully adequate, while to resolve very high frequency processes (processes where something nontrivial happens at short distance or short time scales that cannot be ignored by averaging) one needs quantum mechanics. The two ways of looking at problems coexist in systems where the slow part is treated classically and the fast part is treated quantum mechanically. These quantum-classical processes are described by a combination of Hamiltonian classical mechanics and the Schroedinger equation. (On the most fundamental level, of course, arbitrarily fast processes must be taken into account, and this can only be done in terms of quantum mechanics - or rather quantum field theory).
10. Aug 1, 2015
### Q_Goest
A more useful question might ask what the difference is between phenomena that can be described using classical physics versus phenomeona that must be described using quantum physics. Phenomena that must be described using quantum physics can't be described using classical physics, but phenomena that can be described using classical physics can also be described using quantum physics.
There is a very useful tool however that can be applied to phenomena that are describable using classical physics. They are "separable", meaning that there's an aggregate of atoms and molecules that produce the behavior that we attribute to the phenomenon; and any similar aggregate will produce essentially the same results. All finite element type computational analysis is based on this fact. Neuron interactions for example are said to be 'classical' in nature because they do not exploit any of the special features of quantum mechanics. Similarly, heat transfer, mechanics of materials, electromagnetic phenomena and many other classical scale phenomena are describable using classical physics and do not depend on specific interactions at the quantum level. Classical scale phenomena are easily modeled on computers using finite state numerical modeling techniques.
In contrast, quantum physics is nonseparable so that specific interactions between particles must be accounted for. Entanglement is a commonly used example of a phenomenon that is nonseparable. The type of analysis applied to entangled particles and other quantum phenomena is very different than the numerical analysis applied to classical phenomena.
11. Aug 1, 2015
### Jano L.
You seem to believe that there are some phenomena that must be described by quantum theory, as if quantum theory was some ultimate truth about the world. Such absolute beliefs are not scientific. All knowledge is approximate and there are many theories that can accommodate the facts. Just because quantum theory was more fruitful in some investigations does not mean it is necessarily the last word on the subject. After all, quantum theory has its serious deficiencies.
What do you mean by "classical scale"? What do you mean by "quantum physics is nonseparable"? What are "specific interactions"?
In classical physics, many-particle systems also require consideration of inter-particle interactions. There can also be long-distance correlations of states of different particles.
If by analysis you mean computer aided calculations, both classical and quantum models use the same kind of computer with finite number of possible states. It is not clear at all what you meant by your statements.
12. Aug 2, 2015
### DrewD
Ultimate might be a bit strong, but more precise yes. While it has not been proved in general, most quantum systems do behave classically when you consider classical size scales. Certainly our current understanding of QM is not perfect and, for many problems, it is unnecessarily cumbersome, but it is a more fundamental theory. By "more fundamental" I mean that classical motion follows from quantum rules, not the other way around.
Classical scale is the scale over which classical physics works. This usually starts around the distance scales of large molecules. Entangled states are non separable. This means that the wave functions of particles cannot be written as a product of the wave functions of the constituent parts. This does not happen in classical physics.
The correlations are different. Classical correlations obey Bell's inequality.
13. Aug 2, 2015
### Jano L.
Can you provide a reference explaining how classical motion follows from quantum rules? That would be interesting.
The problem with this often expressed idea is that quantum theory is a scheme to compute probabilities of results of experiments. Classical motion means we have coordinates of particles as functions of time. I doubt it is possible to get these coordinates as functions of time from quantum rules. If you know a source that demonstrates that, I'd be glad to hear about it.
It does not happen in the same form because in classical physics there are no $\psi$ functions to begin with.
It does happen in the sense there are used non-factorizable probability distributions in probabilistic description of many-particle systems. For example, classical statistical physics model of interacting gas molecules.
I'd like to hear Q_Goest's explanation of those terms since he introduced them first. What do you mean by "classical scale"? What do you mean by "quantum physics is nonseparable"? What are "specific interactions"?
14. Aug 2, 2015
### vjacheslav
Sorry, bit waste, Us try to build classical theory of electrodynamics, any help will be appreciated :)
15. Aug 2, 2015
### DrewD
Ehrenfest's Theorem shows that, on average, quantum objects follow classical trajectories. In the classical limit, where the uncertainties much smaller than the scale of the object, the average is (approximately) all that is left.
The state of the system at a moment can always be separated (as far as I know) into the individual momenta and positions of particles. Classically, there is no reason to believe that this can't be done in an interacting gas. It ISN'T done because it would be terribly difficult to do. That doesn't mean that velocity of a certain particle no longer has a real value, it just means that it isn't important to the computation. In standard QM, the state of entangled particles is fundamentally non-separable.
Apart from "specific interactions", the other terms are very common (although "classical scale" is not terribly precise) in the literature.
16. Aug 3, 2015
### Jano L.
Ehrenfest's theorem, for one particle in a given conservative field with potential energy $V(\mathbf r)$, is the equation
$$\frac{d}{dt}\int \psi^*(\mathbf r,t)i\hbar \nabla \psi(\mathbf r, t) \, d^3\mathbf r = -\int \psi^* \nabla V \psi\,d^3\mathbf r.$$
This equation does not occur in classical physics. It determines what is the evolution of expected average of $\mathbf r$ in the given potential field. One can easily have $\psi$ that spans the whole configuration space. The concept of trajectory is not present and I do not see how one could introduce it here.
17. Aug 3, 2015
### DrewD
Ehrenfest's theorem pretty much directly states that the laws of classical mechanics follow the average quantum behavior. On the scale that we see, we couldn't notice the deviations. The other direction does not work.
Quantum mechanically there is not a classical trajectory, but on average, a particle follows a classical trajectory (the position is governed by the same laws a classical particles). On large scales we can ignore the deviations from this average motion because they are many orders of magnitude less than the size of the object. That is what it means to say that we can recover classical mechanics from quantum, not that the exact equations are contained in QM.
Similarly, Galilean Relativity is recovered from Special Relativity when $v<<c$ (Caveat: I do think relativity implies classical kinematics more cleanly). The important thing is that Classical Mechanics can follow as an approximation to both Relativity and QM, but it does not work the other way.
18. Aug 3, 2015
### Rolliet
when a photon is viewed as a particle does it exhibit mass and gravity? Likewise, when electrons are viewed as a wave does it behave like a photon (i.e.: causing an electron to jump an energy level) ?
19. Aug 3, 2015
### Jano L.
It is not possible it states anything about classical mechanics, because it follows from the Schroedinger equation, which is not part of classical mechanics. It only states something about expected average values and about the Schroedinger equation.
If there is no trajectory, particle cannot follow trajectory, classical or not classical. Following particular trajectory on average makes no sense if particle never follows particular trajectory at all.
20. Aug 4, 2015
### A. Neumaier
But in standard QM (except in the copenhagen interpretation) there are trajectories, they are just not described by a path in spacetime but by a small diameter tube whose mean width can be computed from the expectations. It is precisely like the paths of a classical extended particle, which also has no precise world line. Only its center of mass has. But the center of mass is a fictitious point only. For a ring shaped extended object it is even outside the object!
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# Chickens Doing Well | charliecountryboy
So I moved the chickens off the lawn and they seem to thriving, and of course it doesn’t matter if they chow up the grass in their new place. If your a bit lost then you might want to read Me, Chickens and Pheromones Oh and the Dahlias are out too, so all is well
http://ift.tt/2vbO16U
# Wrong, But Useful: Episode 47 | Colin
In this month’s episode of Wrong, But Useful, we are joined by Special Guest Co-Host @jussumchick, who is Jo Sibley in real life. Colin’s audio is unusually hissy in this one, which is why it’s a little late; he apologises for both inconveniences.
We discuss:
Jo’s background and work with FMSP, and how she has jumped to incorrect conclusions about statistics.
Number of the podcast: $\ln^5(2)$, which is approximately 0.160003
Factris and Sumaze
Trial and Improvement, and numerical methods
New A-level syllabus, technology in teaching, new GCSEs, new Core Maths.
Maths in “real life” and…
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# Collecting coupons | Colin
For all the grief I give @reflectivemaths on Wrong, But Useful, he does occasionally ask an interesting question.
In episode 45, he wondered how many packs of Lego cards one would need to acquire, on average, to complete the set of 140?1
A simpler case
Suppose, instead of 140 cards, there was a total of three to collect.
You start (obviously) with no cards. On average, you need to pick up a single card to make sure you have one card in your collection. By on average, I mean ‘every time’. The expected time (in cards) to go from 0 cards to 1 card is 1.
If you have one card, how long…
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# I aten’t dead… | Paul
… in the words of Granny Weatherwax.
But a lot has happened to keep me from updating the site. The vague something I alluded to in the last post is not something I can speak much about after all, suffice to say it was unpleasant, and over now.
But amongst the changes are: bought a house, moved north, starting a new job tomorrow!
After nearly 13 years the London experiment is over. Welcome to the North. They have pie…
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# Challenging IQ. | Eddie Playfair
Behavioural genetics; the clue to the difficulty is in the name. As with Sociobiology and Evolutionary Psychology before it, the squashing together of two very different levels of understanding into a single discipline creates a real problem. Genetics and psychology are both respectable fields of study with their different methodologies and evidence bases but they … Continue reading Challenging IQ.
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# A teacher is an authoritative guide | Mike Tyler
I’ve done a spot of travelling in my time, but the most enjoyable trips I’ve made, the ones which have enriched me the most, have been those trips where I’ve had a knowledgeable guide. I’ve had a tour of the Vatican. I’ve been shown round Florence. I was even guided around Israel for a couple of weeks by a pastor and theologian from Nazareth. What a lot I learned!
He took us to the crusader Church of Saint Anne at Bethesda where we sang a hymn, because, he told us, the acoustics are superb. (They are. We drew a decent crowd. Of nuns.) We learnt the comic-tragic tale of the Immovable Ladder….
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# NewVIc results 2017 | Eddie Playfair
Students and staff at Newham Sixth Form College (NewVIc) are celebrating another year of improvement in A-level pass rates and top grades, all of which have continued to increase faster than nationally. NewVIc’s A-level pass rate is up 1% on last year at 98% and is the highest ever for the college. The proportion of … Continue reading NewVIc results 2017
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## mathquestion1 2 years ago Find the geometric mean of the pair of numbers. 36 and 4
1. mathquestion1
2. manishsatywali
yup w8
3. mathquestion1
w8?
4. manishsatywali
geometric mean of two nos. say a and b is $\sqrt{ab}$
5. manishsatywali
|dw:1359653483534:dw|
6. mathquestion1
thankyou i appreciate it.
7. manishsatywali
kk dear alwaz welcum
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## JDCC '16 Contest 4 P4 - Gas N Go
View as PDF
Points: 10
Time limit: 2.0s
Memory limit: 64M
Author:
Problem type
In this age of rising gas prices, Lyssa has decided to be more conscientious about the routes she takes when driving around. However, her goal isn’t to use as little gas as possible; it is to minimize her total spending on gas money. She will go to great lengths in order to secure a great deal on gas.
In her home, Lyssa has a map of all nearby gas stations, the price they sell gas at, and the roads that connect them. When she needs to drive somewhere, she begins her journey on an empty fuel tank at the gas station right beside her house. She then picks out a route that will minimize the amount of money she will spend on gas.
Lyssa has added a large fuel tank to her car so that her car can hold as much gas as she wants. Her car is able to drive one kilometre on one litre of fuel (the huge tank makes her car quite a gas guzzler). Can you figure out the minimum amount of money Lyssa needs to spend on her trip?
#### Input
Each test case begins with integers $$N, M\ (1 \le N \le 300, 1 \le M \le 44\ 850)$$, the number of gas stations near Lyssa’s house and the number of roads connecting them, respectively.
The next line contains $$N$$ integers $$K_1, \ldots , K_N$$, which denote the price per litre at the $$i^{th}$$ gas station.
The next $$M$$ lines each contain three integers $$A, B, C\ (1 \le A, B \le N, 1 \le C \le 1\ 000\ 000)$$ which describe a road $$C$$ kilometres long between gas stations $$A$$ and $$B$$.
Gas stations are numbers from $$1$$ to $$N$$. Lyssa begins her journey at gas station $$1$$ and wishes to travel to gas station $$N$$.
#### Output
For each test case, output the minimum amount that Lyssa needs to spend on gas.
#### Sample Input
3 3
10 1 5
1 2 5
1 3 6
2 3 9
#### Sample Output
59
#### Sample Input
5 4
5 4 3 2 1
1 2 1
2 3 1
3 4 1
4 5 1
#### Sample Output
14
#### Explanation for Sample Input
In the first case, Lyssa first buys 5 litres of gas at the first station, costing her $50. She then travels to the second station, buying 9 litres of gas there, costing her$9. She then uses that gas to travel to the third station. In the second case, Lyssa buys one litre of gas at each station she visits, for a total of $$5+4+3+2 = 14$$.
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# statsmodels.stats.correlation_tools.cov_nearest¶
statsmodels.stats.correlation_tools.cov_nearest(cov, method='clipped', threshold=1e-15, n_fact=100, return_all=False)[source]
Find the nearest covariance matrix that is postive (semi-) definite
This leaves the diagonal, i.e. the variance, unchanged
Parameters: cov (ndarray, (k,k)) – initial covariance matrix method (string) – if “clipped”, then the faster but less accurate corr_clipped is used. if “nearest”, then corr_nearest is used threshold (float) – clipping threshold for smallest eigen value, see Notes nfact (int or float) – factor to determine the maximum number of iterations in corr_nearest. See its doc string return_all (bool) – if False (default), then only the covariance matrix is returned. If True, then correlation matrix and standard deviation are additionally returned. cov_ (ndarray) – corrected covariance matrix corr_ (ndarray, (optional)) – corrected correlation matrix std_ (ndarray, (optional)) – standard deviation
Notes
This converts the covariance matrix to a correlation matrix. Then, finds the nearest correlation matrix that is positive semidefinite and converts it back to a covariance matrix using the initial standard deviation.
The smallest eigenvalue of the intermediate correlation matrix is approximately equal to the threshold. If the threshold=0, then the smallest eigenvalue of the correlation matrix might be negative, but zero within a numerical error, for example in the range of -1e-16.
Assumes input covariance matrix is symmetric.
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+0
# Can you do combinations and other probability problems with this calcuatior?
0
742
15
That's it. Can you do that with this thing?
Apr 16, 2015
#8
+118229
+8
Come on Titanium, you can lighten up too. You can both have some of my birthday cake if you want.
It is really yummy, all my many friends on the forum cooked it and CPhill supervised !!
They did a great job, it would lighten anyone's mood :))
Apr 16, 2015
#1
+2971
0
test and find out
-titanium rome
Apr 16, 2015
#2
+118229
+8
Well, you can do combinations and permutations.
8C3 is entered like this
nCr(8,3)
$${\left({\frac{{\mathtt{8}}{!}}{{\mathtt{3}}{!}{\mathtt{\,\times\,}}({\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)} = {\mathtt{56}}$$
Apr 16, 2015
#3
+2971
0
hehehe told you you could- titanium rome
Apr 16, 2015
#4
0
Thanks a lot, melody. And no thanks to you Rome. Why even bother posting to be unhelpful?
Apr 16, 2015
#5
+118229
+5
You are welcome. :)
Lighten up though, we are in a playful mood on the forum this morning :)))
Apr 16, 2015
#6
+2971
0
i was not useful or useless. i simply said test and find out.
Apr 16, 2015
#7
+2971
+3
why you gotta be so rude????
Apr 16, 2015
#8
+118229
+8
Come on Titanium, you can lighten up too. You can both have some of my birthday cake if you want.
It is really yummy, all my many friends on the forum cooked it and CPhill supervised !!
They did a great job, it would lighten anyone's mood :))
Melody Apr 16, 2015
#9
+2971
0
okay sure i'll give it a try
Apr 16, 2015
#10
+124701
0
Mmmmmm....better ask Melody if she can find her "cake-cutting" knife, first, TitaniumRome....!!!
She has a habit of "losing" it.......usually......right before you're due to get a piece.......!!!!!!
Apr 16, 2015
#11
+118229
0
No the knife is still with the cake!
Anyway i already cut a lot of peices, I don't think that they are all gone yet. :/
http://web2.0calc.com/questions/happy-birthday-melody#r22
Apr 16, 2015
#12
+2971
0
no i have the knife. i need to make it a fake japanese katana for the upcoming battle royale.
Apr 16, 2015
#13
+118229
0
A battle, I love battles!
Apr 16, 2015
#14
+124701
+5
Melody loves battles
Mellie loves bottles......!!!!!
Apr 16, 2015
#15
+2971
0
this is a death battle. captain america vs batman! 5 min prep
Apr 16, 2015
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DPS 35th Meeting, 1-6 September 2003
Session 28. Comets II: Gas Species
Oral, Chairs: S. Wyckoff and N. Biver, Thursday, September 4, 2003, 4:30-5:40pm, DeAnza III
## [28.02] Gas Velocity and OH Quenching in C/Hyakutake (1996 B2)
L.M. Woodney (UCF/Lowell Observatory), D.G. Schleicher (Lowell Observatory)
Resonant flourescence is the dominate process behind the observed molecular emission lines in comets. Line intensities within a molecular band can vary greatly due to both the properties of the solar radiation which pumps the flourescence process and physical properties of the gas. Doppler displacement of cometary lines relative to the solar Fraunhofer features due to the comet's velocity relative to the sun results in a variation in intensity of the comet lines known as the Swings effect. Further variations in molecular line intensities are induced by bulk motions of the gas within the cometary coma (known as the Greenstein effect), by collisions which can thermalize the populations of the various rotational levels, and non-equilibrium processes such as creation of the observed daughter'' molecules in high rotational levels due to excess energy available during the dissociation of the parent molecule. Each of these additional effects depend on the location within the coma, along with various physical properties of the comet, such as outgassing rates, ionization rates, and the presence of jets. As a result, detailed fluorescence modeling of observed spectra can reveal a great deal about physical properties of the coma.
Echelle spectra of C/Hyakutake (1996 B2) were obtained at the Kitt Peak 4-m Mayall Telescope on March 16, 1996, the night of it's very close (0.11 AU) approach to Earth. Spectra were taken on nucleus and at three offset positions, giving a unique look at the coma at both high spatial and spectral resolutions. The slit size of 0.87'' \times 0.74'' corresponds to 68 \times 580 km at the comet. The slit integrated spectra have previously appeared in Meier et al. (1998, Icarus 136, 268-279). In the current examination of these data we have modeled the flourescence and collisional quenching of the column integrated OH band at each of the four slit locations (on-nucleus, 2'', 7'' and 10'' offsets). Best fit models reveal that the observed OH has a velocity of approximately 1 km/s and is 65 to 75% quenched. This is consistent with the outflow velocity determined by Combi et al. (1999, ApJ 512,961-968) from CN, C2, NH2 and O(1D) spectra. We are currently doing flourescence modeling of the NH and CN bands, and any new results on these molecules will be presented.
This research is supported by NASA.
Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.
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2 added 68 characters in body
First of all, I am aware of the questions about the Zariski topology asked here and I am also aware of the discussion at the Secret Blogging Seminar. But I could not find an answer to a question that bugged me right from my first steps in algebraic geometry: how can I really motivate the Zariski topology on a scheme?
For example in classical algebraic geometry over an algebraically closed field I can define the Zariski topology as the coarsest $T_1$-topology such that all polynomial functions are continuous. I think that this is a great definition when I say that I am working with polynomials and want to make my algebraic set into a local ringed space. But what can I say in the general case of an affine scheme?
Of course I can say that I want to have a fully faithful functor from rings into local ringed spaces and this construction works, but this is not a motivation.
For example for the prime spectrum itself, all motivations I came across so far are as follows: well, over an algebraically closed field we can identify the points with maximal ideals, but in general inverse images of maximal ideals are not maximal ideals, so let's just take prime ideals and...wow, it works. But now that I know that one gets the prime spectrum from the corresponding functor (one can of course also start with a functor) by imposing an equivalence relation on geometric points (which I find very geometric!), I finally found a great motivation for this. What is left is the Zariski topology..topology, and so far I just came across similar strange motivations as above...
1
# How can I really motivate the Zariski topology on a scheme?
First of all, I am aware of the questions about the Zariski topology asked here and I am also aware of the discussion at the Secret Blogging Seminar. But I could not find an answer to a question that bugged me right from my first steps in algebraic geometry: how can I really motivate the Zariski topology on a scheme?
For example in classical algebraic geometry over an algebraically closed field I can define the Zariski topology as the coarsest $T_1$-topology such that all polynomial functions are continuous. I think that this is a great definition when I say that I am working with polynomials and want to make my algebraic set into a local ringed space. But what can I say in the general case of an affine scheme?
Of course I can say that I want to have a fully faithful functor from rings into local ringed spaces and this construction works, but this is not a motivation.
For example for the prime spectrum itself, all motivations I came across so far are as follows: well, over an algebraically closed field we can identify the points with maximal ideals, but in general inverse images of maximal ideals are not maximal ideals, so let's just take prime ideals and...wow, it works. But now that I know that one gets the prime spectrum from the corresponding functor (one can of course also start with a functor) by imposing an equivalence relation on geometric points (which I find very geometric!), I finally found a great motivation for this. What is left is the Zariski topology...
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# Is there a semantic way to typeset table headers in LaTeX?
Usually, when I add tables I use \usepackage{booktabs} and code that looks like this:
\begin{table}[ht]
\centering
\begin{tabular}{l|rrr}
\toprule
Country / Property & Population & Area & HDI \\\midrule
France & $66 \cdot 10^6$ & $\SI{668763}{\km\squared}$ & 0.89 \\
Germany & $81 \cdot 10^6$ & $\SI{357167}{\km\squared}$ & 0.92 \\
United States & $317 \cdot 10^6$ & $\SI{9629091}{\km\squared}$ & 0.94 \\\bottomrule
\end{tabular}
\label{table:countries}
\end{table}
But is there any semantic way to mark the table header row?
Or a way to change the style of a complete row / column?
## MWE
\documentclass[a4paper]{scrartcl}
\usepackage{amssymb, amsmath} % needed for math
\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf
\usepackage[margin=2.5cm]{geometry} %layout
\usepackage{siunitx}
\usepackage{booktabs}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Begin document %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\newcolumntype{+}{>{\global\let\currentrowstyle\relax}}
\newcolumntype{^}{>{\currentrowstyle}}
\newcommand{\rowstyle}[1]{\gdef\currentrowstyle{#1}%
#1\ignorespaces
}
\begin{table}[ht]
\centering
\begin{tabular}{+l|^r^r^r}
\toprule
\rowstyle{\bfseries}%
Country / Property & Population & Area & HDI \\\midrule
France & $66 \cdot 10^6$ & $\SI{668763}{\km\squared}$ & 0.89 \\
Germany & $81 \cdot 10^6$ & $\SI{357167}{\km\squared}$ & 0.92 \\
United States & $317 \cdot 10^6$ & $\SI{9629091}{\km\squared}$ & 0.94 \\\bottomrule
\end{tabular}
\label{table:countries}
\end{table}
\end{document}
## What I've seen so far
On www.latex-community.org I have seen this:
\newcolumntype{+}{>{\global\let\currentrowstyle\relax}}
\newcolumntype{^}{>{\currentrowstyle}}
\newcommand{\rowstyle}[1]{\gdef\currentrowstyle{#1}%
#1\ignorespaces
}
\begin{table}[ht]
\centering
\begin{tabular}{+l|^r^r^r}
\toprule
\rowstyle{\bfseries}%
Country / Property & Population & Area & HDI \\\midrule
France & $66 \cdot 10^6$ & $\SI{668763}{\km\squared}$ & 0.89 \\
Germany & $81 \cdot 10^6$ & $\SI{357167}{\km\squared}$ & 0.92 \\
United States & $317 \cdot 10^6$ & $\SI{9629091}{\km\squared}$ & 0.94 \\\bottomrule
\end{tabular}
\label{table:countries}
\end{table}
• Please complete your code to provide a compilable document. That is much easier to work with than mere fragments. I'm actually not really at all clear what you are asking. What sort of markup do you want? And obviously you can change the style of a column when you specify the settings for the environment. (A row is a bit trickier.) longtable defines \endhead and \endfirsthead and similarly for the footer. Other packages do similar things but I'm not sure if that's what you mean or not. – cfr Aug 25 '14 at 1:44
• @cfr: I want to make sure that I have a consistent way in which I show my tables. Hence I would like to have something like \headercell{content} where I can specify what the header should look like. Of course, I could define a macro myself. But I would like to know if there already exists something like this that eventually allows more sophisticated options like "add a border like \midrule between header and content" or an option that I only have to state once "the following row / column is a header and not do it for every single cell. – Martin Thoma Aug 25 '14 at 2:42
• @Mico: I think I'll write an article about it as soon as I have some free time and leave a comment here. Or, probably better, contact you via chat. I think that does eventually not belong here. (I've removed my comment and will remove this comment, too.) – Martin Thoma Aug 25 '14 at 11:13
Rather than try to improve the display of the information given in the top left-hand cell, it may be more fruitful to disentangle the information and create two groups of columns -- a "country" column and a "property" column, with the latter getting three sub-columns (population, area, and HDI).
To enhance the readability of the table, it's probably also a good idea to remove common factors (\cdot 10^6 and \km\squared) from the cells and place that information in the header section. From a point of view of programming aesthetics, it's probably also a good idea to choose S as the column type for columns 2, 3, and 4, rather than giving them a generic r type and then overlaying various cells with \SI macros.
I wouldn't rule out categorically the use of bold face for material provided in the header cells. More often than not, though, use of bold face smacks of a desperate (and frequently futile) attempt to rescue an improperly designed table from irrelevance.
The screenshot below shows the output of your original code as well as the result of implementing the suggestions given above. If I wanted to improve the table some more, I'd probably start with stating the countries' areas in thousands of square kilometers -- and round off the decimals completely.
\documentclass{article}
\usepackage{booktabs,siunitx,caption}
\begin{document}
\begin{table}[ht]
\label{table:countries}
\centering
\begin{tabular}{l|rrr}
\toprule
Country / Property & Population & Area & HDI \\\midrule
France & $66 \cdot 10^6$ & $\SI{668763}{\km\squared}$ & 0.89 \\
Germany & $81 \cdot 10^6$ & $\SI{357167}{\km\squared}$ & 0.92 \\
United States & $317 \cdot 10^6$ & $\SI{9629091}{\km\squared}$ & 0.94 \\\bottomrule
\end{tabular}
\bigskip
\begin{tabular}{lS[table-format=3.0]
S[table-format=7.0]
S[table-format=1.2]}
\toprule
Country & \multicolumn{3}{c}{Property}\\
\cmidrule{2-4}
& {Population} & {Area} & {HDI} \\
& {(mio.)} & {(km\textsuperscript{2})}\\
\midrule
France & 66 & 668763 & 0.89 \\
Germany & 81 & 357167 & 0.92 \\
United States & 317 & 9629091 & 0.94 \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
• I find the “Property” header useless, as it adds no information. – egreg Aug 25 '14 at 9:13
Table can also be created as shown below.
\documentclass{article}
\usepackage{booktabs,siunitx,caption}
\begin{document}
\begin{table}[ht]
\label{table:countries}
\centering
\begin{tabular*}{1.2\textwidth}{r|r|r||r|r|r||r|r|r}
\toprule
\multicolumn{9}{c}{Country}\\
\midrule
\multicolumn{3}{c}{France} & \multicolumn{3}{c}{Germany} & \multicolumn{3}{c}{United States}\\
\midrule
\multicolumn{3}{c}{Property}& \multicolumn{3}{c}{Property}& \multicolumn{3}{c}{Property}\\
\midrule
Population & Area &{HDI}& Population & Area &{HDI}&Population & Area &{HDI}\\
{(mio.)}& {(km\textsuperscript{2})}& &{(mio.)}& {(km\textsuperscript{2})}& &{(mio.)}& {(km\textsuperscript{2})}&\\
\midrule
66 & 668763 & 0.89 & 81 & 357167 & 0.92 & 317 & 9629091 & 0.94 \\
\bottomrule
\end{tabular*}
\end{table}
\end{document}
output:
• Is it a good idea to specify a table width that's 20 percent larger than the width of the text block? – Mico Aug 25 '14 at 9:16
• While viewing the whole page with text and tables it may add some visual impact – murugan Aug 25 '14 at 9:33
• But how do you know that making the table 20% wider than the text block won't also make the table exceed the physical width of the paper that the document might get printed on? That'll make for terrible visual impact, won't it? In general, unless you can be absolutely sure that it's permissible to expand the width of the text block, it is simply not a good idea to let anything exceed that width. – Mico Aug 25 '14 at 13:16
• Thanks. Absolutely correct. Don't expand the width of the text block beyond the actual width designed with a view to get the document printed. – murugan Aug 25 '14 at 13:40
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{}
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## Section2.2Recursive Sequences and Projection Functions
###### Overview
When looking for patterns in sequences, we usually explore two possibilities. One approach is to look at the values of individual terms and see if there is an explicit formula relating the index with the formula. There were several examples of this in the previous section. Another approach is to look for a pattern in how terms are generated from earlier terms. For example, the sequence $(7,10,13,16,\ldots)$ is easy to recognize that each term is found by adding $3$ to the previous term.
In this section, we consider recursively defined sequences. Arithmetic and geometric sequences are two familiar examples of sequences with recursive definitions. We review some basic ideas about functions. We will learn about projection functions used in such recursive definitions. We visualize the role of projection functions as maps between sequence values and through cobweb diagrams.
### Subsection2.2.1Arithmetic and Geometric Sequences
We often think of sequences in terms of a pattern for how to find the values. When a sequence can be defined so that the next value can found knowing only the previous value, we say the sequence has a recursive definition. The simplest pattern-based sequences follow simple recursive patterns.
An arithmetic sequence is a sequence whose terms change by a fixed increment or difference. For example, consider the sequence introduced above,
\begin{equation*} x = (7, 10, 13, 16, \ldots). \end{equation*}
The pattern for this sequence was that we add 3 to each term in the sequence to find the next term. The value 3 is called the increment or difference of the sequence. It is called the increment because there is a pattern of adding the same value to values in the sequence:
\begin{gather*} x_2=x_1 + 3 = 7+3,\\ x_3 = x_2 + 3 = 10+3,\\ x_4=x_3+3 = 13+3,\\ \vdots \end{gather*}
It is called the difference because each of those equations can be rewritten as a difference of values:
\begin{gather*} x_2-x_1 = 3,\\ x_3 - x_2 = 3,\\ x_4-x_3=3,\\ \vdots \end{gather*}
A geometric sequence is a sequence whose terms change by a fixed multiple or ratio. An example of a geometric sequence is given by
\begin{equation*} u= (2, 6, 18, 54, \ldots). \end{equation*}
Each term is found by multiplying the previous term by 3, which is the multiple or ratio of the sequence. We call the value 3 the multiple because of the pattern
\begin{gather*} u_2 = 3 u_1 = 3 \cdot 2,\\ u_3 = 3 u_2 = 3 \cdot 6,\\ u_4 = 3 u_3 = 3 \cdot 18,\\ \vdots \end{gather*}
It is call the ratio if we rewrite the equations as a ratio of a value to its previous value
\begin{gather*} \frac{u_2}{u_1} = 3,\\ \frac{u_3}{u_2} = 3,\\ \frac{u_4}{u_3} = 3,\\ \ldots \end{gather*}
For recursively defined sequences, the equation that describes the relationship between consecutive terms of the sequence is called the recurrence relation. When the recurrence relation for a sequence $x$ is solved for the next value as a dependent variable in terms of an expression involving of the previous term, we call this map or function the projection function because it allows us to project future values based on current values.
### Subsection2.2.2Functions as Maps
Before we discuss more about projection functions, we take a short diversion to review some core concepts about functions in general. Functions are at the heart of everything we do in calculus. Unfortunately, many students have subtle misconceptions about how to think about functions. We want to use our emphasis on sequences to come to terms with these ideas. Be prepared to think about functions from many different points of view. We begin by thinking of a function as a map between variables.
###### Definition2.2.1Function
Given two related variables, say $x$ and $y\text{,}$ such that there is a rule or relation that defines a map $x \mapsto y\text{,}$ we say that the map is a function. (We will make this more precise later. 1 The precise definition needs to address the domain of the function and clarify what is a map when there is no defining expression.)
Similar to other mathematical objects like variables and sequences, functions are usually represented by symbols for their names. Letter symbols like $f$ or $g$ are particularly common. We would write $f : x \mapsto y$ to say that the name of the function representing the map from a variable $x$ to $y$ is $f\text{.}$ The independent variable $x$ is the input for the function; the dependent variable $y$ is the output of the function.
We often use function notation, writing $y = f(x)\text{.}$ The parentheses in function notation indicate that whatever is inside is the value for the input, not multiplication. So this equation says that the dependent variable $y$ is equal to the output of the function $f$ when the input has the value represented by $x\text{.}$ We usually read the equation, “$y$ equals the value of $f$ of $x\text{.}$” When we have an equation expressing $y$ as an explicit expression involving $x\text{,}$ that expression can be used to define the function.
###### Example2.2.2
Consider the equation $2x+5y = 10\text{,}$ which relates the variables $x$ and $y\text{.}$ Because we can solve for the variable $y$ to be a dependent variable,
\begin{equation*} y = -\frac{2}{5}x + 2, \end{equation*}
the equation defines a function $x \mapsto y\text{.}$ We can choose any name for this function (other than the symbols $x$ or $y\text{,}$ obviously). We might choose to use the name $P$ and write this as a map
\begin{equation*} P : x \mapsto y = -\frac{2}{5}x+2\text{.} \end{equation*}
Using the usual function notation, we would instead write
\begin{equation*} y = P(x) = -\frac{2}{5}x+2\text{.} \end{equation*}
When we wrote explicit formulas for the value of a sequence with the index as the independent variable, we noted that we had a map from the index to the value of the sequence. That was an example of a function.
###### Example2.2.3
For the explicitly defined sequence $x_n = 3n-2\text{,}$ $n=1, 2, 3, \ldots\text{,}$ the equation defines a map $n \mapsto x_n = 3n-2\text{.}$ We could name the function $S\text{,}$ for example, and write $S(n) = 3n-2$ so that $x_n = S(n)\text{.}$
### Subsection2.2.3Projection Functions
We now return to the concept of a recursively defined sequence and the projection function. A sequence is recursive if the same rule is used to go from one value of the sequence to the next. For our earlier example of an arithmetic sequence, we had a pattern of equations
\begin{gather*} x_2 = x_1 + 3,\\ x_3 = x_2 + 3,\\ x_4=x_3+3,\\ \vdots \end{gather*}
The rule was always the same, but the symbols were different because they involved different index values.
We need some notation to capture the idea of consecutive values of a sequence. If $n$ represents the value of the index for a sequence, then $n+1$ represents the value of the index for the subsequent term of the sequence and $n-1$ represents the value of the index for the preceding term of the sequence. For example, if $n=3\text{,}$ then $x_n$ would be $x_3\text{,}$ $x_{n+1}$ would be $x_4\text{,}$ and $x_{n-1}$ would be $x_2\text{.}$ All of our equations follow the pattern
\begin{equation*} x_{n} = x_{n-1} + 3\text{,} \end{equation*}
where the first equation corresponds to $n=2\text{,}$ the second to $n=3\text{,}$ and so forth. Equivalently, we could think of all of the equations as following the pattern
\begin{equation*} x_{n+1} = x_{n} + 3\text{,} \end{equation*}
but now the first equation comes from $n=1$ and the second from $n=2\text{.}$ This equation which relates $x_{n}$ and $x_{n-1}$ is called a recurrence relation or recursive equation for the sequence. Because the equation has been written with $x_{n}$ as a dependent variable in terms of the value of $x_{n-1}\text{,}$ we actually have a projection function.
###### Definition2.2.4Projection Function
Suppose a sequence $x$ is defined by a recurrence relation of the form
\begin{equation*} x_{n} = f(x_{n-1}). \end{equation*}
The function $f$ defining the relation $x_{n-1} \mapsto x_{n}$ is called the projection function. Equivalently, we could write the recurrence relation in terms of a previous value as
\begin{equation*} x_{n+1} = f(x_{n})\text{.} \end{equation*}
For a sequence with a recurrence relation $x_{n} = x_{n-1} + 3\text{,}$ the projection function is $f : x_{n-1} \mapsto x_{n} = x_{n-1} + 3\text{.}$ The function $f$ takes a value as an input and maps it to an output that is that value plus 3. I find it useful to imagine the independent variable in a function as if it were a box, as in
\begin{equation*} f(x_{n-1}) = x_{n-1} + 3 \quad \Leftrightarrow \quad f(\square) = \square + 3\text{.} \end{equation*}
Whatever is between the parentheses for the input of a function will go in the box of the formula. With this understanding, any variable can be used as a placeholder for the input: $f(x) = x+3$ and $f(a)=a+3$ describe the same mapping rule.
When we have a projection function for a sequence defined recursively, we can apply the function repeatedly to calculate values for the sequence. Many sequences can use the same projection function. We need an initial value to begin the process.
###### Example2.2.5
A sequence $u = (u_n)_{n=0}^{\infty}$ is defined recursively by the projection function $f(x)=2x-5$ and an initial value $u_0 = 3\text{.}$ Find the next four terms of the sequence.
Solution
The projection function defines the map $u_{n-1} \mapsto u_{n}$ according to the rule $f(x)=2x-5$ or $f(\square) = 2 \cdot \square - 5\text{.}$ It tells us that if we use an input coming from a sequence value, the output of the function will be the next sequence value. We were given an initial value $u_0 = 3\text{.}$ Using the recursive equation for $n=1$ and the preceding value $u_0=3$ as the input to $f\text{,}$ the output will be the value $u_1\text{:}$
\begin{equation*} u_1 = f(u_0) = f(3) = 2(3) - 5 = 1\text{.} \end{equation*}
Now that we know $u_1\text{,}$ we can use that value as an input to get $u_2\text{,}$ and so on:
\begin{align*} u_2 &= f(u_1) = 2(1) - 5 = -3,\\ u_3 &= f(u_2) = 2(-3) - 5 = -11,\\ u_4 &= f(u_3) = 2(-11) - 5 = -27. \end{align*}
Sometimes, a recurrence relation is not written with the new sequence value isolated. To identify the projection function, we need to solve for the new value of the sequence.
###### Example2.2.6
A sequence is defined by the recurrence relation
\begin{equation*} w_{n+1}-w_n = 1.4 w_n - \frac{3}{w_n}, \quad n \ge -1, \end{equation*}
and an initial value $w_{-1}=1\text{.}$ Find the recursive equation corresponding to the projection function, $w_n \mapsto w_{n+1}\text{,}$ and find $f(x)\text{.}$ Use this to find $w_0$ and $w_1\text{.}$
Solution
To find the recursive equation, we need to solve for $w_{n+1}\text{.}$
\begin{gather*} w_{n+1}-w_n = 1.4 w_n - \frac{3}{w_n}\\ w_{n+1} = 2.4 w_n - \frac{3}{w_n} \end{gather*}
This recursive equation gives us a map from a current value $w_n$ to the next value $w_{n+1}$ in the sequence, $w_n \mapsto w_{n+1}\text{,}$ which is the projection function
\begin{equation*} w_{n+1} = f(w_n) = 2.4 w_n - \frac{3}{w_n}. \end{equation*}
This means that using an input $x$ gives
\begin{equation*} f(x) = 2.4 x - \frac{3}{x}. \end{equation*}
Once we have the map, we can repeatedly use the projection function to find subsequent values of the sequence.
\begin{align*} w_{-1} &= 1\\ w_{0} &= f(w_{-1}) = f(1)\\ &= 2.4(1)-\frac{3}{1} = -0.6\\ w_{1} &= f(w_0) = f(-0.6)\\ &= 2.4(-0.6)-\frac{3}{-0.6} = 3.56 \end{align*}
### Subsection2.2.4Arithmetic and Geometric Sequences Revisited
The arithmetic and geometric sequences have simple explicit formulas. We use these formulas to illustrate the idea of a sequence as a map from the index to the sequence value.
The explicit formula for an arithmetic sequence is a special case of a linear function. The increment of the sequence represents the slope. The initial value gives us a known point. Knowing how many steps away from the given point along with the increment allows us to compute other sequence values.
###### Example2.2.7
Find the explicit formula for the arithmetic sequence $x=(7,10,13,16,\ldots)\text{.}$ Use the formula to find $x_{100}\text{.}$
Solution
The initial value $x_1=7$ means our function will be a map $n \mapsto x_n$ that takes an input $n=1$ to an output $x_1=7\text{.}$ The increment of 3 that appears in the recursive equation $x_{n} = x_{n-1} + 3$ means that the function increases by 3 for every increment of the index by 1. That is, the slope is $m=+3\text{.}$ The value of $x_n$ will equal 7 plus 3 times the number of increments in the index,
\begin{equation*} x_n = 7 + 3(n-1)\text{.} \end{equation*}
We could find an equivalent expression after using the distributive property,
\begin{equation*} x_n = 4 + 3n\text{.} \end{equation*}
Because we now have the function $n \mapsto x_n\text{,}$ we can find the value of the sequence for any index using this expression. To find $x_{100}\text{,}$ we use $n=100$ and the map $n \mapsto x_n\text{,}$
\begin{equation*} x_{100} = 4 + 3 \cdot 100 = 304\text{.} \end{equation*}
The following theorem provides the formula for the explicit formula of any arithmetic sequence.
The explicit formula for a geometric sequence is a special case of an exponential function. The multiple for the sequence corresponds to the base of the exponential. An initial value gives us a known point. The formula will count how many increments the index has changed and multiply by the base to that power.
###### Example2.2.9
Find the explicit formula for the geometric sequence $u=(48,24,12,6,3,\ldots)\text{.}$ Use the formula to find $u_{20}\text{.}$
Solution
The sequence $u$ is geometric because the ratio of the sequence value to its predecessor is always the same.
\begin{gather*} \frac{u_2}{u_1} = \frac{24}{48} = \frac{1}{2}\\ \frac{u_3}{u_2} = \frac{12}{24} = \frac{1}{2}\\ \frac{u_4}{u_3} = \frac{6}{12} = \frac{1}{2}\\ \frac{u_5}{u_4} = \frac{3}{6} = \frac{1}{2} \end{gather*}
The recursive formula for the sequence multiplies the previous sequence value by $\rho=\frac{1}{2}\text{,}$
\begin{equation*} u_{n} = \frac{1}{2} \cdot u_{n-1}\text{.} \end{equation*}
The initial value $u_1=48$ means our function will be a map $n \mapsto x_n$ that takes an input $n=1$ to an output $x_1=48\text{.}$
Each time the index is incremented by 1, the value of the sequence is multiplied by $\rho=\frac{1}{2}\text{.}$ We can count the number of increments for the index $n$ by the expression $n-1\text{.}$ Because repeated multiplication is a power, we obtain an explicit formula
\begin{equation*} u_{n} = u_1 \cdot \rho^{n-1} = 48 \cdot \left( \frac{1}{2} \right)^{n-1}\text{.} \end{equation*}
Using the properties of powers, this is equivalent to
\begin{equation*} u_{n} = \frac{48}{2^{n-1}}. \end{equation*}
With the function $n \mapsto u_n\text{,}$ we can find the value of the sequence for any index using this expression. To find $u_{20}\text{,}$ we use $n=20$ and the map $n \mapsto u_n\text{,}$
\begin{equation*} u_{20} = \frac{48}{2^{19}}. \end{equation*}
If we rewrite $48 = 16 \cdot 3 = 2^4 \cdot 3$ and then simplify the fraction, this is equivalent to
\begin{equation*} u_{20} = \frac{3}{2^{15}} = \frac{3}{32768}. \end{equation*}
The general formula for a geometric sequence is provided in the following theorem.
### Subsection2.2.5Graphical Representations of Projections
If we think about a function as a map between two number lines, then the process of using a projection function to find values in a sequence can be visualized using such a mapping. Consider two number lines. The top number line will represent the current value of the sequence or the input of the function. The bottom number line will represent the next value of the sequence or the output of the function. The projection function defines the rule for how we go from the input to the output. Because the process repeats, we also go from the output number line to the same value on the input number line.
###### Example2.2.11
For the sequence defined by the projection function $f(x) = 2x-5$ and initial value $u_0 = 3\text{,}$ the mapping used to generate the first few terms of the sequence can be represented graphically as shown below.
###### Example2.2.12
For the sequence defined by the projection function
\begin{equation*} w_{n+1} = 2.4 w_n - \frac{3}{w_n} \end{equation*}
and initial value $w_{-1} = 1\text{,}$ the mapping used to generate the first few terms of the sequence can be represented graphically as shown below.
The graph of a function $f$ shows all points $(x,y)$ in the plane where $y=f(x)\text{.}$ Where a mapping visualizes a function as going from the input number line to the output number line, a graph visualizes a function by thinking of the $x$-axis as the input number line and the vertical position of the graph in the $y$-direction as the output. It is as if there were a separate vertical number line parallel to the $y$-axis (and perpendicular to the $x$-axis) through every value on the $x$-axis. The point on the graph corresponds precisely to the location of the output for the function.
We can use the graph of a projection function to visualize how to generate a recursive sequence. The algorithm we use follows the same pattern as we used in the mapping and generates what is called a cobweb diagram in the plane.
###### Example2.2.14
Draw the first four iterations of the cobweb diagram for the sequence $u$ with projection function $f(x) = 2x-5$ and initial value $u_0=3\text{.}$
Solution
We start by drawing the graphs $y=f(x)=2x-5$ and $y=x$ on the same graph. We then start with a point on the $x$-axis at $x=3$ corresponding to the value of $u_0=3\text{.}$ We want to use this value to find the next value in the sequence $u_1\text{.}$ This use the projection function, so we go up to the value of the function $f(3)=1\text{,}$ drawing a vertical line segment to the point $(3,1)\text{.}$ We now know $u_1=1$ and we need to use this as a new input for the projection function. So the next step is to draw a horizontal segment to $y=x$ at the point $(1,1)\text{.}$ Now that our $x$-value is $1\text{,}$ we can repeat the process and use the function to find $u_2=f(1)=-3\text{,}$ drawing a vertical segment down to the point $(1,-3)$ and then a horizontal segment to $(-3,-3)\text{.}$
### Subsection2.2.6Summary
• A sequence $x$ is recursive when the relation between consecutive values of the sequence is the same for every index. An equation describing this relation is called a recurrence relation. If we can solve for $x_{n}$ as a dependent variable with $x_{n-1}$ as the independent variable, the corresponding equation is called the recursive equation.
• An arithmetic sequence with common difference $c$ has a projection function $f(x)=x+c\text{,}$ a recursive relation
\begin{equation*} x_{n}=x_{n-1} + c\text{,} \end{equation*}
and an explicit formula given a known value for $x_k\text{,}$
\begin{equation*} x_n = x_k + \beta(n-k). \end{equation*}
• A geometric sequence with common ratio $\rho$ has a projection function $f(x)=\rho x\text{,}$ a recursive relation
\begin{equation*} x_{n}=\rho \cdot x_{n-1}\text{,} \end{equation*}
and an explicit formula given a known value for $x_k\text{,}$
\begin{equation*} x_n = x_k \cdot \rho^{n-k}. \end{equation*}
• We think of functions as maps from the value of one variable to the value of another variable. For a sequence $x\text{,}$ the map from the index $n$ to the sequence value $x_n$ is called the explicit function of the sequence. For a recursive sequence, the map from one sequence value $x_{n-1}$ to the next sequence value $x_{n}$ is called the projection function.
• The graph of a function uses values on the $x$-axis as input values and the vertical position of the graph as output values. A cobweb diagram uses the graph of a projection function with repeatedly updated inputs to generate a visual representation of a recursive sequence.
### Subsection2.2.7Exercises
Determine if each sequence is arithmetic, geometric, or neither. For each sequence that is arithmetic or geometric, (i) state the recursive equation for the sequence, (ii) find the projection function $f(x)\text{,}$ (iii) state an explicit formula for the sequence, and (iv) use the explicit formula to find the value with index 20.
###### 1
$u = (u_n)_{n=0}^{\infty} = (-8, -2, 4, 10, \ldots)$
###### 2
$t = (t_k)_{k=2}^{\infty} = (27, 23, 19, 15, \ldots)$
###### 3
$v = (v_k)_{k=-2}^{\infty} = (12, 16, 21, 27, \ldots)$
###### 4
$w = (w_k)_{k=1}^{\infty} = (4, 20, 100, 500, \ldots)$
###### 5
$z = (z_i)_{i=0}^{\infty} = (27, 18, 12, 8, \ldots)$
Each problem gives a projection function and an initial value that together determine a sequence recursively. Find the four terms following the initial value. Illustrate the sequence as a map between two number lines.
###### 6
$P = (P_t)_{t=0}^{\infty}$ with $P_0 = 400$ and projection function $f(x) = x + 25\text{.}$
###### 7
$u = (u_n)_{n=0}^{\infty}$ with $u_0 = 3$ and projection function $f(x) = 1.5x + 1\text{.}$
###### 8
$u = (u_n)_{n=0}^{\infty}$ with $u_0 = -3$ and projection function $f(x) = 1.5x + 1\text{.}$
###### 9
$w = (w_i)_{i=1}^{\infty}$ with $w_{1} = 4$ and projection function $f(x) = 2.5x - 6\text{.}$
###### 10
$w = (w_i)_{i=1}^{\infty}$ with $w_{1} = 5$ and projection function $f(x) = 2.5x - 6\text{.}$
###### 11
$z = (z_j)_{j=0}^{\infty}$ with $z_{0} = 16$ and projection function $f(x) = \sqrt{x}\text{.}$
Each problem defines a sequence recursively. Give the formula of the projection function $f(x)\text{.}$ Create the cobweb diagram for the sequence corresponding to the first five values of the sequence.
###### 12
$Q = (Q_t)_{t=0}^{\infty}$ with $Q_{0} = 3$ and $Q_{t} = Q_{t-1} + 4\text{.}$
###### 13
$c = (c_k)_{k=0}^{\infty}$ with $c_{0} = 10$ and $c_{k+1} = 0.75 c_k\text{.}$
###### 14
$S = (S_n)_{n=0}^{\infty}$ with $S_{0} = 10$ and $S_{n} = 0.8 S_{n-1} + 4\text{.}$
###### 15
$P = (P_t)_{t=0}^{\infty}$ with $P_{0} = 1$ and $\displaystyle P_{t+1} = \frac{20 P_t}{P_t + 10}\text{.}$
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How Many 9's?
Algebra Level 2
If $$N=999,999,999,999,999,999,999$$ then how many 9's are there in $$N^2$$?
×
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The Fundamental Theorem of Calculus Lesson 7.4. 2 Definite Integral Recall that the definite integral was defined as But … finding the limit is not often.
Presentation on theme: "The Fundamental Theorem of Calculus Lesson 7.4. 2 Definite Integral Recall that the definite integral was defined as But … finding the limit is not often."— Presentation transcript:
The Fundamental Theorem of Calculus Lesson 7.4
2 Definite Integral Recall that the definite integral was defined as But … finding the limit is not often convenient We need a better way!
3 Fundamental Theorem of Calculus Given function f(x), continuous on [a, b] Let F(x) be any antiderivative of f Then we claim that The definite integral is equal to the difference of the two antiderivatives Shazzam !
4 What About + C ? The constant C was needed for the indefinite integral It is not needed for the definite integral The C's cancel out by subtraction
5 You Gotta Try It Consider What is F(x), the antiderivative? Evaluate F(5) – F(0)
6 Properties Bringing out a constant factor The integral of a sum is the sum of the integrals
7 Properties Splitting an integral f must be continuous on interval containing a, b, and c
8 Example Consider Which property is being used to find F(x), the antiderivative? Evaluate F(4) – F(0)
9 Try Another What is Hint … combine to get a single power of x What is F(x)? What is F(3) – F(1)?
10 When Substitution Is Used Consider u = 4m 3 + 2 du = 12m 2 It is best to change the new limits to be in terms of u When m = 0, u = 2 When m = 3, u = 110
11 Area Why would this definite integral give a negative area? The f(x) values are negative You must take this into account if you want the area between the axis and the curve
12 Assignment Lesson 7.4A Page 399 Exercises 1 – 43 odd Lesson 7.4B Page 401 Exercises 53 – 65 odd
Download ppt "The Fundamental Theorem of Calculus Lesson 7.4. 2 Definite Integral Recall that the definite integral was defined as But … finding the limit is not often."
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Homework Help Question & Answers
# please provide the answers clearly 7. Suppose a Truc-False test has 20 questions (a) In how...
please provide the answers clearly
7. Suppose a Truc-False test has 20 questions (a) In how many ways may a student mark the test, if 6 questions are scored correctly and 14 incorrectly? (b) State which theorem from the text is applicable to solving part (a) (c) In how many ways may a student mark the test, if 10 questions are scored correctly and 10 incorrectly? 8. A baseball fan has a pair of tickets to 5 different home games of the Chicago Cubs. If the fan how many ways may he take one of them along to each of has four friends who like basebal the five games?
Answer #1
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$(a)~We~can~select~6~questions~(which~are~answered~correctly)~out~of~20\\ ~in~\binom{20}{6}~ways.\\ Hence~total~of~ways~that~a~student~answers~6~correctly~out~of~20=\binom{20}{6}=\frac{(20)!}{6!(14)!}=38760.\\ (b)~The~number~of~ways~in~which~a~set~of~r~objects~can~be~formed~out~of~n~different~objects~is\\ \binom{n}{r}.\\ (c)~Required~no.~of~ways=\binom{20}{10}=\frac{(20)!}{(10)!(10)!}=184756\\ 8.~Since~the~fan~has~4~friends~and~he~has~a~pair~of~tickets~of~5~games~then\\ he~can~take~any~one~of~his~4~friends~along~to~each~of~the~five~games~in~5^4~ways.\\ Hence~total~no.~of~ways=5^4.$
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# a “… doesn't match its definition” problem, that I don't understand
I managed to extract from my code the following MnWE which shows the problem i encounter :
Example 1
\begin{document}
\newcommand{\createDATA}[1]{
\xdef\DATA{}
\newcommand{\test}[2][]{
\xdef\DATA{\DATA args=##1 , ##2 }
}
\test[x]{\macom[x]{blabla}}
}
\newcommand{\macom}[2][q]{AAA}
\createDATA
\DATA
\end{document}
The compilation gives an error : ! Use of \\test doesn't match its definition. which I can't understand. On the other hand, notice that if in the definition of \createDATA I replace \macom by a command without optional argument, then it works :
Example 2
\begin{document}
\newcommand{\createDATA}[1]{
\xdef\DATA{}
\newcommand{\test}[2][]{
\xdef\DATA{\DATA args=##1 , ##2 }
}
\test[x]{\macomm{blabla}}
}
\newcommand{\macomm}[1]{BBB}
\createDATA
\DATA
\end{document}
It is very mysterious to me...
-
It's quite hard to understand what you're trying to achieve. But the problem is using a command with optional argument inside an \xdef. The error message is not quite informative, however. – egreg Jun 18 '12 at 17:59
This is the problem with minimal examples ... they sometimes have not meaning. This one just illustrates a problem, that i encounter in my code (which has a meaning!) – nicolas roy Jun 18 '12 at 18:03
You are trying to \edef (\xdef = \global\edef) the macro \macom. However, as \macom is a command with an optional argument, this cannot be done safely. You need to either not do an \edef, use the LaTeX protected mechanism:
\documentclass{article}
\begin{document}
\makeatletter
\newcommand{\createDATA}[1]{%
\xdef\DATA{}%
\newcommand{\test}[2][]{%
\protected@xdef\DATA{\DATA args=##1 , ##2 }%
}%
\test[x]{\macom[x]{blabla}}%
}
\makeatother
\newcommand{\macom}[2][q]{AAA}
\createDATA
\DATA
\end{document}
or make \macrom engine robust using the e-TeX extensions, for example
\documentclass{article}
\usepackage{etoolbox}
\begin{document}
\newcommand{\createDATA}[1]{%
\xdef\DATA{}%
\newcommand{\test}[2][]{%
\xdef\DATA{\DATA args=##1 , ##2 }%
}%
\test[x]{\macom[x]{blabla}}%
}
\newrobustcmd{\macom}[2][q]{AAA}
\createDATA
\DATA
\end{document}
(By the way, you have a lot of extraneous spaces in your commands: I've added % to kill line ends and deal with these.)
For more on what robust, protected and 'fragile' means, see What is the difference between Fragile and Robust commands?
The reason that you cannot \edef a command with optional arguments is that these are picked up using the TeX primitive \futurelet. This performs an assignment, and assignments are not expandable. On the other hand, grabbing a mandatory argument does not require any tricks, so it is expandable.
[It's a bit more complex than that, as there are ways of expandably testing for optional arguments. These are more restrictive than the non-expandable approach, and the LaTeX2e kernel therefore goes with comprehensive-but-non-expandable. For pre-constructed methods for both expandable and non-expandable optional argument grabbing, with automatically robust functions and lots of additional cleverness, see the LaTeX3 xparse module.]
-
As egreg has commented on the question, I have no idea why there is an \edef being used here, hence saying that one (perhaps the most obvious) option is to simply avoid it entirely. – Joseph Wright Jun 18 '12 at 18:00
Could you please explain why one can not safely \edef a command with optional argument, but can do it without optional argument. – nicolas roy Jun 18 '12 at 18:01
@nicolasroy No optional argument is a necessary condition for a macro to be safe in an \edef. Not sufficient. To be safe it must expand to unexpandable tokens without any intervening assignment. It's also important to note that the expansions are "all the way down". – egreg Jun 18 '12 at 18:06
@nicolasroy I've added some detail. There are other questions on the site which focus specifically on expandability. – Joseph Wright Jun 18 '12 at 18:08
– Joseph Wright Jun 18 '12 at 18:11
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# How should I store & read level map?
Ok, so I am trying to create a level map, but I don't know how I should store it. Should I use an array for every level? I feel like that wouldn't be very efficient though. I'm not sure what I should do. Any thoughts?
EDIT: Currently I am storing the single map as a 2D Array, it looks like
int test_array[][] = { {...}, {...} }
I am iterating through each element and for every '1' or '2', draw a block. Is there a better way to do this?
• Seems your asking us how you should form a data structure; but your not telling us anything about what is in that data structure. That makes it impossible to give a useful answer. Jan 17 '17 at 19:57
• There are countless of options. There is no single best one, only the one which is best for your game. We don't know how your software architecture looks, so we can't help you with this decision. But if you elaborate more about what you tried and what problems you encountered, we might be able to help you. Jan 17 '17 at 19:58
• pick a format. at the moment, Tiled is popular, and still worked on mapeditor.org/download.html Jan 17 '17 at 21:44
• Thank you for suggesting that program. Ill give it a shot! Ill reply back later if it worked for me! Jan 19 '17 at 2:14
• So i've fixed it. I use a txt file and read them with a BufferedReader. Jan 23 '17 at 0:28
If you are making a platformer or top down rpg style game an array can be very usefull.
As long as you can consistently convert from world coordinates to array coordinates (and back), you can easily iterate only through a subsection of the array that represents what is on the screen by controlling the start and end of the two loops you are using for iterating through the array.
I would recommend creating a "tile" or "square" object or enumerated that you store into the map array rather than ints. Each item in the enumerated list can have a different sprite variable, movement cost variable, ect.
That way you avoid having a bunch of if statements and having to keep track of what variables do what, you can just do testArray[y][x].drawImage(xgridSize,ygridSize); or something along those lines.
This will make it harder to edit your level in a text editor, but making a crude level editor won't take too long and is worth the time.
You might also consider making maps an object (and have them store their tile arrangement in an array). This can be useful, because there might be a bunch of information that you want to save in a level that wouldn't belong in the array.
For example, what level is next, where do enemies start and what enemies are there. You can roll all of that information into a map object.
• I fixed it! I use a buffered reader to read the txt file i've created which holds the map content. Jan 23 '17 at 0:28
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## IsTim Group Title Simple dimensional analysis: To cancel out "s" in J/S, do I multiply or divide J/s by s? s in both cases are the same. one year ago one year ago
1. IsTim Group Title
This is part of a physics question, but I thought it was simple algebra, and deserved to be let free here.
2. whpalmer4 Group Title
joules are kg m^2/s^2 $J/s= \frac{{kg}*m^2}{s^2}*\frac{1}{s}=\frac{{kg}*m^2}{s^3}$ Right?
3. IsTim Group Title
I think this is extremely over-complicating the original intent of this thread...but...yes?
4. IsTim Group Title
Simply asking how to cancel out "s" in this situation.
5. whpalmer4 Group Title
Where are you canceling the s? Maybe with more context I can give you a better answer.
6. IsTim Group Title
In J/S
7. whpalmer4 Group Title
They don't cancel out. J/s = watts, and watts are kg m^2 / s^3, just like I showed above.
8. whpalmer4 Group Title
Remember, dividing by s is equivalent to multiplying by 1/s.
9. IsTim Group Title
well, you know, the same well you can "remove" distance (m) in speed (m/s) to get time (t) by
10. IsTim Group Title
t=v/d? t=d/v?
11. IsTim Group Title
Man, can not realize I forgot this so fast.
12. whpalmer4 Group Title
d = vt m = (m/s)*(s) m = m But there's no cancellation in J/s...
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## Q. 2.14
A new scale N of temperature is devised in such a way that the freezing point of ice is 100°N and boiling point is 400°N. What is the temperature reading on this new scale when the temperature is 150°C? At what temperature both the Celsius and new temperature scale reading would be the same?
## Verified Solution
Let t°N = ax + b
So that 100 = a$x_i$+ b
400 = a$x_s$ + b
\begin{aligned}a &=\frac{300}{x_s-x_i} \\b &=100-\frac{300 x_i}{x_s-x_i} \\t^{\circ} N &=\frac{300 x}{x_s-x_i}+100-\frac{300 x_i}{x_s-x_i} \\&=\frac{300\left(x-x_i\right)}{x_s-x_i}+100\end{aligned}
Also $t^{\circ} C =100 \frac{100\left(x-x_i\right)}{x_s-x_i}$
$\therefore$ t°N = 3 t°C + 100
When t°C = 150, then
t°N = 3 × 150 + 100 = 550
For t°N = t°C
t°C = 3t°C + 100
t°C = – 50
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Forty before Forty
Well, years passed and life got in the way and as is always the way, I did not complete my 40B40 however what I have done is added all the challenges to my bucket list and I will continue to work on them from there.
Forty before Forty
It has come to my attention that I am not getting any younger, in fact, I am approaching a certain so called life milestone.
At the time of writing this I am 36 and in three and a half years I will be the big Four Zero (bet that makes you feel old TOM.) In realising that this milestone was approaching I thought I should really do something with the time in the three and a half years to mark the last years of my thirties.
At this point, I should offer a nod and a tip of the hat to 39 Dreams and 40 things to do before I’m 40. As not long after the realising that the milestone was close and I should do something, I stumbled across these websites and thus Forty before Forty was born.
I have set myself 38 challenges (yes I know but keep reading) to complete in the three and a half years. The challenges range from reading books to capsizing kayaks from cooking dishes to climbing mountains the full this can be found on the Forty before Forty page (This has now been closed).
You’re probably not asking why do this? but I am going to tell you. For one reason I get forty posts from it, secondly, I often feel I don’t challenge myself enough so this is my chance to do it. The plan will be to mark challenges in progress in Orange and challenges completed in Green, I also plan to write a post and provide photographic evidence of completion.
The small print - I am not a multi millionaire and I have a family so challenges like, meet everyone of your twitter
followers or fly to every continent will be removed unless your paying for me and my family.
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# Converting a Large Analysis Project to a Reproducible Research Framework Part 2
## How easy would it be to convert an existing large MATLAB/R project to using GNU Make?
In these tutorials, we will find out together!
Welcome to Part II where we will start converting individual MATLAB scripts into a series of scripts that can be automatically created using the Make utility.
In the last tutorial, we created a combined manuscript. This manuscript contains the roadmap for what assets to create (and their order) to create a reproducible research project.
#### Platform agnostic
In this project, we are demonstrating the capabilities of MATLAB, R, and Make on the Windows platform due to it being the most challenging. For example, the Windows version of MATLAB cannot truly be run without the GUI present as either the Mac or Linux version. Also, Make must be installed on Windows, whereas it is installed by default on most Linux installations and can be installed on Mac by installing the xcode development application.
## Automating MATLAB scripts
### It’s all about targets and dependencies
The strategy for creating Make versions of MATLAB scripts remains similar to any other Make project. Focus on your target files and dependencies. Remember that each dependency must also be a target file unless it exists prior to your analysis.
For example, you might have a spreadsheet that contains clinical values and group assignments. This spreadsheet is an original asset that does not have a dependency. When you reference a Makefile, let’s call it ‘group_assignments.csv’, it must exist in your source folder to avoid getting an error.
On the other hand, you might want to wrangle your group_assignments.csv to change group labels and exclude certain subjects. In this case, you may opt to create a new file in the Build folder named “validated_group_assigments.csv'. Subsequent scripts will look for this file (rather than the original) so instructions on how to create ‘'validated_group_assigments.csv” from “group_assigments.csv” must be specified in the Makefile. It is also good practice as your original source files remain untouched.
### Start with data models, then move on to tables and figures
The number of figures and tables in any analysis is usually equal to or greater than the number of data models. We often present data models in many different ways to make our points clear.
It plays to the strength of the Make approach to create one or more data models and then use those models as dependencies in other data models, figures, and tables.
## Step 1: Edit a common Matlab file that stores shared paths, variables, and functions.
Functional programming languages like Matlab can be a joy and pain to work with. In particular, Matlab is highly dependent on specifying particular paths to the files you want to include in your project. In addition, given Matlab’s relatively enormous overhead, you want to reduce the duplication of code as much as possible.
We have included a file matlab_00_common.m to serve as a common include file in each of your Malab scripts. Why the odd name? Matlab has very specific naming conventions for files! If you name your file something different, just update the beginning of each of your scripts. In fact, in a complex analysis having more than one possible include file may increase your flexibility and increase the efficiency of your code.
Also, remember that we will be using Matlab both through the GUI for development and also running it from the command line for efficiency. This forces us to write code that is both compatible by running line by line but also can run the entire file at once. Different users have various advice on how to accomplish this, but in our research we have one method that seems to work well in almost every situation.
The template is to create an Matlab script file (“m”) that contains the code to create your environment as well as a main function of your analysis in the same file. We will have plenty of examples of this below for clarification. Each Model file should output a MAT file which contains variables of interest to be used by other analysis. In some cases, creating a CSV file or Parquet file may be more appropriate.
Let’s open matlab_00_common.m and update our variables to reflect our current system needs. Notice that we add two commands to ensure that the entire Matlab environment is wiped clean (including resetting default paths) prior to any operations. This is essential to making sure that your results can be replicated on new systems. Finally, the IsBatchModeis a logical variable that will either be TRUEif running from the command line (such as through Makefile) or through the interactive GUI (as during development).
%=========================================================================%
% CREATE REPRODUCIBLE ENVIRONMENT %
%=========================================================================%
clear all;
restoredefaultpath();
IsBatchMode = batchStartupOptionUsed;
Next we add variables that represent pathnames to common software toolboxes that will be used by our analysis. Since we wipe the Matlab path clean on each run, this is essential to reassigning paths on each script run. The HTP path refers to our internal tool box which contains RepMake scripts and other useful EEG functions.
%=========================================================================%
% TOOLBOX CONFIGURATION %
% high throughput pipline: github.com/cincibrainlab/htp_minimum.git %
%=========================================================================%
EEGLAB_PATH = 'E:/Research Software/eeglab2021';
HTP_PATH = 'C:/Users/ernie/Dropbox/htp_minimum';
BRAINSTORM_PATH = 'E:/Research Software/brainstorm3';
FIELDTRIP_PATH = 'E:/Research Software/fieldtrip-master';
Next we customize specific paths and information regarding our dataset. This is information that should be useful to any script within this project. Notice that the MATLAB and R build paths are different. That is because my R build path is on a limited space cloud drive and the MATLAB build path is on a storage drive for larger analysis projects. It is simple to use the same path if desired.
Finally, the format our datasets are stored in is consistent with our high throughput pipeline (htp) which makes “objects” for each piece of EEG data (which point to a large EEG data file). This includes a CSV file and a MAT file of the objects. This code could be removed and replaced with your custom form of loading data such as in a cell array.
%=========================================================================%
% DIRECTORY CONFIGURATION %
%=========================================================================%
syspath.MatlabBuild = 'E:/data/CommBioEEGRev/MatlabBuild/';
syspath.RBuild = 'C:/Users/ernie/Dropbox/cbl/CommBioEEGRev/Build/';
% adding both build folders to MATLAB path
%=========================================================================%
% DATA CONFIGURATION %
%=========================================================================%
syspath.htpdata = 'E:/postdata/P1_70FXS_71_TDC/';
keyfiles.datacsv = fullfile(syspath.htpdata, 'A00_ANALYSIS/A2109130720_subjTable_htp2bst_Stage4.csv');
keyfiles.datamat = fullfile(syspath.htpdata, 'A00_ANALYSIS/A2109130720_subjTable_htp2bst_Stage4.mat');
Finally, under custom functions you can place any functions that may be used by other project scripts. In this case, I have a simple class called repMakeClass which contains useful functions for working with Makefiles.
%=========================================================================%
% CUSTOM FUNCTIONS %
%=========================================================================%
r = repmakeClass;
When this is complete, try running your matlab_00_common.m file. Not much will happen, however, your Matlab environment will be prepared for the next steps!
## Step 2: Generating a Data model from the command line through Make
The fruit of all your labor setting up the environment will pay off in this next section. At this point, you will notice a dramatic decrease in the size of your script files because you are really only asking your script file to accomplish one major goal.
For the next task, we will load our EEG dataset and save the relevant details in a MAT file for further use. Given the potential for high storage needs, we will use the MATLAB Build folder instead of the R build folder.
We are going to use our template to basically create the following script:
1. Data file in
2. Computation or creation
3. Data file out
### A. Include the common Matlab file of your choosing to set the environment
Start with opening the model_template.m file. This generic template can be used to create a MAT file from MATLAB code. After reading the header instructions you will notice our common include file (easy to change). Remember that the Common file will clear your current environment, so save any work or variables you need now!
%=========================================================================%
% Step 1: Load common packages, data, and functions. %
% ========================================================================%
matlab_00_common
### B. Add a basename that will keep your file names consistent.
The basename is a critical variable to ensure the naming of your file stays extremely consistent through this process. Our recommendation is that any Build file should match the source file name with the addition of the type of asset that it is. This will allow you to keep track of hundreds of files with very little confusion. In this case, we name the basename “loadDataset” and the target files will be automatically called ‘model_loadDataset’.
%=========================================================================%
% Step 2: Customize basename for script %
%=========================================================================%
prefix = ['model_' basename];
### C. Specify any preexisting data you need in your current file
For most projects, data models will require additional input from preexisting data files. This section is reserved for any variables that you would like to create to be used by the rest of the script. Our default setup includes the option of loading a MAT file. We make generous use of the MATLAB missing keyword in these scripts as an easy way of telling what parameters are active or not.
### D. Develop and Run the Data Model in the MATLAB GUI
%=========================================================================%
% CONSTRUCT MODEL %
%=========================================================================%
p = htpPortableClass; % MATLAB object / methods / properties
p.importDataObjects( keyfiles.datacsv, keyfiles.datamat, syspath.htpdata );
p.updateBasePaths( syspath.htpdata );
%=========================================================================%
% EXPORT ENVIRONMENT %
%=========================================================================%
save(target_file, 'p', 'syspath', 'keyfiles')
The hard work from the previous sections have now paid off! Let’s look at the actual code for loading our dataset and saving it to a MAT file. Here we are using htp functions (from our pipeline toolkit) to load the information to our raw data files, update their relative file paths, and then save the variable in a MAT file.
The target file Build\model_loadDataset.mat can now be used across multiple other asset scripts.
### E. Final Step: Automate the Data Model Build using Make
Next, we will automate this relatively simple Build using Make. Open your template Makefile and let’s make some edits. Remember that Make loves shorthand so don’t be intimidated by any of the syntax!
#### Test if your MATLAB is working from the command line
MATLAB must work from the command line for Make to activate and run your script! Let’s test our MATLAB command in a terminal window (should work on Mac, Windows, or Linux). In this case, I am going to open Windows terminal and run the command matlab -nogui -nosplash -batch . If matlab is available, Windows will complain that the nogui option is invalid (this is for Linux and Mac) but essentially tell you that it needs a script to run. Troubleshooting instructions here.
### Edit our Makefile: Setup short cuts
After reading the header, notice the first section defining shortcuts used by Make for the rest of the file. In particular confirm you MB (Matlab build directory) and your B (Build directory) are correct. Make syntax is simple but rigid: no extra spaces! Don’t forget to end your path with a “/” so it seamlessly fits into the filename when you use it later.
Don’t forget to flip your \ to / when you are using Windows for maximal compatibility.
#==============================================================================#
# CONFIGURATION #
#==============================================================================#
# SHORTCUTS ============================================================#
# definition: shortcut [commands or paths] #
# usage: $(shortcut) # #==============================================================================# SHELL=/bin/bash R = RScript --verbose Matlab = matlab /minimize /nosplash /nodesktop /batch MB = E:/data/CommBioEEGRev/MatlabBuild/#MATLAB Build B = C:/Users/ernie/Dropbox/cbl/CommBioEEGRev/Build/ S = Source/ ### Edit the Makefile to include our top-level “recipes” Next, we add our highest level targets to Makefile. At the highest level, we define allas depending on matlab. matlab refers to a series of dependencies that are the output of each of our MATLAB scripts. Since we currently only have one script, our recently created model_loadDataset.m the remainder of our Makefile will be quite short. ### Add an entry to tell Make how to create model_loadDataset.m Let’s create recipe to create our first target file model_loadDataset.mat. #==============================================================================# # MATLAB RECIPIES # #==============================================================================# # MODEL: Import EEG dataset information$(MB)model_loadDataset.mat: model_loadDataset.m
$(Matlab) "target_file='$@';, run $^" Let’s make sense of this Make shorthand! • Any line that starts with # is simply a comment. • the : is the dividing marker between the target file and the dependencies • following the last dependency, a new line and a tab tells Make to pay attention to a command • a tab is NOT a few spaces, but an actual tab character • When you see a $ and () think either variable or function
• $@ is a short hand to refer to the target file or what is left of the : • $^ is short hand to refer to the right of the : or all the dependencies
• The MATLAB shorthand is used in this code as defined at the beginning of the file. It would be equally valid to use the command spelled out: matlab /minimize /nosplash /nodesktop /batch
• To specify the target file that we want, we added it directly as an variable in the batch command. To be more clear, "target_file='$@';, run$^" instructs Make to place the filename of the target file ($@) and replace the $^ with the script name from the dependency.
• Remember that Make is not analysis software. It is a very sophisticated macro software. You could simply run the command (without the shorthand) from the Makefile on the command prompt to test if it works.
Let’s try that now!
First identify the working directory of your new Makefile and MATLAB scripts:
Next, open a terminal window and change to your working directory. Finally run the command make matlab. To break the suspense, since you have already tested these scripts in the GUI, they should work fine from the command line. Remember, that we have ensured a fresh clean environment with each run. If you forget to define the target_filein the MATLAB command from Make you will end up with whatever default name you specified in the file.
If we check our MATLAB Build folder we will see the newly made MAT file. This filename holds special significance to Make. Let’s see a little bit of what makes Make so powerful.
First, let’s run the command make matlab again. Make will check the date and time of the target file and the source file and decide if the file should be rebuilt. In this case, the target file is more recent than the source file so Make does not rebuild the file.
PS C:\Users\ernie\Dropbox\cbl\CommBioEEGRev\Source\MATLAB> make matlab
make: Nothing to be done for matlab'.
PS C:\Users\ernie\Dropbox\cbl\CommBioEEGRev\Source\MATLAB>
### Watch Make in action as we update the original source file.
Now open the model_loadDataset.m file in MATLAB. Let’s make a small change. I added “I made a small mod” to the successful save file message.
Now when I run the command make matlab`, the system detects that the source file is more recent than the target file and reruns the code.
## Summary of Part 2
In this lesson, we created a common MATLAB resource file, developed a standalone script to create a data model, and ran the script through the command line. We then hooked the script and the output file into Make so the process could be automated with a single command.
Relax and breathe a sigh of relief! You will simply need to repeat this process as you build your scripts adding Makefile entries as you go. The true genius of Make is difficult to demonstrate with only one file, but we’ll leave that for tomorrow.
In Part 3, we will add additional data models and begin to construct Figures and Tables.
##### Ernest Pedapati, M.D., M.S.
###### Associate Professor of Psychiatry
Physician and Neuroscientist interested in neurodevelopmental conditions.
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# A decision maker faces a trade-off between longevity and quality of life. His preference relation
A decision maker faces a trade-off between longevity and quality of life. His
preference relation ranks lotteries on the set of all certain outcomes of the form ( q , t ) , defined as “a life of quality q and length t ” (where q and t are nonnegative numbers). Assume that the preference relation satisfies von Neumann–Morgenstern assumptions and that it also satisfies
• Indifference between “high” and “low” quality of life when longevity is 0.
• Expected longevity and quality of life are desirable.
1. Formalize the two assumptions.
2. Show that the preference relation derived from maximizing the expec- tation of the function v ( q ) t , where v is a strictly increasing function and v ( q ) > 0 for all q , satisfies the assumptions.
3. Show that all preference relations satisfying the above assumptions can be represented by an expected utility function of the form v ( q ) t , where v is a positive and increasing function.
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# Revision history [back]
### Why does calc get confused by .setFormula('=MAX(4.5,3)')?
I've been using setFormula in my python calc macro for a few days, and it's worked fine with all the '=(A4 * B4) -D3' formulas I've needed. But now I need to use some functions, and it's acting flaky. For the line:
sheet.getCellByPosition(column, row).setFormula('=MAX(4)')
The cell content is 4 (as expected).
sheet.getCellByPosition(column, row).setFormula('=MAX(4,3)')
The cell content is #NAME? That is not what I expected.
If I double=click on the #NAME? cell, I see the correct formula (=MAX(4,3)). If I then ^A to select the formula, ^X to cut it, and ^V to immediately paste the formula back in, then hit Enter, the cell responds with the correct value of 4.
This is the simplest form of the problem I could find. I found it because this much longer formula:
setFormula('=-' + quantity_cell + '*100*MAX(((0.25*' + underlying_cell + ')+MAX(' + underlying_cell + '-' + strike_cell + ',0) +' + price_cell + '), (0.15*' + strike_cell + '+' + price_cell + '))')
Behaves the same way, except instead of #NAME?, the error in the cell is Err:508. Again, an in-place cut and paste will make the formula work, but I'd like to have calc display it correctly without the intervention.
I suspect this is a bug, but perhaps there's a work-around?
This is LO 5.1.2.2, and the problem occurs under Ubuntu 16.04 and Windows 10.
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On digraphs without onion star immersions - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :
## On digraphs without onion star immersions
(1) , (1, 2) , (1) , (1)
1
2
#### Abstract
The $t$-onion star is the digraph obtained from a star with $2t$ leaves by replacing every edge by a triple of arcs, where in $t$ triples we orient two arcs away from the center, and in the remaining $t$ triples we orient two arcs towards the center. Note that the $t$-onion star contains, as an immersion, every digraph on $t$ vertices where each vertex has outdegree at most $2$ and indegree at most $1$, or vice versa. We investigate the structure in digraphs that exclude a fixed onion star as an immersion. The main discovery is that in such digraphs, for some duality statements true in the undirected setting we can prove their directed analogues. More specifically, we show the next two statements. There is a function $f\colon \mathbb{N}\to \mathbb{N}$ satisfying the following: If a digraph $D$ contains a set $X$ of $2t+1$ vertices such that for any $x,y\in X$ there are $f(t)$ arc-disjoint paths from $x$ to $y$, then $D$ contains the $t$-onion star as an immersion. There is a function $g\colon \mathbb{N}\times \mathbb{N}\to \mathbb{N}$ satisfying the following: If $x$ and $y$ is a pair of vertices in a digraph $D$ such that there are at least $g(t,k)$ arc-disjoint paths from $x$ to $y$ and there are at least $g(t,k)$ arc-disjoint paths from $y$ to $x$, then either $D$ contains the $t$-onion star as an immersion, or there is a family of $2k$ pairwise arc-disjoint paths with $k$ paths from $x$ to $y$ and $k$ paths from $y$ to $x$.
### Dates and versions
hal-03882374 , version 1 (02-12-2022)
### Identifiers
• HAL Id : hal-03882374 , version 1
• ARXIV :
### Cite
Łukasz Bożyk, Oscar Defrain, Karolina Okrasa, Michał Pilipczuk. On digraphs without onion star immersions. 2022. ⟨hal-03882374⟩
### Export
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<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 3.12: Special Right Triangles, 30-60-90
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Identify and use the ratios involved with \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangles.
• Identify and use ratios involved with equilateral triangles.
## Equilateral Triangles
Remember that an equilateral triangle has sides that all have the same length. Equilateral triangles are also equiangular — all angles have the same measure. In an equilateral triangle, all angles measure exactly \begin{align*}60^\circ\end{align*}.
Equilateral triangles are also ___________________.
Notice what happens when you divide an equilateral triangle in half:
This equilateral triangle is divided into 2 equal parts using an altitude, which is a line that is perpendicular to the base of the triangle. Since the altitude is perpendicular to the base, it makes a \begin{align*}90^\circ\end{align*} angle with the base.
• An altitude is a line that is ______________________________ to the base of a triangle.
The altitude also splits the top \begin{align*}60^\circ \end{align*} angle in the picture in half. Therefore, the angles on either side of the altitude are \begin{align*}30^\circ\end{align*} (because \begin{align*}60^\circ \div 2 = 30^\circ\end{align*}).
Each resulting right triangle created is a \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle:
• The hypotenuse of the resulting triangle is the side of the original, and the shorter leg is half of an original side.
• The altitude makes a \begin{align*}90^\circ\end{align*} angle at the base and splits the \begin{align*}60^\circ\end{align*} angle into two __________ angles.
This is why the hypotenuse is always twice the length of the shorter leg in a \begin{align*}30^\circ - 60^\circ - 90^\circ \end{align*} triangle, like in the picture below (where the original equilateral triangle had a side of length 10):
Again, the hypotenuse of a \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle is always double the length of the side opposite the \begin{align*}30^\circ\end{align*} angle. You can use this information to solve problems about equilateral triangles.
In a \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle, the_____________ is double the shortest side.
The ________________ is the longest side of any right triangle.
In a \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle, the side _______________ the \begin{align*}30^\circ\end{align*} angle is the shortest side.
## \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} Triangles
This important type of right triangle has angles measuring \begin{align*}30^\circ, 60^\circ,\end{align*} and \begin{align*}90^\circ\end{align*}.
Just as you found a constant ratio between the sides of an isosceles right triangle, you can find constant ratios here as well. Use the Pythagorean Theorem to discover these important relationships.
Example 1
Find the length of the missing leg in the following triangle. Use the Pythagorean Theorem to find your answer.
Just like you did for\begin{align*} 45^\circ - 45^\circ - 90^\circ\end{align*} triangles, use the Pythagorean Theorem to find the missing side.
In this diagram, you are given two measurements:
• The hypotenuse (which is side ___________ ) is 2 cm and
• The shorter leg (which is side ___________ ) is 1 cm
Substitute these values into the Pythagorean Theorem \begin{align*}(a^2+ b^2 = c^2)\end{align*} to find the length of the missing leg \begin{align*}( b )\end{align*}:
\begin{align*}& \ \ \ a^2+ b^2 = \ \ c^2\\ & \ \ \ 1^2+ b^2 = \ \ 2^2\\ & \ \quad 1+ b^2 = \ \ 4\\ & - 1 \qquad \ \ \ -1\\ & \ \ \ \qquad b^2 = \ \ 3\\ & \ \qquad \quad b = \ \ \sqrt{3}\end{align*}
You can leave the answer in radical form as shown, or use your calculator to find the approximate value of \begin{align*}b\approx1.732 \ cm\end{align*}.
We can try this again using a hypotenuse of 6 feet.
Recall that since the \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle comes from an equilateral triangle, you know that the length of the shorter leg is half the length of the hypotenuse.
So the hypotenuse, \begin{align*}c\end{align*}, is 6 feet.
Therefore, the shorter leg, \begin{align*}a\end{align*} in the diagram on the previous page, is 3 feet (half of 6.)
\begin{align*}& \quad a^2+b^2 \ = \ c^2\\ & \quad 3^2+b^2 \ = \ 6^2\\ & \quad \ 9+b^2 \ = \ 36\\ & - 9 \qquad \ \ \ -9\\ & \qquad \quad b^2 \ = \ 27\\ & \qquad \ \quad b \ = \ \sqrt{27}\\ & \qquad \ \ \quad \ = \ \sqrt{9} \times \sqrt{3} = 3\sqrt{3} \ ft \approx 5.196 \ ft\end{align*}
The special relationship is as follows:
In all \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangles,
• the hypotenuse will always be twice the length of the shorter leg,
• and the longer leg is always the product of the length of the shorter leg and \begin{align*}\sqrt{3}\end{align*}.
In ratio form, the sides, in order from shortest to longest are in the extended ratio
\begin{align*}x:x\sqrt{3}:2x\end{align*}
If we use ratio form, where the ratio is \begin{align*} x:x\sqrt{3}:2x\end{align*}
We can substitute any number in for \begin{align*}x\end{align*} and the sides of the triangle will relate to each other in the same proportion.
For instance, if \begin{align*} x = 4\end{align*}, the ratio is \begin{align*} 4 : 4\sqrt{3} : 2(4)\end{align*} or \begin{align*} 4 : 4\sqrt{3}: 8\end{align*} and if \begin{align*} x = 7\end{align*}, the ratio is \begin{align*}7 : 7\sqrt{3} : 2(7)\end{align*} or \begin{align*}7 : 7\sqrt{3}: 14\end{align*}
Example 2
What is the length of the missing leg in the triangle below?
You could use the Pythagorean Theorem for this problem (like in Example 1), but using the special proportional relationship in a \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle that you just learned is a much easier way!
The special relationship is:
• the hypotenuse is _____________________ the length of the shorter leg, and
• the longer leg is the _______________________ of the length of the shorter leg and \begin{align*}\sqrt{3}\end{align*}
First, you know that the hypotenuse is 16 because it is across from the right angle.
Therefore, the other 2 sides are the legs in this triangle.
You also know that the longer leg is across from the \begin{align*}60^\circ\end{align*} angle.
Since the length of the longer leg is the product of the shorter leg and \begin{align*}\sqrt{3}\end{align*}, you can easily calculate this length:
The short leg is 8 inches, so the longer leg will be \begin{align*}8\sqrt{3}\end{align*} inches or about 13.86 inches.
Example 3
What is AC below?
To find the length of segment \begin{align*}\overline {AC}\end{align*}, identify its relationship to the rest of the triangle. Since it is an altitude, it forms two congruent triangles with angles measuring \begin{align*}30^\circ, 60^\circ\end{align*}, and \begin{align*}90^\circ.\end{align*}
So, \begin{align*}AC\end{align*} will be the product of \begin{align*}BC\end{align*} (the shorter leg) and \begin{align*}\sqrt{3}\end{align*}:
\begin{align*} AC & = BC \sqrt{3}\\ & = 4 \sqrt{3}\end{align*}
\begin{align*}AC = 4\sqrt{3}\end{align*} yards, or approximately 6.93 yards.
1. Draw a \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle and label its angle measures.
\begin{align*}{\;}\end{align*}
\begin{align*}{\;}\end{align*}
\begin{align*}{\;}\end{align*}
\begin{align*}{\;}\end{align*}
2. From shortest to longest sides, what ratio does every \begin{align*} 30^\circ - 60^\circ - 90^\circ\end{align*} triangle follow?
________ : ________ : ________
Example 4
The diagram below shows the shadow a flagpole casts at a certain time of day.
If the length of the shadow cast by the flagpole is 13m, what is the height of the flagpole and what is the length of the hypotenuse of the right triangle shown?
The picture shows that this triangle has angles of \begin{align*} 30^\circ, 60^\circ,\end{align*} and \begin{align*}90^\circ\end{align*} (This assumes that the flagpole is perpendicular to the ground, but that is a safe assumption). Although the \begin{align*}30^\circ\end{align*} angle is not written into the picture, you can tell that the top angle is \begin{align*}30^\circ\end{align*} because \begin{align*}180 - (90 + 60) = 30.\end{align*}
The height of the flagpole is the longer leg in the triangle, so use the special right triangle ratios (along with the given height of the base of the triangle) to find the length of the missing sides, the flagpole height and the hypotenuse.
The longer leg is the product of the shorter leg and \begin{align*}\sqrt{3}\end{align*}.
The length of the shorter leg is given as 13 meters, so the height of the flagpole is \begin{align*}13\sqrt{3} \ m.\end{align*}
To find the length of the hypotenuse, use the hypotenuse of a \begin{align*}30^\circ - 60^\circ - 90^\circ\end{align*} triangle.
It will always be twice the length of the shorter leg, so it will equal \begin{align*}13 \cdot 2\end{align*}, or 26 meters.
What is the length of the altitude in the triangle below?
## Graphic Organizer for Lessons 9 and 10
Special Triangles
Label all angles and side lengths for the triangles below. If the shortest side of each triangle is length \begin{align*}x\end{align*}, what are the other sides?
Show Hide Details
Description
Authors:
Tags:
8 , 9 , 10
Date Created:
Feb 23, 2012
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## Intermediate Algebra (6th Edition)
$y=5$ This is a function.
$y=5$ This is a function. This is a horizontal line passing through (0,5). This graph passes the vertical line test.
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# Write formulas for the indicated partial derivatives for the multivariable function.g(k, m) = k^4m^5 − 3kma)g_kb)g_mc)g_m|_(k=2)
Multivariable functions
Write formulas for the indicated partial derivatives for the multivariable function.
$$\displaystyle{g{{\left({k},{m}\right)}}}={k}^{{4}}{m}^{{5}}−{3}{k}{m}$$
a)$$\displaystyle{g}_{{k}}$$
b)$$\displaystyle{g}_{{m}}$$
c)$$\displaystyle{g}_{{m}}{\mid}_{{{k}={2}}}$$
2021-01-28
$$\displaystyle{g{{\left({k},{m}\right)}}}={k}^{{4}}{m}^{{5}}−{3}{k}{m}$$ (1)
a) Differentiating with respect to x partially, we have
$$\displaystyle\frac{{\partial{g}}}{{\partial{k}}}=\frac{\partial}{{\partial{k}}}{\left[{k}^{{4}}{m}^{{5}}−{3}{k}{m}\right]}$$
$$\displaystyle\Rightarrow\frac{{\partial{g}}}{{\partial{k}}}={4}{k}^{{3}}{m}^{{5}}-{3}{m}$$
b) Differentiating with respect to x partially, we have
$$\displaystyle\frac{{\partial{g}}}{{\partial{m}}}=\frac{\partial}{{\partial{m}}}{\left[{k}^{{4}}{m}^{{5}}−{3}{k}{m}\right]}$$
$$\displaystyle\Rightarrow\frac{{\partial{g}}}{{\partial{m}}}={5}{k}^{{4}}{m}^{{4}}-{3}{k}$$
c) $$\displaystyle{g}_{{m}}{\left|_{\left({k}={2}\right)}=\frac{{\partial{q}}}{{\partial{m}}}\right|}_{{{k}={2}}}={5}\cdot{\left({2}\right)}^{{4}}{m}^{{4}}-{3}\cdot{2}$$
$$\displaystyle{g}_{{m}}{\mid}_{{{k}={2}}}={80}{m}^{{4}}-{6}$$
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시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB111100.000%
## 문제
You are in charge of security at a top-secret government research facility. Recently your government has captured a live extra-terrestrial (ET) life form, and is hosting an open day for fellow researchers. Of course, not all the guests can be trusted, so they are assigned different security clearance levels. Only guests with a level 5 rating will be allowed into the lab where the extra-terrestrial is being held; other than that, everyone is free to roam throughout the rest of the facility. Each room in the facility is connected via one-way airlocks, so that you can pass through the door in only one direction.
To protect your precious ET you will put in place enhanced security measures (in the form of armed guards) on the route leading to the room containing the ET, but not in the room itself — the guards do not have sufficient clearance to enter the room containing the ET. The guards will check the identity and the security rating of all guests trying to pass through the room in which they are stationed, so you would like to place the guards where they will cause the minimum amount of irritation to the guests who have no intention of visiting the ET. The room where the guards must be placed thus satisfies the following two conditions:
1. In order to get to the room containing the ET, the guests must pass through the room containing the guards;
2. There is no other room with this property that is closer to the room containing the ET — remember, the guards cannot be placed in the room containing the ET itself.
The diagram below illustrates one possible map of your facility:
Note that placing the guards in room 2 would satisfy the first condition, but room 3 is closer to the ET, so the guards must be placed in room 3.
## 입력
The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs.
All guests enter through room 0, the entrance to your facility. Your program accepts a sequence of lines containing integers. The first line consists of two integers: the number of rooms, and the room in which the ET is being held (out of his own free will, of course). The rest of the input is a sequence of lines consisting of only two integers, specifying where the airlock-doors are located. The first number on these lines specifies the source room, and the second the destination room. Remember: you can pass only from the source room to the destination room.
## 출력
For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.
The output of your program consists only of a single line:
Put guards in room N.
where N is the room you’ve decided to place the guards.
## 예제 입력 1
9 4
0 2
2 3
3 4
5 3
5 4
3 6
6 5
6 7
6 8
4 7
0 1
1 7
7 0
## 예제 출력 1
Put guards in room 3.
## 힌트
The diagram on the right illustrates the Sample Input sequence below.
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# Reverse Engineering the WMD Editor
We’ve been quite happy with the WMD Markdown editor on Stack Overflow, kindly provided by the author, John Fraser of AttackLabs.
However, there are definitely some outstanding bugs and issues with it that we’d like to fix. Progress on this front has been severely hampered by three problems:
1. We only have obfuscated / minified versions of the WMD editor JavaScript code.
2. I’ve been unable to reach John over the last 4 months.
3. My JavaScript skills are average at best.
I’m not sure what happened to John, because he was super responsive and enthusiastic early on. He helped us out in a bunch of large and small ways with the WMD implementation. Originally he planned to give me a drop of the un-obfuscated/minified WMD source. But I never heard back from him, and he seems to have fallen off the face of the planet in the last 4-6 months. I’ve sent him brief emails like clockwork every few weeks, but there’s no response. I hate to be naggy, but the alternatives are.. bad.
So it is with great regret and heavy hearts that we undertake the painful odyssey of manually un-minifying/obfuscating the WMD code ourselves. Chris Jester-Young, one of the earliest Stack Overflow users, has invested in a substantial amount of effort in this already. He’s set up a git repository for our progress so far:
http://github.com/cky/wmd/tree
(I should add that Chris, like myself, is a git noob, so be gentle!)
1. How will we coordinate the changes? Do we want to have a forum where people can post links to their repositories? (My repository is writable by me only — but Git being a distributed VCS, this is not a problem, people just clone their own.) Or do you prefer to have a central repository that everyone checks into? In this case, I’m happy to check things into it — or you can import it from my repository.
2. How will we manage “knowledge transfer”, such as it were? It would help people if I could write some notes (in a wiki or something, so others can update it) on how to go about the translation. Maybe use a community-modded Stack Overflow question dedicated to this? Ideas welcome.
I’ll try to get more changes checked in periodically, but I still have a ton of projects to clear, so getting the ball rolling with other coders would probably be a good idea.
The easiest way forward is to somehow get a source code drop from John Fraser to start with. If anyone knows him, or knows someone that knows him, can you please try to get in touch? Otherwise it’s back to the salt mines of de-minifiying/obfuscating the JavaScript, until we get it all done.
Beyond that, I’d like to create a Stack Overflow branch of the WMD code, under a very permissive license. We have some needs specific to our website, of course, but I’d like to give our modifications, improvements, and bugfixes back to the greater community as well.
My gut feeling is that we should go with a “real” code hosting solution for this project, perhaps Google Code or the like..
Filed under design
Grégoire Cachet Dec 28 2008
Go to http://github.com/ for social git hosting. People can branch each other easily.
Wilerson Dec 28 2008
Since you’re already considering git, what about github? It has a wiki, it’s free for open source projects, and it’s easy to get links to other people repositories.
github is indeed a nice idea, and I’m thinking about it.
However, I am currently extremely short on time (and anyone who looks at my reputation history will see the near-plateau in my rep gains, for the same reason), so if you have a github account, you’re welcome to clone off my repository, and work from that.
Ditto for anyone who wishes to set up a Google Code, Launchpad, Sourceforge, or whatever project. :-)
It would still be a good idea to dedicate a wiki page (or SO community question, or whatever) to coordinate this, though!
Chakrit Dec 28 2008
I think Google Code is the more natural choice. There are more tools for subversion than for git, especially for windows folks. And I think most of us is still git noob like you, let alone the concepts of distributed VCS
Creating an account on http://github.com and sending the code there would have taken less time imho. And that already includes a free wiki/readme display/webpage plus ssh/git/forking and whatnot.
Even though git is distributed, having one central “authoritative” repository is still the preferred way to go. And having it on github just plain makes it easy for everyone to send changes to it — via the ‘forking inbox’, instead of git-patches via mail.
1. No need for a forum to post links to repositories, and all that stuff.
2. free wiki built into github.
3. lots of other coders that know javascript and git, freely available on github.com as well.
Okay, the githubbers win. :-) I now have a github account with the wmd project: http://github.com/cky/wmd/tree
Bernard Dec 28 2008
I would help, but my JS-fu is weak. Sorry.
@Cody (if he reads this): I would be keen to see if you have a way to programmatically translate the whole lot to Pyvascript.
You know you just can’t resist…and it’d be the Best Way Ever to promote Pyvascript. :-P
Just to check, are we okay on the licensing of all of this? I can’t see any licence in the WMD download, but I’m uneasy about reverse engineering something and then making it open without explicit permission.
It sounds like John Fraser was *planning* on this being okay, but it would be nice to have proper confirmation. And yes, I do understand that if we could easily get in touch with him this probably wouldn’t be necessary in the first place :)
I really don’t want to rain on anyone’s parade, but equally I’d hate to see Stack Overflow in legal trouble over this.
If it’s all legally okay, then best of luck! I’d love to help, but my JavaScript is almost certainly significantly worse then Jeff’s.
Ah, cool. I’d only been on the wmd-editor.com site, which didn’t mention that (or I didn’t see it, which is equally likely). Tally ho :)
tanda Dec 28 2008
So, what are the things that you will like to fix?
> what are the things that you will like to fix?
Until we find John, simple reverse engineering is all that is needed.. a version that isn’t obfuscated or using single character variable names.
http://www.google.com/search?q=javascript+beautifier ought to take care of the minification. I didn’t see you mention it, so I thought I would in case you just missed it for some reason or another.
As for obfuscation, that could mean many things, but I guess variable names are useless. At least having beautified the code you could read it easier and not worry about indenting / newlining as you rename variables and functions.
Derek Dec 29 2008
Jeff, it doesn’t look to me like John ever actually released wmd under the MIT license. He just indicated his plans to do so.
> I’m refactoring the code, and *will be releasing WMD under the MIT license soon*. For now you can download the most recent release (wmd-1.0.1.zip) and use it freely.
You’re going to be on some pretty shaky ground releasing it yourself. It’s probably something he’s not going to mind, but then again he might. People can get pretty weird about stuff they’ve written.
Take a look at this: http://wmd-editor.com/terms
Did you ever happen to click on something saying you agreed to that?
Derek and Will — the current WMD code is here:
**under the MIT license** .. click through to the above page for proof!
tvanfosson Dec 30 2008
Jeff — except that there is no code at code.google.com except the link to the code that seems to be referenced as pre-MIT license on the main page. I couldn’t find anything in the repository there anyway.
> Please visit wmd.googlecode.com for information on the next release, which will be open source. (The API will be changing a lot; it wasn’t really meant for public consumption.)
So it looks like the MIT license on the Google Code page refers to the forthcoming rewrite, not the current version. The old page refers to wmd being free to use but doesn’t mention any distribution rights. I would guess that reverse engineering the code for interoperability would probably be OK, but branching this version would not.
shawn Dec 31 2008
ill stick to the reverse-engineer now, worry about copyright bullshit later model. very excited about using git for the first time :D
I’m sorry, but I’m with Jon and the rest on this one – make absolutely certain that the code you are planning on adapting is released under the licence you think it is, otherwise you may run into difficulties later, whether these range from simply being disallowed to continue using/distributing the code to a lawsuit, not that I expect the original author is the sort of person to go to such lengths, but he would be entitled to.
If there’s any uncertainty about this, then you need to seek proper legal advice, or perhaps take the “simple” option – that is, not use the code, and start a community project to create the toolbar from scratch – I’m sure there’s a huge number of Stack Overflow users who would relish the opportunity to get involved and help shape part of the site.
> My gut feeling is that we should go with a “real” code hosting solution for this project, perhaps Google Code or the like..
How is GitHub not a “real” code hosting solution? I would be disappointed if you standardized on Google Code as the “official” repo, as GitHub offers so many benefits, including the incredibly easy forking and collaboration tools.
@Kevin, The ‘My gut feeling is that we should go with a “real” code hosting solution’ is, I believe, a reflection on Chris Jester-Young’s original git repo for this project, which was located on a personal URL rather than being based on a hosted solution such as Google Code, Github, etc.
However, Jeff has at some point updated the post to point to the Github repo which, it has to be said, does make the comment look like a slight against Github.
Derek Jan 13 2009
Jeff, it looks like you’re right. I missed the license link off to the right. I think he still didn’t explicitly release it under the MIT license, since the code is actually hosted elsewhere, but it’s close enough. Even if he got really weird and tried to sue, you’d have a pretty good case, especially with the “use it freely” statement he made.
“What about the Dufrains? Who can eat at a time like this?”
So what happened to John Frasier?
Jason S Jan 28 2009
just curious: how are you doing the WYSIWYG diffs?
e.g.:
http://stackoverflow.com/revisions/463653/list
Is there any reason why WMD is packed/obfuscated? Seems strange if it’s under the MIT license and free
I’m trying to intercept the image click button for a CMS but having problems with _8s in the source (a successful obfuscation obviously). I’ll take a look at the SO source instead though.
MarkItUp seems to be a good alternative for WMD
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Comment
Share
Q)
# Which of the following are tangents to the circle $x^2+y^2-4x+8y+12=0$ from $(5-3)$?
$(1)\; x+y+2=0$
$(2)\; x+y-2= 0$
$(3)\; 7x-y+32= 0$
$(4)\; 7x+y-32=0$
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For the formation of each compound, write a balanced chemical equation corresponding to the standard enthalpy of formation of each compound. Use Table T1 to calculate $$ΔH^o_{rxn}$$ for the water–gas shift reaction, which is used industrially on an enormous scale to obtain H2(g): $\ce{ CO ( g ) + H2O (g ) -> CO2 (g) + H2 ( g )} \nonumber$. \Delta H_{f}^{o} \left [ \left (C_{2}H_{4} \right )_{4}Pb \right ] & = & \left [1 \; mol \;PbO \;\times 219.0 \;kJ/mol \right ]+\left [8 \; mol \;CO_{2} \times \left (-393.5 \; kJ/mol \right )\right ] \\ In all honesty, enthalpy is a broader term than energy because it accounts for pressure and volume in addition to all that energy accounts for. Standard enthalpy change of formation (data table) These tables include heat of formation data gathered from a variety of sources, including the primary and secondary literature, as well as … Then insert the appropriate quantities into Equation $$\ref{7.8.5}$$ to get the equation for. The converse is also true; the standard enthalpy of reaction is positive for an endothermic reaction. "Products minus reactants" summations are typical of state functions. This form will calculate the enthalpy of formation of a species using ab initio results and experimental enthalpies of formation. Example $$\PageIndex{3}$$: tetraethyllead. The standard conditions for which most thermochemical data are tabulated are a pressure of 1 atmosphere (atm) for all gases and a concentration of 1 M for all species in solution (1 mol/L). Its symbol is ΔfH⦵. Hydrogen chloride contains one atom of hydrogen and one atom of chlorine. Convert $$ΔH^ο_{comb}$$ per gram given in the problem to $$ΔH^ο_{comb}$$ per mole by multiplying $$ΔH^ο_{comb}$$ per gram by the molar mass of tetraethyllead. The standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states. The overall enthalpy change for the conversion of the elements to products (6 mol of carbon dioxide and 6 mol of liquid water) is therefore −4075.8 kJ. To demonstrate the use of tabulated ΔHο values, we will use them to calculate $$ΔH_{rxn}$$ for the combustion of glucose, the reaction that provides energy for your brain: $C_{6}H_{12}O_{6} \left ( s \right ) + 6O_{2}\left ( g \right ) \rightarrow 6CO_{2}\left ( g \right ) + 6H_{2}O\left ( l \right ) \label{7.8.6}$, $\Delta H_{f}^{o} =\left \{ 6\Delta H_{f}^{o}\left [ CO_{2}\left ( g \right ) \right ] + 6\Delta H_{f}^{o}\left [ H_{2}O\left ( g \right ) \right ] \right \} - \left \{ \Delta H_{f}^{o}\left [ C_{6}H_{12}O_{6}\left ( s \right ) \right ] + 6\Delta H_{f}^{o}\left [ O_{2}\left ( g \right ) \right ] \right \} \label{7.8.7}$, From Table T1, the relevant ΔHοf values are ΔHοf [CO2(g)] = -393.5 kJ/mol, ΔHοf [H2O(l)] = -285.8 kJ/mol, and ΔHοf [C6H12O6(s)] = -1273.3 kJ/mol. The standard enthalpy of formation of any element in its most stable form is zero by definition. Thus, for the formation of FeO(s), Note that now we are using kJ/mol as the unit because it is understood that the enthalpy … Based on the energy released in combustion per gram, which is the better fuel — glucose or palmitic acid? The standard pressure value p = 10 Pa (= 100 kPa = 1 bar) is recommended by IUPAC, although prior to 1982 the value 1.00 atm (101.325 kPa) was used. Enthalpy of formation. Example. Missed the LibreFest? Also, called standard enthalpy of formation, the molar heat of formation of a … Legal. The values of all terms other than $$ΔH^o_f [\ce{(C2H5)4Pb}]$$ are given in Table T1. Tetraethyllead is a highly poisonous, colorless liquid that burns in air to give an orange flame with a green halo. Ammonium sulfate, $$\ce{(NH4)2SO4}$$, is used as a fire retardant and wood preservative; it is prepared industrially by the highly exothermic reaction of gaseous ammonia with sulfuric acid: $\ce{2NH3(g) + H2SO4(aq) \rightarrow (NH4)2SO4(s)} \nonumber$. Elemental Carbon. The superscript Plimsollon this symbol indicates that the process has occurred under st… The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Similarly, hydrogen is H2(g), not atomic hydrogen (H). The combustion of fats such as palmitic acid releases more than twice as much energy per gram as the combustion of sugars such as glucose. However the standard enthalpy of combustion is readily measurable using bomb calorimetry. Modified by Joshua Halpern (Howard University). This is one reason many people try to minimize the fat content in their diets to lose weight. For example, the formation of lithium fluoride. The combustion products are $$\ce{CO2(g)}$$, $$\ce{H2O(l)}$$, and red $$\ce{PbO(s)}$$. The standard enthalpy of reaction $$\Delta{H_{rxn}^o}$$ is the enthalpy change that occurs when a reaction is carried out with all reactants and products in their standard states. The elemental form of each atom is that with the lowest enthalpy in the standard state. Formula. It is possible to predict heats of formation for simple unstrained organic compounds with the heat of formation group additivity method. [1] There is no standard temperature. Consider the general reaction, $aA + bB \rightarrow cC + dD \label{7.8.3}$. When a substance changes from solid to liquid, liquid to gas or solid to gas, there are specific enthalpies involved in these changes. We can also measure the enthalpy change for another reaction, such as a combustion reaction, and then use it to calculate a compound’s $$ΔH^ο_f$$ which we cannot obtain otherwise. H 2 (g). Because the standard states of elemental hydrogen and elemental chlorine are H2(g) and Cl2(g), respectively, the unbalanced chemical equation is. B The energy released by the combustion of 1 g of palmitic acid is, $$\Delta H_{comb}^{o} \; per \; gram =\left ( \dfrac{9977.3 \; kJ}{\cancel{1 \; mol}} \right ) \left ( \dfrac{\cancel{1 \; mol}}{256.42 \; g} \right )= -38.910 \; kJ/g \nonumber$$, As calculated in Equation $$\ref{7.8.8}$$, ΔHοf of glucose is −2802.5 kJ/mol. One exception is, When a reaction is reversed, the magnitude of Δ, When the balanced equation for a reaction is multiplied by an integer, the corresponding value of Δ, The change in enthalpy for a reaction can be calculated from the enthalpies of formation of the reactants and the products. Asked for: $$ΔH^ο_{comb}$$ per mole and per gram. Given that the enthalpy of vaporization for water is: H 2 O (l) H 2 O (g) H vap = + 44.0 kJ/mole Calculate H for each of the following processes: a. Working out an enthalpy change of reaction from enthalpy changes of formation This is the commonest use of simple Hess's Law cycles that you are likely to come across. The enthalpy change for the formation of 1 mol of a compound from its component elements when the component elements are each in their standard states. \end{matrix} \nonumber \]. In addition, each pure substance must be in its standard state, which is usually its most stable form at a pressure of 1 atm at a specified temperature. The combustion of methane (CH4 + 2 O2 → CO2 + 2 H2O) is equivalent to the sum of the hypothetical decomposition into elements followed by the combustion of the elements to form carbon dioxide and water: Solving for the standard of enthalpy of formation. The standard heat of formation is the enthalpy change associated with the formation of one mole of a compound from its elements in their standard states. Enthalpy of formation is basically a special case of standard enthalpy of reaction where two or more reactants combine to form one mole of the product. Use the data in Table T1 to calculate the standard enthalpy of formation of ammonium sulfate (in kilojoules per mole). This is the energy released by the combustion of 1 mol of palmitic acid. The enthalpies of the reactants and products for the formation of are: The negative sign shows that the reaction, if it were to proceed, would be exothermic; that is, methane is enthalpically more stable than hydrogen gas and carbon. The enthalpy change associated with this process is called the enthalpy of formation(or heat of formation), ΔH f, where the subscript f indicates that the substance has been formed from its constituent elements. The heat of reaction is then minus the sum of the standard enthalpies of formation of the reactants (each being multiplied by its respective stoichiometric coefficient, ν) plus the sum of the standard enthalpies of formation of the products (each also multiplied by its respective stoichiometric coefficient), as shown in the equation below:[4]. Write the balanced chemical equation for the combustion of tetraethyl lead. Although graphite and diamond are both forms of elemental carbon, graphite is slightly more stable at 1 atm pressure and 25°C than diamond is. … Thermochemical properties of selected substances at 298.15 K and 1 atm, Key concepts for doing enthalpy calculations, Examples: standard enthalpies of formation at 25 °C, https://en.wikipedia.org/w/index.php?title=Standard_enthalpy_of_formation&oldid=991894827, Creative Commons Attribution-ShareAlike License, For a gas: the hypothetical state it would have assuming it obeyed the ideal gas equation at a pressure of 1 bar, For an element: the form in which the element is most stable under 1 bar of pressure. & & \left [12,480.2 \; kJ/mol \; \left ( C_{2}H_{5} \right )_{4}Pb \right ]\\ The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 °C or 298.15 K). The standard enthalpy of formation of any element in its most stable form is zero by definition. The standard enthalpy of formation of any element in its standard state is zero by definition. To avoid confusion caused by differences in reaction conditions and ensure uniformity of data, the scientific community has selected a specific set of conditions under which enthalpy changes are measured. We assume a temperature of 25°C (298 K) for all enthalpy changes given in this text, unless otherwise indicated. Hydrogen. The magnitude of $$ΔH^ο$$ is the sum of the standard enthalpies of formation of the products, each multiplied by its appropriate coefficient, minus the sum of the standard enthalpies of formation of the reactants, also multiplied by their coefficients: $\Delta H_{rxn}^{o} = \underbrace{ \left [c\Delta H_{f}^{o}\left ( C \right ) + d\Delta H_{f}^{o}\left ( D \right ) \right ] }_{\text{products} } - \underbrace{ \left [a\Delta H_{f}^{o}\left ( A \right ) + b\Delta H_{f}^{o}\left ( B \right ) \right ]}_{\text{reactants }} \label{7.8.4}$, $\Delta H_{rxn}^{o} = \sum m\Delta H_{f}^{o}\left ( products \right ) - \sum n\Delta H_{f}^{o}\left ( reactants \right ) \label{7.8.5}$. balanced chemical equation for its formation from elements in standard states. Values of the heat of formation for a number of substances are given in Table A.9 in SB&VW. So the formation of salt releases almost 4 kJ of energy per mole. A standard enthalpy of formation Δ H f ° Δ H f ° is an enthalpy change for a reaction in which exactly 1 mole of a pure substance is formed from free elements in their most stable states under standard state conditions. have a standard enthalpy of formation of zero, as there is no change involved in their formation. The standard enthalpy of formation refers to the quantity of energy essential to produce one mole of a mixture from its composition of elements.. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Example $$\PageIndex{1}$$: Enthalpy of Formation. The standard heat of formation (standard enthalpy of formation) of a compound is defined as the enthalpy change for the reaction in which elements in their standard states produce products. Hence graphite is the standard state of carbon. Enthalpy of formation (ΔHf) is the enthalpy change for the formation of 1 mol of a compound from its component elements, such as the formation of carbon dioxide from carbon and oxygen. The figure shows two pathways from reactants (middle left) to products (bottom). Glucose is not unique; most compounds cannot be prepared by the chemical equations that define their standard enthalpies of formation. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Note that you have two moles of nitromethane, so we had to double the value for heat … Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. Watch the recordings here on Youtube! The alternative hypothetical pathway consists of four separate reactions that convert the reactants to the elements in their standard states (upward purple arrow at left) and then convert the elements into the desired products (downward purple arrows at right). It can be thought of as energy in most cases. Also notice in Table T1 that the standard enthalpy of formation of O2(g) is zero because it is the most stable form of oxygen in its standard state. Enthalpy is similar to energy. Elements in their standard states make no contribution to the enthalpy calculations for the reaction, since the enthalpy of an element in its standard state is zero. Given enough time, diamond will revert to graphite under these conditions. Long-chain fatty acids such as palmitic acid ($$\ce{CH3(CH2)14CO2H}$$) are one of the two major sources of energy in our diet ($$ΔH^o_f$$ =−891.5 kJ/mol). The reactions that convert the reactants to the elements are the reverse of the equations that define the $$ΔH^ο_f$$ values of the reactants. Consequently, the enthalpy changes are, \begin{align} \Delta H_{1}^{o} &= \Delta H_{f}^{o} \left [ glucose \left ( s \right ) \right ] \nonumber \\[4pt] &= -1 \; \cancel{mol \; glucose}\left ( \dfrac{1273.3 \; kJ}{1 \; \cancel{mol \; glucose}} \right ) \nonumber \\[4pt] &= +1273.3 \; kJ \nonumber \\[4pt] \Delta H_{2}^{o} &= 6 \Delta H_{f}^{o} \left [ O_{2} \left ( g \right ) \right ] \nonumber \\[4pt] & =6 \; \cancel{mol \; O_{2}}\left ( \dfrac{0 \; kJ}{1 \; \cancel{mol \; O_{2}}} \right ) \nonumber \\[4pt] &= 0 \; kJ \end{align} \label{7.8.9}. The unbalanced chemical equation is thus, This equation can be balanced by inspection to give, Palmitic acid, the major fat in meat and dairy products, contains hydrogen, carbon, and oxygen, so the unbalanced chemical equation for its formation from the elements in their standard states is as follows: $\ce{C(s, graphite) + H2(g) + O2(g) \rightarrow CH3(CH2)14CO2H(s)} \nonumber$, There are 16 carbon atoms and 32 hydrogen atoms in 1 mol of palmitic acid, so the balanced chemical equation is, $\ce{ Na (s) + \dfrac{1}{2}Cl2 (g) \rightarrow NaCl (s)} \nonumber$, $\ce{H_{2} (g) + \dfrac{1}{8}S8 (s) + 2O2 ( g) \rightarrow H2 SO4( l) } \nonumber$, $\ce{2C(s) + O2(g) + 2H2(g) -> CH3CO2H(l)} \nonumber$, Tabulated values of standard enthalpies of formation can be used to calculate enthalpy changes for any reaction involving substances whose $$\Delta{H_f^o}$$ values are known. If the standard enthalpy of the products is less than the standard enthalpy of the reactants, the standard enthalpy of reaction is negative. In order to quantify the enthalpy of reaction for a given reaction, one approach is to use the standard enthalpies of formation for all of the molecules involved. Enthalpy of formation ($$ΔH_f$$) is the enthalpy change for the formation of 1 mol of a compound from its component elements, such as the formation of carbon dioxide from carbon and oxygen. The standard heat of formation of any element in its most stable form is defined to be zero. Enthalpy of formation ∆H f - is the enthalpy change that occurs when one mole of compound in its standard state if formed from its element in their standard states under standard conditions. This procedure is illustrated in Example $$\PageIndex{3}$$. State of an element is its state at 25°C and 101.3 kPa been determined for large! ( in kilojoules per gram one atom of hydrogen bromide from hydrogen and bromine more direct pathway is the green. The products is less than enthalpy of formation standard state of an element can determined! For simple unstrained organic compounds with the heat of formation is zero from hydrogen bromine... And compiled in chemical and physical reference works, such as the enthalpy of formation ( Δ H )... ), not atomic hydrogen ( H ) labeled \ ( \ce H2SO4. And constant temperature process and 101.3 kPa lead enthalpy of formation ΔH^o_f\ ) values are always in... Heat of formation of a enthalpy of formation using ab initio results and experimental of. Also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and (... Information contact us at info @ libretexts.org or check out our status page at https: //status.libretexts.org less! However the standard enthalpy of formation is zero acid, we must start with the lowest enthalpy in the with! 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That define their standard states ( oxygen gas, solid Carbon in the form of graphite, etc. to... Typical of state functions the lattice energy. [ 3 ] solid Carbon in the problem kilojoules... Tetraethyllead is a highly poisonous, colorless liquid that burns in air to give an orange with. Been determined for a number of substances are given in Table A.9 in SB & VW } \ ) products... Such as the enthalpy of reaction is negative, not atomic hydrogen ( H.... Produce a compound from its elements under standard conditions of reaction is positive an! Cc BY-NC-SA 3.0 corresponding to the standard enthalpy of formation and little 0tells it...
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# Persistence length of a polymer chain
I'm trying to calculate the persistence length (Lp) of a polymer chain using Mathematica. The first and simplest method is to compare the EuclideanDistance between two points on the polymer and arc length separating the points. This works for me. I'll describe how I implemented this now and then give the other method based on tangent-tangent angle correlations which should also work but I'm having trouble with. Hopefully someone might know about this stuff and be able to help. This article describes what I'm trying to do. I've put some more references and a helpful figure at the end. Two of the linked articles at the end are free/open access and I can provide copies of the other linked articles if people are interested and cannot retrieve them.
You can get a sample dataset here, units are in microns but it doesn't really matter:
data = Uncompress@Import["http://pastebin.com/raw.php?i=60aazeuc"]
In the literature traced curves from pixel-based images are often smoothed using a weighted moving average
smoothdata = MovingAverage[data, {1, 2, 4, 2, 1}];
To calculate the arc length lets interpolate along the curve with a cubic spline to a parametrized curve (starting at 0).
f = Interpolation[Transpose[{Range[0, Length[smoothdata] - 1], smoothdata}],
Method -> "Spline", InterpolationOrder -> 3];
To find the length along the curve I based it on @Szabolcs answer.
v = FunctionInterpolation[Norm[f'[t]], {t, 0, Length[smoothdata] - 1}]
dist = Derivative[-1][v]
totallength = dist[Length[smoothdata] - 1];
invdist = FunctionInterpolation[InverseFunction[dist][d],
{d, 0, totallength}]
The invdist function returns the parameter along the curve for a given length.
Now I made a function that takes a window of arc length x (in microns) and translates it along the curve (in 5 nm steps) and then returns the mean of the square of the EuclideanDistance between the end points of all the subsets of the curve. This is repeated for a range of arc lengths and then the result
distance[x_] :=
Mean[
Table[
EuclideanDistance[f[invdist[t]], f[invdist[t + x]]]^2,
{t, 0, totallength - x, 0.005}
]
];
Now we can run the function:
tofit = ParallelTable[{x, distance[x]}, {x, 0, totallength, 0.1}]
and fit the result (dropping the first (0,0) point) to the model from the literature:
fit = NonlinearModelFit[
Rest@tofit, {4 Lp s (1 - (2 Lp /s) (1 - Exp[-s/(2 Lp)]))}, {Lp}, s,
MaxIterations -> 1000, Method -> "NMinimize"
];
Ta da! It works. Lets plot the data and the fit.
Show[
ListPlot[tofit, Joined -> True, PlotRange -> All],
Plot[fit[x], {x, 0, totallength}, PlotStyle -> {Red, Dashed}]
]
In this case Lp is 0.79 microns, sounds reasonable.
The other method to measure the persistence length is based on the angle between tangents on the curve separated by a certain arc length. See: this graphic stolen from the linked paper. Using the cubic spline fit its easy to calculate the tangent vectors at a point. This next function similarly translates a window of arc length x along the curve except this time it finds the dot product (cosine of the angle) of the unit tangent vectors at the endpoints of the window and returns the mean of all the dot products (cosines of the angles).
cosinecorrelation[x_] :=
Mean[
Table[
Dot[Normalize[f'[invdist[t]]], Normalize[f'[invdist[t + x]]]],
{t, 0, totallength - x, 0.005}
]
];
This should result in an exponential decay <cos(theta)> = Exp[-x/Lp], However, I get basically a linear function, also the values drop below zero. As far as I can tell that shouldn't happen... Does something look wrong with what I did?
ListPlot[
ParallelTable[{x, cosinecorrelation[x]},
{x, 0, totallength, 0.1}
],
Joined -> True, PlotRange -> All
]
The next method is to look at the mean square angle (instead of the cosine of the angle), <theta^2> = -x/Lp which should be a linear function of arc length, x. However, (warning, potentially stupid question follows), when I use ArcCos I always get a positive angle (same with VectorAngle), even when the dot product is negative. This must have to do with how Mathematica defines ArcCos, how, can I make it so negative dot products give the equivalent negative angle. Here is my broken function, based on the MMA ArcCos
anglesquaredcorrelation[x_] :=
Mean[
Table[
(ArcCos[Dot[Normalize[f'[invdist[t]]], Normalize[f'[invdist[t + x]]]]])^2,
{t, 0, totallength - x, 0.005}
]
];
An alternative implementation, based on VectorAngle, which confusingly doesn't seem to give the same values for larger x.
vectorangle[x_] :=
Mean[
Table[
VectorAngle[f'[invdist[t]], f'[invdist[t + x]]]^2,
{t, 0, totallength - x, 0.005}
];
Any help would be greatly appreciated! For interested parties much of the theory was presented in this 1979 paper based on earlier work by Landau and Lifshitz (Landau, L. D. & Lifshitz, E. M. (1958) Statistical Physics, Course of Theoretical Physics, Vol. 5, Pergamon, London.)
Here is a helpful set of plots and equations from another paper:
Open access article this time: PDF, and another open access paper PDF.
• Sqrt[#.#] &[...] could be written as Norm[...] Aug 1 '12 at 19:26
• The ArcCos doc page says: For real z between -1 and 1, the results are always in the range 0 to pi. I believe this is the standard convention. (see also Wikipedia) Aug 1 '12 at 19:42
• @SjoerdC.deVries, I added an image borrowed from a paper that illustrates the bending angle and how they have negative angles. Aug 1 '12 at 20:04
• Your cosinecorrelation looks perfectly reasonable, judging from the data. To see an exponential decay you would either need a much wigglier chain, or to average over many data sets. Your vectorangle and anglesquaredcorrelation gave exactly the same results when I tried them. Try re-running your code with a fresh kernel. If you want a signed angle between tangents, I suggest instead of ArcCos[a.b] you use ArcTan@@a - ArcTan@@b Aug 2 '12 at 12:10
• @s0rce is your data 2D $(X,Y)$, or 3D $(\phi,\theta)$? In my opinion MovingAverage introduces an artificial correlation on your data, which is actually what you need to measure. Feb 20 '14 at 18:58
You say your data is a list of $(X,Y)$ so it looks like this:
ListLinePlot[data, Frame -> True, FrameLabel -> {"X", "Y"}]
Far from been a random coil where the definition of persistent length makes sense. Let see, we want to calculate the average $\cos(\theta) = \hat{v_1} \cdot \hat{v_1}$, as a function of the contour distance, so I use Dot[v1, v2]/(Norm[v1] Norm[v2]) versus Total[Norm /@ Differences[data[[i ;; i + j]] for all possible combinations of $\vec{v_1}$, $\vec{v_2}$
cosThetaList = Flatten[
Table[
Table[
With[
{
v1 = data[[i]] - data[[i + 1]]
, v2 = data[[i + j]] - data[[i + j + 1]]
},
N[{Total[Norm /@ Differences[data[[i ;; i + j]]]], Dot[v1, v2]/(
Norm[v1] Norm[v2])}]]
, {j, 1, Length[data] - i - 1}]
, {i, 1, Length[data] - 2}
], 1];
Now for the average value
avgCosTheta = MovingAverage[Sort[cosThetaList, #1[[1]] > #2[[1]] &], 100];
ListLinePlot[
avgCosTheta
, PlotRange -> All
, Frame -> True
, FrameLabel -> {"Contour length", "<Cos[\[Theta]]>"}
]
Which resembles your result. In my opinion, is that the randomness implicit in the model that defines the persistent length is not present in your data, probably because the length of your polymer is too short or the physics is different from a random walk with partial memory.
Probably a way to define $P$ regardless the non-exponential shape of the curve, would be to find the value of the contour distance at which the cosine crosses $\exp(-1)$, in this case approximately $P\approx1.07$ in whatever the units your data was on.
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# Properties
Label 525.2.q.f Level 525 Weight 2 Character orbit 525.q Analytic conductor 4.192 Analytic rank 0 Dimension 16 CM no Inner twists 4
# Related objects
## Newspace parameters
Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 525.q (of order $$6$$, degree $$2$$, not minimal)
## Newform invariants
Self dual: no Analytic conductor: $$4.19214610612$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{15}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q -\beta_{1} q^{2} + ( -\beta_{1} + \beta_{7} - \beta_{8} + \beta_{12} - \beta_{13} + \beta_{15} ) q^{3} + ( \beta_{5} + \beta_{9} ) q^{4} + ( \beta_{2} + \beta_{4} + \beta_{5} + 2 \beta_{6} - \beta_{9} + \beta_{11} ) q^{6} + ( -\beta_{1} + 2 \beta_{7} + \beta_{10} + \beta_{15} ) q^{7} + ( \beta_{1} - \beta_{7} - \beta_{10} - \beta_{12} + \beta_{13} ) q^{8} + ( 1 - \beta_{3} + \beta_{4} - \beta_{5} + \beta_{6} - \beta_{9} - \beta_{11} ) q^{9} +O(q^{10})$$ $$q -\beta_{1} q^{2} + ( -\beta_{1} + \beta_{7} - \beta_{8} + \beta_{12} - \beta_{13} + \beta_{15} ) q^{3} + ( \beta_{5} + \beta_{9} ) q^{4} + ( \beta_{2} + \beta_{4} + \beta_{5} + 2 \beta_{6} - \beta_{9} + \beta_{11} ) q^{6} + ( -\beta_{1} + 2 \beta_{7} + \beta_{10} + \beta_{15} ) q^{7} + ( \beta_{1} - \beta_{7} - \beta_{10} - \beta_{12} + \beta_{13} ) q^{8} + ( 1 - \beta_{3} + \beta_{4} - \beta_{5} + \beta_{6} - \beta_{9} - \beta_{11} ) q^{9} + ( \beta_{3} - \beta_{5} + \beta_{9} ) q^{11} + ( -\beta_{1} - \beta_{7} + 2 \beta_{8} + \beta_{10} - 3 \beta_{12} + \beta_{14} ) q^{12} + ( \beta_{14} + \beta_{15} ) q^{13} + ( 1 + \beta_{2} + \beta_{4} + 2 \beta_{5} + 3 \beta_{6} - \beta_{9} + 2 \beta_{11} ) q^{14} + ( 1 + \beta_{2} - 2 \beta_{3} + \beta_{6} + \beta_{9} + \beta_{11} ) q^{16} + ( -3 \beta_{12} - \beta_{13} + \beta_{14} + \beta_{15} ) q^{17} + ( -\beta_{1} + 2 \beta_{8} - \beta_{10} - \beta_{12} - \beta_{13} - 2 \beta_{14} ) q^{18} + ( -1 - \beta_{4} + \beta_{5} + \beta_{11} ) q^{19} + ( 1 + \beta_{2} - \beta_{3} + \beta_{5} - 2 \beta_{6} - \beta_{9} ) q^{21} + ( \beta_{1} + \beta_{7} - 3 \beta_{8} + 2 \beta_{10} - 2 \beta_{12} + 2 \beta_{13} + \beta_{14} - \beta_{15} ) q^{22} + ( \beta_{1} + 2 \beta_{10} - 4 \beta_{12} + 2 \beta_{13} - 2 \beta_{15} ) q^{23} + ( -1 - \beta_{2} + \beta_{3} - \beta_{4} + \beta_{5} + \beta_{6} ) q^{24} + ( \beta_{2} - 2 \beta_{3} - \beta_{4} - \beta_{5} - \beta_{6} - \beta_{11} ) q^{26} + ( \beta_{1} - \beta_{7} - 4 \beta_{8} - 2 \beta_{10} + 4 \beta_{12} - 3 \beta_{14} + \beta_{15} ) q^{27} + ( -3 \beta_{7} + 3 \beta_{8} + \beta_{10} - 2 \beta_{12} + 2 \beta_{13} - 2 \beta_{15} ) q^{28} + ( 3 + 2 \beta_{2} - 2 \beta_{3} - 2 \beta_{4} - 3 \beta_{5} + 4 \beta_{6} - \beta_{9} - \beta_{11} ) q^{29} + ( -3 \beta_{3} - \beta_{4} - 3 \beta_{5} - \beta_{6} + 3 \beta_{9} - \beta_{11} ) q^{31} + ( -3 \beta_{7} + 6 \beta_{8} - 3 \beta_{12} + \beta_{13} + \beta_{14} - \beta_{15} ) q^{32} + ( \beta_{1} + 2 \beta_{7} + 2 \beta_{8} + 4 \beta_{10} - 2 \beta_{12} - \beta_{13} + \beta_{14} ) q^{33} + ( -1 - 3 \beta_{2} + 3 \beta_{3} - \beta_{5} - 2 \beta_{6} - \beta_{9} - \beta_{11} ) q^{34} + ( -1 + \beta_{2} + 4 \beta_{3} + \beta_{4} + 2 \beta_{5} + 2 \beta_{6} - 2 \beta_{9} ) q^{36} + ( \beta_{1} - 2 \beta_{7} + 3 \beta_{8} + 2 \beta_{10} - 3 \beta_{12} - 2 \beta_{13} + 2 \beta_{15} ) q^{37} + ( 3 \beta_{12} - \beta_{13} + \beta_{14} + \beta_{15} ) q^{38} + ( 2 - 2 \beta_{2} + \beta_{3} + \beta_{6} - 2 \beta_{11} ) q^{39} + ( -3 - 2 \beta_{4} + \beta_{5} - 2 \beta_{6} + \beta_{9} - \beta_{11} ) q^{41} + ( -4 \beta_{1} + \beta_{7} + 4 \beta_{8} - \beta_{10} - \beta_{12} - 2 \beta_{13} - \beta_{14} ) q^{42} + ( -3 \beta_{8} - \beta_{10} + \beta_{12} - \beta_{13} ) q^{43} + ( 2 - 6 \beta_{2} + 2 \beta_{4} - 2 \beta_{5} - 2 \beta_{11} ) q^{44} + ( -8 \beta_{2} + 4 \beta_{3} + \beta_{5} - 2 \beta_{6} + \beta_{9} ) q^{46} + ( -2 \beta_{8} - 2 \beta_{10} + 2 \beta_{12} + 2 \beta_{13} - 2 \beta_{15} ) q^{47} + ( -\beta_{1} + 4 \beta_{8} + \beta_{10} + \beta_{14} + \beta_{15} ) q^{48} + ( -3 + \beta_{2} - 2 \beta_{3} + 2 \beta_{4} + \beta_{5} - 2 \beta_{6} - 2 \beta_{9} + 3 \beta_{11} ) q^{49} + ( -1 - 2 \beta_{2} + 4 \beta_{3} - 2 \beta_{5} + \beta_{6} - 3 \beta_{9} - 3 \beta_{11} ) q^{51} + ( 3 \beta_{7} + 3 \beta_{8} + \beta_{10} - 2 \beta_{12} - \beta_{13} - \beta_{14} + 2 \beta_{15} ) q^{52} + ( -4 \beta_{7} - 4 \beta_{8} - 4 \beta_{10} + 4 \beta_{12} - 4 \beta_{15} ) q^{53} + ( -2 + 7 \beta_{2} - 4 \beta_{3} - 2 \beta_{4} + 2 \beta_{6} + 2 \beta_{11} ) q^{54} + ( -\beta_{3} - 3 \beta_{4} + \beta_{5} + 3 \beta_{9} + \beta_{11} ) q^{56} + ( -\beta_{1} - \beta_{7} + 3 \beta_{8} - \beta_{10} - \beta_{12} + \beta_{13} + 2 \beta_{14} - 2 \beta_{15} ) q^{57} + ( -2 \beta_{1} + 4 \beta_{7} + 2 \beta_{10} - 5 \beta_{13} - 3 \beta_{14} + 2 \beta_{15} ) q^{58} + ( -2 \beta_{2} + \beta_{3} + 2 \beta_{4} + \beta_{5} - 4 \beta_{6} + \beta_{9} - 2 \beta_{11} ) q^{59} + ( 3 \beta_{4} - 3 \beta_{5} + 3 \beta_{6} - 4 \beta_{9} + \beta_{11} ) q^{61} + ( 4 \beta_{1} + 4 \beta_{7} - 4 \beta_{8} - \beta_{10} + \beta_{12} - \beta_{13} - 4 \beta_{14} + 4 \beta_{15} ) q^{62} + ( -\beta_{1} + \beta_{7} - 5 \beta_{8} - 4 \beta_{10} + 2 \beta_{12} - \beta_{13} - 2 \beta_{14} + 4 \beta_{15} ) q^{63} + ( -1 - \beta_{2} - \beta_{3} - \beta_{4} - 3 \beta_{5} - \beta_{6} + 4 \beta_{9} - 4 \beta_{11} ) q^{64} + ( -4 - 6 \beta_{2} + 7 \beta_{3} + 3 \beta_{4} + 2 \beta_{5} - 6 \beta_{6} - 4 \beta_{9} + \beta_{11} ) q^{66} + ( 2 \beta_{1} - \beta_{7} + \beta_{8} + \beta_{10} - \beta_{15} ) q^{67} + ( -2 \beta_{1} + 4 \beta_{7} + 2 \beta_{8} + 2 \beta_{10} - 2 \beta_{12} + 2 \beta_{13} + 4 \beta_{14} + 2 \beta_{15} ) q^{68} + ( -6 - \beta_{2} + 6 \beta_{3} + \beta_{4} + 3 \beta_{5} - 6 \beta_{6} - 3 \beta_{9} + 3 \beta_{11} ) q^{69} + ( -2 + \beta_{2} - \beta_{3} + \beta_{4} - 3 \beta_{6} - \beta_{9} - \beta_{11} ) q^{71} + ( -\beta_{1} - 3 \beta_{7} + 2 \beta_{8} - \beta_{10} - \beta_{12} + \beta_{13} + 2 \beta_{14} - 4 \beta_{15} ) q^{72} + ( 3 \beta_{7} - 2 \beta_{8} + \beta_{12} + 2 \beta_{13} + 2 \beta_{14} - 2 \beta_{15} ) q^{73} + ( -12 + 7 \beta_{3} - 2 \beta_{4} + \beta_{5} - 8 \beta_{6} - \beta_{9} - 2 \beta_{11} ) q^{74} + ( 1 + 3 \beta_{2} - 3 \beta_{3} - 2 \beta_{4} - \beta_{5} + \beta_{9} + \beta_{11} ) q^{76} + ( 2 \beta_{1} - 4 \beta_{8} + 3 \beta_{10} - \beta_{12} - 3 \beta_{13} - 2 \beta_{14} ) q^{77} + ( 3 \beta_{1} - 3 \beta_{7} - 3 \beta_{8} - 3 \beta_{10} + 3 \beta_{12} + \beta_{13} - \beta_{14} + \beta_{15} ) q^{78} + ( 11 + 2 \beta_{2} - 4 \beta_{3} - 3 \beta_{4} - 3 \beta_{5} + 8 \beta_{6} + 2 \beta_{9} - \beta_{11} ) q^{79} + ( -5 + \beta_{2} - 4 \beta_{3} + 2 \beta_{4} + 2 \beta_{5} + \beta_{9} + \beta_{11} ) q^{81} + ( 6 \beta_{1} - 2 \beta_{8} - 2 \beta_{10} + 2 \beta_{12} - \beta_{13} - \beta_{14} + 2 \beta_{15} ) q^{82} + ( \beta_{1} + \beta_{7} - 6 \beta_{8} - 2 \beta_{14} + 2 \beta_{15} ) q^{83} + ( -3 + 3 \beta_{2} + 3 \beta_{3} + \beta_{4} + 6 \beta_{5} + \beta_{6} + \beta_{9} + 4 \beta_{11} ) q^{84} + ( 1 - 2 \beta_{2} + \beta_{4} - \beta_{5} - \beta_{9} ) q^{86} + ( 3 \beta_{1} - 4 \beta_{7} - 3 \beta_{8} - 4 \beta_{10} + 10 \beta_{12} - 3 \beta_{13} - 2 \beta_{14} - \beta_{15} ) q^{87} + ( 4 \beta_{1} - 2 \beta_{7} - 4 \beta_{8} - 4 \beta_{10} + 4 \beta_{13} - 4 \beta_{14} ) q^{88} + ( 3 + 4 \beta_{2} - 8 \beta_{3} + \beta_{4} + \beta_{5} + 4 \beta_{6} + 5 \beta_{9} + 6 \beta_{11} ) q^{89} + ( -\beta_{2} - \beta_{3} - \beta_{4} + 2 \beta_{5} - 4 \beta_{6} + 3 \beta_{9} ) q^{91} + ( 3 \beta_{1} - 3 \beta_{7} - 8 \beta_{8} - 5 \beta_{10} + 11 \beta_{12} + 5 \beta_{13} ) q^{92} + ( 4 \beta_{1} - 2 \beta_{7} + 3 \beta_{8} + 4 \beta_{10} + \beta_{12} + 3 \beta_{13} + 3 \beta_{14} ) q^{93} + ( 8 - 6 \beta_{3} - 2 \beta_{5} + 4 \beta_{6} + 2 \beta_{9} ) q^{94} + ( 2 + 4 \beta_{2} + \beta_{3} - 3 \beta_{4} + 3 \beta_{5} + 4 \beta_{6} + 3 \beta_{9} + \beta_{11} ) q^{96} + ( -3 \beta_{1} + 3 \beta_{7} - \beta_{8} - 2 \beta_{10} + 2 \beta_{13} + 3 \beta_{14} + 3 \beta_{15} ) q^{97} + ( -8 \beta_{1} + 3 \beta_{7} + 8 \beta_{8} + \beta_{10} - 2 \beta_{13} + \beta_{14} - \beta_{15} ) q^{98} + ( -\beta_{2} + 3 \beta_{3} - \beta_{4} - 2 \beta_{5} - 11 \beta_{6} + \beta_{9} - 3 \beta_{11} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - 6q^{4} + 10q^{6} + 10q^{9} + O(q^{10})$$ $$16q - 6q^{4} + 10q^{6} + 10q^{9} + 24q^{14} + 2q^{16} - 18q^{19} + 38q^{21} - 32q^{24} - 12q^{26} - 42q^{31} + 18q^{36} + 6q^{39} - 60q^{41} - 14q^{46} + 8q^{49} - 12q^{51} - 34q^{54} - 42q^{56} + 24q^{59} + 30q^{61} - 76q^{64} + 44q^{66} + 26q^{69} - 108q^{74} + 58q^{79} - 82q^{81} + 6q^{84} + 18q^{86} + 6q^{89} - 6q^{91} + 48q^{94} - 6q^{96} + 68q^{99} + O(q^{100})$$
Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{16} + 11 x^{14} + 85 x^{12} + 332 x^{10} + 940 x^{8} + 1064 x^{6} + 880 x^{4} + 128 x^{2} + 16$$:
$$\beta_{0}$$ $$=$$ $$1$$ $$\beta_{1}$$ $$=$$ $$\nu$$ $$\beta_{2}$$ $$=$$ $$($$$$-13 \nu^{14} - 127 \nu^{12} - 1059 \nu^{10} - 4226 \nu^{8} - 14630 \nu^{6} - 20976 \nu^{4} - 28864 \nu^{2} + 3416$$$$)/17208$$ $$\beta_{3}$$ $$=$$ $$($$$$8072 \nu^{14} + 83435 \nu^{12} + 619005 \nu^{10} + 2199943 \nu^{8} + 5759872 \nu^{6} + 4542924 \nu^{4} + 4197620 \nu^{2} + 1131680$$$$)/2357496$$ $$\beta_{4}$$ $$=$$ $$($$$$-1699 \nu^{14} - 18896 \nu^{12} - 149820 \nu^{10} - 612405 \nu^{8} - 1879598 \nu^{6} - 2699154 \nu^{4} - 3252680 \nu^{2} - 749364$$$$)/392916$$ $$\beta_{5}$$ $$=$$ $$($$$$-9357 \nu^{14} - 91521 \nu^{12} - 672151 \nu^{10} - 2181786 \nu^{8} - 5398232 \nu^{6} - 1173004 \nu^{4} - 1016664 \nu^{2} + 2648608$$$$)/1571664$$ $$\beta_{6}$$ $$=$$ $$($$$$15229 \nu^{14} + 164807 \nu^{12} + 1267309 \nu^{10} + 4851724 \nu^{8} + 13616468 \nu^{6} + 14343892 \nu^{4} + 12681936 \nu^{2} + 272784$$$$)/1571664$$ $$\beta_{7}$$ $$=$$ $$($$$$15229 \nu^{15} + 164807 \nu^{13} + 1267309 \nu^{11} + 4851724 \nu^{9} + 13616468 \nu^{7} + 14343892 \nu^{5} + 12681936 \nu^{3} + 1844448 \nu$$$$)/1571664$$ $$\beta_{8}$$ $$=$$ $$($$$$427 \nu^{15} + 4723 \nu^{13} + 36549 \nu^{11} + 143882 \nu^{9} + 409832 \nu^{7} + 483588 \nu^{5} + 417712 \nu^{3} + 112384 \nu$$$$)/34416$$ $$\beta_{9}$$ $$=$$ $$($$$$-21101 \nu^{14} - 238093 \nu^{12} - 1862467 \nu^{10} - 7521662 \nu^{8} - 21834704 \nu^{6} - 27514780 \nu^{4} - 22775544 \nu^{2} - 3194176$$$$)/1571664$$ $$\beta_{10}$$ $$=$$ $$($$$$-30473 \nu^{15} - 308177 \nu^{13} - 2306547 \nu^{11} - 7971934 \nu^{9} - 20873260 \nu^{7} - 11665404 \nu^{5} - 10957532 \nu^{3} + 8495368 \nu$$$$)/2357496$$ $$\beta_{11}$$ $$=$$ $$($$$$-13411 \nu^{14} - 150080 \nu^{12} - 1163096 \nu^{10} - 4612487 \nu^{8} - 13036508 \nu^{6} - 15171236 \nu^{4} - 11170948 \nu^{2} - 1684584$$$$)/785832$$ $$\beta_{12}$$ $$=$$ $$($$$$-82961 \nu^{15} - 892865 \nu^{13} - 6850017 \nu^{11} - 26014876 \nu^{9} - 72425530 \nu^{7} - 72742140 \nu^{5} - 58172408 \nu^{3} + 5684968 \nu$$$$)/4714992$$ $$\beta_{13}$$ $$=$$ $$($$$$14088 \nu^{15} + 160481 \nu^{13} + 1257754 \nu^{11} + 5136186 \nu^{9} + 15012495 \nu^{7} + 19847572 \nu^{5} + 17571096 \nu^{3} + 4461244 \nu$$$$)/785832$$ $$\beta_{14}$$ $$=$$ $$($$$$29781 \nu^{15} + 319213 \nu^{13} + 2439960 \nu^{11} + 9179749 \nu^{9} + 25256949 \nu^{7} + 24011448 \nu^{5} + 18177892 \nu^{3} - 1445260 \nu$$$$)/785832$$ $$\beta_{15}$$ $$=$$ $$($$$$40479 \nu^{15} + 445749 \nu^{13} + 3442334 \nu^{11} + 13442445 \nu^{9} + 37944739 \nu^{7} + 42566624 \nu^{5} + 33653328 \nu^{3} + 2711404 \nu$$$$)/785832$$
$$1$$ $$=$$ $$\beta_0$$ $$\nu$$ $$=$$ $$\beta_{1}$$ $$\nu^{2}$$ $$=$$ $$\beta_{9} + 2 \beta_{6} + \beta_{5}$$ $$\nu^{3}$$ $$=$$ $$-\beta_{13} + \beta_{12} + \beta_{10} + 5 \beta_{7} - 5 \beta_{1}$$ $$\nu^{4}$$ $$=$$ $$-5 \beta_{11} + \beta_{9} - 13 \beta_{6} - 6 \beta_{5} - 6 \beta_{4} - 2 \beta_{3} + \beta_{2} - 7$$ $$\nu^{5}$$ $$=$$ $$-7 \beta_{15} + 7 \beta_{14} + 7 \beta_{13} - 5 \beta_{12} + 10 \beta_{8} - 25 \beta_{7}$$ $$\nu^{6}$$ $$=$$ $$32 \beta_{11} - 32 \beta_{9} + 25 \beta_{6} + 7 \beta_{5} + 25 \beta_{4} + 9 \beta_{3} + 9 \beta_{2} + 29$$ $$\nu^{7}$$ $$=$$ $$43 \beta_{15} - 41 \beta_{14} - 2 \beta_{13} + 22 \beta_{12} - 43 \beta_{10} - 64 \beta_{8} + 125 \beta_{1}$$ $$\nu^{8}$$ $$=$$ $$-41 \beta_{11} + 127 \beta_{9} + 168 \beta_{6} + 127 \beta_{5} + 41 \beta_{4} + 63 \beta_{3} - 126 \beta_{2}$$ $$\nu^{9}$$ $$=$$ $$-22 \beta_{15} - 22 \beta_{14} - 231 \beta_{13} - 65 \beta_{12} + 231 \beta_{10} + 148 \beta_{8} + 631 \beta_{7} - 631 \beta_{1}$$ $$\nu^{10}$$ $$=$$ $$-653 \beta_{11} + 231 \beta_{9} - 1453 \beta_{6} - 884 \beta_{5} - 884 \beta_{4} - 802 \beta_{3} + 401 \beta_{2} - 569$$ $$\nu^{11}$$ $$=$$ $$-1285 \beta_{15} + 1455 \beta_{14} + 1455 \beta_{13} - 483 \beta_{12} + 170 \beta_{10} + 796 \beta_{8} - 3221 \beta_{7}$$ $$\nu^{12}$$ $$=$$ $$4676 \beta_{11} - 4676 \beta_{9} + 3391 \beta_{6} + 1285 \beta_{5} + 3391 \beta_{4} + 2427 \beta_{3} + 2427 \beta_{2} + 2587$$ $$\nu^{13}$$ $$=$$ $$8245 \beta_{15} - 7103 \beta_{14} - 1142 \beta_{13} + 7138 \beta_{12} - 8245 \beta_{10} - 9352 \beta_{8} + 16615 \beta_{1}$$ $$\nu^{14}$$ $$=$$ $$-7103 \beta_{11} + 17757 \beta_{9} + 19024 \beta_{6} + 17757 \beta_{5} + 7103 \beta_{4} + 14241 \beta_{3} - 28482 \beta_{2}$$ $$\nu^{15}$$ $$=$$ $$-7138 \beta_{15} - 7138 \beta_{14} - 39101 \beta_{13} - 32139 \beta_{12} + 39101 \beta_{10} + 35620 \beta_{8} + 86501 \beta_{7} - 86501 \beta_{1}$$
## Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$$.
$$n$$ $$127$$ $$176$$ $$451$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1 + \beta_{6}$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
299.1
1.16543 − 2.01859i 1.03144 − 1.78651i 0.539169 − 0.933868i 0.192865 − 0.334053i −0.192865 + 0.334053i −0.539169 + 0.933868i −1.03144 + 1.78651i −1.16543 + 2.01859i 1.16543 + 2.01859i 1.03144 + 1.78651i 0.539169 + 0.933868i 0.192865 + 0.334053i −0.192865 − 0.334053i −0.539169 − 0.933868i −1.03144 − 1.78651i −1.16543 − 2.01859i
−1.16543 + 2.01859i −1.23297 1.21646i −1.71646 2.97300i 0 3.89248 1.07116i −2.39840 1.11699i 3.33995 0.0404447 + 2.99973i 0
299.2 −1.03144 + 1.78651i −1.61429 + 0.627739i −1.12774 1.95330i 0 0.543588 3.53142i −2.64573 0.00953166i 0.527019 2.21189 2.02671i 0
299.3 −0.539169 + 0.933868i 1.46840 + 0.918594i 0.418594 + 0.725026i 0 −1.64956 + 0.876010i 0.929227 + 2.47720i −3.05945 1.31237 + 2.69772i 0
299.4 −0.192865 + 0.334053i −0.983691 + 1.42561i 0.925606 + 1.60320i 0 −0.286507 0.603555i −1.17656 2.36975i −1.48553 −1.06470 2.80471i 0
299.5 0.192865 0.334053i 0.983691 1.42561i 0.925606 + 1.60320i 0 −0.286507 0.603555i 1.17656 + 2.36975i 1.48553 −1.06470 2.80471i 0
299.6 0.539169 0.933868i −1.46840 0.918594i 0.418594 + 0.725026i 0 −1.64956 + 0.876010i −0.929227 2.47720i 3.05945 1.31237 + 2.69772i 0
299.7 1.03144 1.78651i 1.61429 0.627739i −1.12774 1.95330i 0 0.543588 3.53142i 2.64573 + 0.00953166i −0.527019 2.21189 2.02671i 0
299.8 1.16543 2.01859i 1.23297 + 1.21646i −1.71646 2.97300i 0 3.89248 1.07116i 2.39840 + 1.11699i −3.33995 0.0404447 + 2.99973i 0
374.1 −1.16543 2.01859i −1.23297 + 1.21646i −1.71646 + 2.97300i 0 3.89248 + 1.07116i −2.39840 + 1.11699i 3.33995 0.0404447 2.99973i 0
374.2 −1.03144 1.78651i −1.61429 0.627739i −1.12774 + 1.95330i 0 0.543588 + 3.53142i −2.64573 + 0.00953166i 0.527019 2.21189 + 2.02671i 0
374.3 −0.539169 0.933868i 1.46840 0.918594i 0.418594 0.725026i 0 −1.64956 0.876010i 0.929227 2.47720i −3.05945 1.31237 2.69772i 0
374.4 −0.192865 0.334053i −0.983691 1.42561i 0.925606 1.60320i 0 −0.286507 + 0.603555i −1.17656 + 2.36975i −1.48553 −1.06470 + 2.80471i 0
374.5 0.192865 + 0.334053i 0.983691 + 1.42561i 0.925606 1.60320i 0 −0.286507 + 0.603555i 1.17656 2.36975i 1.48553 −1.06470 + 2.80471i 0
374.6 0.539169 + 0.933868i −1.46840 + 0.918594i 0.418594 0.725026i 0 −1.64956 0.876010i −0.929227 + 2.47720i 3.05945 1.31237 2.69772i 0
374.7 1.03144 + 1.78651i 1.61429 + 0.627739i −1.12774 + 1.95330i 0 0.543588 + 3.53142i 2.64573 0.00953166i −0.527019 2.21189 + 2.02671i 0
374.8 1.16543 + 2.01859i 1.23297 1.21646i −1.71646 + 2.97300i 0 3.89248 + 1.07116i 2.39840 1.11699i −3.33995 0.0404447 2.99973i 0
$$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 374.8 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
21.g even 6 1 inner
105.p even 6 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 525.2.q.f 16
3.b odd 2 1 525.2.q.e 16
5.b even 2 1 inner 525.2.q.f 16
5.c odd 4 1 105.2.s.c 8
5.c odd 4 1 525.2.t.g 8
7.d odd 6 1 525.2.q.e 16
15.d odd 2 1 525.2.q.e 16
15.e even 4 1 105.2.s.d yes 8
15.e even 4 1 525.2.t.f 8
21.g even 6 1 inner 525.2.q.f 16
35.f even 4 1 735.2.s.k 8
35.i odd 6 1 525.2.q.e 16
35.k even 12 1 105.2.s.d yes 8
35.k even 12 1 525.2.t.f 8
35.k even 12 1 735.2.b.c 8
35.l odd 12 1 735.2.b.d 8
35.l odd 12 1 735.2.s.l 8
105.k odd 4 1 735.2.s.l 8
105.p even 6 1 inner 525.2.q.f 16
105.w odd 12 1 105.2.s.c 8
105.w odd 12 1 525.2.t.g 8
105.w odd 12 1 735.2.b.d 8
105.x even 12 1 735.2.b.c 8
105.x even 12 1 735.2.s.k 8
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.2.s.c 8 5.c odd 4 1
105.2.s.c 8 105.w odd 12 1
105.2.s.d yes 8 15.e even 4 1
105.2.s.d yes 8 35.k even 12 1
525.2.q.e 16 3.b odd 2 1
525.2.q.e 16 7.d odd 6 1
525.2.q.e 16 15.d odd 2 1
525.2.q.e 16 35.i odd 6 1
525.2.q.f 16 1.a even 1 1 trivial
525.2.q.f 16 5.b even 2 1 inner
525.2.q.f 16 21.g even 6 1 inner
525.2.q.f 16 105.p even 6 1 inner
525.2.t.f 8 15.e even 4 1
525.2.t.f 8 35.k even 12 1
525.2.t.g 8 5.c odd 4 1
525.2.t.g 8 105.w odd 12 1
735.2.b.c 8 35.k even 12 1
735.2.b.c 8 105.x even 12 1
735.2.b.d 8 35.l odd 12 1
735.2.b.d 8 105.w odd 12 1
735.2.s.k 8 35.f even 4 1
735.2.s.k 8 105.x even 12 1
735.2.s.l 8 35.l odd 12 1
735.2.s.l 8 105.k odd 4 1
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(525, [\chi])$$:
$$T_{2}^{16} + \cdots$$ $$T_{11}^{8} - 28 T_{11}^{6} + 636 T_{11}^{4} - 168 T_{11}^{3} - 4132 T_{11}^{2} + 888 T_{11} + 21904$$ $$T_{13}^{8} - 21 T_{13}^{6} + 123 T_{13}^{4} - 135 T_{13}^{2} + 36$$
## Hecke Characteristic Polynomials
$p$ $F_p(T)$
$2$ $$1 - 5 T^{2} + 9 T^{4} + 8 T^{6} - 64 T^{8} + 120 T^{10} - 32 T^{12} - 368 T^{14} + 1104 T^{16} - 1472 T^{18} - 512 T^{20} + 7680 T^{22} - 16384 T^{24} + 8192 T^{26} + 36864 T^{28} - 81920 T^{30} + 65536 T^{32}$$
$3$ $$1 - 5 T^{2} + 33 T^{4} - 110 T^{6} + 430 T^{8} - 990 T^{10} + 2673 T^{12} - 3645 T^{14} + 6561 T^{16}$$
$5$
$7$ $$1 - 4 T^{2} - 26 T^{4} - 244 T^{6} + 3907 T^{8} - 11956 T^{10} - 62426 T^{12} - 470596 T^{14} + 5764801 T^{16}$$
$11$ $$( 1 + 16 T^{2} - 2 T^{4} + 30 T^{5} + 268 T^{6} + 1548 T^{7} + 21079 T^{8} + 17028 T^{9} + 32428 T^{10} + 39930 T^{11} - 29282 T^{12} + 28344976 T^{14} + 214358881 T^{16} )^{2}$$
$13$ $$( 1 + 83 T^{2} + 3217 T^{4} + 76058 T^{6} + 1197778 T^{8} + 12853802 T^{10} + 91880737 T^{12} + 400625147 T^{14} + 815730721 T^{16} )^{2}$$
$17$ $$1 + 76 T^{2} + 3024 T^{4} + 74528 T^{6} + 1179962 T^{8} + 10465632 T^{10} - 4424000 T^{12} - 1753904276 T^{14} - 37267323453 T^{16} - 506878335764 T^{18} - 369496904000 T^{20} + 252614914528608 T^{22} + 8231128701597242 T^{24} + 150247993412663072 T^{26} + 1761849645382797264 T^{28} + 12796714818514470604 T^{30} + 48661191875666868481 T^{32}$$
$19$ $$( 1 + 9 T + 100 T^{2} + 657 T^{3} + 4723 T^{4} + 26244 T^{5} + 148996 T^{6} + 704196 T^{7} + 3331528 T^{8} + 13379724 T^{9} + 53787556 T^{10} + 180007596 T^{11} + 615506083 T^{12} + 1626797043 T^{13} + 4704588100 T^{14} + 8044845651 T^{15} + 16983563041 T^{16} )^{2}$$
$23$ $$1 - 53 T^{2} + 399 T^{4} + 18308 T^{6} - 55297 T^{8} - 3303501 T^{10} - 170695622 T^{12} - 2962951637 T^{14} + 281105182152 T^{16} - 1567401415973 T^{18} - 47767633556102 T^{20} - 489036707347389 T^{22} - 4330362553083457 T^{24} + 758436567299485892 T^{26} + 8743935148376108079 T^{28} -$$$$61\!\cdots\!77$$$$T^{30} +$$$$61\!\cdots\!61$$$$T^{32}$$
$29$ $$( 1 - 53 T^{2} + 3250 T^{4} - 128951 T^{6} + 4063174 T^{8} - 108447791 T^{10} + 2298663250 T^{12} - 31525636013 T^{14} + 500246412961 T^{16} )^{2}$$
$31$ $$( 1 + 21 T + 262 T^{2} + 2415 T^{3} + 17293 T^{4} + 101304 T^{5} + 505090 T^{6} + 2328618 T^{7} + 11769748 T^{8} + 72187158 T^{9} + 485391490 T^{10} + 3017947464 T^{11} + 15970448653 T^{12} + 69139399665 T^{13} + 232525964422 T^{14} + 577764896331 T^{15} + 852891037441 T^{16} )^{2}$$
$37$ $$1 + 97 T^{2} + 5532 T^{4} + 186305 T^{6} + 3327797 T^{8} + 12794040 T^{10} + 1243533586 T^{12} + 183679377646 T^{14} + 10522943320200 T^{16} + 251457067997374 T^{18} + 2330582149071346 T^{20} + 32826006305802360 T^{22} + 11688818589319942037 T^{24} +$$$$89\!\cdots\!45$$$$T^{26} +$$$$36\!\cdots\!92$$$$T^{28} +$$$$87\!\cdots\!33$$$$T^{30} +$$$$12\!\cdots\!41$$$$T^{32}$$
$41$ $$( 1 + 15 T + 218 T^{2} + 1791 T^{3} + 14136 T^{4} + 73431 T^{5} + 366458 T^{6} + 1033815 T^{7} + 2825761 T^{8} )^{4}$$
$43$ $$( 1 - 304 T^{2} + 41758 T^{4} - 3395548 T^{6} + 179098699 T^{8} - 6278368252 T^{10} + 142762292158 T^{12} - 1921694366896 T^{14} + 11688200277601 T^{16} )^{2}$$
$47$ $$1 + 268 T^{2} + 36732 T^{4} + 3628040 T^{6} + 294880202 T^{8} + 20635855860 T^{10} + 1272375350416 T^{12} + 70342526859604 T^{14} + 3494142383383395 T^{16} + 155386641832865236 T^{18} + 6208785822293297296 T^{20} +$$$$22\!\cdots\!40$$$$T^{22} +$$$$70\!\cdots\!22$$$$T^{24} +$$$$19\!\cdots\!60$$$$T^{26} +$$$$42\!\cdots\!12$$$$T^{28} +$$$$68\!\cdots\!92$$$$T^{30} +$$$$56\!\cdots\!21$$$$T^{32}$$
$53$ $$1 - 104 T^{2} + 3204 T^{4} + 8144 T^{6} - 2651158 T^{8} - 214376472 T^{10} + 18555084688 T^{12} + 949831131304 T^{14} - 128029390162317 T^{16} + 2668075647832936 T^{18} + 146408543184054928 T^{20} - 4751517542968956888 T^{22} -$$$$16\!\cdots\!38$$$$T^{24} +$$$$14\!\cdots\!56$$$$T^{26} +$$$$15\!\cdots\!64$$$$T^{28} -$$$$14\!\cdots\!76$$$$T^{30} +$$$$38\!\cdots\!21$$$$T^{32}$$
$59$ $$( 1 - 12 T - 80 T^{2} + 1164 T^{3} + 7690 T^{4} - 80082 T^{5} - 434420 T^{6} + 1772232 T^{7} + 28861927 T^{8} + 104561688 T^{9} - 1512216020 T^{10} - 16447161078 T^{11} + 93182506090 T^{12} + 832171884036 T^{13} - 3374442691280 T^{14} - 29863817817828 T^{15} + 146830437604321 T^{16} )^{2}$$
$61$ $$( 1 - 15 T + 223 T^{2} - 2220 T^{3} + 19711 T^{4} - 141723 T^{5} + 816310 T^{6} - 5175267 T^{7} + 31433836 T^{8} - 315691287 T^{9} + 3037489510 T^{10} - 32168428263 T^{11} + 272915371951 T^{12} - 1875003788220 T^{13} + 11489043482503 T^{14} - 47141142540315 T^{15} + 191707312997281 T^{16} )^{2}$$
$67$ $$1 + 484 T^{2} + 128562 T^{4} + 23999600 T^{6} + 3478000361 T^{8} + 410568162660 T^{10} + 40599889512562 T^{12} + 3416547531270040 T^{14} + 246775367829948324 T^{16} + 15336881867871209560 T^{18} +$$$$81\!\cdots\!02$$$$T^{20} +$$$$37\!\cdots\!40$$$$T^{22} +$$$$14\!\cdots\!01$$$$T^{24} +$$$$43\!\cdots\!00$$$$T^{26} +$$$$10\!\cdots\!82$$$$T^{28} +$$$$17\!\cdots\!36$$$$T^{30} +$$$$16\!\cdots\!81$$$$T^{32}$$
$71$ $$( 1 - 464 T^{2} + 99532 T^{4} - 12936548 T^{6} + 1114829374 T^{8} - 65213138468 T^{10} + 2529275433292 T^{12} - 59438531739344 T^{14} + 645753531245761 T^{16} )^{2}$$
$73$ $$1 - 335 T^{2} + 63708 T^{4} - 7606879 T^{6} + 587709533 T^{8} - 19770442248 T^{10} - 1697574900854 T^{12} + 348751235496070 T^{14} - 32202831466789560 T^{16} + 1858495333958557030 T^{18} - 48208141150002997814 T^{20} -$$$$29\!\cdots\!72$$$$T^{22} +$$$$47\!\cdots\!73$$$$T^{24} -$$$$32\!\cdots\!71$$$$T^{26} +$$$$14\!\cdots\!68$$$$T^{28} -$$$$40\!\cdots\!15$$$$T^{30} +$$$$65\!\cdots\!61$$$$T^{32}$$
$79$ $$( 1 - 29 T + 294 T^{2} - 1975 T^{3} + 27377 T^{4} - 260496 T^{5} + 598654 T^{6} - 2403434 T^{7} + 77714340 T^{8} - 189871286 T^{9} + 3736199614 T^{10} - 128434687344 T^{11} + 1066336367537 T^{12} - 6077186388025 T^{13} + 71467711923174 T^{14} - 556913360598611 T^{15} + 1517108809906561 T^{16} )^{2}$$
$83$ $$( 1 - 535 T^{2} + 130150 T^{4} - 19183249 T^{6} + 1908109846 T^{8} - 132153402361 T^{10} + 6176700478150 T^{12} - 174913099752415 T^{14} + 2252292232139041 T^{16} )^{2}$$
$89$ $$( 1 - 3 T - 53 T^{2} - 2820 T^{3} + 14227 T^{4} + 160275 T^{5} + 3467116 T^{6} - 26593569 T^{7} - 193500020 T^{8} - 2366827641 T^{9} + 27463025836 T^{10} + 112988906475 T^{11} + 892633862707 T^{12} - 15747047646180 T^{13} - 26340008420933 T^{14} - 132694004686587 T^{15} + 3936588805702081 T^{16} )^{2}$$
$97$ $$( 1 + 368 T^{2} + 81676 T^{4} + 12257504 T^{6} + 1385094598 T^{8} + 115330855136 T^{10} + 7230717554956 T^{12} + 306533697813872 T^{14} + 7837433594376961 T^{16} )^{2}$$
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# Tag Info
7
One idea that comes to mind is the fact that a connected graph has a Eulerian circuit if and only if every vertex has even degree. Another idea that comes to mind is just the Fundamental Theorem of Calculus. If you have a rather boring video of a car's speedometer as the car travels from A to B, then you can figure out the total distance the car has ...
6
This is a service course for students who are mostly engineering majors. Therefore any drastic change in notation like this is likely to be a bad idea. Leaving out $d\textbf{S}$ and $dV$ would be particularly unfortunate, since leaving out the $dx$ is such a common student mistake anyway in freshman calculus. Also, any notation that has the wrong units is a ...
5
I think you are being harsh in your criticism of the classical notation. Of course, at the mathematician's end of the spectrum, the notation you promote towards the end of your question has merit. But I have taught vector calculus for many years, and find the classical notations that provoke you do in fact help learners decode theorems and calculations. ...
5
Here are two similar ideas. (1) The shortest geodesic between two points on the surface of a polyhedron (generally) bends as it crosses edges, when viewed globally in $\mathbb{R}^3$, but from the local point of view of an ant walking along the path, it is straight, i.e., straight when each crossed edge is unfolded flat. This is commonly illustrated on a ...
2
Local-to-global is a big thing in algebra, starting with (Hasse-)Minkowski's result that if you have a solution to a quadratic form modulo all prime powers and in the reals, you also have one over the integers. (See Theorem 2.4 here for the Minkowskian statement without $p$-adic numbers, which is otherwise a bit difficult to find in a quick web search.) ...
Only top voted, non community-wiki answers of a minimum length are eligible
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St. Charles Lwanga School Kitui 2021/2022 KCSE Results Analysis, Grade Count
St. Charles Lwanga School Kitui recorded an impressive result in the 2021 KCSE exams. The school recorded a mean score of 8.95 points which is a B(plain)
Out of the 221 candidates who sat for the 2021 KCSE exams, a total of 214 candidates attained the direct university entry grade. This translates to 96.83258% direct entry.
HERE IS THE SCHOOL’S 2021 KCSE RESULTS ANALYSIS IN FULL
GRADE A A- B+ B B- C+ C C- D+ D D- E X Y P NO OF CANDIDATES 4 24 50 63 48 25 6 0 1 0 0 0 0 0 0 MSS 8.95 . . . . . . . . . . . . . . SCHOOL MEAN GRADE B(plain) . . . . . . . . . . . . . . UNIVERSITY DIRECT ENTRY 214 . . . . . . . . . . . . . . TOTAL CANDIDATES 221 . . . . . . . . . . . . . . % DIRECT ENTRY 96.83258 . . . . . . . . . . . . . .
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Eigen 3.4.90 (git rev a4098ac676528a83cfb73d4d26ce1b42ec05f47c)
Eigen::ColPivHouseholderQR< MatrixType_ > Class Template Reference
## Detailed Description
template<typename MatrixType_>
class Eigen::ColPivHouseholderQR< MatrixType_ >
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
Template Parameters
MatrixType_ the type of the matrix of which we are computing the QR decomposition
This class performs a rank-revealing QR decomposition of a matrix A into matrices P, Q and R such that
$\mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}$
by using Householder transformations. Here, P is a permutation matrix, Q a unitary matrix and R an upper triangular matrix.
This decomposition performs column pivoting in order to be rank-revealing and improve numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.
This class supports the inplace decomposition mechanism.
MatrixBase::colPivHouseholderQr()
Inheritance diagram for Eigen::ColPivHouseholderQR< MatrixType_ >:
## Public Member Functions
MatrixType::RealScalar absDeterminant () const
ColPivHouseholderQR ()
Default Constructor. More...
template<typename InputType >
ColPivHouseholderQR (const EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix. More...
template<typename InputType >
ColPivHouseholderQR (EigenBase< InputType > &matrix)
Constructs a QR factorization from a given matrix. More...
ColPivHouseholderQR (Index rows, Index cols)
Default Constructor with memory preallocation. More...
const PermutationTypecolsPermutation () const
template<typename InputType >
ColPivHouseholderQR< MatrixType > & compute (const EigenBase< InputType > &matrix)
Index dimensionOfKernel () const
const HCoeffsType & hCoeffs () const
HouseholderSequenceType householderQ () const
ComputationInfo info () const
Reports whether the QR factorization was successful. More...
const Inverse< ColPivHouseholderQRinverse () const
bool isInjective () const
bool isInvertible () const
bool isSurjective () const
MatrixType::RealScalar logAbsDeterminant () const
const MatrixType & matrixQR () const
const MatrixType & matrixR () const
RealScalar maxPivot () const
Index nonzeroPivots () const
Index rank () const
ColPivHouseholderQRsetThreshold (const RealScalar &threshold)
ColPivHouseholderQRsetThreshold (Default_t)
template<typename Rhs >
const Solve< ColPivHouseholderQR, Rhs > solve (const MatrixBase< Rhs > &b) const
RealScalar threshold () const
Public Member Functions inherited from Eigen::SolverBase< ColPivHouseholderQR< MatrixType_ > >
ColPivHouseholderQR< MatrixType_ > & derived ()
const ColPivHouseholderQR< MatrixType_ > & derived () const
const Solve< ColPivHouseholderQR< MatrixType_ >, Rhs > solve (const MatrixBase< Rhs > &b) const
SolverBase ()
ConstTransposeReturnType transpose () const
Public Member Functions inherited from Eigen::EigenBase< Derived >
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
Derived & derived ()
const Derived & derived () const
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
EIGEN_CONSTEXPR Index size () const EIGEN_NOEXCEPT
Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index Index
The interface type of indices. More...
## ◆ ColPivHouseholderQR() [1/4]
template<typename MatrixType_ >
Eigen::ColPivHouseholderQR< MatrixType_ >::ColPivHouseholderQR ( )
inline
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via ColPivHouseholderQR::compute(const MatrixType&).
## ◆ ColPivHouseholderQR() [2/4]
template<typename MatrixType_ >
Eigen::ColPivHouseholderQR< MatrixType_ >::ColPivHouseholderQR ( Index rows, Index cols )
inline
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
ColPivHouseholderQR()
## ◆ ColPivHouseholderQR() [3/4]
template<typename MatrixType_ >
template<typename InputType >
Eigen::ColPivHouseholderQR< MatrixType_ >::ColPivHouseholderQR ( const EigenBase< InputType > & matrix )
inlineexplicit
Constructs a QR factorization from a given matrix.
This constructor computes the QR factorization of the matrix matrix by calling the method compute(). It is a short cut for:
ColPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
qr.compute(matrix);
compute()
## ◆ ColPivHouseholderQR() [4/4]
template<typename MatrixType_ >
template<typename InputType >
Eigen::ColPivHouseholderQR< MatrixType_ >::ColPivHouseholderQR ( EigenBase< InputType > & matrix )
inlineexplicit
Constructs a QR factorization from a given matrix.
This overloaded constructor is provided for inplace decomposition when MatrixType is a Eigen::Ref.
ColPivHouseholderQR(const EigenBase&)
## ◆ absDeterminant()
template<typename MatrixType >
MatrixType::RealScalar Eigen::ColPivHouseholderQR< MatrixType >::absDeterminant
Returns
the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.
Note
This is only for square matrices.
Warning
a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use logAbsDeterminant() instead.
logAbsDeterminant(), MatrixBase::determinant()
## ◆ colsPermutation()
template<typename MatrixType_ >
const PermutationType & Eigen::ColPivHouseholderQR< MatrixType_ >::colsPermutation ( ) const
inline
Returns
a const reference to the column permutation matrix
## ◆ compute()
template<typename MatrixType_ >
template<typename InputType >
ColPivHouseholderQR< MatrixType > & Eigen::ColPivHouseholderQR< MatrixType_ >::compute ( const EigenBase< InputType > & matrix )
Performs the QR factorization of the given matrix matrix. The result of the factorization is stored into *this, and a reference to *this is returned.
class ColPivHouseholderQR, ColPivHouseholderQR(const MatrixType&)
## ◆ dimensionOfKernel()
template<typename MatrixType_ >
Index Eigen::ColPivHouseholderQR< MatrixType_ >::dimensionOfKernel ( ) const
inline
Returns
the dimension of the kernel of the matrix of which *this is the QR decomposition.
Note
This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
## ◆ hCoeffs()
template<typename MatrixType_ >
const HCoeffsType & Eigen::ColPivHouseholderQR< MatrixType_ >::hCoeffs ( ) const
inline
Returns
a const reference to the vector of Householder coefficients used to represent the factor Q.
## ◆ householderQ()
template<typename MatrixType >
ColPivHouseholderQR< MatrixType >::HouseholderSequenceType Eigen::ColPivHouseholderQR< MatrixType >::householderQ
Returns
the matrix Q as a sequence of householder transformations. You can extract the meaningful part only by using:
qr.householderQ().setLength(qr.nonzeroPivots())
## ◆ info()
template<typename MatrixType_ >
ComputationInfo Eigen::ColPivHouseholderQR< MatrixType_ >::info ( ) const
inline
Reports whether the QR factorization was successful.
Note
This function always returns Success. It is provided for compatibility with other factorization routines.
Returns
Success
## ◆ inverse()
template<typename MatrixType_ >
const Inverse< ColPivHouseholderQR > Eigen::ColPivHouseholderQR< MatrixType_ >::inverse ( ) const
inline
Returns
the inverse of the matrix of which *this is the QR decomposition.
Note
If this matrix is not invertible, the returned matrix has undefined coefficients. Use isInvertible() to first determine whether this matrix is invertible.
## ◆ isInjective()
template<typename MatrixType_ >
bool Eigen::ColPivHouseholderQR< MatrixType_ >::isInjective ( ) const
inline
Returns
true if the matrix of which *this is the QR decomposition represents an injective linear map, i.e. has trivial kernel; false otherwise.
Note
This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
## ◆ isInvertible()
template<typename MatrixType_ >
bool Eigen::ColPivHouseholderQR< MatrixType_ >::isInvertible ( ) const
inline
Returns
true if the matrix of which *this is the QR decomposition is invertible.
Note
This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
## ◆ isSurjective()
template<typename MatrixType_ >
bool Eigen::ColPivHouseholderQR< MatrixType_ >::isSurjective ( ) const
inline
Returns
true if the matrix of which *this is the QR decomposition represents a surjective linear map; false otherwise.
Note
This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
## ◆ logAbsDeterminant()
template<typename MatrixType >
MatrixType::RealScalar Eigen::ColPivHouseholderQR< MatrixType >::logAbsDeterminant
Returns
the natural log of the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.
Note
This is only for square matrices.
This method is useful to work around the risk of overflow/underflow that's inherent to determinant computation.
absDeterminant(), MatrixBase::determinant()
## ◆ matrixQR()
template<typename MatrixType_ >
const MatrixType & Eigen::ColPivHouseholderQR< MatrixType_ >::matrixQR ( ) const
inline
Returns
a reference to the matrix where the Householder QR decomposition is stored
## ◆ matrixR()
template<typename MatrixType_ >
const MatrixType & Eigen::ColPivHouseholderQR< MatrixType_ >::matrixR ( ) const
inline
Returns
a reference to the matrix where the result Householder QR is stored
Warning
The strict lower part of this matrix contains internal values. Only the upper triangular part should be referenced. To get it, use
matrixR().template triangularView<Upper>()
const MatrixType & matrixR() const
Definition: ColPivHouseholderQR.h:206
For rank-deficient matrices, use
matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>()
Index rank() const
Definition: ColPivHouseholderQR.h:257
## ◆ maxPivot()
template<typename MatrixType_ >
RealScalar Eigen::ColPivHouseholderQR< MatrixType_ >::maxPivot ( ) const
inline
Returns
the absolute value of the biggest pivot, i.e. the biggest diagonal coefficient of R.
## ◆ nonzeroPivots()
template<typename MatrixType_ >
Index Eigen::ColPivHouseholderQR< MatrixType_ >::nonzeroPivots ( ) const
inline
Returns
the number of nonzero pivots in the QR decomposition. Here nonzero is meant in the exact sense, not in a fuzzy sense. So that notion isn't really intrinsically interesting, but it is still useful when implementing algorithms.
rank()
## ◆ rank()
template<typename MatrixType_ >
Index Eigen::ColPivHouseholderQR< MatrixType_ >::rank ( ) const
inline
Returns
the rank of the matrix of which *this is the QR decomposition.
Note
This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
## ◆ setThreshold() [1/2]
template<typename MatrixType_ >
ColPivHouseholderQR & Eigen::ColPivHouseholderQR< MatrixType_ >::setThreshold ( const RealScalar & threshold )
inline
Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine when pivots are to be considered nonzero. This is not used for the QR decomposition itself.
When it needs to get the threshold value, Eigen calls threshold(). By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method setThreshold(const RealScalar&), your value is used instead.
Parameters
threshold The new value to use as the threshold.
A pivot will be considered nonzero if its absolute value is strictly greater than $$\vert pivot \vert \leqslant threshold \times \vert maxpivot \vert$$ where maxpivot is the biggest pivot.
If you want to come back to the default behavior, call setThreshold(Default_t)
## ◆ setThreshold() [2/2]
template<typename MatrixType_ >
ColPivHouseholderQR & Eigen::ColPivHouseholderQR< MatrixType_ >::setThreshold ( Default_t )
inline
Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.
You should pass the special object Eigen::Default as parameter here.
qr.setThreshold(Eigen::Default);
See the documentation of setThreshold(const RealScalar&).
## ◆ solve()
template<typename MatrixType_ >
template<typename Rhs >
const Solve< ColPivHouseholderQR, Rhs > Eigen::ColPivHouseholderQR< MatrixType_ >::solve ( const MatrixBase< Rhs > & b ) const
inline
This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists.
Parameters
b the right-hand-side of the equation to solve.
Returns
a solution.
This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use MatrixBase::isApprox() directly, for instance like this:
bool a_solution_exists = (A*result).isApprox(b, precision);
This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get inf or nan values.
If there exists more than one solution, this method will arbitrarily choose one.
Example:
Matrix3f m = Matrix3f::Random();
Matrix3f y = Matrix3f::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the matrix y:" << endl << y << endl;
Matrix3f x;
x = m.colPivHouseholderQr().solve(y);
assert(y.isApprox(m*x));
cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
static const RandomReturnType Random()
Definition: Random.h:115
Output:
Here is the matrix m:
-1 -0.0827 -0.906
-0.737 0.0655 0.358
0.511 -0.562 0.359
Here is the matrix y:
0.869 0.662 0.0594
-0.233 -0.931 0.342
0.0388 -0.893 -0.985
Here is a solution x to the equation mx=y:
-0.117 0.626 -0.278
-0.667 1.18 1.56
-0.77 -1.53 0.0985
## ◆ threshold()
template<typename MatrixType_ >
RealScalar Eigen::ColPivHouseholderQR< MatrixType_ >::threshold ( ) const
inline
Returns the threshold that will be used by certain methods such as rank().
See the documentation of setThreshold(const RealScalar&).
The documentation for this class was generated from the following file:
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C covered with Pointers and Strings [Deep Study]
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# C covered with Pointers and Strings [Deep Study]
Pointers and Strings: Learn the core concepts of Pointers and Strings in C language. All concepts are covered in deep.
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What Will I Learn?
• write their own codes
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Requirements
• An operating system with internet connection.
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Description
Do you want to get a sound knowledge of C programming language?
If yes, then this is the right course for you. This course is specially designed for the programmers of C language. This gives you a sound knowledge of the main concepts of C computer language.
You would be able to learn all the main concepts from scratch. The examples are displayed on the screen so that you could understand all the concepts better. This course speeds up your process of writing codes by explaining you all the concepts in the smoothest possible way. This course is designed in such a way that all the front end concepts that you need to know in today's scenario are covered in it.
The main concepts that are explained in these videos are pointers and strings. The way to use their commands is explained in depth. By taking this course you would master C language and could stand at great heights in your field. All the concepts are explained with examples so as to clear every concept in an easy way.
There are basic requirements for this course. If you are keen to learn computer languages then you would already have a little knowledge of coding C. And this is what this course needs, just a little knowledge of C language. If by any chance, you do not have much knowledge of coding through C language then it is not an issue as the way all the concepts are explained makes it very cosy to understand. The only mandatory thing to learn this programming language is to practice.
This course is going to benefit you in many ways. You would stand ahead in your field with the highest pay as you would have mastered this language. You would write your own codes and at last you would be able to understand others codes and help them enhance their skills by teaching them. Teaching is the best way to learn concepts to the core as what I'm doing here you can do later to strengthen your concepts. Therefore, go on guys and enroll now. Get keen to learn your favorite computer language.
Who is the target audience?
• Beginners
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Students Who Viewed This Course Also Viewed
Curriculum For This Course
205 Lectures
24:41:15
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Introduction to Pointers
2 Lectures 13:52
Preview 06:43
Introduction to pointers Part 2
07:09
+
Basics of Pointers
4 Lectures 30:26
Playing with pointers
05:49
Preview 05:24
Pointer to Pointer
10:25
Increment or Decrement on Pointers
08:48
+
4 Lectures 38:02
Preview 09:49
Passing pointers to functions
05:49
Pointers pointing to the function
07:45
Program to reverse a given number
14:39
+
Introduction to Strings
2 Lectures 13:01
Strings Part 1
06:16
Strings Part 2
06:45
+
Basics of strings
4 Lectures 25:59
Preview 05:36
Joining two strings
07:21
Join two strings with given size
06:57
Copy one string to other string
06:05
+
Bonus Section
2 Lectures 05:27
02:23
Let's make it best course
03:04
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Decision making and branching
187 Lectures 22:34:28
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# zbMATH — the first resource for mathematics
A Lévy-driven asset price model with bankruptcy and liquidity risk. (English) Zbl 1383.62232
Ferger, Dietmar (ed.) et al., From statistics to mathematical finance. Festschrift in honour of Winfried Stute. Cham: Springer (ISBN 978-3-319-50985-3/hbk; 978-3-319-50986-0/ebook). 387-416 (2017).
Summary: We present a new asset price model, which is an enhancement of the exponential Lévy model. The possibility of bankruptcy is modelled by a single jump to zero, whereby higher probabilities for this event lead to lower asset prices. We emphasize in particular the dependence between the asset price and the probability of default. Explicit valuation formulas for European options are established by using the Fourier-based valuation method. The formulas can numerically be computed fast and thus allow to calibrate the model to market data. On markets which are not perfectly liquid, the law of one price does no longer hold and the cost of unhedgeable risks has to be taken into account. This aspect is incorporated in the recently developed two price theory (see [D. B. Madan and A. Cherny, Int. J. Theor. Appl. Finance 13, No. 8, 1149–1177 (2010; Zbl 1208.91148)]), which is discussed and applied to the proposed defaultable asset price model.
For the entire collection see [Zbl 1383.62010].
##### MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics 60G51 Processes with independent increments; Lévy processes 60H30 Applications of stochastic analysis (to PDEs, etc.) 91B25 Asset pricing models (MSC2010)
##### Keywords:
asset price model; liquidity risk
Full Text:
##### References:
[1] Andersen, L. and D. Buffum (2004). Calibration and implementation of convertible bond models. $$The Journal of Computational Finance$$ $$7$$ , 1-34. [2] Bachelier, L. (1900). $$Théorie de la Spéculation$$ . Ph. D. thesis, École Normale Superieure Paris. [3] Barndorff-Nielsen, O. and N. Shephard (2001). Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. $$Journal of the Royal Statistical Society, Series B$$ $$63(2)$$ , 167-241. · Zbl 0983.60028 [4] Bäurer, P. (2015). $$Credit and Liquidity Risk in Lévy Asset Price Models$$ . Ph. D. thesis, Universität Freiburg. [5] Bielecki, T. and M. Rutkowski (2004). $$Credit Risk: Modeling, Valuation and Hedging.$$ (2. ed.). Springer. · Zbl 1134.91023 [6] Black, F. and M. Scholes (1973). The pricing of options and corporate liabilities. $$The Journal of Political Economy$$ $$81(3)$$ , 637-654. · Zbl 1092.91524 [7] Brigo, D. and F. Mercurio (2001). $$Interest Rate Models - Theory and Practice$$ . Springer. · Zbl 1038.91040 [8] Carr, P., H. Geman, D. Madan, and M. Yor (2002). The fine structure of asset returns: An empirical investigation. $$Journal of Business$$ $$75(2)$$ , 305-332. [9] Carr, P., H. Geman, D. Madan, and M. Yor (2007). Self-decomposability and option pricing. $$Mathematical Finance$$ $$17(1)$$ , 31-57. · Zbl 1278.91157 [10] Carr, P. and D. Madan (2010). Local volatility enhanced by a jump to default. $$SIAM Journal of Financial Mathematics$$ $$1(1)$$ , 2-15. · Zbl 1197.91183 [11] Cherny, A. and D. Madan (2010). Markets as a counterparty: An introduction to conic finance. $$International Journal of Theoretical and Applied Finance$$ $$13(08)$$ , 1149-1177. · Zbl 1208.91148 [12] Cont, R. and P. Tankov (2004). $$Financial Modelling with Jump Processes$$ . Chapman and Hall/CRC. · Zbl 1052.91043 [13] Cont, R. and E. Voltchkova (2005). Integro-differential equations for option prices in exponential Lévy models. $$Finance and Stochastics$$ $$9(3)$$ , 299-325. · Zbl 1096.91023 [14] Davis, M. and F. Lischka (2002). Convertible bonds with market risk and credit risk. In D. Y. R. Chan, Y-K. Kwok and Q. Zhang (Eds.), $$Applied Probability$$ , Studies in Advanced Mathematics, pp. 45-58. American Mathematical Society/International Press. · Zbl 1029.91033 [15] Delbaen, F. and W. Schachermayer (2006). $$The Mathematics of Arbitrage$$ . Springer. · Zbl 1106.91031 [16] Eberlein, E. (2001). Application of generalized hyperbolic Lévy motions to finance. In O. Barndorff-Nielsen, T. Mikosch, and S. Resnick (Eds.), $$Lévy Processes: Theory and Applications$$ , pp. 319-336. Birkhäuser. · Zbl 0982.60045 [17] Eberlein, E., K. Glau, and A. Papapantoleon (2010). Analysis of Fourier transform valuation formulas and applications. $$Applied Mathematical Finance$$ $$17(3)$$ , 211-240. · Zbl 1233.91267 [18] Eberlein, E. and U. Keller (1995). Hyperbolic distributions in finance. $$Bernoulli$$ $$1(3)$$ , 281-299. · Zbl 0836.62107 [19] Eberlein, E. and K. Prause (2002). The generalized hyperbolic model: Financial derivatives and risk measures. In H. Geman, D. Madan, S. Pliska, and T. Vorst (Eds.), $$Mathematical Finance: Bachelier Congress 2000$$ , Springer Finance, pp. 245-267. Springer. · Zbl 0996.91067 [20] Eberlein, E. and S. Raible (1999). Term structure models driven by general Lévy processes. $$Mathematical Finance$$ $$9(1)$$ , 31-53. · Zbl 0980.91020 [21] Hull, J. and A. White (1990). Pricing interest rate derivative securities. $$The Review of Financial Studies$$ $$3(4)$$ , 573-592. · Zbl 1386.91152 [22] Jacod, J. and A. Shiryaev (2003). $$Limit Theorems for Stochastic Processes$$ (2. ed.). Springer. · Zbl 1018.60002 [23] Kluge, W. (2005). $$Time-inhomogeneous Lévy Processes in Interest Rate and Credit Risk Models.$$ Ph. D. thesis, Universität Freiburg. · Zbl 1135.60017 [24] Linetsky, V. (2006). Pricing equity derivatives subject to bankruptcy. $$Mathematical Finance$$ $$16(2)$$ , 255-282. · Zbl 1145.91351 [25] Madan, D., M. Konikov, and M. Marinescu (2004). Credit and basket default swaps. $$The Journal of Credit Risk$$ $$2(1)$$ , 67-87. [26] Madan, D. and F. Milne (1991). Option pricing with V.G. martingale component. $$Mathematical Finance$$ $$1(4)$$ , 39-55. · Zbl 0900.90105 [27] Madan, D. and E. Seneta (1990). The variance gamma (V.G.) model for share market returns. $$Journal of Business$$ $$63(4)$$ , 511-524. [28] Merton, R. (1973). Theory of rational option pricing. $$The Bell Journal of Economics and Management Science$$ $$4(1)$$ , 141-183. · Zbl 1257.91043 [29] Protter, P. E. (2005). $$Stochastic Integration and Differential Equations$$ (2. ed.). Springer. · Zbl 1041.60005 [30] Samuelson, P. (1965). Rational theory of warrant pricing. $$Industrial Management Review$$ $$6$$ (2), 13-32. [31] Sato, K.-I. (1999). $$Lévy Processes and Infinitely Divisible Distributions$$ . Cambridge University Press. [32] Schoutens, W. and J. Cariboni (2009). $$Lévy Processes in Credit Risk$$ . Wiley Finance. · Zbl 1192.91008 [33] Vasicek, O. (1977). An equilibrium characterization of the term structure. $$Journal of Financial Economics$$ $$5(2)$$ , 177-188. · Zbl 1372.91113
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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Outlook: BEZANT RESOURCES PLC is assigned short-term Ba1 & long-term Ba1 estimated rating.
Time series to forecast n: 16 Mar 2023 for (n+6 month)
Methodology : Modular Neural Network (Emotional Trigger/Responses Analysis)
## Abstract
BEZANT RESOURCES PLC prediction model is evaluated with Modular Neural Network (Emotional Trigger/Responses Analysis) and ElasticNet Regression1,2,3,4 and it is concluded that the LON:BZT stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Buy
## Key Points
1. Investment Risk
2. Which neural network is best for prediction?
3. What are the most successful trading algorithms?
## LON:BZT Target Price Prediction Modeling Methodology
We consider BEZANT RESOURCES PLC Decision Process with Modular Neural Network (Emotional Trigger/Responses Analysis) where A is the set of discrete actions of LON:BZT stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(ElasticNet Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (Emotional Trigger/Responses Analysis)) X S(n):→ (n+6 month) $\stackrel{\to }{S}=\left({s}_{1},{s}_{2},{s}_{3}\right)$
n:Time series to forecast
p:Price signals of LON:BZT stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## LON:BZT Stock Forecast (Buy or Sell) for (n+6 month)
Sample Set: Neural Network
Stock/Index: LON:BZT BEZANT RESOURCES PLC
Time series to forecast n: 16 Mar 2023 for (n+6 month)
According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Buy
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for BEZANT RESOURCES PLC
1. The methods used to determine whether credit risk has increased significantly on a financial instrument since initial recognition should consider the characteristics of the financial instrument (or group of financial instruments) and the default patterns in the past for comparable financial instruments. Despite the requirement in paragraph 5.5.9, for financial instruments for which default patterns are not concentrated at a specific point during the expected life of the financial instrument, changes in the risk of a default occurring over the next 12 months may be a reasonable approximation of the changes in the lifetime risk of a default occurring. In such cases, an entity may use changes in the risk of a default occurring over the next 12 months to determine whether credit risk has increased significantly since initial recognition, unless circumstances indicate that a lifetime assessment is necessary
2. An entity shall assess separately whether each subgroup meets the requirements in paragraph 6.6.1 to be an eligible hedged item. If any subgroup fails to meet the requirements in paragraph 6.6.1, the entity shall discontinue hedge accounting prospectively for the hedging relationship in its entirety. An entity also shall apply the requirements in paragraphs 6.5.8 and 6.5.11 to account for ineffectiveness related to the hedging relationship in its entirety.
3. The methods used to determine whether credit risk has increased significantly on a financial instrument since initial recognition should consider the characteristics of the financial instrument (or group of financial instruments) and the default patterns in the past for comparable financial instruments. Despite the requirement in paragraph 5.5.9, for financial instruments for which default patterns are not concentrated at a specific point during the expected life of the financial instrument, changes in the risk of a default occurring over the next 12 months may be a reasonable approximation of the changes in the lifetime risk of a default occurring. In such cases, an entity may use changes in the risk of a default occurring over the next 12 months to determine whether credit risk has increased significantly since initial recognition, unless circumstances indicate that a lifetime assessment is necessary
4. For the purpose of determining whether a forecast transaction (or a component thereof) is highly probable as required by paragraph 6.3.3, an entity shall assume that the interest rate benchmark on which the hedged cash flows (contractually or non-contractually specified) are based is not altered as a result of interest rate benchmark reform.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
BEZANT RESOURCES PLC is assigned short-term Ba1 & long-term Ba1 estimated rating. BEZANT RESOURCES PLC prediction model is evaluated with Modular Neural Network (Emotional Trigger/Responses Analysis) and ElasticNet Regression1,2,3,4 and it is concluded that the LON:BZT stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Buy
### LON:BZT BEZANT RESOURCES PLC Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCBaa2
Balance SheetCC
Leverage RatiosB3B2
Cash FlowB1C
Rates of Return and ProfitabilityBa1Ba1
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 81 out of 100 with 520 signals.
## References
1. Imbens GW, Rubin DB. 2015. Causal Inference in Statistics, Social, and Biomedical Sciences. Cambridge, UK: Cambridge Univ. Press
2. Babula, R. A. (1988), "Contemporaneous correlation and modeling Canada's imports of U.S. crops," Journal of Agricultural Economics Research, 41, 33–38.
3. Hastie T, Tibshirani R, Wainwright M. 2015. Statistical Learning with Sparsity: The Lasso and Generalizations. New York: CRC Press
4. J. Baxter and P. Bartlett. Infinite-horizon policy-gradient estimation. Journal of Artificial Intelligence Re- search, 15:319–350, 2001.
5. Imbens G, Wooldridge J. 2009. Recent developments in the econometrics of program evaluation. J. Econ. Lit. 47:5–86
6. S. Bhatnagar, H. Prasad, and L. Prashanth. Stochastic recursive algorithms for optimization, volume 434. Springer, 2013
7. Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C, et al. 2016a. Double machine learning for treatment and causal parameters. Tech. Rep., Cent. Microdata Methods Pract., Inst. Fiscal Stud., London
Frequently Asked QuestionsQ: What is the prediction methodology for LON:BZT stock?
A: LON:BZT stock prediction methodology: We evaluate the prediction models Modular Neural Network (Emotional Trigger/Responses Analysis) and ElasticNet Regression
Q: Is LON:BZT stock a buy or sell?
A: The dominant strategy among neural network is to Buy LON:BZT Stock.
Q: Is BEZANT RESOURCES PLC stock a good investment?
A: The consensus rating for BEZANT RESOURCES PLC is Buy and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of LON:BZT stock?
A: The consensus rating for LON:BZT is Buy.
Q: What is the prediction period for LON:BZT stock?
A: The prediction period for LON:BZT is (n+6 month)
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# performance_counters¶
The contents of this module can be included with the header hpx/modules/performance_counters.hpp. These headers may be used by user-code but are not guaranteed stable (neither header location nor contents). You are using these at your own risk. If you wish to use non-public functionality from a module we strongly suggest only including the module header hpx/modules/performance_counters.hpp, not the particular header in which the functionality you would like to use is defined. See Public API for a list of names that are part of the public HPX API.
namespace hpx
namespace performance_counters
Functions
bool action_invocation_counter_discoverer(hpx::actions::detail::invocation_count_registry const ®istry, counter_info const &info, counter_path_elements &p, discover_counter_func const &f, discover_counters_mode mode, error_code &ec)
namespace hpx
namespace performance_counters
template<typename Derived>
class base_performance_counter
Public Types
typedef Derived type_holder
typedef hpx::performance_counters::server::base_performance_counter base_type_holder
Public Functions
base_performance_counter()
base_performance_counter(hpx::performance_counters::counter_info const &info)
void finalize()
Private Types
typedef hpx::components::component_base<Derived> base_type
namespace hpx
namespace performance_counters
Functions
bool default_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
Default discovery function for performance counters; to be registered with the counter types. It will pass the counter_info and the error_code to the supplied function.
bool locality_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
Default discoverer function for performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
/<objectname>(locality#<locality_id>/total)/<instancename>
bool locality_pool_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
Default discoverer function for performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
/<objectname>(locality#<locality_id>/pool#<pool_name>/total)/<instancename>
bool locality0_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
Default discoverer function for AGAS performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
/<objectname>{locality#0/total}/<instancename>
bool locality_thread_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
Default discoverer function for performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
bool locality_pool_thread_counter_discoverer(counter_info const &info, discover_counter_func const &f, discover_counters_mode mode, error_code &ec)
Default discoverer function for performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
bool locality_pool_thread_no_total_counter_discoverer(counter_info const &info, discover_counter_func const &f, discover_counters_mode mode, error_code &ec)
Default discoverer function for performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
This is essentially the same as above just that locality#*/total is not supported.
bool locality_numa_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
Default discoverer function for performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
naming::gid_type locality_raw_counter_creator(counter_info const&, hpx::util::function_nonser<std::int64_t(bool)> const&, error_code&, )
Creation function for raw counters. The passed function is encapsulating the actual value to monitor. This function checks the validity of the supplied counter name, it has to follow the scheme:
/<objectname>(locality#<locality_id>/total)/<instancename>
naming::gid_type locality_raw_values_counter_creator(counter_info const&, hpx::util::function_nonser<std::vector<std::int64_t>(bool)> const&, error_code&, )
naming::gid_type agas_raw_counter_creator(counter_info const&, error_code&, char const*const)
Creation function for raw counters. The passed function is encapsulating the actual value to monitor. This function checks the validity of the supplied counter name, it has to follow the scheme:
/agas(<objectinstance>/total)/<instancename>
bool agas_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
Default discoverer function for performance counters; to be registered with the counter types. It is suitable to be used for all counters following the naming scheme:
/agas(<objectinstance>/total)/<instancename>
naming::gid_type local_action_invocation_counter_creator(counter_info const&, error_code&)
bool local_action_invocation_counter_discoverer(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)
namespace hpx
namespace performance_counters
Functions
bool parse_counter_name(std::string const &name, path_elements &elements)
struct instance_elements
Public Members
instance_name parent_
instance_name child_
instance_name subchild_
struct instance_name
Public Members
std::string name_
std::string index_
bool basename_ = false
struct path_elements
Public Members
std::string object_
instance_elements instance_
std::string counter_
std::string parameters_
namespace hpx
namespace performance_counters
Typedefs
typedef hpx::util::function_nonser<naming::gid_type(counter_info const&, error_code&)> create_counter_func
This declares the type of a function, which will be called by HPX whenever a new performance counter instance of a particular type needs to be created.
typedef hpx::util::function_nonser<bool(counter_info const&, error_code&)> discover_counter_func
This declares a type of a function, which will be passed to a discover_counters_func in order to be called for each discovered performance counter instance.
typedef hpx::util::function_nonser<bool(counter_info const&, discover_counter_func const&, discover_counters_mode, error_code&)> discover_counters_func
This declares the type of a function, which will be called by HPX whenever it needs to discover all performance counter instances of a particular type.
Enums
enum counter_type
Values:
counter_text
counter_text shows a variable-length text string. It does not deliver calculated values.
Formula: None Average: None Type: Text
counter_raw
counter_raw shows the last observed value only. It does not deliver an average.
Formula: None. Shows raw data as collected. Average: None Type: Instantaneous
counter_monotonically_increasing
counter_average_base
counter_average_base is used as the base data (denominator) in the computation of time or count averages for the counter_average_count and counter_average_timer counter types. This counter type collects the last observed value only.
Formula: None. This counter uses raw data in factional calculations without delivering an output. Average: SUM (N) / x Type: Instantaneous
counter_average_count
counter_average_count shows how many items are processed, on average, during an operation. Counters of this type display a ratio of the items processed (such as bytes sent) to the number of operations completed. The ratio is calculated by comparing the number of items processed during the last interval to the number of operations completed during the last interval.
Formula: (N1 - N0) / (D1 - D0), where the numerator (N) represents the number of items processed during the last sample interval, and the denominator (D) represents the number of operations completed during the last two sample intervals. Average: (Nx - N0) / (Dx - D0) Type: Average
counter_aggregating
counter_aggregating applies a function to an embedded counter instance. The embedded counter is usually evaluated repeatedly after a fixed (but configurable) time interval.
Formula: F(Nx)
counter_average_timer
counter_average_timer measures the average time it takes to complete a process or operation. Counters of this type display a ratio of the total elapsed time of the sample interval to the number of processes or operations completed during that time. This counter type measures time in ticks of the system clock. The variable F represents the number of ticks per second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: ((N1 - N0) / F) / (D1 - D0), where the numerator (N) represents the number of ticks counted during the last sample interval, the variable F represents the frequency of the ticks, and the denominator (D) represents the number of operations completed during the last sample interval. Average: ((Nx - N0) / F) / (Dx - D0) Type: Average
counter_elapsed_time
counter_elapsed_time shows the total time between when the component or process started and the time when this value is calculated. The variable F represents the number of time units that elapse in one second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: (D0 - N0) / F, where the nominator (D) represents the current time, the numerator (N) represents the time the object was started, and the variable F represents the number of time units that elapse in one second. Average: (Dx - N0) / F Type: Difference
counter_histogram
counter_histogram exposes a histogram of the measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
The first three values in the returned array represent the lower and upper boundaries, and the size of the histogram buckets. All remaining values in the returned array represent the number of measurements for each of the buckets in the histogram.
counter_raw_values
counter_raw_values exposes an array of measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
counter_text
counter_text shows a variable-length text string. It does not deliver calculated values.
Formula: None Average: None Type: Text
counter_raw
counter_raw shows the last observed value only. It does not deliver an average.
Formula: None. Shows raw data as collected. Average: None Type: Instantaneous
counter_monotonically_increasing
counter_average_base
counter_average_base is used as the base data (denominator) in the computation of time or count averages for the counter_average_count and counter_average_timer counter types. This counter type collects the last observed value only.
Formula: None. This counter uses raw data in factional calculations without delivering an output. Average: SUM (N) / x Type: Instantaneous
counter_average_count
counter_average_count shows how many items are processed, on average, during an operation. Counters of this type display a ratio of the items processed (such as bytes sent) to the number of operations completed. The ratio is calculated by comparing the number of items processed during the last interval to the number of operations completed during the last interval.
Formula: (N1 - N0) / (D1 - D0), where the numerator (N) represents the number of items processed during the last sample interval, and the denominator (D) represents the number of operations completed during the last two sample intervals. Average: (Nx - N0) / (Dx - D0) Type: Average
counter_aggregating
counter_aggregating applies a function to an embedded counter instance. The embedded counter is usually evaluated repeatedly after a fixed (but configurable) time interval.
Formula: F(Nx)
counter_average_timer
counter_average_timer measures the average time it takes to complete a process or operation. Counters of this type display a ratio of the total elapsed time of the sample interval to the number of processes or operations completed during that time. This counter type measures time in ticks of the system clock. The variable F represents the number of ticks per second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: ((N1 - N0) / F) / (D1 - D0), where the numerator (N) represents the number of ticks counted during the last sample interval, the variable F represents the frequency of the ticks, and the denominator (D) represents the number of operations completed during the last sample interval. Average: ((Nx - N0) / F) / (Dx - D0) Type: Average
counter_elapsed_time
counter_elapsed_time shows the total time between when the component or process started and the time when this value is calculated. The variable F represents the number of time units that elapse in one second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: (D0 - N0) / F, where the nominator (D) represents the current time, the numerator (N) represents the time the object was started, and the variable F represents the number of time units that elapse in one second. Average: (Dx - N0) / F Type: Difference
counter_histogram
counter_histogram exposes a histogram of the measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
The first three values in the returned array represent the lower and upper boundaries, and the size of the histogram buckets. All remaining values in the returned array represent the number of measurements for each of the buckets in the histogram.
counter_raw_values
counter_raw_values exposes an array of measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
enum counter_status
Status and error codes used by the functions related to performance counters.
Values:
status_valid_data
No error occurred, data is valid.
status_new_data
Data is valid and different from last call.
status_invalid_data
Some error occurred, data is not value.
status_already_defined
The type or instance already has been defined.
status_counter_unknown
The counter instance is unknown.
status_counter_type_unknown
The counter type is unknown.
status_generic_error
A unknown error occurred.
status_valid_data
No error occurred, data is valid.
status_new_data
Data is valid and different from last call.
status_invalid_data
Some error occurred, data is not value.
status_already_defined
The type or instance already has been defined.
status_counter_unknown
The counter instance is unknown.
status_counter_type_unknown
The counter type is unknown.
status_generic_error
A unknown error occurred.
Functions
std::string &ensure_counter_prefix(std::string &name)
std::string ensure_counter_prefix(std::string const &counter)
std::string &remove_counter_prefix(std::string &name)
std::string remove_counter_prefix(std::string const &counter)
char const *get_counter_type_name(counter_type state)
Return the readable name of a given counter type.
bool status_is_valid(counter_status s)
counter_status add_counter_type(counter_info const &info, error_code &ec)
naming::id_type get_counter(std::string const &name, error_code &ec)
naming::id_type get_counter(counter_info const &info, error_code &ec)
Variables
constexpr const char counter_prefix[] = "/counters"
constexpr std::size_t counter_prefix_len = (sizeof(counter_prefix) / sizeof(counter_prefix[0])) - 1
struct counter_info
Public Functions
counter_info(counter_type type = counter_raw)
counter_info(std::string const &name)
counter_info(counter_type type, std::string const &name, std::string const &helptext = "", std::uint32_t version = HPX_PERFORMANCE_COUNTER_V1, std::string const &uom = "")
Public Members
counter_type type_
The type of the described counter.
std::uint32_t version_
The version of the described counter using the 0xMMmmSSSS scheme
counter_status status_
The status of the counter object.
std::string fullname_
The full name of this counter.
std::string helptext_
The full descriptive text for this counter.
std::string unit_of_measure_
The unit of measure for this counter.
Private Functions
void serialize(serialization::output_archive &ar, const unsigned int)
void serialize(serialization::input_archive &ar, const unsigned int)
Friends
friend hpx::performance_counters::hpx::serialization::access
struct counter_path_elements : public hpx::performance_counters::counter_type_path_elements
#include <counters.hpp>
A counter_path_elements holds the elements of a full name for a counter instance. Generally, a full name of a counter instance has the structure:
/objectname{parentinstancename::parentindex/instancename#instanceindex} /countername#parameters
Public Types
typedef counter_type_path_elements base_type
Public Functions
counter_path_elements()
counter_path_elements(std::string const &objectname, std::string const &countername, std::string const ¶meters, std::string const &parentname, std::string const &instancename, std::int64_t parentindex = -1, std::int64_t instanceindex = -1, bool parentinstance_is_basename = false)
counter_path_elements(std::string const &objectname, std::string const &countername, std::string const ¶meters, std::string const &parentname, std::string const &instancename, std::string const &subinstancename, std::int64_t parentindex = -1, std::int64_t instanceindex = -1, std::int64_t subinstanceindex = -1, bool parentinstance_is_basename = false)
Public Members
std::string parentinstancename_
the name of the parent instance
std::string instancename_
the name of the object instance
std::string subinstancename_
the name of the object sub-instance
std::int64_t parentinstanceindex_
the parent instance index
std::int64_t instanceindex_
the instance index
std::int64_t subinstanceindex_
the sub-instance index
bool parentinstance_is_basename_
the parentinstancename_
Private Functions
void serialize(serialization::output_archive &ar, const unsigned int)
void serialize(serialization::input_archive &ar, const unsigned int)
Friends
friend hpx::performance_counters::hpx::serialization::access
member holds a base counter name
struct counter_type_path_elements
#include <counters.hpp>
A counter_type_path_elements holds the elements of a full name for a counter type. Generally, a full name of a counter type has the structure:
/objectname/countername
i.e. /queue/length
Subclassed by hpx::performance_counters::counter_path_elements
Public Functions
counter_type_path_elements()
counter_type_path_elements(std::string const &objectname, std::string const &countername, std::string const ¶meters)
Public Members
std::string objectname_
the name of the performance object
std::string countername_
contains the counter name
std::string parameters_
optional parameters for the counter instance
Protected Functions
void serialize(serialization::output_archive &ar, const unsigned int)
void serialize(serialization::input_archive &ar, const unsigned int)
Friends
friend hpx::performance_counters::hpx::serialization::access
Defines
HPX_PERFORMANCE_COUNTER_V1
namespace hpx
namespace performance_counters
Enums
enum counter_type
Values:
counter_text
counter_text shows a variable-length text string. It does not deliver calculated values.
Formula: None Average: None Type: Text
counter_raw
counter_raw shows the last observed value only. It does not deliver an average.
Formula: None. Shows raw data as collected. Average: None Type: Instantaneous
counter_monotonically_increasing
counter_average_base
counter_average_base is used as the base data (denominator) in the computation of time or count averages for the counter_average_count and counter_average_timer counter types. This counter type collects the last observed value only.
Formula: None. This counter uses raw data in factional calculations without delivering an output. Average: SUM (N) / x Type: Instantaneous
counter_average_count
counter_average_count shows how many items are processed, on average, during an operation. Counters of this type display a ratio of the items processed (such as bytes sent) to the number of operations completed. The ratio is calculated by comparing the number of items processed during the last interval to the number of operations completed during the last interval.
Formula: (N1 - N0) / (D1 - D0), where the numerator (N) represents the number of items processed during the last sample interval, and the denominator (D) represents the number of operations completed during the last two sample intervals. Average: (Nx - N0) / (Dx - D0) Type: Average
counter_aggregating
counter_aggregating applies a function to an embedded counter instance. The embedded counter is usually evaluated repeatedly after a fixed (but configurable) time interval.
Formula: F(Nx)
counter_average_timer
counter_average_timer measures the average time it takes to complete a process or operation. Counters of this type display a ratio of the total elapsed time of the sample interval to the number of processes or operations completed during that time. This counter type measures time in ticks of the system clock. The variable F represents the number of ticks per second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: ((N1 - N0) / F) / (D1 - D0), where the numerator (N) represents the number of ticks counted during the last sample interval, the variable F represents the frequency of the ticks, and the denominator (D) represents the number of operations completed during the last sample interval. Average: ((Nx - N0) / F) / (Dx - D0) Type: Average
counter_elapsed_time
counter_elapsed_time shows the total time between when the component or process started and the time when this value is calculated. The variable F represents the number of time units that elapse in one second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: (D0 - N0) / F, where the nominator (D) represents the current time, the numerator (N) represents the time the object was started, and the variable F represents the number of time units that elapse in one second. Average: (Dx - N0) / F Type: Difference
counter_histogram
counter_histogram exposes a histogram of the measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
The first three values in the returned array represent the lower and upper boundaries, and the size of the histogram buckets. All remaining values in the returned array represent the number of measurements for each of the buckets in the histogram.
counter_raw_values
counter_raw_values exposes an array of measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
counter_text
counter_text shows a variable-length text string. It does not deliver calculated values.
Formula: None Average: None Type: Text
counter_raw
counter_raw shows the last observed value only. It does not deliver an average.
Formula: None. Shows raw data as collected. Average: None Type: Instantaneous
counter_monotonically_increasing
counter_average_base
counter_average_base is used as the base data (denominator) in the computation of time or count averages for the counter_average_count and counter_average_timer counter types. This counter type collects the last observed value only.
Formula: None. This counter uses raw data in factional calculations without delivering an output. Average: SUM (N) / x Type: Instantaneous
counter_average_count
counter_average_count shows how many items are processed, on average, during an operation. Counters of this type display a ratio of the items processed (such as bytes sent) to the number of operations completed. The ratio is calculated by comparing the number of items processed during the last interval to the number of operations completed during the last interval.
Formula: (N1 - N0) / (D1 - D0), where the numerator (N) represents the number of items processed during the last sample interval, and the denominator (D) represents the number of operations completed during the last two sample intervals. Average: (Nx - N0) / (Dx - D0) Type: Average
counter_aggregating
counter_aggregating applies a function to an embedded counter instance. The embedded counter is usually evaluated repeatedly after a fixed (but configurable) time interval.
Formula: F(Nx)
counter_average_timer
counter_average_timer measures the average time it takes to complete a process or operation. Counters of this type display a ratio of the total elapsed time of the sample interval to the number of processes or operations completed during that time. This counter type measures time in ticks of the system clock. The variable F represents the number of ticks per second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: ((N1 - N0) / F) / (D1 - D0), where the numerator (N) represents the number of ticks counted during the last sample interval, the variable F represents the frequency of the ticks, and the denominator (D) represents the number of operations completed during the last sample interval. Average: ((Nx - N0) / F) / (Dx - D0) Type: Average
counter_elapsed_time
counter_elapsed_time shows the total time between when the component or process started and the time when this value is calculated. The variable F represents the number of time units that elapse in one second. The value of F is factored into the equation so that the result is displayed in seconds.
Formula: (D0 - N0) / F, where the nominator (D) represents the current time, the numerator (N) represents the time the object was started, and the variable F represents the number of time units that elapse in one second. Average: (Dx - N0) / F Type: Difference
counter_histogram
counter_histogram exposes a histogram of the measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
The first three values in the returned array represent the lower and upper boundaries, and the size of the histogram buckets. All remaining values in the returned array represent the number of measurements for each of the buckets in the histogram.
counter_raw_values
counter_raw_values exposes an array of measured values instead of a single value as many of the other counter types. Counters of this type expose a counter_value_array instead of a counter_value. Those will also not implement the get_counter_value() functionality. The results are exposed through a separate get_counter_values_array() function.
enum counter_status
Values:
status_valid_data
No error occurred, data is valid.
status_new_data
Data is valid and different from last call.
status_invalid_data
Some error occurred, data is not value.
status_already_defined
The type or instance already has been defined.
status_counter_unknown
The counter instance is unknown.
status_counter_type_unknown
The counter type is unknown.
status_generic_error
A unknown error occurred.
status_valid_data
No error occurred, data is valid.
status_new_data
Data is valid and different from last call.
status_invalid_data
Some error occurred, data is not value.
status_already_defined
The type or instance already has been defined.
status_counter_unknown
The counter instance is unknown.
status_counter_type_unknown
The counter type is unknown.
status_generic_error
A unknown error occurred.
enum discover_counters_mode
Values:
discover_counters_minimal
discover_counters_full
Functions
counter_status get_counter_type_name(counter_type_path_elements const &path, std::string &result, error_code &ec = throws)
Create a full name of a counter type from the contents of the given counter_type_path_elements instance.The generated counter type name will not contain any parameters.
counter_status get_full_counter_type_name(counter_type_path_elements const &path, std::string &result, error_code &ec = throws)
Create a full name of a counter type from the contents of the given counter_type_path_elements instance. The generated counter type name will contain all parameters.
counter_status get_counter_name(counter_path_elements const &path, std::string &result, error_code &ec = throws)
Create a full name of a counter from the contents of the given counter_path_elements instance.
counter_status get_counter_instance_name(counter_path_elements const &path, std::string &result, error_code &ec = throws)
Create a name of a counter instance from the contents of the given counter_path_elements instance.
counter_status get_counter_type_path_elements(std::string const &name, counter_type_path_elements &path, error_code &ec = throws)
Fill the given counter_type_path_elements instance from the given full name of a counter type.
counter_status get_counter_path_elements(std::string const &name, counter_path_elements &path, error_code &ec = throws)
Fill the given counter_path_elements instance from the given full name of a counter.
counter_status get_counter_name(std::string const &name, std::string &countername, error_code &ec = throws)
Return the canonical counter instance name from a given full instance name.
counter_status get_counter_type_name(std::string const &name, std::string &type_name, error_code &ec = throws)
Return the canonical counter type name from a given (full) instance name.
counter_status complement_counter_info(counter_info &info, counter_info const &type_info, error_code &ec = throws)
Complement the counter info if parent instance name is missing.
counter_status complement_counter_info(counter_info &info, error_code &ec = throws)
counter_status add_counter_type(counter_info const &info, create_counter_func const &create_counter, discover_counters_func const &discover_counters, error_code &ec = throws)
counter_status discover_counter_types(discover_counter_func const &discover_counter, discover_counters_mode mode = discover_counters_minimal, error_code &ec = throws)
Call the supplied function for each registered counter type.
counter_status discover_counter_types(std::vector<counter_info> &counters, discover_counters_mode mode = discover_counters_minimal, error_code &ec = throws)
Return a list of all available counter descriptions.
counter_status discover_counter_type(std::string const &name, discover_counter_func const &discover_counter, discover_counters_mode mode = discover_counters_minimal, error_code &ec = throws)
Call the supplied function for the given registered counter type.
counter_status discover_counter_type(counter_info const &info, discover_counter_func const &discover_counter, discover_counters_mode mode = discover_counters_minimal, error_code &ec = throws)
counter_status discover_counter_type(std::string const &name, std::vector<counter_info> &counters, discover_counters_mode mode = discover_counters_minimal, error_code &ec = throws)
Return a list of matching counter descriptions for the given registered counter type.
counter_status discover_counter_type(counter_info const &info, std::vector<counter_info> &counters, discover_counters_mode mode = discover_counters_minimal, error_code &ec = throws)
bool expand_counter_info(counter_info const&, discover_counter_func const&, error_code&)
call the supplied function will all expanded versions of the supplied counter info.
This function expands all locality#* and worker-thread#* wild cards only.
counter_status remove_counter_type(counter_info const &info, error_code &ec = throws)
Remove an existing counter type from the (local) registry.
Note
This doesn’t remove existing counters of this type, it just inhibits defining new counters using this type.
counter_status get_counter_type(std::string const &name, counter_info &info, error_code &ec = throws)
Retrieve the counter type for the given counter name from the (local) registry.
lcos::future<naming::id_type> get_counter_async(std::string name, error_code &ec = throws)
Get the global id of an existing performance counter, if the counter does not exist yet, the function attempts to create the counter based on the given counter name.
lcos::future<naming::id_type> get_counter_async(counter_info const &info, error_code &ec = throws)
Get the global id of an existing performance counter, if the counter does not exist yet, the function attempts to create the counter based on the given counter info.
void get_counter_infos(counter_info const &info, counter_type &type, std::string &helptext, std::uint32_t &version, error_code &ec = throws)
Retrieve the meta data specific for the given counter instance.
void get_counter_infos(std::string name, counter_type &type, std::string &helptext, std::uint32_t &version, error_code &ec = throws)
Retrieve the meta data specific for the given counter instance.
struct counter_value
Public Functions
counter_value(std::int64_t value = 0, std::int64_t scaling = 1, bool scale_inverse = false)
template<typename T>
T get_value(error_code &ec = throws) const
Retrieve the ‘real’ value of the counter_value, converted to the requested type T.
Public Members
std::uint64_t time_
The local time when data was collected.
std::uint64_t count_
The invocation counter for the data.
std::int64_t value_
The current counter value.
std::int64_t scaling_
The scaling of the current counter value.
counter_status status_
The status of the counter value.
bool scale_inverse_
If true, value_ needs to be divided by scaling_, otherwise it has to be multiplied.
Private Functions
void serialize(serialization::output_archive &ar, const unsigned int)
void serialize(serialization::input_archive &ar, const unsigned int)
Friends
friend hpx::performance_counters::hpx::serialization::access
struct counter_values_array
Public Functions
counter_values_array(std::int64_t scaling = 1, bool scale_inverse = false)
counter_values_array(std::vector<std::int64_t> &&values, std::int64_t scaling = 1, bool scale_inverse = false)
counter_values_array(std::vector<std::int64_t> const &values, std::int64_t scaling = 1, bool scale_inverse = false)
template<typename T>
T get_value(std::size_t index, error_code &ec = throws) const
Retrieve the ‘real’ value of the counter_value, converted to the requested type T.
Public Members
std::uint64_t time_
The local time when data was collected.
std::uint64_t count_
The invocation counter for the data.
std::vector<std::int64_t> values_
The current counter values.
std::int64_t scaling_
The scaling of the current counter values.
counter_status status_
The status of the counter value.
bool scale_inverse_
If true, value_ needs to be divided by scaling_, otherwise it has to be multiplied.
Private Functions
void serialize(serialization::output_archive &ar, const unsigned int)
void serialize(serialization::input_archive &ar, const unsigned int)
Friends
friend hpx::performance_counters::hpx::serialization::access
namespace hpx
namespace performance_counters
Functions
void install_counter(naming::id_type const &id, counter_info const &info, error_code &ec = throws)
Install a new performance counter in a way, which will uninstall it automatically during shutdown.
namespace hpx
namespace performance_counters
Functions
counter_status install_counter_type(std::string const &name, hpx::util::function_nonser<std::int64_t(bool)> const &counter_value, std::string const &helptext = "", std::string const &uom = "", counter_type type = counter_raw, error_code &ec = throws, )
Install a new generic performance counter type in a way, which will uninstall it automatically during shutdown.
The function install_counter_type will register a new generic counter type based on the provided function. The counter type will be automatically unregistered during system shutdown. Any consumer querying any instance of this this counter type will cause the provided function to be called and the returned value to be exposed as the counter value.
The counter type is registered such that there can be one counter instance per locality. The expected naming scheme for the counter instances is: '/objectname{locality#<*>/total}/countername' where ‘<*>’ is a zero based integer identifying the locality the counter is created on.
Note
As long as ec is not pre-initialized to hpx::throws this function doesn’t throw but returns the result code using the parameter ec. Otherwise it throws an instance of hpx::exception.
Return
If successful, this function returns status_valid_data, otherwise it will either throw an exception or return an error_code from the enum counter_status (also, see note related to parameter ec).
Note
The counter type registry is a locality based service. You will have to register each counter type on every locality where a corresponding performance counter will be created.
Parameters
• name: [in] The global virtual name of the counter type. This name is expected to have the format /objectname/countername.
• counter_value: [in] The function to call whenever the counter value is requested by a consumer.
• helptext: [in, optional] A longer descriptive text shown to the user to explain the nature of the counters created from this type.
• uom: [in] The unit of measure for the new performance counter type.
• type: [in] Type for the new performance counter type.
• ec: [in,out] this represents the error status on exit, if this is pre-initialized to hpx::throws the function will throw on error instead.
counter_status install_counter_type(std::string const &name, hpx::util::function_nonser<std::vector<std::int64_t>(bool)> const &counter_value, std::string const &helptext = "", std::string const &uom = "", error_code &ec = throws, )
Install a new generic performance counter type returning an array of values in a way, that will uninstall it automatically during shutdown.
The function install_counter_type will register a new generic counter type that returns an array of values based on the provided function. The counter type will be automatically unregistered during system shutdown. Any consumer querying any instance of this this counter type will cause the provided function to be called and the returned array value to be exposed as the counter value.
The counter type is registered such that there can be one counter instance per locality. The expected naming scheme for the counter instances is: '/objectname{locality#<*>/total}/countername' where ‘<*>’ is a zero based integer identifying the locality the counter is created on.
Note
As long as ec is not pre-initialized to hpx::throws this function doesn’t throw but returns the result code using the parameter ec. Otherwise it throws an instance of hpx::exception.
Return
If successful, this function returns status_valid_data, otherwise it will either throw an exception or return an error_code from the enum counter_status (also, see note related to parameter ec).
Note
The counter type registry is a locality based service. You will have to register each counter type on every locality where a corresponding performance counter will be created.
Parameters
• name: [in] The global virtual name of the counter type. This name is expected to have the format /objectname/countername.
• counter_value: [in] The function to call whenever the counter value (array of values) is requested by a consumer.
• helptext: [in, optional] A longer descriptive text shown to the user to explain the nature of the counters created from this type.
• uom: [in] The unit of measure for the new performance counter type.
• ec: [in,out] this represents the error status on exit, if this is pre-initialized to hpx::throws the function will throw on error instead.
void install_counter_type(std::string const &name, counter_type type, error_code &ec = throws)
Install a new performance counter type in a way, which will uninstall it automatically during shutdown.
The function install_counter_type will register a new counter type based on the provided counter_type_info. The counter type will be automatically unregistered during system shutdown.
Return
If successful, this function returns status_valid_data, otherwise it will either throw an exception or return an error_code from the enum counter_status (also, see note related to parameter ec).
Note
The counter type registry is a locality based service. You will have to register each counter type on every locality where a corresponding performance counter will be created.
Note
As long as ec is not pre-initialized to hpx::throws this function doesn’t throw but returns the result code using the parameter ec. Otherwise it throws an instance of hpx::exception.
Parameters
• name: [in] The global virtual name of the counter type. This name is expected to have the format /objectname/countername.
• type: [in] The type of the counters of this counter_type.
• ec: [in,out] this represents the error status on exit, if this is pre-initialized to hpx::throws the function will throw on error instead.
counter_status install_counter_type(std::string const &name, counter_type type, std::string const &helptext, std::string const &uom = "", std::uint32_t version = HPX_PERFORMANCE_COUNTER_V1, error_code &ec = throws)
Install a new performance counter type in a way, which will uninstall it automatically during shutdown.
The function install_counter_type will register a new counter type based on the provided counter_type_info. The counter type will be automatically unregistered during system shutdown.
Return
If successful, this function returns status_valid_data, otherwise it will either throw an exception or return an error_code from the enum counter_status (also, see note related to parameter ec).
Note
The counter type registry is a locality based service. You will have to register each counter type on every locality where a corresponding performance counter will be created.
Note
As long as ec is not pre-initialized to hpx::throws this function doesn’t throw but returns the result code using the parameter ec. Otherwise it throws an instance of hpx::exception.
Parameters
• name: [in] The global virtual name of the counter type. This name is expected to have the format /objectname/countername.
• type: [in] The type of the counters of this counter_type.
• helptext: [in] A longer descriptive text shown to the user to explain the nature of the counters created from this type.
• uom: [in] The unit of measure for the new performance counter type.
• version: [in] The version of the counter type. This is currently expected to be set to HPX_PERFORMANCE_COUNTER_V1.
• ec: [in,out] this represents the error status on exit, if this is pre-initialized to hpx::throws the function will throw on error instead.
counter_status install_counter_type(std::string const &name, counter_type type, std::string const &helptext, create_counter_func const &create_counter, discover_counters_func const &discover_counters, std::uint32_t version = HPX_PERFORMANCE_COUNTER_V1, std::string const &uom = "", error_code &ec = throws)
Install a new generic performance counter type in a way, which will uninstall it automatically during shutdown.
The function install_counter_type will register a new generic counter type based on the provided counter_type_info. The counter type will be automatically unregistered during system shutdown.
Note
As long as ec is not pre-initialized to hpx::throws this function doesn’t throw but returns the result code using the parameter ec. Otherwise it throws an instance of hpx::exception.
Return
If successful, this function returns status_valid_data, otherwise it will either throw an exception or return an error_code from the enum counter_status (also, see note related to parameter ec).
Note
The counter type registry is a locality based service. You will have to register each counter type on every locality where a corresponding performance counter will be created.
Parameters
• name: [in] The global virtual name of the counter type. This name is expected to have the format /objectname/countername.
• type: [in] The type of the counters of this counter_type.
• helptext: [in] A longer descriptive text shown to the user to explain the nature of the counters created from this type.
• version: [in] The version of the counter type. This is currently expected to be set to HPX_PERFORMANCE_COUNTER_V1.
• create_counter: [in] The function which will be called to create a new instance of this counter type.
• discover_counters: [in] The function will be called to discover counter instances which can be created.
• uom: [in] The unit of measure of the counter type (default: “”)
• ec: [in,out] this represents the error status on exit, if this is pre-initialized to hpx::throws the function will throw on error instead.
namespace hpx
namespace performance_counters
Functions
std::vector<performance_counter> discover_counters(std::string const &name, error_code &ec = throws)
struct performance_counter : public components::client_base<performance_counter, server::base_performance_counter>
Public Types
using base_type = components::client_base<performance_counter, server::base_performance_counter>
Public Functions
performance_counter()
performance_counter(std::string const &name)
performance_counter(std::string const &name, hpx::id_type const &locality)
performance_counter(id_type const &id)
performance_counter(future<id_type> &&id)
performance_counter(hpx::future<performance_counter> &&c)
future<counter_info> get_info() const
counter_info get_info(launch::sync_policy, error_code &ec = throws) const
future<counter_value> get_counter_value(bool reset = false)
counter_value get_counter_value(launch::sync_policy, bool reset = false, error_code &ec = throws)
future<counter_value> get_counter_value() const
counter_value get_counter_value(launch::sync_policy, error_code &ec = throws) const
future<counter_values_array> get_counter_values_array(bool reset = false)
counter_values_array get_counter_values_array(launch::sync_policy, bool reset = false, error_code &ec = throws)
future<counter_values_array> get_counter_values_array() const
counter_values_array get_counter_values_array(launch::sync_policy, error_code &ec = throws) const
future<bool> start()
bool start(launch::sync_policy, error_code &ec = throws)
future<bool> stop()
bool stop(launch::sync_policy, error_code &ec = throws)
future<void> reset()
void reset(launch::sync_policy, error_code &ec = throws)
future<void> reinit(bool reset = true)
void reinit(launch::sync_policy, bool reset = true, error_code &ec = throws)
future<std::string> get_name() const
std::string get_name(launch::sync_policy, error_code &ec = throws) const
template<typename T>
future<T> get_value(bool reset = false)
template<typename T>
T get_value(launch::sync_policy, bool reset = false, error_code &ec = throws)
template<typename T>
future<T> get_value() const
template<typename T>
T get_value(launch::sync_policy, error_code &ec = throws) const
Private Static Functions
template<typename T>
static T extract_value(future<counter_value> &&value)
namespace hpx
namespace performance_counters
struct performance_counter_base
Public Functions
virtual ~performance_counter_base()
Destructor, needs to be virtual to allow for clean destruction of derived objects
virtual counter_info get_counter_info() const = 0
virtual counter_value get_counter_value(bool reset = false) = 0
virtual counter_values_array get_counter_values_array(bool reset = false) = 0
virtual void reset_counter_value() = 0
virtual void set_counter_value(counter_value const&) = 0
virtual bool start() = 0
virtual bool stop() = 0
virtual void reinit(bool reset) = 0
namespace hpx
namespace performance_counters
class performance_counter_set
Public Functions
performance_counter_set(bool print_counters_locally = false)
Create an empty set of performance counters.
performance_counter_set(std::string const &names, bool reset = false)
Create a set of performance counters from a name, possibly containing wild-card characters
performance_counter_set(std::vector<std::string> const &names, bool reset = false)
void add_counters(std::string const &names, bool reset = false, error_code &ec = throws)
Add more performance counters to the set based on the given name, possibly containing wild-card characters
void add_counters(std::vector<std::string> const &names, bool reset = false, error_code &ec = throws)
std::vector<counter_info> get_counter_infos() const
Retrieve the counter infos for all counters in this set.
std::vector<hpx::future<counter_value>> get_counter_values(bool reset = false) const
Retrieve the values for all counters in this set supporting this operation
std::vector<counter_value> get_counter_values(launch::sync_policy, bool reset = false, error_code &ec = throws) const
std::vector<hpx::future<counter_values_array>> get_counter_values_array(bool reset = false) const
Retrieve the array-values for all counters in this set supporting this operation
std::vector<counter_values_array> get_counter_values_array(launch::sync_policy, bool reset = false, error_code &ec = throws) const
std::vector<hpx::future<void>> reset()
Reset all counters in this set.
void reset(launch::sync_policy, error_code &ec = throws)
std::vector<hpx::future<bool>> start()
Start all counters in this set.
bool start(launch::sync_policy, error_code &ec = throws)
std::vector<hpx::future<bool>> stop()
Stop all counters in this set.
bool stop(launch::sync_policy, error_code &ec = throws)
std::vector<hpx::future<void>> reinit(bool reset = true)
Re-initialize all counters in this set.
void reinit(launch::sync_policy, bool reset = true, error_code &ec = throws)
void release()
Release all references to counters in the set.
std::size_t size() const
Return the number of counters in this set.
template<typename T>
hpx::future<std::vector<T>> get_values(bool reset = false) const
template<typename T>
std::vector<T> get_values(launch::sync_policy, bool reset = false, error_code &ec = throws) const
std::size_t get_invocation_count() const
Protected Functions
bool find_counter(counter_info const &info, bool reset, error_code &ec)
Protected Static Functions
template<typename T>
static std::vector<T> extract_values(std::vector<hpx::future<counter_value>> &&values)
Private Types
typedef lcos::local::spinlock mutex_type
Private Members
mutex_type mtx_
std::vector<counter_info> infos_
std::vector<naming::id_type> ids_
std::vector<std::uint8_t> reset_
std::uint64_t invocation_count_
bool print_counters_locally_
namespace hpx
namespace performance_counters
class registry
Public Functions
registry()
void clear()
Reset registry by deleting all stored counter types.
counter_status add_counter_type(counter_info const &info, create_counter_func const &create_counter, discover_counters_func const &discover_counters, error_code &ec = throws)
Add a new performance counter type to the (local) registry.
counter_status discover_counter_types(discover_counter_func discover_counter, discover_counters_mode mode, error_code &ec = throws)
Call the supplied function for all registered counter types.
counter_status discover_counter_type(std::string const &fullname, discover_counter_func discover_counter, discover_counters_mode mode, error_code &ec = throws)
Call the supplied function for the given registered counter type.
counter_status discover_counter_type(counter_info const &info, discover_counter_func const &f, discover_counters_mode mode, error_code &ec = throws)
counter_status get_counter_create_function(counter_info const &info, create_counter_func &create_counter, error_code &ec = throws) const
Retrieve the counter creation function which is associated with a given counter type.
counter_status get_counter_discovery_function(counter_info const &info, discover_counters_func &func, error_code &ec) const
Retrieve the counter discovery function which is associated with a given counter type.
counter_status remove_counter_type(counter_info const &info, error_code &ec = throws)
Remove an existing counter type from the (local) registry.
Note
This doesn’t remove existing counters of this type, it just inhibits defining new counters using this type.
counter_status create_raw_counter_value(counter_info const &info, std::int64_t *countervalue, naming::gid_type &id, error_code &ec = throws)
Create a new performance counter instance of type raw_counter based on given counter value.
counter_status create_raw_counter(counter_info const &info, hpx::util::function_nonser<std::int64_t()> const &fnaming::gid_type &id, error_code &ec = throws, )
Create a new performance counter instance of type raw_counter based on given function returning the counter value.
counter_status create_raw_counter(counter_info const &info, hpx::util::function_nonser<std::int64_t(bool)> const &f, naming::gid_type &id, error_code &ec = throws, )
Create a new performance counter instance of type raw_counter based on given function returning the counter value.
counter_status create_raw_counter(counter_info const &info, hpx::util::function_nonser<std::vector<std::int64_t>()> const &fnaming::gid_type &id, error_code &ec = throws, )
Create a new performance counter instance of type raw_counter based on given function returning the counter value.
counter_status create_raw_counter(counter_info const &info, hpx::util::function_nonser<std::vector<std::int64_t>(bool)> const &f, naming::gid_type &id, error_code &ec = throws, )
Create a new performance counter instance of type raw_counter based on given function returning the counter value.
counter_status create_counter(counter_info const &info, naming::gid_type &id, error_code &ec = throws)
Create a new performance counter instance based on given counter info.
counter_status create_statistics_counter(counter_info const &info, std::string const &base_counter_name, std::vector<std::size_t> const ¶meters, naming::gid_type &id, error_code &ec = throws)
Create a new statistics performance counter instance based on given base counter name and given base time interval (milliseconds).
counter_status create_arithmetics_counter(counter_info const &info, std::vector<std::string> const &base_counter_names, naming::gid_type &id, error_code &ec = throws)
Create a new arithmetics performance counter instance based on given base counter names.
counter_status create_arithmetics_counter_extended(counter_info const &info, std::vector<std::string> const &base_counter_names, naming::gid_type &id, error_code &ec = throws)
Create a new extended arithmetics performance counter instance based on given base counter names.
counter_status add_counter(naming::id_type const &id, counter_info const &info, error_code &ec = throws)
Add an existing performance counter instance to the registry.
counter_status remove_counter(counter_info const &info, naming::id_type const &id, error_code &ec = throws)
remove the existing performance counter from the registry
counter_status get_counter_type(std::string const &name, counter_info &info, error_code &ec = throws)
Retrieve counter type information for given counter name.
Public Static Functions
static registry &instance()
Protected Functions
counter_type_map_type::iterator locate_counter_type(std::string const &type_name)
counter_type_map_type::const_iterator locate_counter_type(std::string const &type_name) const
Private Types
typedef std::map<std::string, counter_data> counter_type_map_type
Private Members
counter_type_map_type countertypes_
struct counter_data
Public Functions
counter_data(counter_info const &info, create_counter_func const &create_counter, discover_counters_func const &discover_counters)
Public Members
counter_info info_
create_counter_func create_counter_
discover_counters_func discover_counters_
namespace hpx
namespace performance_counters
namespace server
template<typename Operation>
class arithmetics_counter : public hpx::performance_counters::server::base_performance_counter, public components::component_base<arithmetics_counter<Operation>>
Public Types
typedef arithmetics_counter type_holder
typedef base_performance_counter base_type_holder
Public Functions
arithmetics_counter()
arithmetics_counter(counter_info const &info, std::vector<std::string> const &base_counter_names)
hpx::performance_counters::counter_value get_counter_value(bool reset = false)
Overloads from the base_counter base class.
bool start()
bool stop()
void reset_counter_value()
the following functions are not implemented by default, they will just throw
void finalize()
Private Types
typedef components::component_base<arithmetics_counter<Operation>> base_type
Private Members
performance_counter_set counters_
namespace hpx
namespace performance_counters
namespace server
template<typename Statistic>
class arithmetics_counter_extended : public hpx::performance_counters::server::base_performance_counter, public components::component_base<arithmetics_counter_extended<Statistic>>
Public Types
typedef arithmetics_counter_extended type_holder
typedef base_performance_counter base_type_holder
Public Functions
arithmetics_counter_extended()
arithmetics_counter_extended(counter_info const &info, std::vector<std::string> const &base_counter_names)
hpx::performance_counters::counter_value get_counter_value(bool reset = false)
Overloads from the base_counter base class.
bool start()
bool stop()
void reset_counter_value()
the following functions are not implemented by default, they will just throw
void finalize()
Private Types
typedef components::component_base<arithmetics_counter_extended<Statistic>> base_type
Private Members
performance_counter_set counters_
namespace hpx
namespace performance_counters
namespace server
class base_performance_counter : public hpx::performance_counters::performance_counter_base, public component_tag
Public Types
typedef components::component<base_performance_counter> wrapping_type
typedef base_performance_counter base_type_holder
Public Functions
base_performance_counter()
base_performance_counter(counter_info const &info)
void finalize()
finalize() will be called just before the instance gets destructed
counter_info get_counter_info_nonvirt() const
counter_value get_counter_value_nonvirt(bool reset)
counter_values_array get_counter_values_array_nonvirt(bool reset)
void set_counter_value_nonvirt(counter_value const &info)
void reset_counter_value_nonvirt()
bool start_nonvirt()
bool stop_nonvirt()
void reinit_nonvirt(bool reset)
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, get_counter_info_nonvirt, get_counter_info_action)
Each of the exposed functions needs to be encapsulated into an action type, allowing to generate all required boilerplate code for threads, serialization, etc. The get_counter_info_action retrieves a performance counters information.
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, get_counter_value_nonvirt, get_counter_value_action)
The get_counter_value_action queries the value of a performance counter.
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, get_counter_values_array_nonvirt, get_counter_values_array_action)
The get_counter_value_action queries the value of a performance counter.
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, set_counter_value_nonvirt, set_counter_value_action)
The set_counter_value_action.
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, reset_counter_value_nonvirt, reset_counter_value_action)
The reset_counter_value_action.
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, start_nonvirt, start_action)
The start_action.
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, stop_nonvirt, stop_action)
The stop_action.
HPX_DEFINE_COMPONENT_ACTION(base_performance_counter, reinit_nonvirt, reinit_action)
The reinit_action.
Public Static Functions
static components::component_type get_component_type()
static void set_component_type(components::component_type t)
Protected Functions
virtual void reset_counter_value()
the following functions are not implemented by default, they will just throw
virtual void set_counter_value(counter_value const&)
virtual counter_value get_counter_value(bool)
virtual counter_values_array get_counter_values_array(bool)
virtual bool start()
virtual bool stop()
virtual void reinit(bool)
virtual counter_info get_counter_info() const
Protected Attributes
hpx::performance_counters::counter_info info_
util::atomic_count invocation_count_
namespace hpx
namespace performance_counters
namespace server
class elapsed_time_counter : public hpx::performance_counters::server::base_performance_counter, public components::component_base<elapsed_time_counter>
Public Types
typedef elapsed_time_counter type_holder
typedef base_performance_counter base_type_holder
Public Functions
elapsed_time_counter()
elapsed_time_counter(counter_info const &info)
hpx::performance_counters::counter_value get_counter_value(bool reset)
void reset_counter_value()
the following functions are not implemented by default, they will just throw
bool start()
bool stop()
void finalize()
finalize() will be called just before the instance gets destructed
Private Types
typedef components::component_base<elapsed_time_counter> base_type
namespace hpx
namespace agas
Functions
void primary_namespace_register_counter_types(error_code &ec = throws)
naming::gid_type primary_namespace_statistics_counter(std::string const &name)
HPX_DEFINE_PLAIN_ACTION(primary_namespace_statistics_counter, primary_namespace_statistics_counter_action)
namespace hpx
namespace performance_counters
namespace server
class raw_counter : public hpx::performance_counters::server::base_performance_counter, public components::component_base<raw_counter>
Public Types
typedef raw_counter type_holder
typedef base_performance_counter base_type_holder
Public Functions
raw_counter()
raw_counter(counter_info const &info, hpx::util::function_nonser<std::int64_t(bool)> f)
hpx::performance_counters::counter_value get_counter_value(bool reset = false)
void reset_counter_value()
the following functions are not implemented by default, they will just throw
void finalize()
finalize() will be called just before the instance gets destructed
Private Types
typedef components::component_base<raw_counter> base_type
Private Members
hpx::util::function_nonser<std::int64_t(bool)> f_
bool reset_
namespace hpx
namespace performance_counters
namespace server
class raw_values_counter : public hpx::performance_counters::server::base_performance_counter, public components::component_base<raw_values_counter>
Public Types
typedef raw_values_counter type_holder
typedef base_performance_counter base_type_holder
Public Functions
raw_values_counter()
raw_values_counter(counter_info const &info, hpx::util::function_nonser<std::vector<std::int64_t>(bool)> f)
hpx::performance_counters::counter_values_array get_counter_values_array(bool reset = false)
void reset_counter_value()
the following functions are not implemented by default, they will just throw
void finalize()
finalize() will be called just before the instance gets destructed
Private Types
typedef components::component_base<raw_values_counter> base_type
Private Members
hpx::util::function_nonser<std::vector<std::int64_t>bool)> hpx::performance_counters::server::raw_values_counter::f_
bool reset_
namespace hpx
namespace performance_counters
namespace server
template<typename Statistic>
class statistics_counter : public hpx::performance_counters::server::base_performance_counter, public components::component_base<statistics_counter<Statistic>>
Public Types
typedef statistics_counter type_holder
typedef base_performance_counter base_type_holder
Public Functions
statistics_counter()
statistics_counter(counter_info const &info, std::string const &base_counter_name, std::size_t parameter1, std::size_t parameter2, bool reset_base_counter)
hpx::performance_counters::counter_value get_counter_value(bool reset = false)
Overloads from the base_counter base class.
bool start()
bool stop()
void reset_counter_value()
the following functions are not implemented by default, they will just throw
void on_terminate()
void finalize()
finalize() will be called just before the instance gets destructed
Protected Functions
bool evaluate_base_counter(counter_value &value)
bool evaluate()
bool ensure_base_counter()
Private Types
typedef components::component_base<statistics_counter<Statistic>> base_type
typedef lcos::local::spinlock mutex_type
Private Functions
statistics_counter *this_()
Private Members
mutex_type mtx_
hpx::util::interval_timer timer_
base time interval in milliseconds
std::string base_counter_name_
name of base counter to be queried
naming::id_type base_counter_id_
std::unique_ptr<detail::counter_type_from_statistic_base> value_
counter_value prev_value_
bool has_prev_value_
std::size_t parameter1_
std::size_t parameter2_
bool reset_base_counter_
|
{}
|
# 17.2: Chemical Defenses (2023)
1. Last updated
2. Save as PDF
• Page ID
5216
Learning Objectives
• Describe how enzymes in body fluids provide protection against infection or disease
• List and describe the function of antimicrobial peptides, complement components, cytokines, and acute-phase proteins
• Describe similarities and differences among classic, alternate, and lectin complement pathways
In addition to physical defenses, the innate nonspecific immune system uses a number of chemical mediators that inhibit microbial invaders. The term “chemical mediators” encompasses a wide array of substances found in various body fluids and tissues throughout the body. Chemical mediators may work alone or in conjunction with each other to inhibit microbial colonization and infection.
Some chemical mediators are endogenously produced, meaning they are produced by human body cells; others are produced exogenously, meaning that they are produced by certain microbes that are part of the microbiome. Some mediators are produced continually, bathing the area in the antimicrobial substance; others are produced or activated primarily in response to some stimulus, such as the presence of microbes.
#### Chemical and Enzymatic Mediators Found in Body Fluids
Fluids produced by the skin include examples of both endogenous and exogenous mediators. Sebaceous glands in the dermis secrete an oil called sebum that is released onto the skin surface through hair follicles. This sebum is an endogenous mediator, providing an additional layer of defense by helping seal off the pore of the hair follicle, preventing bacteria on the skin’s surface from invading sweat glands and surrounding tissue (Figure $$\PageIndex{1}$$). Certain members of the microbiome, such as the bacterium Propionibacterium acnes and the fungus Malassezia, among others, can use lipase enzymes to degrade sebum, using it as a food source. This produces oleic acid, which creates a mildly acidic environment on the surface of the skin that is inhospitable to many pathogenic microbes. Oleic acid is an example of an exogenously produced mediator because it is produced by resident microbes and not directly by body cells.
Environmental factors that affect the microbiota of the skin can have a direct impact on the production of chemical mediators. Low humidity or decreased sebum production, for example, could make the skin less habitable for microbes that produce oleic acid, thus making the skin more susceptible to pathogens normally inhibited by the skin’s low pH. Many skin moisturizers are formulated to counter such effects by restoring moisture and essential oils to the skin.
The digestive tract also produces a large number of chemical mediators that inhibit or kill microbes. In the oral cavity, saliva contains mediators such as lactoperoxidase enzymes, and mucus secreted by the esophagus contains the antibacterial enzyme lysozyme. In the stomach, highly acidic gastric fluid kills most microbes. In the lower digestive tract, the intestines have pancreatic and intestinal enzymes, antibacterial peptides (cryptins), bile produced from the liver, and specialized Paneth cells that produce lysozyme. Together, these mediators are able to eliminate most pathogens that manage to survive the acidic environment of the stomach.
In the urinary tract, urine flushes microbes out of the body during urination. Furthermore, the slight acidity of urine (the average pH is about 6) inhibits the growth of many microbes and potential pathogens in the urinary tract.
The female reproductive system employs lactate, an exogenously produced chemical mediator, to inhibit microbial growth. The cells and tissue layers composing the vagina produce glycogen, a branched and more complex polymer of glucose. Lactobacilli in the area ferment glycogen to produce lactate, lowering the pH in the vagina and inhibiting transient microbiota, opportunistic pathogens like Candida (a yeast associated with vaginal infections), and other pathogens responsible for sexually transmitted diseases.
In the eyes, tears contain the chemical mediators lysozyme and lactoferrin, both of which are capable of eliminating microbes that have found their way to the surface of the eyes. Lysozyme cleaves the bond between NAG and NAM in peptidoglycan, a component of the cell wall in bacteria. It is more effective against gram-positive bacteria, which lack the protective outer membrane associated with gram-negative bacteria. Lactoferrin inhibits microbial growth by chemically binding and sequestering iron. This effectually starves many microbes that require iron for growth.
In the ears, cerumen (earwax) exhibits antimicrobial properties due to the presence of fatty acids, which lower the pH to between 3 and 5.
The respiratory tract uses various chemical mediators in the nasal passages, trachea, and lungs. The mucus produced in the nasal passages contains a mix of antimicrobial molecules similar to those found in tears and saliva (e.g., lysozyme, lactoferrin, lactoperoxidase). Secretions in the trachea and lungs also contain lysozyme and lactoferrin, as well as a diverse group of additional chemical mediators, such as the lipoprotein complex called surfactant, which has antibacterial properties.
Exercise $$\PageIndex{1}$$
1. Explain the difference between endogenous and exogenous mediators
2. Describe how pH affects antimicrobial defenses
#### Antimicrobial Peptides
The antimicrobial peptides (AMPs) are a special class of nonspecific cell-derived mediators with broad-spectrum antimicrobial properties. Some AMPs are produced routinely by the body, whereas others are primarily produced (or produced in greater quantities) in response to the presence of an invading pathogen. Research has begun exploring how AMPs can be used in the diagnosis and treatment of disease.
AMPs may induce cell damage in microorganisms in a variety of ways, including by inflicting damage to membranes, destroying DNA and RNA, or interfering with cell-wall synthesis. Depending on the specific antimicrobial mechanism, a particular AMP may inhibit only certain groups of microbes (e.g., gram-positive or gram-negative bacteria) or it may be more broadly effective against bacteria, fungi, protozoa, and viruses. Many AMPs are found on the skin, but they can also be found in other regions of the body.
A family of AMPs called defensins can be produced by epithelial cells throughout the body as well as by cellular defenses such as macrophages and neutrophils (see Cellular Defenses). Defensins may be secreted or act inside host cells; they combat microorganisms by damaging their plasma membranes. AMPs called bacteriocins are produced exogenously by certain members of the resident microbiota within the gastrointestinal tract. The genes coding for these types of AMPs are often carried on plasmids and can be passed between different species within the resident microbiota through lateral or horizontal gene transfer.
There are numerous other AMPs throughout the body. The characteristics of a few of the more significant AMPs are summarized in Table $$\PageIndex{1}$$.
Table $$\PageIndex{1}$$: Characteristics of Selected Antimicrobial Peptides (AMPs)
AMP Secreted by Body site Pathogens inhibited Mode of action
Bacteriocins Resident microbiota Gastrointestinal tract Bacteria Disrupt membrane
Cathelicidin Epithelial cells, macrophages, and other cell types Skin Bacteria and fungi Disrupts membrane
Defensins Epithelial cells, macrophages, neutrophils Throughout the body Fungi, bacteria, and many viruses Disrupt membrane
Dermicidin Sweat glands Skin Bacteria and fungi Disrupts membrane integrity and ion channels
Histatins Salivary glands Oral cavity Fungi Disrupt intracellular function
Exercise $$\PageIndex{2}$$
Why are antimicrobial peptides (AMPs) considered nonspecific defenses?
#### Plasma Protein Mediators
Many nonspecific innate immune factors are found in plasma, the fluid portion of blood. Plasma contains electrolytes, sugars, lipids, and proteins, each of which helps to maintain homeostasis (i.e., stable internal body functioning), and contains the proteins involved in the clotting of blood. Additional proteins found in blood plasma, such as acute-phase proteins, complement proteins, and cytokines, are involved in the nonspecific innate immune response.
Plasma versus Serum
There are two terms for the fluid portion of blood: plasma and serum. How do they differ if they are both fluid and lack cells? The fluid portion of blood left over after coagulation (blood cell clotting) has taken place is serum. Although molecules such as many vitamins, electrolytes, certain sugars, complement proteins, and antibodies are still present in serum, clotting factors are largely depleted. Plasma, conversely, still contains all the clotting elements. To obtain plasma from blood, an anticoagulant must be used to prevent clotting. Examples of anticoagulants include heparin and ethylene diamine tetraacetic acid (EDTA). Because clotting is inhibited, once obtained, the sample must be gently spun down in a centrifuge. The heavier, denser blood cells form a pellet at the bottom of a centrifuge tube, while the fluid plasma portion, which is lighter and less dense, remains above the cell pellet.
#### Acute-Phase Proteins
The acute-phase proteins are another class of antimicrobial mediators. Acute-phase proteins are primarily produced in the liver and secreted into the blood in response to inflammatory molecules from the immune system. Examples of acute-phase proteins include C-reactive protein, serum amyloid A, ferritin, transferrin, fibrinogen, and mannose-binding lectin. Each of these proteins has a different chemical structure and inhibits or destroys microbes in some way (Table $$\PageIndex{1}$$).
Table $$\PageIndex{2}$$: Some Acute-Phase Proteins and Their Functions
Some Acute-Phase Proteins and Their Functions
C-reactive protein Coats bacteria (opsonization), preparing them for ingestion by phagocytes
Serum amyloid A
Ferritin Bind and sequester iron, thereby inhibiting the growth of pathogens
Transferrin
Fibrinogen Involved in formation of blood clots that trap bacterial pathogens
Mannose-binding lectin Activates complement cascade
#### The Complement System
The complement system is a group of plasma protein mediators that can act as an innate nonspecific defense while also serving to connect innate and adaptive immunity (discussed in the next chapter). The complement system is composed of more than 30 proteins (including C1 through C9) that normally circulate as precursor proteins in blood. These precursor proteins become activated when stimulated or triggered by a variety of factors, including the presence of microorganisms. Complement proteins are considered part of innate nonspecific immunity because they are always present in the blood and tissue fluids, allowing them to be activated quickly. Also, when activated through the alternative pathway (described later in this section), complement proteins target pathogens in a nonspecific manner.
The process by which circulating complement precursors become functional is called complement activation. This process is a cascade that can be triggered by one of three different mechanisms, known as the alternative, classical, and lectin pathways.
The alternative pathway is initiated by the spontaneous activation of the complement protein C3. The hydrolysis of C3 produces two products, C3a and C3b. When no invader microbes are present, C3b is very quickly degraded in a hydrolysis reaction using the water in the blood. However, if invading microbes are present, C3b attaches to the surface of these microbes. Once attached, C3b will recruit other complement proteins in a cascade (Figure $$\PageIndex{2}$$).
The classical pathway provides a more efficient mechanism of activating the complement cascade, but it depends upon the production of antibodies by the specific adaptive immune defenses. To initiate the classical pathway, a specific antibody must first bind to the pathogen to form an antibody-antigen complex. This activates the first protein in the complement cascade, the C1 complex. The C1 complex is a multipart protein complex, and each component participates in the full activation of the overall complex. Following recruitment and activation of the C1 complex, the remaining classical pathway complement proteins are recruited and activated in a cascading sequence (Figure $$\PageIndex{2}$$).
The lectin activation pathway is similar to the classical pathway, but it is triggered by the binding of mannose-binding lectin, an acute-phase protein, to carbohydrates on the microbial surface. Like other acute-phase proteins, lectins are produced by liver cells and are commonly upregulated in response to inflammatory signals received by the body during an infection (Figure $$\PageIndex{2}$$).
Although each complement activation pathway is initiated in a different way, they all provide the same protective outcomes: opsonization, inflammation, chemotaxis, and cytolysis. The term opsonization refers to the coating of a pathogen by a chemical substance (called an opsonin) that allows phagocytic cells to recognize, engulf, and destroy it more easily. Opsonins from the complement cascade include C1q, C3b, and C4b. Additional important opsonins include mannose-binding proteins and antibodies. The complement fragments C3a and C5a are well-characterized anaphylatoxins with potent proinflammatory functions. Anaphylatoxins activate mast cells, causing degranulation and the release of inflammatory chemical signals, including mediators that cause vasodilation and increased vascular permeability. C5a is also one of the most potent chemoattractants for neutrophils and other white blood cells, cellular defenses that will be discussed in the next section.
The complement proteins C6, C7, C8, and C9 assemble into a membrane attack complex (MAC), which allows C9 to polymerize into pores in the membranes of gram-negative bacteria. These pores allow water, ions, and other molecules to move freely in and out of the targeted cells, eventually leading to cell lysis and death of the pathogen (Figure $$\PageIndex{2}$$). However, the MAC is only effective against gram-negative bacteria; it cannot penetrate the thick layer of peptidoglycan associated with cell walls of gram-positive bacteria. Since the MAC does not pose a lethal threat to gram-positive bacterial pathogens, complement-mediated opsonization is more important for their clearance.
#### Cytokines
Cytokines are soluble proteins that act as communication signals between cells. In a nonspecific innate immune response, various cytokines may be released to stimulate production of chemical mediators or other cell functions, such as cell proliferation, cell differentiation, inhibition of cell division, apoptosis, and chemotaxis.
When a cytokine binds to its target receptor, the effect can vary widely depending on the type of cytokine and the type of cell or receptor to which it has bound. The function of a particular cytokine can be described as autocrine, paracrine, or endocrine (Figure $$\PageIndex{3}$$). In autocrine function, the same cell that releases the cytokine is the recipient of the signal; in other words, autocrine function is a form of self-stimulation by a cell. In contrast, paracrine function involves the release of cytokines from one cell to other nearby cells, stimulating some response from the recipient cells. Last, endocrine function occurs when cells release cytokines into the bloodstream to be carried to target cells much farther away.
Three important classes of cytokines are the interleukins, chemokines, and interferons. The interleukins were originally thought to be produced only by leukocytes (white blood cells) and to only stimulate leukocytes, thus the reasons for their name. Although interleukins are involved in modulating almost every function of the immune system, their role in the body is not restricted to immunity. Interleukins are also produced by and stimulate a variety of cells unrelated to immune defenses.
The chemokines are chemotactic factors that recruit leukocytes to sites of infection, tissue damage, and inflammation. In contrast to more general chemotactic factors, like complement factor C5a, chemokines are very specific in the subsets of leukocytes they recruit.
Interferons are a diverse group of immune signaling molecules and are especially important in our defense against viruses. Type I interferons (interferon-α and interferon-β) are produced and released by cells infected with virus. These interferons stimulate nearby cells to stop production of mRNA, destroy RNA already produced, and reduce protein synthesis. These cellular changes inhibit viral replication and production of mature virus, slowing the spread of the virus. Type I interferons also stimulate various immune cells involved in viral clearance to more aggressively attack virus-infected cells. Type II interferon (interferon-γ) is an important activator of immune cells (Figure $$\PageIndex{4}$$).
#### Inflammation-Eliciting Mediators
Many of the chemical mediators discussed in this section contribute in some way to inflammation and fever, which are nonspecific immune responses discussed in more detail in Inflammation and Fever. Cytokines stimulate the production of acute-phase proteins such as C-reactive protein and mannose-binding lectin in the liver. These acute-phase proteins act as opsonins, activating complement cascades through the lectin pathway.
Some cytokines also bind mast cells and basophils, inducing them to release histamine, a proinflammatory compound. Histamine receptors are found on a variety of cells and mediate proinflammatory events, such as bronchoconstriction (tightening of the airways) and smooth muscle contraction.
In addition to histamine, mast cells may release other chemical mediators, such as leukotrienes. Leukotrienes are lipid-based proinflammatory mediators that are produced from the metabolism of arachidonic acid in the cell membrane of leukocytes and tissue cells. Compared with the proinflammatory effects of histamine, those of leukotrienes are more potent and longer lasting. Together, these chemical mediators can induce coughing, vomiting, and diarrhea, which serve to expel pathogens from the body.
Certain cytokines also stimulate the production of prostaglandins, chemical mediators that promote the inflammatory effects of kinins and histamines. Prostaglandins can also help to set the body temperature higher, leading to fever, which promotes the activities of white blood cells and slightly inhibits the growth of pathogenic microbes (see Inflammation and Fever).
Another inflammatory mediator, bradykinin, contributes to edema, which occurs when fluids and leukocytes leak out of the bloodstream and into tissues. It binds to receptors on cells in the capillary walls, causing the capillaries to dilate and become more permeable to fluids.
Exercise $$\PageIndex{3}$$
1. What do the three complement activation pathways have in common?
2. Explain autocrine, paracrine, and endocrine signals.
3. Name two important inflammation-eliciting mediators.
Clinical Focus: Part 2
To relieve the constriction of her airways, Angela is immediately treated with antihistamines and administered corticosteroids through an inhaler, and then monitored for a period of time. Though her condition does not worsen, the drugs do not seem to be alleviating her condition. She is admitted to the hospital for further observation, testing, and treatment.
Following admission, a clinician conducts allergy testing to try to determine if something in her environment might be triggering an allergic inflammatory response. A doctor orders blood analysis to check for levels of particular cytokines. A sputum sample is also taken and sent to the lab for microbial staining, culturing, and identification of pathogens that could be causing an infection.
Exercise $$\PageIndex{4}$$
1. Which aspects of the innate immune system could be contributing to Angela’s airway constriction?
2. Why was Angela treated with antihistamines?
3. Why would the doctor be interested in levels of cytokines in Angela’s blood?
Table $$\PageIndex{3}$$ provides a summary of the chemical defenses discussed in this section.
Table $$\PageIndex{3}$$: Chemical Defenses of Nonspecific Innate Immunity
Defense Examples Function
Chemicals and enzymes in body fluids Sebum from sebaceous glands Provides oil barrier protecting hair follicle pores from pathogens
Oleic acid from sebum and skin microbiota Lowers pH to inhibit pathogens
Lysozyme in secretions Kills bacteria by attacking cell wall
Acid in stomach, urine, and vagina Inhibits or kills bacteria
Digestive enzymes and bile Kill bacteria
Lactoferrin and transferrin Bind and sequester iron, inhibiting bacterial growth
Surfactant in lungs Kills bacteria
Antimicrobial peptides Defensins, bacteriocins, dermicidin, cathelicidin, histatins, Kill bacteria by attacking membranes or interfering with cell functions
Plasma protein mediators Acute-phase proteins (C-reactive protein, serum amyloid A, ferritin, fibrinogen, transferrin, and mannose-binding lectin) Inhibit the growth of bacteria and assist in the trapping and killing of bacteria
Complements C3b and C4b Opsonization of pathogens to aid phagocytosis
Complement C5a Chemoattractant for phagocytes
Complements C3a and C5a Proinflammatory anaphylatoxins
Cytokines Interleukins Stimulate and modulate most functions of immune system
Chemokines Recruit white blood cells to infected area
Interferons Alert cells to viral infection, induce apoptosis of virus-infected cells, induce antiviral defenses in infected and nearby uninfected cells, stimulate immune cells to attack virus-infected cells
Inflammation-eliciting mediators Histamine Promotes vasodilation, bronchoconstriction, smooth muscle contraction, increased secretion and mucus production
Leukotrienes Promote inflammation; stronger and longer lasting than histamine
Prostaglandins Promote inflammation and fever
Bradykinin Increases vasodilation and vascular permeability, leading to edema
## Key Concepts and Summary
• Numerous chemical mediators produced endogenously and exogenously exhibit nonspecific antimicrobial functions.
• Many chemical mediators are found in body fluids such as sebum, saliva, mucus, gastric and intestinal fluids, urine, tears, cerumen, and vaginal secretions.
• Antimicrobial peptides (AMPs) found on the skin and in other areas of the body are largely produced in response to the presence of pathogens. These include dermcidin, cathelicidin, defensins, histatins, and bacteriocins.
• Plasma contains various proteins that serve as chemical mediators, including acute-phase proteins, complement proteins, and cytokines.
• The complement system involves numerous precursor proteins that circulate in plasma. These proteins become activated in a cascading sequence in the presence of microbes, resulting in the opsonization of pathogens, chemoattraction of leukocytes, induction of inflammation, and cytolysis through the formation of a membrane attack complex (MAC).
• Cytokines are proteins that facilitate various nonspecific responses by innate immune cells, including production of other chemical mediators, cell proliferation, cell death, and differentiation.
• Cytokines play a key role in the inflammatory response, triggering production of inflammation-eliciting mediators such as acute-phase proteins, histamine, leukotrienes, prostaglandins, and bradykinin.
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# How to align column names in the second row?
Here are my example and the code.
\begin{table}[H]
\begin{tabular}{lrrrr}
\toprule
\multirow{2}[3]{*}{Method} & \multicolumn{2}{c}{group} & \multicolumn{2}{c}{variable} \\
\cmidrule(l){2-3} \cmidrule(l){4-5}
& rate & size & rate & size \\
\midrule
s = 1/2 & 0.7668 (0.0058) & 8.78 (0.086) & 0.7184 (0.0067) & 11.07 (0.098) \\
s = 1/4 & 0.7768 (0.0066) & 12.81 (0.099) & 0.6732 (0.0063) & 15.29 (0.103) \\
\bottomrule
\end{tabular}
\end{table}
My question is rather simple. I wish to keep the column names (rate, size) in the second row centered, while the numbers in the table aligned to right. How could I achieve that? Moreover, how to use cmidrule, especially what does its first option do? I tried to change to \cmidrule{lr} and cmidrule{r}, but seems no difference to me.
Thanks for the help.
• \multicolumnn can also be used for a single column to overwrite the column specification.
• The first argument of \cmidrule specifies some trimming. The example uses (lr). Then you will see, the line is also shorter at the right side.
Example:
\documentclass{article}
\usepackage{booktabs}
\usepackage{multirow}
\begin{document}
\begin{table}
\begin{tabular}{lrrrr}
\toprule
\multirow{2}[3]{*}{Method} & \multicolumn{2}{c}{group} &
\multicolumn{2}{c}{variable} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5}
& \multicolumn{1}{c}{rate}
& \multicolumn{1}{c}{size}
& \multicolumn{1}{c}{rate}
& \multicolumn{1}{c}{size} \\
\midrule
s = 1/2 & 0.7668 (0.0058) & 8.78 (0.086) & 0.7184 (0.0067) & 11.07 (0.098)
\\
s = 1/4 & 0.7768 (0.0066) & 12.81 (0.099) & 0.6732 (0.0063) & 15.29 (0.103)
\\
\bottomrule
\end{tabular}
\end{table}
\end{document}
With help of makecell˙package is really simple:
Code:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{multirow,booktabs,makecell}
\begin{document}
\begin{table}
\begin{tabular}{lrrrr}
\toprule
\multirow{2}[3]{*}{Method} & \multicolumn{2}{c}{group} & \multicolumn{2}{c}{variable} \\
\cmidrule(l){2-3} \cmidrule(l){4-5}
`
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# Rank growth of elliptic curves after cubic extensions
Let $E/\mathbb{Q}$ be an elliptic curve and let $N_E(3,X)$ denote the number of cyclic cubic extensions $K/\mathbb{Q}$ of conductor no more than $X$ for which $rank~E(K)> ~rank~ E(\mathbb{Q})$. Then a conjecture of David, Fearnley and Kisilevsky (stemming from considerations in random matrix theory) states that
$\log N_E(3,X) \sim \frac{1}{2}\log X.$
My question is what the conjecture should be if we remove the condition that $K/\mathbb{Q}$ is a $\textit{cyclic}$ extension.
-
Hi Dave, did you look at Kisilevsky's paper "Ranks of elliptic curves in cubic extensions"? (In Number Theory, Analysis and Geometry, D. Goldfeld, J. Jorgenson, P. Jones, D. Ramakrishnan, K. A. Ribet, J. Tate, eds., New York, Springer, 2012). There he proves various rank growth results in general cubic extensions. Perhaps he has some precise growth conjectures there as well? – Tim Dokchitser Jan 10 '13 at 12:16
Hi Tim. I have had a look at that paper and there don't seem to be any precise conjectures, however it may be possible to adapt some of his arguements to find some lower bounds. I'll have another look! – Dave M da C Jan 10 '13 at 14:43
I don't have a full answer, but if $E$ is given in Weierstrass form $y^2=f(x)$, then for most values of $c \in \mathbb{Q}$, if you look at the point with $y=c$ on $E$, you get a point in a cubic extension (usually non-cyclic) given by $f(x)-c^2=0$ which will not be in the division hull of $E(\mathbb{Q})$, i.e. the rank will grow. So the number of such cubic fields of conductor at most $X$ will be a constant times some power of $X$. The total number of cubic fields of conductor at most $X$ is a constant times some other power of $X$.
Well it's easy to get a lower bound $cX^\theta$ for some $c,\theta>0$, but the question is how big $\theta$ can get. For cyclic cubics we're told it might be $1/2 - \epsilon$. For unrestricted cubics, possibly even a positive proportion (i.e. $\theta = 1$), at least if $E$ has a place of bad reduction whose contribution to the root number can change from ${\bf Q}$ to $K$ $-$ or is there a reason that this can't happen (as it presumably doesn't for cyclic cubics if we're to believe the heuristic of David, Fearnley, and Kisilevsky)? – Noam D. Elkies Jan 10 '13 at 2:42
Following the approach that Felipe mentions one can show that there are at least $c_E X^{1/2}$ cubic extensions which show an increase in rank (at least when $j(E) \neq 0$). It would be interesting to know how many more extensions there should be where rank grows which are not of the form $f(x) - c^2$. Perhaps, as Noam suggests, the true exponent of $X$ depends on the reduction types the curve exhibits and is not uniform in $E$ unlike the conjecture above and others like Goldfeld's. – Dave M da C Jan 10 '13 at 14:15
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Corpus ID: 235458658
# On the stability of the stretched Euler-Bernoulli beam on a star-shaped graph
@inproceedings{Mahinzaeim2021OnTS,
title={On the stability of the stretched Euler-Bernoulli beam on a star-shaped graph},
author={Mahyar Mahinzaeim and Genqi Xu and Hai Zhang},
year={2021}
}
• Published 2021
• Mathematics, Physics
We deal with the as yet unresolved exponential stability problem for a stretched Euler–Bernoulli beam on a star-shaped geometric graph with three edges. The edges are hinged with respect to the boundary vertices. The inner vertex is capable of both translation and rotation, the latter of which is subject to a combination of elastic and frictional effects. We present detailed results on the properties of the linear monic operator pencil associated with the spectral problem in Hilbert space… Expand
#### References
SHOWING 1-10 OF 28 REFERENCES
Spectral properties and stability of a nonselfadjoint Euler–Bernoulli beam
• Methods of Functional Analysis and Topology, 23:346–366
• 2017
Introduction To Infinite Dimensional Linear Systems Theory
This introduction to infinite dimensional linear systems theory helps people to enjoy a good book with a cup of tea in the afternoon, instead they juggled with some harmful bugs inside their laptop. Expand
Modeling Analysis And Control Of Dynamic Elastic Multi Link Structures
Thank you very much for reading modeling analysis and control of dynamic elastic multi link structures, and maybe you have knowledge that, people have look hundreds of times for their favorite readings, but end up in malicious downloads. Expand
On the Riesz basis property of root vectors system for $2 \times 2$ Dirac type operators
• Mathematics
• 2015
The paper is concerned with the Riesz basis property of a boundary value problem associated in $L^2[0,1] \otimes \mathbb{C}^2$ with the following $2 \times 2$ Dirac type equation L y = -i B^{-1}Expand
Spectral Theory of Operator Pencils
• Hermite–Biehler Functions, and their Applications. Birkhäuser
• 2015
On the completeness and Riesz basis property of root subspaces of boundary value problems for first order systems and applications
• Mathematics
• 2014
The paper is concerned with the completeness property of root functions of general boundary value problems for $n \times n$ first order systems of ordinary differential equations on a finiteExpand
Introduction to the Spectral Theory of Polynomial Operator Pencils
Operators with compact resolvent which are close to being normal Keldysh pencils Factorization of pencils Selfadjoint pencils.
On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations
• Mathematics
• 2012
The paper is concerned with the completeness problem of root functions of general boundary value problems for first order systems of ordinary differential equations. We introduce and investigate theExpand
Differential Equations on Metric Graph
• WSEAS Press
• 2010
Spectral Properties of a Fourth Order Differential Equation
• Mathematics
• 2006
The eigenvalue problem y(4)(λ, x) − (gy′)′(λ, x) = λ2y(λ, x) with boundary conditions y(λ, 0) = 0, y′′(λ, 0) = 0, y(λ, a) = 0, y′′(λ, a) + iαλy′(λ, a) = 0 is considered, where g ∈ C1[0, a] and α > 0.Expand
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# What is the resonance structure for C_6H_6?
The following diagram represents the resonance structures of benzene, $\text{C"_6"H"_6}$.
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Slow dynamics coupled with cluster formation in ultrasoft-potential glasses
Research paper by Ryoji Miyazaki, Takeshi Kawasaki, Kunimasa Miyazaki
Indexed on: 20 Dec '18Published on: 20 Dec '18Published in: arXiv - Physics - Soft Condensed Matter
Abstract
We numerically investigate slow dynamics of a binary mixture of ultrasoft particles interacting with the generalized Hertzian potential. If the softness parameter, $\alpha$, is small, the particles at high densities start penetrating each other, form clusters, and eventually undergo the glass transition. We find multiple cluster-glass phases characterized by different number of particles per cluster, whose boundary lines are sharply separated by the cluster size. Anomalous logarithmic slow relaxation of the density correlation functions is observed in the vicinity of these glass-glass phase boundaries, which hints the existence of the higher-order dynamical singularities predicted by the mode-coupling theory. Deeply in the cluster glass phases, it is found that the dynamics of a single particle is decoupled from that of the collective fluctuations.
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Trigonal-Pyramidal. Source(s): https://shrink.im/a9Vhb. Note that any one of the resonance structures could be used to predict molecular structure and bond angles. I assume you are referring to ICl4^-. You can quickly refer to the periodic table for the group A number for this information. Get your answers by asking now. For one bond, the bond dipole moment is determined by the difference in electronegativity between the two atoms. The molecular geometry of C2H2Br2 is trigonal planar.The molecular geometry of C2H2Br2 is trigonal planar. When there are lone pairs, you need to look at the structure and recognize the names and bond angles. CCl 4, NH 4 +, SF 4, XeF 4, ClO 4 − AB 5: PCl 5, IF 5, SbF 5, BrF 5: AB 6: SF 6, UF 6 ... and the molecular geometry, which is the arrangement of bonded atoms. Jump to Question. n3 molecular geometry, a. SeO 3 has a trigonal planar molecular structure with all bond angles equal to 120 o. 0 1. fearing. Predict the molecular geometry and bond angle of ClNO. Explain. There is a simple procedure that allows us to predict overall geometry is the VSEPR , … Still have questions? Trigonal- Planar. Lv 4. This chemistry video tutorial explains how to draw lewis structures of molecules and the lewis dot diagram of polyatomic ions. maybe you should just google it or something.. 0 0. Clf4 Lewis Structure. 0 0. Molecular Geometry which is also known as Molecular Structure is the three-dimensional construction or organization of particles in a molecule. Trigonal pyramidal geometry in ammonia. 5. 1 To determine the molecular geometry Draw the Lewis structure Molecular Geometry Molecular Geometry Investigating Molecular Shapes with VSEPR About this Lesson This activity is intended to give the students opportunities to practice drawing Lewis structures and then build the corresponding model. If you are willing to understand the molecular structure of a compound, you can decide its polarity, reactivity, hybridization, shade, magnetism, and genetic movement. • molecular geometry is vital in order to understand the polarity of molecules • crucial to understanding reactions in organic, inorganic and biochemistry. Molecular geometries take into account the number of atoms and the number of lone pair electrons. Before starting any complicated explanations, let’s start with the basics. Home » Chemistry » Hypochlorite Ion {-} Name: Hypochlorite Ion {-} Formula: ClO. 4. b. SeO 2 has a V-shaped molecular structure. —Lewis Dot Structures and Molecule Geometries Worksheet Answer Key 1 Lewis Dot Structures and Molecule Geometries Worksheet Answer Key How to Draw a Lewis Dot Structure 1. These lone pairs are mutually trans. None of these. PCL3 Molecular Geometry. shared pairs=1/2 (electrions required - valence electrons) so SP=1/2 view the full answer. xecl2 molecular geometry, Molecular geometry, the bond lengths and angles, are determined experimentally. Chlorite is the strongest oxidiser of the chlorine oxyanions on the basis of standard half cell potentials. Chapter 8.Molecular Geometry and Bonding Theories (Homework) W a. eleven sigma bonds and two pie bonds b. five sigma bonds and eleven pie bonds c. thirteen sigma bonds and one pi bond d. thirteen sigma bonds and two pie bonds e. eleven sigma bonds and five pie bonds Use the following Lewis structure for acetic acid to answer the following questions: ____ 36. Bent or Angular. The main geometries without lone pair electrons are: linear, trigonal, tetrahedral, trigonal bipyramidal, and octahedral. 1 decade ago. 1 decade ago. VSEPR Theory: a chemistry model used to predict the shape of individual molecules based on electron-pair electrostatic repulsion; VSEPR Model. Molecular structure, which refers only to the placement of atoms in a molecule and not the electrons, is equivalent to electron-pair geometry only when there are no lone electron pairs around the central atom. Our tutors rated the difficulty ofDetermine the molecular geometry of ClF4- ....as medium difficulty. VESPR stands for valence shell electron pair repulsion. Answer Save. Use VSEPR theory (valence shell electron pair repulsion) Boron has 3 valence electrons, and each of the four fluorides contributes one electron to each covalent bond. Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 … In chemical formula you may use: Any chemical element. There is a simple procedure that allows us to predict overall geometry is the VSEPR, Valence Shell Electron Pair Repulsion. The molecular geometry and bond angle of clone is the result of a tetrahedral electron. a) trigonal planar b) tetrahedral c) trigonal pyramidal d) T-shaped e) square planar Im trying to teach myself chemistry and this question has popped up and i have no idea how to answer it and what the question is actually asking? 4 years ago. Or if you need more Molecular vs Electron Geometry practice, you can also practice Molecular vs Electron Geometry practice problems. The two C-H dipoles do not cancel the two C-F dipoles in CH. Molecular Geometry . The nitrogen in ammonia has 5 valence electrons and bonds with three hydrogen atoms to complete the octet.This would result in the geometry of a regular tetrahedron with each bond angle equal to cos −1 (− 1 / 3) ≈ 109.5°. This problem has been solved! Lewis structures can give us an approximate measure of molecular bonding. It is common to be called a bent molecule. Best Answer 93% (30 ratings) first, you have to know how many shared pairs there are. and i cant find any explanation in my notes etc. Using VSEPR theory, this translates to trigonal bipyramidal electron pair geometry, and "see-saw" molecular geometry with a lone pair in the equatorial position. (c) Predict the molecular geometry of $\mathrm{PF}_{4} \mathrm{Cl} .$ How did your answer for part (b) influence Explain what is wrong with each molecular geometry and provide the correct molecular geometry, given the number of lone pairs and bonding groups on the central atom. The molecular geometry of a compound represents the orientation of the different atoms of a molecule in space. Or if you need more Molecular vs Electron Geometry practice, you can also practice Molecular vs Electron Geometry practice problems. 2. the tetrachloroiodide ion. How long does this problem take to solve? (b) Which would you expect to take up more space, a $\mathrm{P}-\mathrm{F}$ bond or a $\mathrm{P}-\mathrm{Cl}$ bond? • Answer the pre-lab questions that appear at the end of this lab exercise. Figure 9.2 illustrates the molecular geometries of AB x molecules in which all the electron domains are bonds—that is, there are no lone pairs on any of the central atoms. 7. You can view video lessons to learn Molecular vs Electron Geometry. determine the molecular geometry, or shape, of ClO2 a. octahedral b. tetrahedral c. trigonal bipyramidal d. trigonal planar e. t-shaped f. bent. A dipole moment measures a separation of charge. Best Answer 100% (4 ratings) Previous question Next question Get more help from Chegg. Thus with two nuclei and one lone pair the shape is bent, or V shaped, which can be viewed as a trigonal planar arrangement with a missing vertex (Figure 9.1 and Figure 9.3). 1. The chlorite ion adopts a bent molecular geometry, due to the effects of the lone pairs on the chlorine atom, with an O–Cl–O bond angle of 111° and Cl–O bond lengths of 156 pm. 3. Octahedral. Molecular geometry, the bond lengths and angles, are determined experimentally. Favorite Answer. What is the difficulty of this problem? clf5 molecular geometry, Our tutors have indicated that to solve this problem you will need to apply the Molecular vs Electron Geometry concept. Anonymous. Molecular Geometry Lewis structures are good for figuring out how atoms are bonded to each other within a molecule and where any lone pairs of electrons are. This produces a set of geometries which depend only on the number of valence shell electron pairs and not on the atoms present. One aspect contains electron and the second dimension includes the bonds. Molecular Geometry The valence shell electron pair repulsion model (VSEPR model) assumes that electron pairs repel one another. Lv 7. ENDMEMO . 2. 8.Trigonal-Bipyramidal. They’re quite flexible in terms of how the atoms can be arranged on the page: bond length and angles between bonds don’t necessarily have to match reality. MnO 4 + ClO 2 = MnO 2 + ClO 4: double replacement: Formula in Hill system is ClO2: Computing molar mass (molar weight) To calculate molar mass of a chemical compound enter its formula and click 'Compute'. Figure $$\PageIndex{1}$$ shows the various molecular geometries for the five VESPR electronic geometries with 2 to 6 electron domains. Cl has 4 bonding pairs around it plus 1 nonbonding pair. Relevance. When there are no lone pairs the molecular geometry is the electron (VESPR) geometry. Hypochlorite Ion {-} ClO Molar Mass, Molecular Weight. The shape of the molecule is based on the number of bond pairs and the number of lone pairs. 1 Answer. Consider the molecule $\mathrm{PF}_{4} \mathrm{Cl}$ (a) Draw a Lewis structure for the molecule, and predict its electron-domain geometry. The molecular geometry is described only by the positions of the nuclei, not by the positions of the lone pairs. Here is the molecular geometry of PCL3. Molecular Geometry : The molecular geometry of a molecule represents the shape of the molecule in space. Key Terms. Question: Predict The Molecular Geometry And Bond Angle Of ClNO. The C-H bond is less polar than the C-F bond. ClF41+ has 34 valence electrons. We would expect the bond angle to be approximately 120 o as expected for trigonal planar geometry. This lesson is included in … Lewis structures can give us an approximate measure of molecular bonding. Determine the molecular geometry of the ion ClO^-2? xecl4 molecular geometry, The structure is square planar, as has been confirmed by neutron diffraction studies, According to VSEPR theory, in addition to four fluoride ligands, the xenon center has two lone pairs of electrons. It applies a theory called VESPR for short. 6. See the answer. Linear. WM Wilson M. The University of Alabama. the molecular geometry arranges the C-F dipoles so that they cancel out and the molecule is nonpolar. What is the molecular geometry of the NO3– ion? Xenon tetrafluoride sublimes at a … Chem Man. • Some sites on the molecule are more open to reaction than other sites – helps in deducing reaction mechanism, with information about the correct orientation of the atoms in the molecule. Find the total sum of valence electrons that each atom contributes to the molecule or polyatomic ion. 4. 7 CHEM 1411. This theory basically says that bonding and non-bonding electron pairs of the central atom in a molecule will repel (push away from) each other in three dimensional space and this gives the molecules their shape. There are two dimensions of Phosphorus Trichloride. Experiment 12 Lewis Dot Structures and Molecular Geometry 12-1 Experiment 12 Lewis Dot Structures and Molecular Geometry Pre-Lab Assignment Before coming to lab: • Read the lab thoroughly. 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• ### NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution(1804.09581)
May 6, 2018 astro-ph.CO, astro-ph.IM
The Crab nebula is a supernova remnant exhibiting a highly polarized synchrotron radiation at radio and millimeter wavelengths. It is the brightest source in the microwave sky with an extension of 7 by 5 arcminutes and commonly used as a standard candle for any experiment which aims at measuring the polarization of the sky. Though its spectral energy distribution has been well characterized in total intensity, polarization data are still lacking at millimetre wavelengths. We report in this paper high resolution (18 arcsec FWHM) observations of the Crab nebula in total intensity and linear polarization at 150 GHz with the NIKA camera. NIKA, operated at the IRAM 30 m telescope from 2012 to 2015, is a camera made of Lumped Element Kinetic Inductance Detectors (LEKIDs) observing the sky at 150 and 260 GHz. From these observations we are able to reconstruct the spatial distribution of the polarization degree and angle of the Crab nebula, which is found to be compatible with previous observations at lower and higher frequencies. Averaging across the source and using other existing data sets we find that the Crab nebula polarization angle is consistent with being constant over a wide range of frequencies with a value of -87.7$^\circ$ +- 0.3 in Galactic coordinates. We also present the first estimation of the Crab nebula spectral energy distribution polarized flux in a wide frequency range: 30-353 GHz. Assuming a single power law emission model we find that the polarization spectral index $\beta_{pol}$ = - 0.347 +- 0.026 is compatible with the intensity spectral index $\beta$ = - 0.323 +- 0.001.
• ### The NIKA2 instrument at 30-m IRAM telescope: performance and results(1712.04003)
Feb. 4, 2018 astro-ph.IM
The New IRAM KID Arrays 2 (NIKA2) consortium has just finished installing and commissioning a millimetre camera on the IRAM 30 m telescope. It is a dual-band camera operating with three frequency multiplexed kilo-pixels arrays of Lumped Element Kinetic Inductance Detectors (LEKID) cooled at 150 mK, designed to observe the intensity and polarisation of the sky at 260 and 150 GHz (1.15 and 2 mm). NIKA2 is today an IRAM resident instrument for millimetre astronomy, such as Intra Cluster Medium from intermediate to distant clusters and so for the follow-up of Planck satellite detected clusters, high redshift sources and quasars, early stages of star formation and nearby galaxies emission. We present an overview of the instrument performance as it has been evaluated at the end of the commissioning phase.
• ### Gravity as the main driver of non-thermal motions in massive star formation(1511.03670)
Oct. 16, 2017 astro-ph.GA, astro-ph.SR
The origin of non-thermal motions in massive star forming regions can be ascribed to turbulence acting against the gravitational collapse, or to the self-gravity itself driving the rapid global collapse. The dependence between velocity dispersion, radius and clouds surface density found by Heyer et al. (2009), $\sigma/R^{1/2}\propto \Sigma^{1/2}$, has been interpreted in terms of global collapse of clouds. In this work we demonstrate that this relation is an expression of a more general relation between accelerations. We introduce the gravo-turbulent acceleration, a$_k$, which describe the non-thermal motions in each region, and the acceleration generated by the gravitational field a$_G$, which is proportional to $\Sigma$. We also introduce a new coefficient, the force partition coefficient $\alpha_{for}$ which is equivalent to the virial parameter but does not distinguish between collapsing and non-collapsing regions. In this work we use the a$_k$ - a$_G$ formalism in the analysis of a new sample of 16 massive starless clumps (MSCls) combined with data from the literature. We show that a$_k$ and a$_G$ are not independent. The non-thermal motions in each region can originate from both local turbulence and self-gravity but overall the data in the a$_k$ vs. a$_G$ diagram demonstrate that the majority of the non-thermal motions originate from self-gravity. We further show that all the MSCls with $\Sigma\geq 0.1$ g cm$^{-2}$ show signs of infall motions, a strong indication that the denser regions are the first to collapse. Finally, we include in the formalism the contribution of an external pressure and the magnetic fields.
• ### Massive 70 micron quiet clumps II: non-thermal motions driven by gravity in massive star formation?(1710.04904)
Oct. 11, 2017 astro-ph.GA
The dynamic activity in massive star forming regions prior to the formation of bright protostars is still not fully investigated. In this work we present observations of HCO+ J=1-0 and N2H+ J=1-0 made with the IRAM 30m telescope towards a sample of 16 Herschel-identified massive 70 micron quiet clumps associated with infrared dark clouds. The clumps span a mass range from 300 M_sun to 2000 M_sun. The N2H+ data show that the regions have significant non-thermal motions with velocity dispersion between 0.28 km s^-1 and 1.5 km s^-1, corresponding to Mach numbers between 2.6 and 11.5. The majority of the 70 micron quiet clumps have asymmetric HCO+ line profiles, indicative of significant dynamical activity. We show that there is a correlation between the degree of line asymmetry and the surface density Sigma of the clumps, with clumps of Sigma>=0.1 g cm^-2 having more asymmetric line profiles, and so are more dynamically active, than clumps with lower Sigma. We explore the relationship between velocity dispersion, radius and Sigma and show how it can be interpreted as a relationship between an acceleration generated by the gravitational field a_G, and the measured kinetic acceleration, a_k, consistent with the majority of the non-thermal motions originating from self-gravity. Finally, we consider the role of external pressure and magnetic fields in the interplay of forces.
• ### Mapping the hot gas temperature in galaxy clusters using X-ray and Sunyaev-Zel'dovich imaging(1706.10230)
July 21, 2017 astro-ph.CO
We propose a method to map the temperature distribution of the hot gas in galaxy clusters that uses resolved images of the thermal Sunyaev-Zel'dovich (tSZ) effect in combination with X-ray data. Application to images from the New IRAM KIDs Array (NIKA) and XMM-Newton allows us to measure and determine the spatial distribution of the gas temperature in the merging cluster MACS J0717.5+3745, at $z=0.55$. Despite the complexity of the target object, we find a good morphological agreement between the temperature maps derived from X-ray spectroscopy only -- using XMM-Newton ($T_{\rm XMM}$) and Chandra ($T_{\rm CXO}$) -- and the new gas-mass-weighted tSZ+X-ray imaging method ($T_{\rm SZ}$). We correlate the temperatures from tSZ+X-ray imaging and those from X-ray spectroscopy alone and find that $T_{\rm SZ}$ is higher than $T_{\rm XMM}$ and lower than $T_{\rm CXO}$ by $\sim 10\%$ in both cases. Our results are limited by uncertainties in the geometry of the cluster gas, contamination from kinetic SZ ($\sim 10\%$), and the absolute calibration of the tSZ map ($7\%$). Investigation using a larger sample of clusters would help minimise these effects.
• ### A multi-instrument non-parametric reconstruction of the electron pressure profile in the galaxy cluster CLJ1226.9+3332(1707.06113)
July 19, 2017 astro-ph.CO
Context: In the past decade, sensitive, resolved Sunyaev-Zel'dovich (SZ) studies of galaxy clusters have become common. Whereas many previous SZ studies have parameterized the pressure profiles of galaxy clusters, non-parametric reconstructions will provide insights into the thermodynamic state of the intracluster medium (ICM). Aims: We seek to recover the non-parametric pressure profiles of the high redshift ($z=0.89$) galaxy cluster CLJ 1226.9+3332 as inferred from SZ data from the MUSTANG, NIKA, Bolocam, and Planck instruments, which all probe different angular scales. Methods: Our non-parametric algorithm makes use of logarithmic interpolation, which under the assumption of ellipsoidal symmetry is analytically integrable. For MUSTANG, NIKA, and Bolocam we derive a non-parametric pressure profile independently and find good agreement among the instruments. In particular, we find that the non-parametric profiles are consistent with a fitted gNFW profile. Given the ability of Planck to constrain the total signal, we include a prior on the integrated Compton Y parameter as determined by Planck. Results: For a given instrument, constraints on the pressure profile diminish rapidly beyond the field of view. The overlap in spatial scales probed by these four datasets is therefore critical in checking for consistency between instruments. By using multiple instruments, our analysis of CLJ 1226.9+3332 covers a large radial range, from the central regions to the cluster outskirts: $0.05 R_{500} < r < 1.1 R_{500}$. This is a wider range of spatial scales than is typical recovered by SZ instruments. Similar analyses will be possible with the new generation of SZ instruments such as NIKA2 and MUSTANG2.
• ### Probing changes of dust properties along a chain of solar-type prestellar and protostellar cores in Taurus with NIKA(1706.08407)
June 26, 2017 astro-ph.GA
The characterization of dust properties in the interstellar medium (ISM) is key for star formation. Mass estimates are crucial to determine gravitational collapse conditions for the birth of new stellar objects in molecular clouds. However, most of these estimates rely on dust models that need further observational constraints from clouds to prestellar and protostellar cores. We present results of a study of dust emissivity changes based on mm-continuum data obtained with the NIKA camera at the IRAM-30m telescope. Observing dust emission at 1.15 mm and 2 mm allows us to constrain the dust emissivity index ($\beta$) in the Rayleigh-Jeans tail of the dust spectral energy distribution (SED) far from its peak emission, where the contribution of other parameters (i.e. dust temperature) is important. Focusing on the Taurus molecular cloud, a low-mass star-forming regions in the Gould Belt, we analyze the emission properties of several distinct objects in the B213 filament: three prestellar cores, two Class-0/I protostellar cores and one Class-II object. By means of the ratio of the two NIKA channel-maps, we show that in the Rayleigh-Jeans approximation the dust emissivity index varies among the objects. For one prestellar and two protostellar cores, we produce a robust study using Herschel data to constrain the dust temperature of the sources. By using the Abel transform inversion technique we get accurate radial $\beta$ profiles. We find systematic spatial variations of $\beta$ in the protostellar cores that is not observed in the prestellar core. While in the former case $\beta$ decreases toward the center, in the latter it remains constant. Moreover, $\beta$ appears anticorrelated with the dust temperature. We discuss the implication of these results in terms of dust grain evolution between pre- and protostellar cores.
• ### Properties of Hi-GAL clumps in the inner Galaxy]{The Hi-GAL compact source catalogue. I. The physical properties of the clumps in the inner Galaxy ($-71.0^{\circ}< \ell < 67.0^{\circ}$)(1706.01046)
June 4, 2017 astro-ph.GA
Hi-GAL is a large-scale survey of the Galactic plane, performed with Herschel in five infrared continuum bands between 70 and 500 $\mu$m. We present a band-merged catalogue of spatially matched sources and their properties derived from fits to the spectral energy distributions (SEDs) and heliocentric distances, based on the photometric catalogs presented in Molinari et al. (2016a), covering the portion of Galactic plane $-71.0^{\circ}< \ell < 67.0^{\circ}$. The band-merged catalogue contains 100922 sources with a regular SED, 24584 of which show a 70 $\mu$m counterpart and are thus considered proto-stellar, while the remainder are considered starless. Thanks to this huge number of sources, we are able to carry out a preliminary analysis of early stages of star formation, identifying the conditions that characterise different evolutionary phases on a statistically significant basis. We calculate surface densities to investigate the gravitational stability of clumps and their potential to form massive stars. We also explore evolutionary status metrics such as the dust temperature, luminosity and bolometric temperature, finding that these are higher in proto-stellar sources compared to pre-stellar ones. The surface density of sources follows an increasing trend as they evolve from pre-stellar to proto-stellar, but then it is found to decrease again in the majority of the most evolved clumps. Finally, we study the physical parameters of sources with respect to Galactic longitude and the association with spiral arms, finding only minor or no differences between the average evolutionary status of sources in the fourth and first Galactic quadrants, or between "on-arm" and "inter-arm" positions.
• ### Massive 70 micron quiet clumps I: evidence of embedded low/intermediate-mass star formation activity(1706.00432)
June 1, 2017 astro-ph.GA, astro-ph.SR
Massive clumps, prior to the formation of any visible protostars, are the best candidates to search for the elusive massive starless cores. In this work we investigate the dust and gas properties of massive clumps selected to be 70 micron quiet, therefore good starless candidates. Our sample of 18 clumps has masses 300 < M < 3000 M_sun, radius 0.54 < R < 1.00 pc, surface densities Sigma > 0.05 g cm^-2 and luminosity/mass ratio L/M < 0.3. We show that half of these 70 micron quiet clumps embed faint 24 micron sources. Comparison with GLIMPSE counterparts shows that 5 clumps embed young stars of intermediate stellar mass up to ~5.5 M_sun. We study the clump dynamics with observations of N2H+ (1-0), HNC (1-0) and HCO+ (1-0) made with the IRAM 30m telescope. Seven clumps have blue-shifted spectra compatible with infall signatures, for which we estimate a mass accretion rate 0.04 < M_dot < 2.0 x 10^-3 M_sun yr^-1, comparable with values found in high-mass protostellar regions, and free-fall time of the order of t_ff = 3 x 10^5 yr. The only appreciable difference we find between objects with and without embedded 24 micron sources is that the infall rate appears to increase from 24 micron dark to 24 micron bright objects. We conclude that all 70 micron quiet objects have similar properties on clump scales, independently of the presence of an embedded protostar. Based on our data we speculate that the majority, if not all of these clumps may already embed faint, low-mass protostellar cores. If these clumps are to form massive stars, this must occur after the formation of these lower mass stars.
• ### Polarimetry at millimeter wavelengths with the NIKA camera: calibration and performance(1609.02042)
Feb. 24, 2017 physics.ins-det, astro-ph.IM
Magnetic fields, which play a major role in a large number of astrophysical processes from galactic to cosmological scales, can be traced via observations of dust polarization as demonstrated by the Planck satellite results. In particular, low-resolution observations of dust polarization have demonstrated that Galactic filamentary structures, where star formation takes place, are associated to well organized magnetic fields. A better understanding of this process requires detailed observations of galactic dust polarization on scales of 0.01 to 0.1 pc. Such high-resolution polarization observations can be carried out at the IRAM 30 m telescope using the recently installed NIKA2 camera, which features two frequency bands at 260 and 150 GHz (respectively 1.15 and 2.05 mm), the 260 GHz band being polarization sensitive. NIKA2 so far in commissioning phase, has its focal plane filled with ~3300 detectors to cover a Field of View (FoV) of 6.5 arcminutes diameter. The NIKA camera, which consisted of two arrays of 132 and 224 Lumped Element Kinetic Inductance Detectors (LEKIDs) and a FWHM (Full-Width-Half-Maximum) of 12 and 18.2 arcsecond at 1.15 and 2.05 mm respectively, has been operated at the IRAM 30 m telescope from 2012 to 2015 as a test-bench for NIKA2. NIKA was equipped of a room temperature polarization system (a half wave plate (HWP) and a grid polarizer facing the NIKA cryostat window). The fast and continuous rotation of the HWP permits the quasi simultaneous reconstruction of the three Stokes parameters, I, Q and U at 150 and 260 GHz. This paper presents the first polarization measurements with KIDs and reports the polarization performance of the NIKA camera and the pertinence of the choice of the polarization setup in the perspective of NIKA2. (abridged)
• ### The Great Observatories All-Sky LIRG Survey: Herschel Image Atlas and Aperture Photometry(1702.01756)
Feb. 6, 2017 astro-ph.GA
Far-infrared (FIR) images and photometry are presented for 201 Luminous and Ultraluminous Infrared Galaxies [LIRGs: log$(L_{\rm IR}/L_\odot) = 11.00 - 11.99$, ULIRGs: log$(L_{\rm IR}/L_\odot) = 12.00 - 12.99$], in the Great Observatories All-Sky LIRG Survey (GOALS) based on observations with the $Herschel$ $Space$ $Observatory$ Photodetector Array Camera and Spectrometer (PACS) and the Spectral and Photometric Imaging Receiver (SPIRE) instruments. The image atlas displays each GOALS target in the three PACS bands (70, 100, and 160 $\mu$m) and the three SPIRE bands (250, 350, and 500 $\mu$m), optimized to reveal structures at both high and low surface brightness levels, with images scaled to simplify comparison of structures in the same physical areas of $\sim$$100\times100$ kpc$^2$. Flux densities of companion galaxies in merging systems are provided where possible, depending on their angular separation and the spatial resolution in each passband, along with integrated system fluxes (sum of components). This dataset constitutes the imaging and photometric component of the GOALS Herschel OT1 observing program, and is complementary to atlases presented for the Hubble Space Telescope (Evans et al. 2017, in prep.), Spitzer Space Telescope (Mazzarella et al. 2017, in prep.), and Chandra X-ray Observatory (Iwasawa et al. 2011, 2017, in prep.). Collectively these data will enable a wide range of detailed studies of AGN and starburst activity within the most luminous infrared galaxies in the local Universe.
• ### Mapping the kinetic Sunyaev-Zel'dovich effect toward MACS J0717.5+3745 with NIKA(1606.07721)
Dec. 8, 2016 astro-ph.CO
Measurement of the gas velocity distribution in galaxy clusters provides insight into the physics of mergers, through which large scale structures form in the Universe. Velocity estimates within the intracluster medium (ICM) can be obtained via the Sunyaev-Zel'dovich (SZ) effect, but its observation is challenging both in term of sensitivity requirement and control of systematic effects, including the removal of contaminants. In this paper we report resolved observations, at 150 and 260 GHz, of the SZ effect toward the triple merger MACS J0717.5+3745 (z=0.55), using data obtained with the NIKA camera at the IRAM 30m telescope. Assuming that the SZ signal is the sum of a thermal (tSZ) and a kinetic (kSZ) component and by combining the two NIKA bands, we extract for the first time a resolved map of the kSZ signal in a cluster. The kSZ signal is dominated by a dipolar structure that peaks at -5.1 and +3.4 sigma, corresponding to two subclusters moving respectively away and toward us and coincident with the cold dense X-ray core and a hot region undergoing a major merging event. We model the gas electron density and line-of-sight velocity of MACS J0717.5+3745 as four subclusters. Combining NIKA data with X-ray observations from XMM-Newton and Chandra, we fit this model to constrain the gas line-of-sight velocity of each component, and we also derive, for the first time, a velocity map from kSZ data (i.e. that is model-dependent). Our results are consistent with previous constraints on the merger velocities, and thanks to the high angular resolution of our data, we are able to resolve the structure of the gas velocity. Finally, we investigate possible contamination and systematic effects with a special care given to radio and submillimeter galaxies. Among the sources that we detect with NIKA, we find one which is likely to be a high redshift lensed submillimeter galaxy.
• ### Non-parametric deprojection of NIKA SZ observations: Pressure distribution in the Planck-discovered cluster PSZ1 G045.85+57.71(1607.07679)
Oct. 5, 2016 astro-ph.CO
The determination of the thermodynamic properties of clusters of galaxies at intermediate and high redshift can bring new insights into the formation of large-scale structures. It is essential for a robust calibration of the mass-observable scaling relations and their scatter, which are key ingredients for precise cosmology using cluster statistics. Here we illustrate an application of high resolution $(< 20$ arcsec) thermal Sunyaev-Zel'dovich (tSZ) observations by probing the intracluster medium (ICM) of the \planck-discovered galaxy cluster \psz\ at redshift $z = 0.61$, using tSZ data obtained with the NIKA camera, which is a dual-band (150 and 260~GHz) instrument operated at the IRAM 30-meter telescope. We deproject jointly NIKA and \planck\ data to extract the electronic pressure distribution from the cluster core ($R \sim 0.02\, R_{500}$) to its outskirts ($R \sim 3\, R_{500}$) non-parametrically for the first time at intermediate redshift. The constraints on the resulting pressure profile allow us to reduce the relative uncertainty on the integrated Compton parameter by a factor of two compared to the \planck\ value. Combining the tSZ data and the deprojected electronic density profile from \xmm\ allows us to undertake a hydrostatic mass analysis, for which we study the impact of a spherical model assumption on the total mass estimate. We also investigate the radial temperature and entropy distributions. These data indicate that \psz\ is a massive ($M_{500} \sim 5.5 \times 10^{14}$ M$_{\odot}$) cool-core cluster. This work is part of a pilot study aiming at optimizing the treatment of the NIKA2 tSZ large program dedicated to the follow-up of SZ-discovered clusters at intermediate and high redshifts. (abridged)
• ### High angular resolution SZ observations with NIKA and NIKA2(1605.09549)
May 31, 2016 astro-ph.CO
NIKA2 (New IRAM KID Arrays) is a dual band (150 and 260 GHz) imaging camera based on Kinetic Inductance Detectors (KIDs) and designed to work at the IRAM 30 m telescope (Pico Veleta, Spain). Built on the experience of the NIKA prototype, NIKA2 has been installed at the 30 m focal plane in October 2015 and the commissioning phase is now ongoing. Through the thermal Sunyaev-Zeldovich (tSZ) effect, NIKA2 will image the ionized gas residing in clusters of galaxies with a resolution of 12 and 18 arcsec FWHM (at 150 and 260 GHz, respectively). We report on the recent tSZ measurements with the NIKA camera and discuss the future objectives for the NIKA2 SZ large Program, 300h of observation dedicated to SZ science. With this program we intend to perform a high angular resolution follow-up of a cosmologically-representative sample of clusters belonging to SZ catalogues, with redshift greater than 0.5. The main output of the program will be the study of the redshift evolution of the cluster pressure profile as well as that of the scaling laws relating the cluster global properties.
• ### The NIKA2 commissioning campaign: performance and first results(1605.08628)
The New IRAM KID Array 2 (NIKA 2) is a dual-band camera operating with three frequency-multiplexed kilopixels arrays of Lumped Element Kinetic Inductance Detectors (LEKID) cooled at 150 mK. NIKA 2 is designed to observe the intensity and polarisation of the sky at 1.15 and 2.0 mm wavelength from the IRAM 30 m telescope. The NIKA 2 instrument represents a huge step in performance as compared to the NIKA pathfinder instrument, which has already shown state-of-the-art detector and photometric performance. After the commissioning planned to be accomplished at the end of 2016, NIKA 2 will be an IRAM resident instrument for the next ten years or more. NIKA 2 should allow the astrophysical community to tackle a large number of open questions reaching from the role of the Galactic magnetic field in star formation to the discrepancy between cluster-based and CMB-based cosmology possibly induced by the unknown cluster physics. We present an overview of the commissioning phase together with some first results.
• ### Hi-GAL, the Herschel infrared Galactic Plane Survey: photometric maps and compact source catalogues. First data release for Inner Milky Way: +68{\deg}> l > -70{\deg}(1604.05911)
April 20, 2016 astro-ph.GA
(Abridged) We present the first public release of high-quality data products (DR1) from Hi-GAL, the {\em Herschel} infrared Galactic Plane Survey. Hi-GAL is the keystone of a suite of continuum Galactic Plane surveys from the near-IR to the radio, and covers five wavebands at 70, 160, 250, 350 and 500 micron, encompassing the peak of the spectral energy distribution of cold dust for 8 < T < 50K. This first Hi-GAL data release covers the inner Milky Way in the longitude range 68{\deg} > l > -70{\deg} in a |b|<1{\deg} latitude strip. Photometric maps have been produced with the ROMAGAL pipeline, that optimally capitalizes on the excellent sensitivity and stability of the bolometer arrays of the {\em Herschel} PACS and SPIRE photometric cameras, to deliver images of exquisite quality and dynamical range, absolutely calibrated with {\em Planck} and {\em IRAS}, and recovering extended emission at all wavelengths and all spatial scales. The compact source catalogues have been generated with the CuTEx algorithm, specifically developed to optimize source detection and extraction in the extreme conditions of intense and spatially varying background that are found in the Galactic Plane in the thermal infrared. Hi-GAL DR1 images will be accessible via a dedicated web-based image cutout service. The DR1 Compact Source Catalogues are delivered as single-band photometric lists containing, in addition to source position, peak and integrated flux and source sizes, a variety of parameters useful to assess the quality and reliability of the extracted sources, caveats and hints to help this assessment are provided. Flux completeness limits in all bands are determined from extensive synthetic source experiments and depend on the specific line of sight along the Galactic Plane. Hi-GAL DR1 catalogues contain 123210, 308509, 280685, 160972 and 85460 compact sources in the five bands, respectively.
• ### High-resolution tSZ cartography of clusters of galaxies with NIKA at the IRAM 30-m telescope(1602.07941)
Feb. 25, 2016 astro-ph.CO
The thermal Sunyaev-Zeldovich effect (tSZ) is a powerful probe to study clusters of galaxies and is complementary with respect to X-ray, lensing or optical observations. Previous arcmin resolution tSZ observations ({\it e.g.} SPT, ACT and Planck) only enabled detailed studies of the intra-cluster medium morphology for low redshift clusters ($z < 0.2$). Thus, the development of precision cosmology with clusters requires high angular resolution observations to extend the understanding of galaxy cluster towards high redshift. NIKA2 is a wide-field (6.5 arcmin field of view) dual-band camera, operated at $100 \ {\rm mK}$ and containing $\sim 3300$ KID (Kinetic Inductance Detectors), designed to observe the millimeter sky at 150 and 260 GHz, with an angular resolution of 18 and 12 arcsec respectively. The NIKA2 camera has been installed on the IRAM 30-m telescope (Pico Veleta, Spain) in September 2015. The NIKA2 tSZ observation program will allow us to observe a large sample of clusters (50) at redshift ranging between 0.5 and 1. As a pathfinder for NIKA2, several clusters of galaxies have been observed at the IRAM 30-m telescope with the NIKA prototype to cover the various configurations and observation conditions expected for NIKA2.
• ### High angular resolution Sunyaev-Zel'dovich observations of MACS J1423.8+2404 with NIKA: Multiwavelength analysis(1510.06674)
Feb. 15, 2016 astro-ph.CO
The prototype of the NIKA2 camera, NIKA, is an instrument operating at the IRAM 30-m telescope, which can observe simultaneously at 150 and 260GHz. One of the main goals of NIKA2 is to measure the pressure distribution in galaxy clusters at high resolution using the thermal SZ (tSZ) effect. Such observations have already proved to be an excellent probe of cluster pressure distributions even at high redshifts. However, an important fraction of clusters host submm and/or radio point sources, which can significantly affect the reconstructed signal. Here we report on <20" resolution observations at 150 and 260GHz of the cluster MACSJ1424, which hosts both radio and submm point sources. We examine the morphology of the tSZ signal and compare it to other datasets. The NIKA data are combined with Herschel satellite data to study the SED of the submm point source contaminants. We then perform a joint reconstruction of the intracluster medium (ICM) electronic pressure and density by combining NIKA, Planck, XMM-Newton, and Chandra data, focusing on the impact of the radio and submm sources on the reconstructed pressure profile. We find that large-scale pressure distribution is unaffected by the point sources because of the resolved nature of the NIKA observations. The reconstructed pressure in the inner region is slightly higher when the contribution of point sources are removed. We show that it is not possible to set strong constraints on the central pressure distribution without accurately removing these contaminants. The comparison with X-ray only data shows good agreement for the pressure, temperature, and entropy profiles, which all indicate that MACSJ1424 is a dynamically relaxed cool core system. The present observations illustrate the possibility of measuring these quantities with a relatively small integration time, even at high redshift and without X-ray spectroscopy.
• ### NIKA 2: next-generation continuum/polarized camera at the IRAM 30 m telescope and its prototype(1602.01605)
Feb. 4, 2016 astro-ph.IM
NIKA 2 (New Instrument of Kids Array) is a next generation continuum and polarized instrument successfully installed in October 2015 at the IRAM 30 m telescope on Pico-Veleta (Granada, Spain). NIKA 2 is a high resolution dual-band camera, operating with frequency multiplexed LEKIDs (Lumped Element Kinetic Inductance Detectors) cooled at 100 mK. Dual color images are obtained thanks to the simultaneous readout of a 1020 pixels array at 2 mm and 1140 x 2 pixels arrays at 1.15 mm with a final resolution of 18 and 12 arcsec respectively, and 6.5 arcmin of Field of View (FoV). The two arrays at 1.15 mm allow us to measure the linear polarization of the incoming light. This will place NIKA 2 as an instrument of choice to study the role of magnetic fields in the star formation process. The NIKA experiment, a prototype for NIKA 2 with a reduced number of detectors (about 400 LEKIDs) and FoV (1.8 arcmin), has been successfully operated at the IRAM 30 telescope in several open observational campaigns. The performance of the NIKA 2 polarization setup has been successfully validated with the NIKA prototype.
• ### The NIKA2 instrument, a dual-band kilopixel KID array for millimetric astronomy(1601.02774)
Jan. 12, 2016 astro-ph.IM
NIKA2 (New IRAM KID Array 2) is a camera dedicated to millimeter wave astronomy based upon kilopixel arrays of Kinetic Inductance Detectors (KID). The pathfinder instrument, NIKA, has already shown state-of-the-art detector performance. NIKA2 builds upon this experience but goes one step further, increasing the total pixel count by a factor $\sim$10 while maintaining the same per pixel performance. For the next decade, this camera will be the resident photometric instrument of the Institut de Radio Astronomie Millimetrique (IRAM) 30m telescope in Sierra Nevada (Spain). In this paper we give an overview of the main components of NIKA2, and describe the achieved detector performance. The camera has been permanently installed at the IRAM 30m telescope in October 2015. It will be made accessible to the scientific community at the end of 2016, after a one-year commissioning period. When this happens, NIKA2 will become a fundamental tool for astronomers worldwide.
• ### First polarised light with the NIKA camera(1508.00747)
Oct. 7, 2015 astro-ph.IM
NIKA is a dual-band camera operating with 315 frequency multiplexed LEKIDs cooled at 100 mK. NIKA is designed to observe the sky in intensity and polarisation at 150 and 260 GHz from the IRAM 30-m telescope. It is a test-bench for the final NIKA2 camera. The incoming linear polarisation is modulated at four times the mechanical rotation frequency by a warm rotating multi-layer Half Wave Plate. Then, the signal is analysed by a wire grid and finally absorbed by the LEKIDs. The small time constant (< 1ms ) of the LEKID detectors combined with the modulation of the HWP enables the quasi-simultaneous measurement of the three Stokes parameters I, Q, U, representing linear polarisation. In this paper we present results of recent observational campaigns demonstrating the good performance of NIKA in detecting polarisation at mm wavelength.
• ### Pressure distribution of the high-redshift cluster of galaxies CL J1226.9+3332 with NIKA(1410.2808)
May 15, 2015 astro-ph.CO
The thermal Sunyaev-Zel'dovich (tSZ) effect is expected to provide a low scatter mass proxy for galaxy clusters since it is directly proportional to the cluster thermal energy. The tSZ observations have proven to be a powerful tool for detecting and studying them, but high angular resolution observations are now needed to push their investigation to a higher redshift. In this paper, we report high angular (< 20 arcsec) resolution tSZ observations of the high-redshift cluster CL J1226.9+3332 (z=0.89). It was imaged at 150 and 260 GHz using the NIKA camera at the IRAM 30-meter telescope. The 150 GHz map shows that CL J1226.9+3332 is morphologically relaxed on large scales with evidence of a disturbed core, while the 260 GHz channel is used mostly to identify point source contamination. NIKA data are combined with those of Planck and X-ray from Chandra to infer the cluster's radial pressure, density, temperature, and entropy distributions. The total mass profile of the cluster is derived, and we find $M_{500} = 5.96^{+1.02}_{-0.79}$ x $10^{14} M_{\odot}$ within the radius $R_{500} = 930^{+50}_{-43}$ kpc, at a 68% confidence level. ($R_{500}$ is the radius within which the average density is 500 times the critical density at the cluster's redshift.) NIKA is the prototype camera of NIKA2, a KIDs (kinetic inductance detectors) based instrument to be installed at the end of 2015. This work is, therefore, part of a pilot study aiming at optimizing tSZ NIKA2 large programs.
• ### Spitzer/infrared spectrograph investigation of MIPSGAL 24 {\mu}m compact bubbles : Low resolution observations(1410.6119)
Oct. 22, 2014 astro-ph.GA
We present Spitzer/IRS low resolution observations of 11 compact circumstellar bubbles from the MIPSGAL 24 {\mu}m Galactic Plane Survey. We find that this set of MIPSGAL bubbles (MBs) is divided into two categories, and that this distinction correlates with the morphologies of the MBs in the mid- IR. The four MBs with central sources in the mid-IR exhibit dust-rich, low excitation spectra, and their 24 {\mu}m emission is accounted for by the dust continuum. The seven MBs without central sources in the mid-IR have spectra dominated by high excitation gas lines (e.g., [O IV] 26.0 {\mu}m, [Ne V] 14.3 and 24.3 {\mu}m, [Ne III] 15.5 {\mu}m), and the [O IV] line accounts for 50 to almost 100% of the 24 {\mu}m emission in five of them. In the dust-poor MBs, the [Ne V] and [Ne III] line ratios correspond to high excitation conditions. Based on comparisons with published IRS spectra, we suggest that the dust-poor MBs are highly excited planetary nebulae with peculiar white dwarfs (e.g., [WR], novae) at their centers. The central stars of the four dust-rich MBs are all massive star candidates. Dust temperatures range from 40 to 100 K in the outer shells. We constrain the extinction along the lines of sight from the IRS spectra. We then derive distance, dust masses, and dust production rate estimates for these objects. These estimates are all consistent with the nature of the central stars. We summarize the identifications of MBs made to date and discuss the correlation between their mid-IR morphologies and natures. Candidate Be/B[e]/LBV and WR stars are mainly "rings" with mid-IR central sources, whereas PNe are mostly "disks" without mid-IR central sources. Therefore we expect that most of the 300 remaining unidentified MBs will be classified as PNe.
• ### Latest NIKA results and the NIKA-2 project(1310.1230)
Sept. 10, 2014 astro-ph.IM
NIKA (New IRAM KID Arrays) is a dual-band imaging instrument installed at the IRAM (Institut de RadioAstronomie Millimetrique) 30-meter telescope at Pico Veleta (Spain). Two distinct Kinetic Inductance Detectors (KID) focal planes allow the camera to simultaneously image a field-of-view of about 2 arc-min in the bands 125 to 175 GHz (150 GHz) and 200 to 280 GHz (240 GHz). The sensitivity and stability achieved during the last commissioning Run in June 2013 allows opening the instrument to general observers. We report here the latest results, in particular in terms of sensitivity, now comparable to the state-of-the-art Transition Edge Sensors (TES) bolometers, relative and absolute photometry. We describe briefly the next generation NIKA-2 instrument, selected by IRAM to occupy, from 2015, the continuum imager/polarimeter slot at the 30-m telescope.
• ### High resolution SZ observations at the IRAM 30-m telescope with NIKA(1409.1137)
Sept. 3, 2014 astro-ph.CO
High resolution observations of the thermal Sunyaev-Zel'dovich (tSZ) effect are necessary to allow the use of clusters of galaxies as a probe for large scale structures at high redshifts. With its high resolution and dual-band capability at millimeter wavelengths, the NIKA camera can play a significant role in this context. NIKA is based on newly developed Kinetic Inductance Detectors (KIDs) and operates at the IRAM 30m telescope, Pico Veleta, Spain. In this paper, we give the status of the NIKA camera, focussing on the KID technology. We then present observations of three galaxy clusters: RX J1347.5-1145 as a demonstrator of the NIKA capabilities and the recent observations of CL J1226.9+3332 (z = 0.89) and MACS J0717.5+3745 (z = 0.55). We also discuss prospects for the final NIKA2 camera, which will have a 6.5 arcminute field of view with about 5000 detectors in two bands at 150 and 260 GHz.
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# Pole (of a function)
An isolated singular point $a$ of single-valued character of an analytic function $f(z)$ of the complex variable $z$ for which $\abs{f(z)}$ increases without bound when $z$ approaches $a$: $\lim_{z\rightarrow a} f(z) = \infty$. In a sufficiently small punctured neighbourhood $V=\set{z\in\C : 0 < \abs{z-a} < R}$ of the point $a \neq \infty$, or $V'=\set{z\in\C : r < \abs{z} < \infty}$ in the case of the point at infinity $a=\infty$, the function $f(z)$ can be written as a Laurent series of special form: $$\label{eq1} f(z) = \sum_{k=-m}^\infty c_k (z-a)^k,\quad \text{a \neq \infty, c_{-m} \neq 0, z \in V},$$ or, respectively, $$\label{eq2} f(z) = \sum_{k=-m}^\infty \frac{c_k}{z^k},\quad \text{a = \infty, c_{-m} \neq 0, z \in V'},$$ with finitely many negative exponents if $a\neq\infty$, or, respectively, finitely many positive exponents if $a=\infty$. The natural number $m$ in these expressions is called the order, or multiplicity, of the pole $a$; when $m=1$ the pole is called simple. The expressions \ref{eq1} and \ref{eq2} show that the function $p(z)=(z-a)^mf (z)$ if $a\neq\infty$, or $p(z)=z^{-m}f(z)$ if $a=\infty$, can be [[Analytic continuation|analytically continued]] to a full neighbourhood of the pole $a$, and, moreover, $p(a) \neq 0$. Alternatively, a pole $a$ of order $m$ can also be characterized by the fact that the function $1/f(z)$ has a zero of multiplicity $m$ at $a$. A point $a=(a_1,\ldots,a_n)$ of the complex space $\C^n$, $n\geq2$, is called a pole of the analytic function $f(z)$ of several complex variables $z=(z_1,\ldots,z_n)$ if the following conditions are satisfied: 1) $f(z)$ is holomorphic everywhere in some neighbourhood $U$ of $a$ except at a set $P \subset U$, $a \in P$; 2) $f(z)$ cannot be analytically continued to any point of $P$; and 3) there exists a function $q(z) \not\equiv 0$, holomorphic in $U$, such that the function $p(z) = q(z)f(z)$, which is holomorphic in $U \setminus P$, can be holomorphically continued to the full neighbourhood $U$, and, moreover, $p(a) \neq 0$. Here also '"UNIQ-MathJax2-QINU"' however, for $n \geq 2$, poles, as with singular points in general, cannot be isolated. ===='"UNIQ--h-0--QINU"'References==== <table><tr><td valign="top">[1]</td> <td valign="top"> B.V. Shabat, "Introduction of complex analysis" , '''2''' , Moscow (1976) (In Russian)</td></tr></table> ===='"UNIQ--h-1--QINU"'Comments==== For $n=1$ see [[#References|[a1]]]. For $n \geq 2$ see [a2], [a3].
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# Set packing
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them share an element).
More formally, given a universe ${\displaystyle {\mathcal {U}}}$ and a family ${\displaystyle {\mathcal {S}}}$ of subsets of ${\displaystyle {\mathcal {U}}}$, a packing is a subfamily ${\displaystyle {\mathcal {C}}\subseteq {\mathcal {S}}}$ of sets such that all sets in ${\displaystyle {\mathcal {C}}}$ are pairwise disjoint. The size of the packing is ${\displaystyle |{\mathcal {C}}|}$. In the set packing decision problem, the input is a pair ${\displaystyle ({\mathcal {U}},{\mathcal {S}})}$ and an integer ${\displaystyle k}$; the question is whether there is a set packing of size ${\displaystyle k}$ or more. In the set packing optimization problem, the input is a pair ${\displaystyle ({\mathcal {U}},{\mathcal {S}})}$, and the task is to find a set packing that uses the most sets.
The problem is clearly in NP since, given k subsets, we can easily verify that they are pairwise disjoint in polynomial time.
The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in the list. It is a maximization problem that can be formulated naturally as an integer linear program, belonging to the class of packing problems.
## Integer linear program formulation
The maximum set packing problem can be formulated as the following integer linear program.
maximize ${\displaystyle \sum _{S\in {\mathcal {S}}}x_{S}}$ (maximize the total number of subsets) subject to ${\displaystyle \sum _{S\colon e\in S}x_{S}\leqslant 1}$ for all ${\displaystyle e\in {\mathcal {U}}}$ (selected sets have to be pairwise disjoint) ${\displaystyle x_{S}\in \{0,1\}}$ for all ${\displaystyle S\in {\mathcal {S}}}$. (every set is either in the set packing or not)
## Complexity
The set packing problem is not only NP-complete, but its optimization version (general maximum set packing problem) has been proven as difficult to approximate as the maximum clique problem; in particular, it cannot be approximated within any constant factor.[1] The best known algorithm approximates it within a factor of ${\displaystyle O({\sqrt {|U|}})}$.[2] The weighted variant can also be approximated as well.[3]
## Packing sets with a bounded size
The problem does have a variant which is more tractable. Given any positive integer k≥3, the k-set packing problem is a variant of set packing in which each set contains at most k elements.
When k=1, the problem is trivial. When k=2, the problem is equivalent to finding a maximum cardinality matching, which can be solved in polynomial time.
For any k≥3, the problem is NP-hard, as it is more general than 3-dimensional matching. However, there are constant-factor approximation algorithms:
• Cygan[4] presented an algorithm that, for any ε>0, attains a (k+1+ε)/3 approximation. The run-time is polynomial in the number of sets and elements, but doubly-exponential in 1/ε.
• Furer and Yu[5] presented an algorithm that attains the same approximation, but with run-time singly-exponential in 1/ε.
## Packing sets with a bounded degree
In another more tractable variant, if no element occurs in more than k of the subsets, the answer can be approximated within a factor of k. This is also true for the weighted version.
## Related problems
### Equivalent problems
Hypergraph matching is equivalent to set packing: the sets correspond to the hyperedges.
The independent set problem is also equivalent to set packing – there is a one-to-one polynomial-time reduction between them:
• Given a set packing problem on a collection ${\displaystyle {\mathcal {S}}}$, build a graph where for each set ${\displaystyle S\in {\mathcal {S}}}$ there is a vertex ${\displaystyle v_{S}}$, and there is an edge between ${\displaystyle v_{S}}$ and ${\displaystyle v_{T}}$ iff ${\displaystyle S\cap T\neq \varnothing }$. Every independent set of vertices in the generated graph corresponds to a set packing in ${\displaystyle {\mathcal {S}}}$.
• Given an independent vertex set problem on a graph ${\displaystyle G(V,E)}$, build a collection of sets where for each vertex ${\displaystyle v}$ there is a set ${\displaystyle S_{v}}$ containing all edges adjacent to ${\displaystyle v}$. Every set packing in the generated collection corresponds to an independent vertex set in ${\displaystyle G(V,E)}$.
This is also a bidirectional PTAS reduction, and it shows that the two problems are equally difficult to approximate.
In the special case when each set contains at most k elements (the k-set packing problem), the intersection graph is (k+1)-claw-free. This is because, if a set intersects some k+1 sets, then at least two of these sets intersect, so there cannot be a (k+1)-claw. So Maximum Independent Set in claw-free graphs[6] can be seen as a generalization of Maximum k-Set Packing.
### Special cases
Graph matching is a special case of set packing in which the size of all sets is 2 (the sets correspond to the edges). In this special case, a maximum-size matching can be found in polynomial time.
3-dimensional matching is a special case in which the size of all sets is 3, and in addition, the elements are partitioned into 3 colors and each set contains exactly one element of each color. This special case is still NP-hard, though it has better constant-factor approximation algorithms than the general case.
### Other related problems
In the set cover problem, we are given a family ${\displaystyle {\mathcal {S}}}$ of subsets of a universe ${\displaystyle {\mathcal {U}}}$, and the goal is to determine whether we can choose k sets that together contain every element of ${\displaystyle {\mathcal {U}}}$. These sets may overlap. The optimization version finds the minimum number of such sets. The maximum set packing need not cover every possible element.
In the exact cover problem, every element of ${\displaystyle {\mathcal {U}}}$ should be contained in exactly one of the subsets. Finding such an exact cover is an NP-complete problem, even in the special case in which the size of all sets is 3 (this special case is called exact 3 cover or X3C). However, if we create a singleton set for each element of S and add these to the list, the resulting problem is about as easy as set packing.
Karp originally showed set packing NP-complete via a reduction from the clique problem.
## Notes
1. ^ Hazan, Elad; Safra, Shmuel; Schwartz, Oded (2006), "On the complexity of approximating k-set packing", Computational Complexity, 15 (1): 20–39, CiteSeerX 10.1.1.352.5754, doi:10.1007/s00037-006-0205-6, MR 2226068, S2CID 1858087. See in particular p. 21: "Maximum clique (and therefore also maximum independent set and maximum set packing) cannot be approximated to within ${\displaystyle O(n^{1-\epsilon })}$ unless NP ⊂ ZPP."
2. ^ Halldórsson, Magnus M.; Kratochvíl, Jan; Telle, Jan Arne (1998). Independent sets with domination constraints. 25th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science. Vol. 1443. Springer-Verlag. pp. 176–185.
3. ^ Halldórsson, Magnus M. (1999). Approximations of weighted independent set and hereditary subset problems. 5th Annual International Conference on Computing and Combinatorics. Lecture Notes in Computer Science. Vol. 1627. Springer-Verlag. pp. 261–270.
4. ^ Cygan, Marek (October 2013). "Improved Approximation for 3-Dimensional Matching via Bounded Pathwidth Local Search". 2013 IEEE 54th Annual Symposium on Foundations of Computer Science: 509–518. arXiv:1304.1424. doi:10.1109/FOCS.2013.61. ISBN 978-0-7695-5135-7. S2CID 14160646.
5. ^ Fürer, Martin; Yu, Huiwen (2014). Fouilhoux, Pierre; Gouveia, Luis Eduardo Neves; Mahjoub, A. Ridha; Paschos, Vangelis T. (eds.). "Approximating the $$k$$-Set Packing Problem by Local Improvements". Combinatorial Optimization. Lecture Notes in Computer Science. Cham: Springer International Publishing. 8596: 408–420. doi:10.1007/978-3-319-09174-7_35. ISBN 978-3-319-09174-7. S2CID 15815885.
6. ^ Neuwohner, Meike (2021-06-07). "An Improved Approximation Algorithm for the Maximum Weight Independent Set Problem in d-Claw Free Graphs". arXiv:2106.03545. {{cite journal}}: Cite journal requires |journal= (help)
|
{}
|
## Torchlight ceguibase.dll error
sprers.eu problems are generally caused by file corruption, or if the DLL file has been accidentally or maliciously removed from the other Torchlight II. Torchlight is a software program developed by Runic Games. sprers.eu - Torchlight (Torchlight game executable); sprers.eu; sprers.eu C:\Program Files\Steam\steamapps\common\Torchlight\sprers.eu; C:\Program Files\Steam\steamapps\common\Torchlight\sprers.eu; C:\Program.
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### What is sprers.eu?
sprers.eu is a dynamic link library file that is part of developed by Runic Games, Inc.. The version of the software: is usually about in size, but the version you have may differ. DLL files are a file format for dynamic link libraries that is used to store several codes and procedures torchlight ceguibase.dll error Windows programs, torchlight ceguibase.dll error. DLL files have been created to allow several programs to use their information simultaneously, thus preserving memory. It also allows the user to modify the encoding of several applications at once without changing the applications themselves. DLLs can be converted to static libraries using MSIL disassemble or DLL to Lib The file format torchlight ceguibase.dll error files is similar to that of DLL. DLL files, and both types of files contain code, data and resources.
The most important facts about sprers.eu:
• Name: sprers.eu
• Software: Torchlight
• Publisher: Runic Games, Inc.
• Publisher URL: sprers.eu
• Help file: sprers.eu
• Known to be up to MB in size on most Windows;
Recommended: Identify sprers.eu related errors
## Torchlight
### A way to uninstall Torchlight from your computer
This web page is about Torchlight for Windows. Here you can find details on how to uninstall it from your PC. It is written by JoWooD. Take a look herewhere you can find out more on JoWooD. Torchlight is normally installed in the C:\Program Files (x86)\JoWooD\Torchlight directory, however this location may differ a lot depending on torchlight ceguibase.dll error user's choice when installing the application. Torchlight's full uninstall command line is sprers.eu /I{4F64A46DFAEADA5F6}. Torchlight's primary file takes around MB ( bytes) and is called sprers.eu
Torchlight installs the following the executables on your PC, occupying about MB (bytes) on disk.
• sprers.eu ( MB)
The current web page applies to Torchlight version only. Click on the links below for other Torchlight versions:
Torchlight has the habit of leaving behind some leftovers.
Directories left on disk:
• C:\Program Files (x86)\JoWooD\Torchlight
The files below remain on your disk when you remove Torchlight:
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\D3DX9_dll
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\JoWood sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\msvcpdll
• C:\Program Files (x86)\JoWooD\Torchlight\msvcrdll
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Plugin_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Plugin_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Plugin_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\programs\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\programs\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\programs\sprers.eum
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\RenderSystem_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\RenderSystem_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\steam_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Torchlight - szybki sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Torchlight_PL_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\translations\sprers.eu
Many times the following registry keys will not be cleaned:
• HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products\D64A46F47FEA2A13DA6F
• HKEY_LOCAL_MACHINE\Software\JoWooD\Torchlight
Use sprers.eu to delete the following additional registry values from the Windows Registry:
• HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products\D64A46F47FEA2A13DA6F\ProductName
### How to erase Torchlight using Advanced Uninstaller PRO
Torchlight is an application by JoWooD. Some people choose to erase it. Sometimes this can be troublesome because deleting this manually requires some advanced knowledge regarding removing Windows programs manually, torchlight ceguibase.dll error. One of the best QUICK approach to erase Torchlight is to use Advanced Uninstaller PRO. Here is how to do this:
1. If you don't have Advanced Uninstaller PRO already installed on your system, add it. This is good because Advanced Uninstaller PRO is one of the best uninstaller and general utility to clean your computer.
2, torchlight ceguibase.dll error. Start Advanced Uninstaller PRO. Take some time to get familiar with Advanced Uninstaller PRO's design and wealth of features available. Advanced Uninstaller PRO is a powerful package of tools.
3. Click on the General Tools category
4. Click on the Uninstall Programs feature
5. A list of the programs existing on your computer will be made available to you
6. Navigate the list of programs until you locate Torchlight or simply activate the Search feature and type in "Torchlight". If it is installed on your PC the Torchlight application will be found automatically. When you click Torchlight in the list of applications, some information about the program is available to you:
• Star rating (in the lower left corner). The star rating tells you the opinion other people have about Torchlight, from "Highly recommended" to "Very dangerous".
• Reviews by other people - Click on the Read reviews button.
• Details about the application you want to uninstall, by pressing the Properties button.
7. Press the Uninstall button. A confirmation dialog will come up, torchlight ceguibase.dll error. Confirm the removal by clicking the Uninstall button. Advanced Uninstaller PRO will uninstall Torchlight.
8. After removing Torchlight, Advanced Uninstaller PRO will ask you to run a cleanup. Press Next to proceed with the cleanup. All the items torchlight ceguibase.dll error Torchlight that have been left behind will be found and you will be able to delete them. By removing Torchlight with Advanced Uninstaller PRO, you can be sure that no registry entries, torchlight ceguibase.dll error, files or folders are left behind on your computer.
Your PC will remain clean, speedy and able to serve you properly.
### Geographical user distribution
Users that fifa 11 appcrash error Torchlight:
• Windows Vista ()
• Windows 7 ()
• Windows XP ()
• Windows ()
Software Application
### Disclaimer
This page is not a piece of advice to remove Torchlight by JoWooD from your computer, nor are we saying that Torchlight by JoWooD is not a good application. This page simply contains detailed instructions on how to remove Torchlight supposing you decide this is what you want to do. The information above contains registry and disk entries that our application Advanced Uninstaller PRO stumbled upon and classified as "leftovers" on other users' computers.
Last update on:
### Torchlight ceguibase.dll error - speaking
sprers.eu problems are generally caused by file corruption, or if the DLL file has been accidentally or maliciously removed from the other Torchlight II files location. Obtaining a new, uninfected copy of your DLL file will usually resolve the problem. We also recommend running a registry scan to clean up any invalid sprers.eu references which could be cause of the error.
The Dynamic Link Library format, typically carrying the DLL file extension, are known as System Files. Below, you find the latest file versions for %%os%% (and other OS versions). Rare or very old versions of sprers.eu may not be in our current file directory, but you can request a version by clicking "Request" next to your target file version. If you cannot find your file version in our database, you can also reach out directly to Runic Games for more help.
Most of your sprers.eu problems should be resolved if the file is placed in the correct file path directory, but it's a good idea to verify it is fixed. We recommend re-loading Torchlight II to test for the issue.
sprers.eu File Summary
File Format:DLL
Application Type:Game
Program:Torchlight II
ID:
Author:Runic Games
File Name:sprers.eu
KB:
SHAb70eaa7a77c1cd0f6afc77e32b29ed
MD5:eccfb71e81cc9b34cd8c4
CRCf5
Product by Solvusoft
WinThruster - Scan your PC for sprers.eu registry errors
Windows
11/10/8/7/Vista/XP
Optional Offer for WinThruster by Solvusoft Terms Uninstall)
### Torchlight 2 Class Builds and Character Progression Guide
• Embermage. Inferno, Frost, Storm.
• Engineer. Blitz, Construction, Aegis.
• Outlander. Warfare, Lore, Sigil.
• Strength.
• Dexterity.
• Focus.
• Vitality.
Sep 25,
Categories Runic Games, Inc.
## Torchlight II
Click here to run a quick scan for Torchlight II as well as connected issues.
Torchlight II error Fix
To Fix (Torchlight II) errors you’ll need to follow the 3 steps below:
Step 1:
Step 2:
Left click the “Scan Now” button
Step 3:
Finally, click ‘Fix DLL Errors‘. The Fix complete.
*File size: MB
Location: C:\Program Files\Steam\steamapps\common\Torchlight II Install size: GB (1,,, bytes) About URL: sprers.eu Help link: sprers.eu Uninstall: "C:\Program Files\Steam\sprers.eu" steam://uninstall/
sprers.eu Behavior: Windows Firewall Allowed Program Name: sprers.eu MD5: cb4cf46dfe05df00cab8ff9a sprers.eu Behavior: Windows Firewall Allowed Program MD5: 5d09c69e0f17adf5b04ea5def sprers.eu MD5: ad3de5ea5dc1bfdf2c7c sprers.eu MD5: 96ddf6db64f36f1a8b2aee sprers.eu MD5: 0c3dc1bebeffbafcf sprers.eu Description: sprers.eu MD5: fc1d7c90cbf8ddc sprers.eu Description: TextureSheeter MD5: dfd7fdfceace32d7e21a sprers.eu MD5: eccfb71e81cc9b34cd8c4 sprers.eu Publisher: NVIDIA Name: NVIDIA Cg Runtime Description: Cg Core Runtime Library MD5: 89d7cdccea67cc4e5c sprers.eu Publisher: Firelight Technologies Name: FMOD Description: FMOD Ex Sound System MD5: ec9e5fbc82d8f7f5e2c1ecd libeaydll Publisher: The OpenSSL Project, sprers.eu Name: The OpenSSL Toolkit Description: OpenSSL Shared Library MD5: 3aadaf96aebccdeff0
When you have Torchlight II error then we strongly recommend that you run an error message scan.
This article provides advice that tells you the best way to successfully treat your Microsoft Windows Torchlight II error messages both by hand and / or automatically. Added to that, this article will allow you to diagnose any common error alerts associated with Torchlight II error code you may be sent.
The Torchlight II error message is the Hexadecimal data format of the error message generated. It’s the normal error message format utilized by Microsoft Windows and other Microsoft Windows compatible applications and driver manufacturers.
This particular code can be used by the supplier to identify the error made. This unique Torchlight II error code features a numeric value and a practical description. Occasionally the error code could have more variables in Torchlight II formatting .This further number and letter code are the location of the storage regions in which the instructions are stored at the time of the error code.
Typically, the Torchlight II error message may be brought on by Windows system file damage. Missing system data files can be a real risk to the health and wellbeing of any pc.
There are numerous events which can have resulted in file errors. An unfinished installation, an unfinished file erasure, bad deletion of applications or equipment. It can also be brought about if the laptop or desktop is contaminated with a trojan or spyware attack or through a poor shutdown of the computer system. Any one of the preceeding actions can end up in the removal or data corruption of Windows system files. This damaged system file will cause absent and wrongly linked documents and archives essential for the proper operation of the program.
There are 2 methods in which to resolve Torchlight II error:
2) Click on the Get started button then select Programs, Accessories, System Tools, then select Restore.
3) From the new window, select “Restore my PC to an earlier date” and after that click on Next.
4) Pick the freshest system restore date in the “select a restoration point” list, and then click Next.
5) Then click ‘Next’ within the verification screen.
6) Restart your laptop or desktop whenever the rescue is completed.
Beginner Computer User Fix (totally automatic):
2) Install application and click on Scan button.
3) Press the Fix Errors button in the software when the diagnostic scan is successfully done.
Here is a link to a different Torchlight II repair program you can try if the previous tool doesn’t work.
Uninstall)
If sprers.eu is missing or corrupted, it can impact many applications, including the operating system, which can prevent you from doing your job or using critical features in critical software.
### Run SFC
The safest way to repair missing or corrupted sprers.eu file caused by your Windows operating system, is to run the built-in System File Checker, which replaces missing or corrupted system files.
To do this, right-click the Start button on your Windows 10 computer to open the WinX menu and click the Command Prompt (Admin) link.
In the CMD window, copy the following command and press Enter :
sfc /scannow
The scan may take 10 minutes, and if it is successfully completed, you must restart your PC. Running sfc /scannow in safe mode or at startup can give better results.
### Update drivers
Sometimes, you’ll get a missing sprers.eu file error while using hardware, such as a printer. This error can be due to an older version of the driver that is not compatible with the updated .dll file, so the printer is looking for a wrong .dll file and can’t find it.
Update your device’s drivers to see if this fixes the problem.
### Startup repair
Startup repair is another way to restore all .dll files like sprers.eu to their original working condition. However, this fix can cause problems in other programs, especially if a program has updated the .dll files.
In most tutorials and guides, authors warn their readers not to download missing sprers.eu files from random and unusable websites that could provide them with malware. This is not without reason, of course. The truth is that the Internet is full of websites that promise users to solve their problems by opening certain applications or programs as soon as possible. Unfortunately, very few can really meet your expectations.
Although less common, a potentially much worse problem is that DLLs that you download from sources other than the provider can sometimes be loaded with viruses or other malware that can infect your PC. This is especially true for websites that are not too careful about where their files come from. And it's not as if these sites will do anything to tell you about their high-risk sources.
Fortunately, the process of installing sprers.eu is quite simple. In short, all you have to do is copy the original DLL file into C:\Windows\System Once the .DLL has been copied, run the following command: regsvr32 sprers.eu and your .DLL will be successfully installed.
The only way to ensure that you get a stable, up-to-date and clean sprers.eu is to get it from the source from which it comes.
(optional offer for Reimage - Website
## Torchlight
### A way to uninstall Torchlight from your computer
This web page is about Torchlight for Windows. Here you can find details on how to uninstall it from your PC. It is written by JoWooD. Take a look herewhere you can find out more on JoWooD. Torchlight is normally installed in the C:\Program Files (x86)\JoWooD\Torchlight directory, however this location may differ a lot depending on the user's choice when installing the application. Torchlight's full uninstall command line is sprers.eu /I{4F64A46DFAEADA5F6}. Torchlight's primary file takes around MB ( bytes) and is called sprers.eu
Torchlight installs the following the executables on your PC, occupying about MB (bytes) on disk.
• sprers.eu ( MB)
The current web page applies to Torchlight version only. Click on the links below for other Torchlight versions:
Torchlight has the habit of leaving behind some leftovers.
Directories left on disk:
• C:\Program Files (x86)\JoWooD\Torchlight
The files below remain on your disk when you remove Torchlight:
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\D3DX9_dll
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\icons\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\JoWood sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\msvcpdll
• C:\Program Files (x86)\JoWooD\Torchlight\msvcrdll
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\music\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Plugin_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Plugin_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Plugin_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\programs\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\programs\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\programs\sprers.eum
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\RenderSystem_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\RenderSystem_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\steam_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Torchlight - szybki sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\Torchlight_PL_sprers.eu
• C:\Program Files (x86)\JoWooD\Torchlight\translations\sprers.eu
Many times the following registry keys will not be cleaned:
• HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products\D64A46F47FEA2A13DA6F
• HKEY_LOCAL_MACHINE\Software\JoWooD\Torchlight
Use sprers.eu to delete the following additional registry values from the Windows Registry:
• HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products\D64A46F47FEA2A13DA6F\ProductName
### How to erase Torchlight using Advanced Uninstaller PRO
Torchlight is an application by JoWooD. Some people choose to erase it. Sometimes this can be troublesome because deleting this manually requires some advanced knowledge regarding removing Windows programs manually. One of the best QUICK approach to erase Torchlight is to use Advanced Uninstaller PRO. Here is how to do this:
1. If you don't have Advanced Uninstaller PRO already installed on your system, add it. This is good because Advanced Uninstaller PRO is one of the best uninstaller and general utility to clean your computer.
2. Start Advanced Uninstaller PRO. Take some time to get familiar with Advanced Uninstaller PRO's design and wealth of features available. Advanced Uninstaller PRO is a powerful package of tools.
3. Click on the General Tools category
4. Click on the Uninstall Programs feature
5. A list of the programs existing on your computer will be made available to you
6. Navigate the list of programs until you locate Torchlight or simply activate the Search feature and type in "Torchlight". If it is installed on your PC the Torchlight application will be found automatically. When you click Torchlight in the list of applications, some information about the program is available to you:
• Star rating (in the lower left corner). The star rating tells you the opinion other people have about Torchlight, from "Highly recommended" to "Very dangerous".
• Reviews by other people - Click on the Read reviews button.
• Details about the application you want to uninstall, by pressing the Properties button.
7. Press the Uninstall button. A confirmation dialog will come up. Confirm the removal by clicking the Uninstall button. Advanced Uninstaller PRO will uninstall Torchlight.
8. After removing Torchlight, Advanced Uninstaller PRO will ask you to run a cleanup. Press Next to proceed with the cleanup. All the items of Torchlight that have been left behind will be found and you will be able to delete them. By removing Torchlight with Advanced Uninstaller PRO, you can be sure that no registry entries, files or folders are left behind on your computer.
Your PC will remain clean, speedy and able to serve you properly.
### Geographical user distribution
Users that installed Torchlight:
• Windows Vista ()
• Windows 7 ()
• Windows XP ()
• Windows ()
Software Application
### Disclaimer
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# Coefficient In A Septic Expansion
What is the coefficient of $$x^3$$ in the expansion of $$(x+2)^7$$?
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# Simple lagrangian problem
aaaa202
## Homework Statement
A uniform thin disk rolls without slipping on a plane and a force is being applied at its center parallel to the plane. Find the lagrangian and thereby the generalized force.
## Homework Equations
Lagranges equation.
## The Attempt at a Solution
This is my first ever exercise of this kind. We first note that U=0 so the lagrangian is simply L=T. We then want to express the kinetic energy T in terms of coordinates, which contain the constraints of the motion implicitly. Therefore we should use polar coordinates. Correct so far?
We then get:
L = T = ½m($\omega$2r2) (1)
And now lagranges equation says:
d/dt[dT/dqj'] - dT/dqj = Qj
where Qj is the generalized force. There is for this motion one equation of the above kind - one for theta and one for r.
Should I now just differentiate with respect to r and $\theta$ and make two separate equations of the above kind of which I can find the components of the generalized force?
I just don't get anything very sensible when I differentiate the expression for L above with the two variables, and when my teacher did it I think he just differentiated with respect to x - why is that? Shouldn't you use the generalized coordinates?
Homework Helper
Gold Member
This is my first ever exercise of this kind. We first note that U=0 so the lagrangian is simply L=T. We then want to express the kinetic energy T in terms of coordinates, which contain the constraints of the motion implicitly. Therefore we should use polar coordinates. Correct so far?
We then get:
L = T = ½m($\omega$2r2) (1)
This is what you would get for a disk that was freely spinning subject to no external forces. You need to include the facts that there is a force being applied to the center of the disk,parallel to the plane (what does that mean for the disk, will it only spin or will it have translational motion as well?) and that the disk rolls without slipping (this should give you some relationship between the motion of the center of the disk, and the angular speed of the disk)
aaaa202
oh yes right.
So T=½Mv2 + ½I$\omega$2 = ½(M$\omega$2R2 + I$\omega$2)
The translational plus rotational kinetic energy. Do I need this? For rolling without slipping v=$\omega$R but I am not sure where to use this.
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aaaa202
hey man, is the above correct?
Staff Emeritus
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