anchor stringlengths 0 150 | positive stringlengths 0 96k | source dict |
|---|---|---|
Number of phrases of LZ compression | Question: It is known that for the number $c(n)$ of phrases / tupel of the LZ compression for binary words of length $n$ the following relation holds:
$$c(n)\leq\frac{n}{(1-\epsilon_n)\log_2 n}$$
With $\epsilon_n\to 0$ for $n\to\infty$.
The proof is made in Thomas & Cover: Elements of Information Theory (Lemma 12.10.1, page 320 in the linked chapter).
I tried to generalize it to an alphabet of size $k$ by adjust the proof step by step, but I failed. So, my question:
How can I prove that the number $c(n)$ of phrases / tupel of the LZ compression is bounded by
$$c(n)\leq\frac{n}{(1-\epsilon_n)\log_k n}$$
for all words of length $n$ over an alphabet of size $k$ with $\epsilon_n\to0$ for $n\to\infty\;?$
Answer: You don't need to redo the proof for this, simply note that $n$ symbols of an alphabet of size $k$ can be represented with $n \log_2(k)$ bits. The Lempel-Ziv bound is then:
$\mbox{# phrases} \leq \frac{n log_2 k}{(1-\epsilon_{n \lg k})log_2(n \log_2 k)}$
Dividing numerator and denominator by $\log_2 k$ then gives:
$\mbox{# phrases} \leq \frac{n}{(1-\epsilon_{n \lg k})\left(log_k(n) + \log_2(\log_2(k))/log_2(k)\right)}$
Since $\epsilon_n \longrightarrow 0$ as $n \longrightarrow \infty$, the result follows. | {
"domain": "cs.stackexchange",
"id": 3017,
"tags": "information-theory, data-compression, lempel-ziv"
} |
Reduce frame rate FPS kinect openni_launch | Question:
Hello everybody,
I am running two programs at the same time so the computational cost is too high. Hence, i thought in reducing the frame rate of the kinect. I am using openni_launch and fuerte. Does anyone know how to reduce the FPS or whether it is possible?
Thank you very much!
Antonio
Originally posted by anto1389 on ROS Answers with karma: 106 on 2013-02-05
Post score: 1
Answer:
You can skip frames to reduce frame rate.
Write this line in the terminal
set param name="camera/driver/data_skip" value="10"
and then run
roslaunch openni_launch openni.launch
This will drop 10 frames and output 2-3Hz data, whereas default value is 0 (which output 30 frames/sec without any dropping)
Originally posted by usman with karma: 81 on 2013-03-14
This answer was ACCEPTED on the original site
Post score: 2
Original comments
Comment by FBernuy on 2013-04-11:
I tried this and didn't work. Instead I used dynamic_reconfigure with the openni running. Here is the command I used: "$ rosrun dynamic_reconfigure dynparam set /camera/driver data_skip 9" | {
"domain": "robotics.stackexchange",
"id": 12747,
"tags": "ros, kinect, ros-fuerte, rate, openni-launch"
} |
Can't publish or echo topics with custom message types from command line | Question:
Hello. I have starting to migrate from ROS1 to ROS2 and have encountered some issues trying to use the topic tools in the command line. I can use the "ros2 topic" tools just fine with message types that came installed with ROS2 humble (std_msgs, etc.). However, I discovered that some of these tools are not working for me for a package I've been porting to ROS2 that contains and uses custom-defined messages. The package which includes the custom messages builds just fine and runs, but I can't call "ros2 topic echo" or "pub" for the topics with the types defined in that package (but work fine on other types).
I've tried to follow this example as closely as possible, and present a minimal package below which replicates this issue for me. The error text when trying to call "ros2 topic pub/echo" (after sourcing the workspace) is displayed at the bottom of my question.
test_msgs/msg/TestMessage.msg
std_msgs/Int16 data
test_msgs/CMakeLists.txt
cmake_minimum_required(VERSION 3.8 FATAL_ERROR)
project(test_msgs)
set(CMAKE_CXX_STANDARD 17)
find_package(ament_cmake REQUIRED)
find_package(rosidl_default_generators REQUIRED)
find_package(std_msgs REQUIRED)
set(MSG_FILES "msg/TestMessage.msg")
rosidl_generate_interfaces(${PROJECT_NAME} ${MSG_FILES} DEPENDENCIES std_msgs)
ament_export_dependencies(rosidl_default_runtime)
ament_package()
test_msgs/package.xml
<package format="3">
<name>test_msgs</name>
<version>0.0.0</version>
<description>No</description>
<maintainer email="no@no.no">No</maintainer>
<license>Test</license>
<buildtool_depend>ament_cmake</buildtool_depend>
<buildtool_depend>rosidl_default_generators</buildtool_depend>
<exec_depend>rosidl_default_runtime</exec_depend>
<test_depend>ament_lint_common</test_depend>
<member_of_group>rosidl_interface_packages</member_of_group>
<export>
<build_type>ament_cmake</build_type>
</export>
</package>
After building, the built interface shows up using the ros2 interface tool:
ros2 interface list | grep test
returns:
pendulum_msgs/msg/RttestResults
test_msgs/msg/TestMessage
as expected. I can also show the fields of the message from the command line without error:
ros2 interface show test_msgs/msg/TestMessage
returns:
int16 data
as expected.
I can publish a topic with a type from the nominal ROS2 distribution:
ros2 topic pub /test std_msgs/Int16 "data: 0"
publisher: beginning loop
publishing #1: std_msgs.msg.Int16(data=0)
However, I get this error when trying to publish a topic with my custom message (after sourcing the workspace, of course):
ros2 topic pub /test test_msgs/msg/TestMessage "data: {data: 0}"
Traceback (most recent call last):
File "/opt/ros/humble/local/lib/python3.10/dist-packages/rosidl_generator_py/import_type_support_impl.py", line 46, in import_type_support
return importlib.import_module(module_name, package=pkg_name)
File "/usr/lib/python3.10/importlib/__init__.py", line 126, in import_module
return _bootstrap._gcd_import(name[level:], package, level)
File "<frozen importlib._bootstrap>", line 1050, in _gcd_import
File "<frozen importlib._bootstrap>", line 1027, in _find_and_load
File "<frozen importlib._bootstrap>", line 1004, in _find_and_load_unlocked
ModuleNotFoundError: No module named 'test_msgs.test_msgs_s__rosidl_typesupport_c'
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/opt/ros/humble/bin/ros2", line 33, in <module>
sys.exit(load_entry_point('ros2cli==0.18.6', 'console_scripts', 'ros2')())
File "/opt/ros/humble/lib/python3.10/site-packages/ros2cli/cli.py", line 89, in main
rc = extension.main(parser=parser, args=args)
File "/opt/ros/humble/lib/python3.10/site-packages/ros2topic/command/topic.py", line 41, in main
return extension.main(args=args)
File "/opt/ros/humble/lib/python3.10/site-packages/ros2topic/verb/pub.py", line 222, in main
return main(args)
File "/opt/ros/humble/lib/python3.10/site-packages/ros2topic/verb/pub.py", line 240, in main
return publisher(
File "/opt/ros/humble/lib/python3.10/site-packages/ros2topic/verb/pub.py", line 275, in publisher
pub = node.create_publisher(msg_module, topic_name, qos_profile)
File "/opt/ros/humble/local/lib/python3.10/dist-packages/rclpy/node.py", line 1290, in create_publisher
check_is_valid_msg_type(msg_type)
File "/opt/ros/humble/local/lib/python3.10/dist-packages/rclpy/type_support.py", line 35, in check_is_valid_msg_type
check_for_type_support(msg_type)
File "/opt/ros/humble/local/lib/python3.10/dist-packages/rclpy/type_support.py", line 29, in check_for_type_support
msg_or_srv_type.__class__.__import_type_support__()
File "/home/squid/ws/install/test_msgs/local/lib/python3.10/dist-packages/test_msgs/msg/_test_message.py", line 29, in __import_type_support__
module = import_type_support('test_msgs')
File "/opt/ros/humble/local/lib/python3.10/dist-packages/rosidl_generator_py/import_type_support_impl.py", line 48, in import_type_support
raise UnsupportedTypeSupport(pkg_name)
rosidl_generator_py.import_type_support_impl.UnsupportedTypeSupport: Could not import 'rosidl_typesupport_c' for package 'test_msgs'
The built python package in my workspace seems to have a number of built typesupport packages for test_msgs as well:
/home/squid/ws/install/test_msgs/local/lib/python3.10/dist-packages/test_msgs$ ls
__init__.py
libtest_msgs__rosidl_generator_py.so
msg
__pycache__
_test_msgs_s.ep.rosidl_typesupport_c.c
_test_msgs_s.ep.rosidl_typesupport_fastrtps_c.c
_test_msgs_s.ep.rosidl_typesupport_introspection_c.c
test_msgs_s__rosidl_typesupport_c.cpython-36m-x86_64-linux-gnu.so
test_msgs_s__rosidl_typesupport_fastrtps_c.cpython-36m-x86_64-linux-gnu.so
test_msgs_s__rosidl_typesupport_introspection_c.cpython-36m-x86_64-linux-gnu.so
Thanks in advance for any help. This issue has had me confused all day.
Originally posted by squidonthebass on ROS Answers with karma: 26 on 2023-07-13
Post score: 0
Original comments
Comment by gvdhoorn on 2023-07-14:
Quick comment: I've seen this happen whenever I forget to source the setup.bash (or local_setup.bash) after building a new msg package. Just something to check.
Comment by squidonthebass on 2023-07-14:
Yeah, I have triple checked this, and unfortunately is not the issue.
Answer:
I finally figured out the issue (and a solution) today. The python IDL interfaces for my version of ROS used python3.10. Despite the normal python install on my machine being python3.10, for whatever reason, when I ran colcon build it was finding a spurious python3.6 install, so the python IDL interfaces for the packages in my workspace were being built using that (and were not compatible with the CLI commands). So the IDL products would be under the path /home/user/ws/install/test_msgs/local/lib/python3.10/dist-packages/test_msgs, but the IDL libraries were test_msgs_s__rosidl_typesupport_*.cpython-3.6-*.so instead of *.cpython-3.10*.so.
I did not find a quick way to specify that colcon/cmake explicitly use python3.10, so I fixed this issue by removing python3.6 from my machine, removing the build, install, and log folders, and doing a fresh build.
Originally posted by squidonthebass with karma: 26 on 2023-08-02
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by gvdhoorn on 2023-08-03:
Good sleuthing. Thanks for posting your findings here. | {
"domain": "robotics.stackexchange",
"id": 38455,
"tags": "ros"
} |
Hot air ballon and a sandbag moving at constant velocity | Question: Suppose you are in a hot air balloon with a sandbag that has a certain mass. The hot air balloon is moving upwards at a constant velocity of $15$ $m$.$s^{-1}$. If you throw the sandbag out of the hot air balloon, will the velocity of the hot air balloon change?
I thought that it will increase, because according to Newton's first law, an object will move in uniform motion unless an unbalanced force acts upon it. If the sandbag is released, there will be an unbalanced force. Or am I wrong? Please help.
Answer: Yes. The velocity of the balloon is determined by the buoyant force of the balloon, determined by its effective density and volume balanced against the density of the surrounding air, balanced against the aerodynamic drag of the balloon, which increases with speed.
When you drop a weight, the buoyancy of the balloon increases. This will cause the upward velocity to increase until the drag on the balloon matches the new buoyancy.
This ignores the effect of decreasing atmospheric density with altitude, which will also, by limiting the buoyancy, cause the rate of climb of the balloon to decrease with altitude until a maximum altitude is reached. | {
"domain": "physics.stackexchange",
"id": 22505,
"tags": "homework-and-exercises, newtonian-mechanics"
} |
Confusion about the construction of the rat's mental map | Question: I'm reading the article "A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology" by Y. Dabaghian, F. Mémoli, L. Frank, G. Carlsson
I try to understand the following graph:
In part a) of the graph, we are seeing a bunch of colored points. These points are in the hippocampus of the rat as opposed to the idea that these points are in the plane on which the rat is moving, and so each point is a place cell of the hippocampus that has fired at some moment in some place of the plane on which the rat is moving. Normally there is a huge number of points in this picture but we chose to put only those who fired, those who did not fire are deleted from the picture of part a). Also, each point (which means each place cell) has one color, and two place cells having the same color designate that the two place cells are considered identical and will be treated as a single place cell in the part b) of the figure.
In part b), we record the time at which each point has fired, with each point being represented by a bar on the time axis and all the bars are identical (same height, and same thickness).
In part c) the picture is in the plane on which the rat is moving as opposed to the idea that the picture of part c) is in the hippocampus of the rat. In part c) we are trying to derive the place fields from part b). Deriving the place fields means here that we are deriving the path that the rat has taken. In particular, place fields are in the plane on which the rat is moving and not in the hippocampus, and each place field in the plane is determined by seeing which place cells in the hippocampus has fired at that area of the plane.
Is my understanding correct? I'm not a specialist but I need to understand each detail of this graph because my work depends on it. My confusion comes from the fact that there are two regions here: the hippocampus of the rat and the plane on which the rat is moving and I need to be sure in which region the picture is.
Answer: You have a couple small misunderstandings that I think are making it hard to understand the figure. There is no map of the hippocampus pictured here!
1) Note: this is a schematic figure. These aren't real data, although there are real data that show this pattern. This is meant to be an easy to understand diagram that explains how place cells work.
2) Panel (a) is EXTERNAL SPACE. Essentially it's a "top down" view of a floor that the rat is running around on.
3) Panel (b) shows spike trains for three different cells: theses cells have been arbitrarily color-coded. The hash shows the times that cells 1, 2, or 3 fired spikes. There are just three cells shown in this figure: there aren't any combinations of cells considered one color or multiple cells in one color, just three cells and three colors.
4) Panel (a) is showing how researchers have connected spiking data, like in (b), to the animal's location. The procedure is this:
Start with a blank map of space.
Record from Cell 1. Every time cell 1 fires, mark a blue dot in panel (a) indicating where the animal was when Cell 1 fired.
Record from Cell 2. Every time cell 2 fires, mark a green dot in panel (a).
Record from Cell 3. Every time cell 3 fires, mark a red dot in panel (a).
(the previous steps could be done for many more than 3 cells simultaneously or in sequence; in this example they are just using 3 cells)
5) Panel (c) is in world space, just like in panel (a), and it shows a hypothesized way that the animal could be using the activity of cells 1, 2, and 3 to determine where it is in space. A researcher recording from cells 1, 2, and 3 could also use those recordings to make a guess of where the animal is. If only cell 3 fires within some window of time (an appropriate window is indicated by the outlined ovals in (b) ), and cells 1 and 2 do not, then the best guess is that the animal is in the upper left area that's shaded only red. If all three cells fire, then the best guess is that the animal is in the very center overlapped region of space.
The dashed line shows a hypothetical path the animal might take through it's environment. If the animal took this path, we'd expect to see place cells firing just like they did in panel (b): first only the blue cell, then blue+green, then all three, then red+green, and finally red only.
6) Very importantly: the animal has way way more cells encoding place than just these three. It would be really confusing to plot them all out in discriminable colors like these, but it is this more complex map with thousands of dimensions that gives the animal a good internal representation of its current location.
Hope this helps! | {
"domain": "biology.stackexchange",
"id": 8098,
"tags": "neuroscience, neurophysiology, neurology, neurotransmitter"
} |
sensor_msgs/Range | Question:
I have a simple sonar sensor running to an Arduino Mega ADK. On the Arduino I have the following code patched together from rosserial_arduino tutorials and the code specific to my sensor:
#include <ros.h>
#include <ros/time.h>
#include <sensor_msgs/Range.h>
#include <Ultrasonic.h>
ros::NodeHandle nh;
sensor_msgs::Range range_msg;
ros::Publisher pub_range( "/ultrasound", & range_msg);
char frameid[] = "/ultrasound";
int inMsec;
#define TRIGGER_PIN 48
#define ECHO_PIN 49
Ultrasonic ultrasonic(TRIGGER_PIN, ECHO_PIN);
void setup()
{
nh.initNode();
nh.advertise(pub_range);
range_msg.radiation_type = sensor_msgs::Range::ULTRASOUND;
range_msg.header.frame_id = frameid;
range_msg.field_of_view = 0.1; // fake
range_msg.min_range = 0.0;
range_msg.max_range = 6.47;
}
long range_time;
void loop()
{
long microsec = ultrasonic.timing();
inMsec = ultrasonic.convert(microsec, Ultrasonic::IN);
//publish the adc value every 50 milliseconds
//since it takes that long for the sensor to stablize
if ( millis() >= range_time ){
int r =0;
range_msg.range = inMsec;
range_msg.header.stamp = nh.now();
pub_range.publish(&range_msg);
range_time = millis() + 50;
}
nh.spinOnce();
}
I know it is publishing as rostopic list shows .ultrasound as one of the running topics. As I expect based on the line
range_msg.radiation_type = sensor_msgs::Range::ULTRASOUND;
it is publishing a Range and that is confirmed by running rostopic type ultrasound.
My subscriber, however, refuses to read this because of the Range type. Here's the code:
#!/usr/bin/env python
import rospy
from std_msgs.msg import String
def callback(data):
rospy.loginfo(rospy.get_name() + ": I heard %s" % data.data)
def listener():
rospy.init_node('listener', anonymous=True)
rospy.Subscriber("ultrasound", Range, callback)
rospy.spin()
if __name__=='__main__':
listener()
based on the simple publisher and subscriber tutorials.
However, when I run it, the error message tells me
Traceback (most recent call last):
rospy.Subscriber("ultrasound", Range, callback)
NameError: global name 'Range' is not defined
I tried changing it to rospy.Range and got
rospy.Subscriber("ultrasound", rospy.Range, callback)
AttributeError: 'module' object has no attribute 'Range'
I understand the error, but have no idea how to fix it. Can I get a gentle-ish shove in the right direction?
Originally posted by richkappler on ROS Answers with karma: 106 on 2014-01-03
Post score: 1
Original comments
Comment by mukut_noob on 2016-04-08:
Hello mate, I am thinking of doing the same but as you have included the file Ultrasound.h, I am asking that this file contains the code that gets the raw data from the sensor?
Answer:
Try adding from sensor_msgs.msg import Range to your Python node with the subscriber.
Originally posted by Thomas D with karma: 4347 on 2014-01-03
This answer was ACCEPTED on the original site
Post score: 3
Original comments
Comment by richkappler on 2014-01-03:
That did the trick, thanks for the answer!
Comment by Kellya on 2014-01-04:
It work for me (y)
Comment by mukut_noob on 2016-04-09:
Hello mate, I am thinking of doing the same but as you have included the file Ultrasound.h, I am asking that this file contains the code that gets the raw data from the sensor? | {
"domain": "robotics.stackexchange",
"id": 16565,
"tags": "ros, rosseral-arduino, ros-hydro"
} |
Cloudsim/Softlayer: gzclient fails to launch on OCU | Question:
After running on the local OCU:
. ros.bash
I have shell variables (printenv | grep GAZ)
GAZEBO_MASTER_URI=http://10.0.0.51:11345
GAZEBO_IP=11.8.0.2
The gzclient launch fails, on a machine that can happily run gazebo locally.
Gazebo multi-robot simulator, version 1.8.0
Copyright (C) 2013 Open Source Robotics Foundation.
Released under the Apache 2 License.
http://gazebosim.org
Msg Waiting for master
Msg Connected to gazebo master @ http://10.0.0.51:11345
Msg Publicized address: 11.8.0.2
Exception [RenderEngine.cc:579] unable to find OpenGL rendering system. OGRE is probably installed incorrectly. Double check the OGRE cmake output, and make sure OpenGL is enabled.
Error [Rendering.cc:38] Failed to load the Rendering engine subsystem
unable to find OpenGL rendering system. OGRE is probably installed incorrectly. Double check the OGRE cmake output, and make sure OpenGL is enabled.
Warning [ModelDatabase.cc:117] GAZEBO_MODEL_DATABASE_URI not set
Warning [ModelDatabase.cc:117] GAZEBO_MODEL_DATABASE_URI not set
Warning [ModelDatabase.cc:202] Unable to connect to model database using [//database.config]. Only locally installed models will be available.
Error [parser.cc:99] Unable to load file[]
Warning [parser.cc:499] XML Attribute[version] in element[sdf] not defined in SDF, ignoring.
Error [parser.cc:719] XML Element[model], child of element[sdf] not defined in SDF. Ignoring.[]
Warning [parser.cc:427] Unable to parse sdf element[]
Error [parser.cc:337] parse as sdf version 1.4 failed, should try to parse as old deprecated format
Error [SDF.cc:1646] Unable to parse sdf string[0 0 0.0 0 0 01.0 1.0 1.00 0 0.0 0 0 01.0 1.0 1.0file://media/materials/scripts/gazebo.materialGazebo/Greytrue]
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Error [WindowManager.cc:96] Unable to create the rendering window
Exception [WindowManager.cc:103] Unable to create the rendering window
Qt has caught an exception thrown from an event handler. Throwing
exceptions from an event handler is not supported in Qt. You must
reimplement QApplication::notify() and catch all exceptions there.
terminate called after throwing an instance of 'gazebo::common::Exception'
Originally posted by cga on Gazebo Answers with karma: 223 on 2013-05-28
Post score: 0
Answer:
Looks like you didn't source the usual /usr/share/drcsim/setup.sh on the OCU, which resulted in bad/unset Gazebo/OGRE paths. I've added that to the User Guide and opened a ticket to add that line to the generated router/ros.bash.
Originally posted by gerkey with karma: 1414 on 2013-05-28
This answer was ACCEPTED on the original site
Post score: 0 | {
"domain": "robotics.stackexchange",
"id": 3322,
"tags": "cloudsim"
} |
ideas for variable with branching data? | Question: I had no idea how to explain this in the title but anyway... Let's say I have a data points like this:
John, Happy | Greedy | Smart | Funny, 0.8
Ann, Smart | Sad | Funny, 0.6
Joel, Greedy | Prideful | Stupid, 0.2
Where the first part is the name the second is there characteristics and the third is their overall character score (how nice they are to be around or something). Is there a good way to work with this data so that I can work out what the best possible combinations are? Assume I have a large enough data set. There may be say 30 of those characteristics and any person can have any number of them and every characteristic is equally valid to every person.
Hopefully that explains it. Essentially I am want a way to organise the traits so that I can say "smart and happy" make a better combination than "sad and greedy". I also need to be able to asses the ultimate combination and be able to compare any two possible combinations.
Answer: It's a regression machine learning problem. Assuming you have 30 characteristics, one-hot encoded into 30 columns. And your target is the character score, min-max scaled into $[0, 1]$.
So we have X.shape=(None, 30), Y.shape=(None,) (just like what ncasas has stated), thus we can train a regression model using your favorite algorithm (linear regression, random forest, even neural network).
After we have this model working, as each person has and only has 3 characters, we can predict the character score for each character combination one by one. The time complexity is roughly $O(n^3)$. However, $n$ is small in your case, so maybe we can just brute-force every score on every combination. That's what you want. | {
"domain": "datascience.stackexchange",
"id": 1452,
"tags": "machine-learning, dataset, statistics"
} |
Validity of the sudden/diabatic approximation | Question: The Schrodinger equation is given by
$$i\hbar\ \frac{\partial}{\partial t}\ \mathcal{U}(t,t_{0})=H\ \mathcal{U}(t,t_{0}),$$
where $\mathcal{U}(t,t_{0})$ is the time evolution operator for evolution of some physical state $|\psi\rangle$ from $t_0$ to $t$.
Rewriting time $t$ as $t=s\ T$, where $s$ is a dimensionless parameter and $T$ is a time scale, the Schrodinger equation becomes as
$$i\ \frac{\partial}{\partial s}\ \mathcal{U}(t,t_{0})=\frac{H}{\hbar/T}\ \mathcal{U}(t,t_{0})=\frac{H}{\hbar\ \Omega}\ \mathcal{U}(t,t_{0}),$$
where $\Omega \equiv 1/T$.
In the sudden/diabatic approximation, $T \rightarrow 0$, which means that $\hbar\ \Omega \gg H$.
Are we allowed to redefine $H$ by adding or subtracting an arbitrary constant?
How does this introduce some overall phase factor in the state vectors?
Why does this imply that $\mathcal{U}(t,t_{0})\rightarrow 1$ as $t\rightarrow 0$?
How does this prove the validity of the sudden approximation?
Answer: Note: This is not a complete answer. However the essence of sudden approximation is as follows.
The sudden approximation is valid if the Hamiltonian varies drastically in a time interval that is very small compared to that required for the system to have a transition in between the corresponding eigen states.
The above time evolution equation of the time evolution operator has a solution that can be approximated as
$$\mathcal{U}(t,t_o)=1-\frac{i}{h}\int_{t_0}^{t}H(t')dt'$$
When you parametrize it in terms of $s$,
$$\mathcal{U}(s)=1-\frac{i}{h}T\int_{0}^{s}H(s')ds'$$
In the limit $T\longrightarrow 0$, we have $\mathcal{U}(s)=1$. Hence for $T\longrightarrow 0$
$$\vert \alpha,t_o;t\rangle=\lim_{T\to 0} \mathcal{U}(t,t_o)\vert\alpha,t_o\rangle=1\vert\alpha,t_o\rangle=\vert\alpha,t_o\rangle$$
i.e., the system remains in the previous eigen ket. The system do not have enough time to adjust to the change as the Hamiltonian suffers a very rapid change. So, in the very small interval of time, $H(t_0)$ changes to $H(t)$. But the system remains in the eigen state of $H(t_0)$, which, in general, need not be the eigen state of the evolved Hamiltonian. Now, how to define the "rapidness" (or, as you asked, when this approximation is valid)?
If $E_a$ and $E_b$ represent the energy eigen values of the Hamiltonian at the instants $t_0$ and $t$ respectively, then the change in the energy levels, $E_{ab}=\hbar\omega_{ab}$. If $T<<2\pi/\omega_{ab}$, then this approximation is valid. | {
"domain": "physics.stackexchange",
"id": 35455,
"tags": "quantum-mechanics, approximations"
} |
ML Retraining project | Question: Tear me to shreds.
The class RandomForestRetrainer will be used to retrain a machine learning algorithm. It has functionality for taking in a directory containing malware or benignware files and splitting them into training and testing sets, creating statistics from these files, creating concatenated mw/bw training/testing stat files, balancing the mw count with bw count via a reduction algorithm, and finally sending them to the ML classifier for training.
p.s. let me know if you want to see code from the other classes
import os
import datetime
from retraining.StatsFile import StatsFile
from retraining.Dataset import Dataset
from retraining.Partitioner import Partitioner
from retraining.GridBasedBalancingRandom import GridBasedBalancingRandom
from retraining.Classifier import Classifier
import config
class RandomForestRetrainer(object):
def __init__(self, previous_mw_dataset=None,
previous_bw_dataset=None):
self.mw_datasets = []
self.bw_datasets = []
self.malware = None
self.benignware = None
self.data_folder = self._initialize_data_folder()
self.balancer = GridBasedBalancingRandom()
self.classifier = Classifier(self.data_folder)
if previous_mw_dataset is not None:
if type(previous_mw_dataset) is not Dataset:
raise TypeError("one or more arguments not of type Dataset")
self.mw_datasets.append(previous_mw_dataset)
if previous_bw_dataset is not None:
if type(previous_bw_dataset) is not Dataset:
raise TypeError("one or more arguments not of type Dataset")
self.bw_datasets.append(previous_bw_dataset)
def add_malware_dataset(self, path):
if type(path) is not str:
raise TypeError("path must be a string")
dataset = self._build_dataset_from_path(path, is_malware=True)
self.mw_datasets.append(dataset)
def add_benignware_dataset(self, path):
if type(path) is not str:
raise TypeError("path must be a string")
dataset = self._build_dataset_from_path(path, is_malware=False)
self.bw_datasets.append(dataset)
def malware_count(self):
return self._count_files_in_datasets(self.mw_datasets)
def benignware_count(self):
return self._count_files_in_datasets(self.bw_datasets)
def concatenate_stat_files(self):
if not self.mw_datasets and not self.bw_datasets:
raise RuntimeError("No datasets have been added")
mw_train, mw_test, bw_train, bw_test = self._create_concatenated_stat_files()
self.malware = Dataset(mw_train, mw_test, is_malware=True)
self.benignware = Dataset(bw_train, bw_test, is_malware=False)
def balance_datasets(self):
if not self.malware and not self.benignware:
raise RuntimeError("Concatenated stat files have not been created")
self.balancer = GridBasedBalancingRandom()
self.balancer.set_malware_dataset(self.malware)
self.balancer.set_benignware_dataset(self.benignware)
self.balancer.balance()
def train(self):
if not self.malware and not self.benignware:
raise RuntimeError("Concatenated stat files have not been created")
self.classifier.add_training_data(self._get_malware_training_stats_path())
self.classifier.add_training_data(self._get_benignware_training_stats_path())
return self.classifier.train()
def run_test_metrics(self):
if not self.malware and not self.benignware:
raise RuntimeError("Concatenated stat files have not been created")
self.classifier.add_testing_data(self._get_malware_testing_stats_path())
self.classifier.add_testing_data(self._get_benignware_testing_stats_path())
return self.classifier.test()
'''
Private
'''
def _initialize_data_folder(self):
data_folder = os.path.join(config.BASE_DATA_FOLDER,
datetime.datetime.now().isoformat())
if not os.path.isdir(config.BASE_DATA_FOLDER):
os.makedirs(config.BASE_DATA_FOLDER)
os.makedirs(data_folder)
return data_folder
def _build_dataset_from_path(self, path, is_malware):
partitioner = Partitioner(path, self.data_folder)
partitioner.process()
training = StatsFile(partitioner.training_stats_file)
testing = StatsFile(partitioner.testing_stats_file)
return Dataset(training, testing, is_malware)
def _count_files_in_datasets(self, datasets):
training = 0
testing = 0
for dataset in datasets:
training += dataset.training_stats.get_count()
testing += dataset.testing_stats.get_count()
return training, testing
def _create_concatenated_stat_files(self):
mw_train_file = open(self._get_malware_training_stats_path(), 'w')
mw_test_file = open(self._get_malware_testing_stats_path(), 'w')
bw_train_file = open(self._get_benignware_training_stats_path(), 'w')
bw_test_file = open(self._get_benignware_testing_stats_path(), 'w')
for dataset in self.mw_datasets:
self._write_stats_to_file(dataset, mw_train_file, mw_test_file)
for dataset in self.bw_datasets:
self._write_stats_to_file(dataset, bw_train_file, bw_test_file)
mw_train_file.close()
mw_test_file.close()
bw_train_file.close()
bw_test_file.close()
mw_train = StatsFile(self._get_malware_training_stats_path())
mw_test = StatsFile(self._get_malware_testing_stats_path())
bw_train = StatsFile(self._get_benignware_training_stats_path())
bw_test = StatsFile(self._get_benignware_testing_stats_path())
return mw_train, mw_test, bw_train, bw_test
def _write_stats_to_file(self, dataset, training_file, testing_file):
training_file.writelines(dataset.training_stats.get_stats())
testing_file.writelines(dataset.testing_stats.get_stats())
def _get_malware_training_stats_path(self):
return os.path.join(self.data_folder, config.CONCATENATED_MALWARE_TRAINING_STATS)
def _get_benignware_training_stats_path(self):
return os.path.join(self.data_folder, config.CONCATENATED_BENIGNWARE_TRAINING_STATS)
def _get_malware_testing_stats_path(self):
return os.path.join(self.data_folder, config.CONCATENATED_MALWARE_TESTING_STATS)
def _get_benignware_testing_stats_path(self):
return os.path.join(self.data_folder, config.CONCATENATED_BENIGNWARE_TESTING_STATS)
Answer: My knowledge of machine learning is a rounding error, so I can’t assess the accuracy of the code. I can provide some feedback on the general programming quality:
There are no comments or documentation. None, nada, zilch. This program would be significantly improved if there were some comments or docstrings, so that I could tell what the code was supposed to do. Explaining the motivation behind the code will make it much easier to read, review and maintain.
You have a lot of checks of the form:
if type(foo) is not bar:
raise TypeError("foo is not of type bar")
One potential risk here is that you don’t cater for inheritance. Suppose I have a subclass of bar called girder. If I pass in a variable of type girder, it will raise a TypeError, even though it probably supports the same interface as bar and is probably fine.
The alternative is to use
if not isinstance(foo, bar):
raise TypeError("foo is not of type bar or of a subclass of bar")
This answer on Stack Overflow explains the difference between type() and isinstance() quite well. I’m not saying you should definitely use one or the other, but unless I had a good reason I’d usually use isinstance().
You add the balancer attribute to the class in the balance_datasets() method. This is sometimes frowned upon – even if you initialise it to None, it’s good to declare all your attributes up front in the constructor. It makes it easier to find out what sort of attributes your class might have.
The one docstring in the file (“private”) is incorrect. Strictly speaking, these are protected methods, not private.
Python doesn’t have access control for methods and attributes. The rules are enforced by convention, and everybody is expected to behave sensibly (“we’re all consenting adults”). https://stackoverflow.com/a/797814
The _initialize_data_folder() method is subject to a race condition. If the base data folder doesn’t exist, but is created between your if statement and the os.makedirs() call, you’ll throw an OSError.
A better approach is to pass the exist_ok method to os.makedirs(), which will suppress the error if the folder already exists.
You have a bunch of methods that start with the word “get”. It would be more Pythonic to decorate these with @property and use them as attributes.
In the _create_concatenated_state_files() method, you should really use with when opening files:
with open(self.malware_training_stats_path, 'w') as mw_train_file,
open(self.malware_testing_stats_path, 'w') as mw_test_file:
for dataset in self.mw_datasets:
self._write_stats_to_file(dataset, mw_train_file, mw_test_file)
This ensures that the file is closed correctly, even if the body throws an exception, and ensures the close() call cannot be forgotten or omitted. | {
"domain": "codereview.stackexchange",
"id": 15864,
"tags": "python, machine-learning"
} |
rosdep and ROS2? | Question:
Can anyone tell me the status of rosdep with regards to ROS2? I'm a little confused by the ROS2 from-source guide since it actually does use rosdep, but only after installing a ton of dependencies by hand. Contrast that with the same guide for ROS1, which only installs enough to get rosinstall files and merge them into a workspace before using rosdep to get all the dependencies.
Originally posted by kyrofa on ROS Answers with karma: 347 on 2018-12-14
Post score: 1
Answer:
The instructions explicitly install dependencies not covered by rosdep keys in ROS packages, e.g. build-essential, cmake, and some tools. That is pretty similar to the ROS 1 instructions in the first section "Installing bootstrap dependencies".
In ROS 2 we additionally need to install a few pip packages just because the available Debian packages are too old.
Anything beyond that is coming in via rosdep - as in ROS 1.
Originally posted by Dirk Thomas with karma: 16276 on 2018-12-14
This answer was ACCEPTED on the original site
Post score: 3 | {
"domain": "robotics.stackexchange",
"id": 32169,
"tags": "ros2, rosdep"
} |
smoothing the robot poses inbetween two known poses | Question: I have a set of N robot poses between point A and B. I use a global localization technique to estimate poses at point A and B. As a result, I have a new corrected pose B'. Please see the figure below.
Considering the poses A and B' are now fixed, how do I smooth out the in-between poses such that there is a smooth transition between A and B'? I know the relative poses between each node in the white trajectory. Please help me formulate this problem. Is this a graph optimization problem? or is there any other simple approach for smoothing out the jump?
Answer: You are right. That is absolutly graph optimization problem. Sorry for the answers above but you don't need spline or acceleration for this.
The graph optimization will find 5 poses above in your figure that reduce your sensor observation error at B as well as all the other inter poses. Graph optimization usually includes constraints on relative poses. That does exactly do the job you want. | {
"domain": "robotics.stackexchange",
"id": 1794,
"tags": "mobile-robot, slam, pose"
} |
The climatological variance of albedo, soil moisture in weather models | Question: Looking at WRF currently but I am sure this applies to most weather models there is a file (specifically LANDUSE.TBL) that specifies USGS derived albedo, soil moisture and other parameters on a biannual basis - one for summer and one for winter.
Why would not these parameters vary on a more seasonal basis and/or on a annual basis? Why are these these variables assumed to be constant? Would not changing vegetation or land cover modifications affect these values on a regional basis as well as their impact on regional climate?
Also would it make sense to model these values on a regional basis after deriving them from remote sensing as indicated in the below mentioned article http://web.maths.unsw.edu.au/~jasone/publications/evansetal2012a.pdf
Answer: WRF model development is done in such a way that users can run the model independently before you start adding more complex options to ingest observations. There is even an "ideal" mode that new users can take advantage of to learn how the system works (not for simulating real Earth situations). In "real" mode, there are typically two types of simulations done: a forecast or a retrospective (historical) simulation. It's important to have real observations ingested into a retrospective simulation, since the intent is to model the event as best you can. However, this is not possible in forecast mode, since the observations do not yet exist. So, it is important to have default lookup tables that characterize your unknowns.
Regarding the values in the LANDUSE.tbl, there are many groups that use the monthly MODIS-derived values to ingest into their simulations that replace some of these values. A "summer" and "winter" lookup table is provided for users in WRF, but those defaults are not appropriate for the best retrospective weather simulations. Forecasting, on the other hand, can use old satellite data (MODIS land-surface data is several days if not weeks old by the time it is processed) but that has error just as a seasonal average would. The values in the LANDUSE.tbl (except surface roughness) will get overwritten with the VEGPARM.TBL values if you use Noah or the RUC Land Surface Model (LSM). Noah uses monthly values as far as I know. RUC might write values on its own... not really sure if it uses the VEGPARM.TBL or not. I'm sure there are experienced WRF modelers out there that can give you more detailed information, e.g. on the WRF modelers forum. | {
"domain": "earthscience.stackexchange",
"id": 390,
"tags": "atmosphere-modelling, climatology, mesoscale-meteorology, wrf"
} |
Ideal gas law, theory vs reality | Question: I am trying to get an idea of the amount of hydrogen that I can store in some pressurized steel tanks underground.
Based on the ideal gas law PV=nRT
I did a simple calculation
pressure = 200bar
volume = 2000Liters
temp = 25C
My results were about
16136.7 moles of hydrogen
1 mole of any gas is about 22.4 liters but that's at standard temperature and pressure.
At these elevated pressure it should be about 361,671 liters?
Answer: Have a look at the following:
https://industry.airliquide.us/volume-compressed-gas-cylinder
Based on this, if you assume a gas cylinder of 47 litres (standard size) at 200 bar fill pressure, you have:
$P_1 V_1 = P_2 V_2$
where:
$P_1$ = 200 bar (above atmospheric pressure) = 201.325 bar (absolute pressure)
$V_1$ = 47 $l$
$P_2 = P_{atm}$ = 1.01325 bar (absolute pressure)
$V_2$ is what you're trying to determine
You end up with $V_2$ = 9338.6 $l$ approximately. | {
"domain": "engineering.stackexchange",
"id": 2782,
"tags": "thermodynamics, pressure, gas, pressure-vessel, compressed-gases"
} |
Reconstruction of Contiuous - Time Signals | Question: In terms of analog signals, we can represent digital signal as :
$$
x[n] \triangleq x_{a}(nT) = \int_{-\infty}^{\infty}X_{a}(f) \, e^{j2\pi f nT} \ \mathrm{d}f
$$
While if we focused on the integral on the right side and according to the Digital Signal Processing by John Proakis, chapter 6.1, we can rewrite it into :
$$
\int_{-\infty}^{\infty}X_{a}(f) \, e^{j2\pi f nT} \ \mathrm{d}f = \sum_{k=-\infty}^{\infty} \int_{(k-1/2)F_{s}}^{(k+1/2)F_{s}}X_{a}(f) \, e^{j2\pi nf/F_{s}} \ \mathrm{d}f
$$
where $ F_{s} \triangleq \frac1T $.
My question is how the second equation comes up ? what does the interval of $(k-1/2)F_{s}$ to $(k+1/2)F_{s}$ means ?
Furthermore, it is stated in the book that "observing the $X_{a}(f)$ in the interval of $(k-1/2)F_{s}$ to $(k+1/2)F_{s}$ is identical to $X_{a}(f-kF_{s})$ in the interval of $-F_{s}/2$ to $F_{s}/2$". Is there any explanation or derivation how both things are identical ?
Thank you so much, hope that my question is clear enough
Answer: Because sampled signals Spectrum will have copies of original spectrum at multiples of $f=F_s$. Even if aliasing happened due to choice of $F_s$, the spectrum of sampled signal $x(n.T_s)$ will be periodic in frequency always with period $F_s$. And you can take any one such $k^{th}$ copy or period and integrate from $\frac{k-1}{2}F_s$ to $\frac{k+1}{2}F_s$. Now if you vary $k$ from $-\infty$ to $\infty$, then it is equivalent to integration on LHS.
Key: Sampling at $F_s$ will create a spectrum which is periodic in frequency with period $F_s$. | {
"domain": "dsp.stackexchange",
"id": 8784,
"tags": "sampling, analog-to-digital, digital-to-analog"
} |
Optical waveguide that can displace a 4D light field | Question: Has anyone invented an optical waveguide that can "pipe" a scene from one place to another unaltered? More precisely, I want to displace (and/or rotate) a 4D light field.
An optical waveguide is an EM waveguide engineered to operate at visible wavelengths.
A light field is a computer graphics concept that represents the RGB intensities and directions of photons in a given linear span of a 3D room.
All the light in a room can be described as a 5D light field: the RGB value at each sample along 5 dimensions:
theta (compass bearing)
phi (inclination)
x (+x = right)
y (+y = down)
z (+z = into scene)
A 5D light field sampled along a 3D linear span comes out as still a 5D light field. But a 5D light field sampled along a 2D linear span (such as the aperture of a camera, eye, or display) comes out as a 4D light field.
Thus, this hypothetical "light field waveguide" could also be summarized as "the perfect periscope" or "fiber optics for images". You would be able to use one of these to, e.g. create a window between any two rooms, even if they are miles apart.
Any ideas on how to make one of these? Don't say light-field-camera -> video-streaming -> light-field-display, because I'm already working on that. ;)
Answer: There is some work, pioneered by Nader Engheta and Mario Silveirinha. The basic idea is to make a waveguide out of a medium whose permeability $\varepsilon$ is close to zero, which basically allows a sort of "classical tunneling", since the phase velocity in the medium is very large. Say, transporting a light field unchanged from one end of the waveguide to the other.
It's been experimentally demonstrated for microwaves, but I doubt that it will be possible with visible wavelengths in the immediate future.
Here are some papers that you could read:
Silveirinha & Engheta (2006). Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials. Phys. Rev. Lett. 97, 157403. http://prl.aps.org/abstract/PRL/v97/i15/e157403 (The original paper.)
Liu, Cheng, Hand, Mock, Cui, Cummer, Smith (2008). Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies. Phys. Rev. Lett. 100, 023903. http://prl.aps.org/abstract/PRL/v100/i2/e023903 (Experimental demonstration for microwaves, using metamaterials, i.e. materials with repeated structures that are smaller than the wavelength.)
Edwards, Alu, Young, Silveirinha, Engheta (2008). Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Phys. Rev. Lett. 100, 033903. http://prl.aps.org/abstract/PRL/v100/i3/e033903 (Published only a week after the above paper, this is another experimental demonstration for microwaves taking a different approach. Instead of using metamaterials, they operate the waveguide at its cutoff point. This makes the effect strictly monochromatic, I think, but the waveguide is much simpler and cheaper to make.)
Silveirinha & Engheta (2009). Transporting an image through a subwavelength hole. Phys. Rev. Lett. 102, 103902. http://prl.aps.org/abstract/PRL/v102/i10/e103902 (Theoretical paper that describes transporting what you call a light field.)
Silveirinha & Engheta (2012). Sampling and squeezing electromagnetic waves through subwavelength ultranarrow regions or openings. Phys. Rev. B 85, 085116. http://prb.aps.org/abstract/PRB/v85/i8/e085116 (Latest updates - I haven't kept abreast of any developments after 2009 so I'm not quite sure what's new here.) | {
"domain": "physics.stackexchange",
"id": 4339,
"tags": "optics, quantum-electrodynamics, quantum-optics, geometric-optics, waveguide"
} |
ROS indigo installation fails on Raspberry pi 2 and 3 | Question:
I tried to follow the instructions below to install ROS indego on raspberry pi 2 and 3,
http://wiki.ros.org/ROSberryPi/Installing%20ROS%20Indigo%20on%20Raspberry%20Pi
Both failed. I used latest image from raspberry website.
Raspberry pi 2 failure - Failing while installing liblz4-dev.
apt-get source -b lz4 command just runs for a very long time and gives below error
Read : 66 MB ==> 59.22% ^CMakefile:226: recipe for target 'test-lz4-basic' failed
make[3]: *** [test-lz4-basic] Interrupt
Makefile:98: recipe for target 'test' failed
make[2]: *** [test] Interrupt
debian/rules:47: recipe for target 'override_dh_auto_test' failed
make[1]: *** [override_dh_auto_test] Interrupt
debian/rules:33: recipe for target 'build' failed
make: *** [build] Error 1
dpkg-buildpackage: error: debian/rules build died from signal 2
Raspberry pi 3 failure - Failing during python installation stage,
sudo apt-get install python-pip python-setuptools python-yaml python-distribute python-docutils python-dateutil python-six
Error message
sub-process /usr/bin/dpkg returned an error code (1)
Do we have any recent image of raspbian Jessie with ROS Indigo installed?
Originally posted by VictorAbraham on ROS Answers with karma: 1 on 2016-11-16
Post score: 0
Answer:
Just asking:
Read : 66 MB ==> 59.22% ^CMakefile
That ^, is that a control character (ie: the ctrl in ctrl+c)? I'm asking because make then reports [test-lz4-basic] Interrupt.
Originally posted by gvdhoorn with karma: 86574 on 2016-11-17
This answer was ACCEPTED on the original site
Post score: 0 | {
"domain": "robotics.stackexchange",
"id": 26266,
"tags": "ros"
} |
Commuting operators and their physical interpretation in QM | Question: I'm studying Quantum Mechanics for the first time at the moment and I have a few questions in mind.
So recently, I saw a proof on that if two operators share the same eigenstates is equivalent to the two operators commuting. Furthermore, the physical interpretation of this is apparently that we can know two physical quantities without uncertainty if this holds. Now here comes my question:
can we interpret an operator as an act of "measuring",
and if we conform ourselves to the previous statement, that the order of measuring doesn't matter if the operators commute?
I can sort of see the answer to 2) intuitevly if one of the physical quantities measured is some scaling factor of the one we are looking for, i.e. velocity and momentum (scaling factor as mass)? We could also do the opposite order, meaning we measure momentum, from which velocity can be found. Maybe this is a bad example. since we are also limited by Heisenberg's uncertainty principle, but I hope you get the idea.
I hope I made myself clear enough.
Answer:
can we interpret an operator as an act of "measuring",
Yes, there is a one-to-one mapping between mathematical operators
(more precisely: self-adjoint operators) and physical observables.
However, the act of measuring the observable $A$ on a physical state
is not directly modeled as applying the operator $A$ to the state
$|\psi\rangle$. It is actually more complicated (see for example
Axioms of Quantum Mechanics):
The measured value is any of the eigenvalues $a_k$ of $A$.
The state collapses from $|\psi\rangle$
to the corresponding eigenvector $|k\rangle$ of $A$.
The measurement outcome is not deterministic.
It will yield eigenvalue $a_k$ and eigenvector $|k\rangle$
with probability $|\langle k|\psi\rangle|^2$.
and if we conform ourselves to the previous statement,
that the order of measuring doesn't matter if the operators commute?
Yes. If two operators $A$ and $B$ commute, then you get the same
results when you measure $A$ first and then $B$ as compared
to the other way round.
There are no accuracy restrictions when you measure both $A$ and $B$, and can you do this in any order:
$$\Delta A\ \Delta B \ge 0.$$
If they don't commute (i.e. $[A,B]\ne 0$),
then you have an uncertainty relation
restricting the accuracies of the two measurements
$$\Delta A\ \Delta B \ge \frac{1}{2}\Big|\langle[A,B]\rangle\Big|.$$
So if you measure $A$ precisely first (i.e. $\Delta A=0$)
then you get a completely imprecise measurement for $B$ (i.e. $\Delta B=\infty$),
and vice versa. | {
"domain": "physics.stackexchange",
"id": 97293,
"tags": "quantum-mechanics, operators, heisenberg-uncertainty-principle, commutator, quantum-measurements"
} |
Why do outside charges do not contribute to net flux of a Gaussian Surface? | Question: I don't quite understand why external charges can be ignored when calculating the net flux of a Gaussian surface. I understand that $\nabla \cdot \vec{E}$ of any point charge equals $0$ and I can reason using equations, but I can't find an intuitive physical understanding. Most arguments I have heard mention that all electric field lines that enter a Gaussian surface must then leave it, and so an external charge has no effect on net flux. But doesn't the flux also depend on the magnitude of the field?
For instance, Let's say I had a particle next to a Gaussian sphere and I look at the electric field line which pierces the sphere at its closest point. Wouldn't the field vector's magnitude be greater when it enters the sphere compared to when it exits because it is farther away when it leaves? And by the equation for flux,
$$\int \vec{E} \cdot \mathrm{d}\vec{A} = \int E \cos (\theta) \ \mathrm{d}A$$
which depends on $E$, wouldn't this have an affect on the net flux?
I'm not sure where my misunderstanding of flux is, but I know that I am clearly missing something huge. Perhaps is it that I have to consider all electric field lines and not just a single one? Or am I incorrectly assuming something about the relationship between the magnitude of the field and the flux through the surface?
Answer: If a charge is kept near a sphere, the charge will not affect the flux of the sphere because flux is dependent on magnitude of electric field and area it pass through. So when the field enters the near end of the sphere the magnitude of electric field is high and the surface pass through is low but when the filed comes out the magnitude of electric field is low but the area it pass through is high. Hence, it compensate and don't affect the flux of the sphere. | {
"domain": "physics.stackexchange",
"id": 84308,
"tags": "electrostatics, electric-fields, charge, gauss-law"
} |
good laser scanner/ lidar for 4 wheel robot? | Question: i was wondering what could be a good laser scanner can someone get for as much as 180$ ? i am planning to use it from SLAM to build a map, so this is why i wanted to ask here ? have anyone tried something that gives a good result?
Answer: My suggestion would be to buy a cheap, second-hand, Neato Robotics XV-15 robot vacuum-cleaner and use the LIDAR from that (you may even be able to buy the LIDAR unit separately).
A lot of guides to using the Neato LIDAR for robots have been published. For example this one from Hackaday describes how to use the Neato LIDAR with the Raspberry Pi.
Just type Neato Lidar robot into Google for more (this will also get you lots more useful background information about the LIDAR sensor itself, which is a bonus). | {
"domain": "robotics.stackexchange",
"id": 1551,
"tags": "mobile-robot, lidar, laser, hardware"
} |
The conmutator of the square of Pauli-Lubanski vector and the generators of Poincare group | Question: I'm working on trying to solve the following problem:
Using the following expressión for the square of Pauli-Lubanski vector:$$W^2=-\frac{1}{2}M_{\mu\nu}M^{\mu\nu}P_{\alpha}P^{\alpha}+M^{\mu\nu}M_{\lambda\nu}P_{\mu}P^{\lambda}$$
show that $$[W^2,P_{\sigma}]=0$$
I know that there are other ways to prove the same result; for example, first showing that $[W_{\mu},P_{\nu}]=0$ but I have to use the formula that it gives to me, because It was deduced on the previous exercise.
My calculations are like following; first of all
$$[W^2,P_{\sigma}]=-\frac{1}{2}[M_{\mu\nu}M^{\mu\nu}P_{\alpha}P^{\alpha},P_{\sigma}]+[M^{\mu\nu}M_{\lambda\nu}P_{\mu}P^{\lambda},P_{\sigma}]$$
but, using the properties of conmutator, the conmutation relations of generators of Poincaré Algebra and renaming indexes I obtain, for the first conmutator on the right side, the following:
$$[M_{\mu\nu}M^{\mu\nu}P_{\alpha}P^{\alpha},P_{\sigma}]=(M_{\mu\nu}[M^{\mu\nu},P_{\sigma}]+[M_{\mu\nu},P_{\sigma}]M^{\mu\nu})P_{\alpha}P^{\alpha}=i(M_{\mu\nu}\eta_{\sigma\lambda}(\eta^{\nu\lambda}P^{\mu}-\eta^{\nu\lambda}P^{\nu})+(\eta_{\nu\sigma}P_{\mu}-\eta_{\mu\sigma}P_{\nu})M^{\mu\nu})P_{\alpha}P^{\alpha}=2i(M_{\mu\sigma}P^{\mu}+\eta_{\nu\sigma}P_{\mu}M^{\mu\nu})P_{\alpha}P^{\alpha}$$
On the other hand, for the second conmutator on the right side I obtain the following:
$$[M^{\mu\nu}M_{\lambda\nu}P_{\mu}P^{\lambda},P_{\sigma}]=[M^{\mu\nu}M_{\lambda\nu},P_{\sigma}]P_{\mu}P^{\lambda}=(M^{\mu\nu}[M_{\lambda\nu},P_{\sigma}]+\eta_{\sigma\epsilon}[M^{\mu\nu},P^{\epsilon}])P_{\mu}P^{\lambda}=(M^{\mu\nu}i(\eta_{\nu\sigma}P_{\lambda}-\eta_{\lambda\sigma}P_{\nu})+i\eta_{\sigma\epsilon}(\eta^{\nu\epsilon}P^{\mu}-\eta^{\mu\epsilon}P^{\nu})M_{\lambda\nu})P_{\mu}P^{\lambda}=i(\eta_{\nu\sigma}M^{\mu\nu}P_{\lambda}P_{\mu}P^{\lambda}+P^{\mu}M_{\lambda\sigma}P_{\mu}P^{\lambda})$$
The problem, accoding to me, comes when I try to compare both expressions using again the conmutation relations of Poincare algebra, because I obtain the following expression:
$$\eta_{\nu\sigma}M^{\mu\nu}P_{\lambda}P_{\mu}P^{\lambda}+P^{\mu}M_{\lambda\sigma}P_{\mu}P^{\lambda}=\eta_{\nu\sigma}([M^{\mu\nu},P_{\mu}]+P_{\mu}M^{\mu\nu})P_{\lambda}P^{\lambda}+([P^{\mu},M_{\lambda\sigma}]+M_{\lambda\sigma}P^{\mu})P_{\mu}P^{\lambda}=\eta_{\nu\sigma}(i\eta_{\mu\alpha}(\eta^{\nu\alpha}P^{\mu}-\eta^{\mu\alpha}P^{\nu})+P_{\mu}M^{\mu\nu})P_{\lambda}P^{\lambda}+M_{\lambda\sigma}P_{\mu}P^{\mu}P^{\lambda}-i\eta^{\mu\alpha}(\eta_{\sigma\alpha}P_{\lambda}-\eta_{\lambda\alpha}P_{\sigma})P_{\mu}P^{\lambda}=(M_{\mu\sigma}P^{\mu}+\eta_{\nu\sigma}P_{\mu}M^{\mu\nu}-3iP_{\sigma})P_{\lambda}P^{\lambda}$$
I have tried for three complete days to eliminate the $3iP_{\sigma}$ term, but I couldn't. I have checked all my calculations, and made it many times using other ways, but I couldn't find where the mistake is, or what I'm doing wrong. Could anybody help me, please?. Am I not considering something?
Note: In some steps I used that $M_{\mu\nu}=-M_{\nu\mu}$ :D
.
Answer: You have a subtle and interesting error. In your second commutator, there are four terms, and you thought that the second and fourth are both zero. Only the second is. The second term contains $M^{\mu\nu}P_\nu P_\mu$, and this is indeed zero because $M^{\mu\nu}$ is antisymmetric while $P_\nu P_\mu$ is symmetric. The fourth term contains $P^\nu M_{\lambda\nu}P^\lambda$, but this is not zero; $M$ and $P$ don't commute, so it isn't the contraction of an antisymmetric tensor with a symmetric tensor. After you use the commutation relation to move the $P$'s together, that part will vanish but the extra terms coming from the commutator won't.
I suggest that your calculation would be a bit nicer if you eliminated $\eta$ by simply using it to raise or lower indices. I would also write the contraction of $P$ with itself as $P^2$ whenever I could. Finally, I would use the commutator of $M$ and $P$ to put each of the two commutators in a “standard” form where $M$ is to the left of $P$. If you do this, you should find that the first commutator is $2i(2M_{\mu\sigma}P^\mu+3iP_\sigma)P^2$ and the second commutator is $i(2M_{\mu\sigma}P^\mu+3iP_\sigma)P^2$. Thus -1/2 times the first, plus the second, is zero.
By the way, in the first line of the second commutator you have a typo where the second $M$ in the second term is missing. | {
"domain": "physics.stackexchange",
"id": 60939,
"tags": "homework-and-exercises, special-relativity, operators, commutator, poincare-symmetry"
} |
Return a List based on very similar data | Question: I am rewriting an old VB.NET app in C#. I will not subject you to the old VB.NET code that I am writing (the original method that I have already refactored was over 700 lines long).
The following is what we call On Demand Reports. There is a stored procedure that these objects fill in for us. I don't have a 100% understanding of why most of what I am doing is just static string text but it is.
What I want to do is to find a better way to represent the List<MyObject> (see the embedded comments).
private IEnumerable<MyObject> GetOnDemandInputsBy(int key)
{
var inputs = new List<MyObject>();
//This is actually called 13 times with different parameter variables (the parameter called parameter) and a different static dictionary
inputs.Add(AssembleMyObject(key, "@BeginTime", MyObjectPropertyConstants.BeginTime()));
inputs.Add(AssembleMyObject(key, "@EndTime", MyObjectPropertyConstants.EndTime()));
return inputs;
}
//This method is fine with me. It is just here for context
private static IEnumerable<MyObjectProperty> AssembleMyObjectProperty(Dictionary<string, string> dictionary)
{
return dictionary.Select(item => new MyObjectProperty {PropertyName = item.Key, PropertyValue = item.Value});
}
//I feel like I am passing to many things into this method and its doing to much
private MyObject AssembleMyObject(int key, string parameter, Dictionary<string, string> dictionary)
{
//this is set to 0 in the constructor, I am not sure why the original developers chose 10 for every new object
_displayOrder += 10;
var MyObject = new MyObject
{
DisplayOrder = _displayOrder,
ParameterName = parameter,
QueryKey = key,
};
MyObject.MyObjectProperties.AddRange(AssembleMyObjectProperty(dictionary));
return MyObject;
}
//This seems like a bad idea as well but all the data is static and I created a separate dictionary for each of the parameter types
public class MyObjectPropertyConstants
{
public static Dictionary<string, string> BeginTime()
{
return new Dictionary<string, string>
{
{"stuff", "@BeginTime"},
{"VISIBLE", "TRUE"},
{"CAPTION", "*beginTime"},
{"DISPLAYTYPE", "DATEPICKER"},
{"DATATYPE", "DATE"},
};
}
public static Dictionary<string, string> EndTime()
{
return new Dictionary<string, string>
{
{"Name", "@EndTime"},
{"VISIBLE", "TRUE"},
{"CAPTION", "*EndTime"},
{"DISPLAYTYPE", "DATEPICKER"},
{"DATATYPE", "DATE"},
};
}
}
As previously states this is the refactored version so far. The original code to do the above chunk is 180 lines. The method that I am rewriting is over 700 lines long.
Any Suggestions?
Answer: var inputs = new List<MyObject>();
inputs.Add(AssembleMyObject(key, "@BeginTime", MyObjectPropertyConstants.BeginTime()));
inputs.Add(AssembleMyObject(key, "@EndTime", MyObjectPropertyConstants.EndTime()));
return inputs;
You could rewrite this to make it more DRY using LINQ into:
return new Func<Dictionary<string, string>>[]
{
MyObjectPropertyConstants.BeginTime,
MyObjectPropertyConstants.EndTime
}.Select(f => AssembleMyObject(key, "@" + f.Name, f()).ToList();
var MyObject
Local variables are usually named in camelCase, e.g. myObject.
public static Dictionary<string, string> BeginTime()
Method should be named using verbs, this looks more like a property. Thought making this into a property would make the above LINQ rewrite more difficult.
new Dictionary<string, string>
{
{"stuff", "@BeginTime"},
{"VISIBLE", "TRUE"},
{"CAPTION", "*beginTime"},
{"DISPLAYTYPE", "DATEPICKER"},
{"DATATYPE", "DATE"},
};
Does order matter here? If it does, you shouldn't use Dictionary, since it doesn't guarantee ordering. | {
"domain": "codereview.stackexchange",
"id": 8682,
"tags": "c#"
} |
Custom simulation using Stage | Question:
Hi,
I want to simulate a custom robot using ROS Diamondback. I figured that Stage is the package I should be using for simulation. I have read up the documentation on setting up a .world file for my simulation and have a world file with a robot and the intended simulation arena. However I am stuck as to how to proceed further. I have some code which does controlling/path planning for my robot, but how do I integrate the code with Stage ?
Could someone point me to some documentation / How-tos on this ?
Thanks,
Sagnik
Originally posted by Sagnik on ROS Answers with karma: 184 on 2011-03-08
Post score: 2
Original comments
Comment by Arkapravo on 2011-10-17:
@Sagnik : Have a look, this is primarily gazebo but there is some information on how to use stage/stageros with world files - http://mobotica.blogspot.com/2011/09/using-gazebo.html
Answer:
A good place to start would be to read over the Stage ROS API available on the stage wiki page. In particular, note that Stage publishes an odom topic for odometry information, a base_scan topic for planar laser scans and subscribes to the cmd_vel topic for velocity commands. Stageros also outputs the tf information required to transform laser scans into the odometry frame.
An important thing to keep in mind is that Stage is not a full-on physics simulation so code that does low-level control may not be appropriate to simulate if it is dependent on physical properties of your platform (I'm referring to things like control loops or PIDs that may need gains tuned to the particular robot platform).
Originally posted by Eric Perko with karma: 8406 on 2011-03-08
This answer was ACCEPTED on the original site
Post score: 2 | {
"domain": "robotics.stackexchange",
"id": 5000,
"tags": "ros, simulation, stage, simulator-stage, ros-diamondback"
} |
If a cart hits a wall, does the weight of it affect how it moves, when the center of gravity is constant? | Question: I have a model that represents a bicycle (a wood block with wheels), and I'm balancing the center of gravity so it's the same as a real bike. However, when the center of mass is kept constant, does the weight of it affect the effect torque has on it when it hits a wall?
I'm planning to measure the angle the back wheel bounces up.
Answer: No. When you hit the wall, the bicycle rotates around the front axis. The angular momentum L that you create for an arbitrary number of mass particles is $$L=\Sigma_i(r_i \times m_iv_i) .$$
If you split location r=R+r_i and v=V+v_i with R and V being center of mass location and velocity, respectively, and r_i and v_i deviation from it, then it can be shown that L does not change when the center of mass does not change.
So, the wood block on wheels should work (in theory). | {
"domain": "physics.stackexchange",
"id": 6079,
"tags": "newtonian-mechanics, torque, models, weight"
} |
Filtering a list of vertices that lie inside a cylinder, with and without LINQ | Question: Since I don't know how LINQ works under the hood, I can't decide what version is best to use in term of rapidity of execution. I've done some testing with my testing data (Point Cloud) but I can't see a clear difference between the two. The only thing I know is that the real life data will be a larger Point Cloud so my guess is that the LINQ would be faster but this is only if LINQ doesn't do a for each under the hood. If it's the case, the 2 functions would be the same. What is your advice?
By the way, cylindre is a 3D cylinder and I want to know which point are inside.
Version 1 without LINQ
for (int i = 0; i < fpc.Vertices.Length; i++)
{
if (cylindre.IsPointInside(fpc.Vertices[i]))
listPoint.Add(fpc.Vertices[i]);
}
Version 2, with LINQ
var insidePoint =
from pt1 in fpc.Vertices
where cylindre.IsPointInside(pt1)
select pt1;
foreach (Point3D pt2 in insidePoint)
{
listPoint.Add(pt2);
}
Answer: Under the hood LINQ will iterate over the collection, just as foreach will. The difference between LINQ and foreach is that LINQ will defer execution until the iteration begins.
Performance wise take a look at this blog post. | {
"domain": "codereview.stackexchange",
"id": 7102,
"tags": "c#, performance, linq, comparative-review"
} |
Naming of bicyclo[2.2.1]hept-5-ene-1,4,5,6-tetramethyl-3-bromo-2-ethyl carboxylate | Question:
I've synthesized a molecule (depicted above) using a Diels-Alder reaction, and I can't find it in any database (I used scifinder for my search), so I need advice about the name.
The name I came up with, based on similar structures is bicyclo[2.2.1]hept-5-ene-1,4,5,6-tetramethyl-3-bromo-2-ethyl carboxylate. Is that correct?
Answer: The individual parts of the proposed name are correct; however, their order of citation in the name is wrong.
The name of the parent hydride is ‘bicyclo[2.2.1]hept-2-ene’. Note that the ending ‘ene’ receives the lowest locant possible (here: ‘2’ since the bicyclic ring system is numbered starting with one of the bridgeheads).
The principal characteristic group is expressed by means of a suffix, which yields the name ‘bicyclo[2.2.1]hept-5-ene-2-carboxylate’. Note that now the characteristic group receives the lowest locant possible (here: ‘2’), which
is cited immediately in front of the suffix. Thus, the locant for the ending ‘ene’ in the functionalized parent hydride is changed to ‘5’.
The other substituents are cited as prefixes in substitutive nomenclature: ‘3-bromo-1,4,5,6-tetramethylbicyclo[2.2.1]hept-5-ene-2-carboxylate’
Finally, the name of the ester is formed according to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), by placing the ‘hydroxylic’ component in front of the name.
P-65.6.3.3.1 Monoesters
Monoesters formed from a monobasic acid and a ‘monohydroxylic’ component are named systematically by placing the ‘hydroxylic’ component denoted by an organyl group (alkyl, aryl, etc.) in front of the name of the acid component expressed as an anion derived from the appropriate acid (…).
Therefore, the preferred IUPAC name (PIN) of the compound given in the question is
‘ethyl 3-bromo-1,4,5,6-tetramethylbicyclo[2.2.1]hept-5-ene-2-carboxylate’. | {
"domain": "chemistry.stackexchange",
"id": 5265,
"tags": "organic-chemistry, nomenclature, esters"
} |
The non-renormalizable $\phi^6-$theory as an effective field theory | Question: Let the non-renormalizable $\phi^6$ theory behaves as a low-energy, effective field theory, and works perfectly well below a finite energy (or momentum) scale $\Lambda$ for a system.
In this theory, all the loop diagrams will be finite if the loop momenta are carefully integrated up to $\Lambda$. This implies that there will be no divergences in scattering amplitudes at any order.
Does this theory still require renormalization? If yes, why?
If yes, then instead of saying $\phi^6$ to be a non-renormalizable theory, shouldn't we say that (i) it is renormalizable at low energy but (ii) non-renormalizable at high energies?
Answer: There's a bit of confusion here.
Whenever you work with a QFT you have to able to define it first. It is not enough to just write down diverging integrals and assert that they correspond to transition amplitudes. This doesn't make sense.
So I assume that what you mean is: define a theory with an explicit momentum-scale cutoff $\Lambda$ such that all the integrals are finite. Consider $\Lambda$ just as physical as other constants like mass $m$ and the coupling constant $\lambda$.
There's a whole bunch of issues with this definition. Like, for example,
It isn't clear how to consistently impose momentum constraints on the loop integrals, as we can pass to different loop momenta integration variables for which different constraints have to apply. Note that you don't care about this subtlety when $\Lambda \gg p$.
The theory with a momentum cut-off isn't Lorentz invariant. It simply isn't. You can, however, neglect this Lorentz violations when $\Lambda \gg p$.
The list can go on, but I think I've made my point already. But say that we somehow found relatively satisfactory answers to all of the questions above. What now?
1. Does this theory still require renormalization? If yes, why?
Yes, it does! Renormalization isn't about getting rid of infinities, and it isn't about getting rid of the unphysical $\Lambda$ (though it achieves both of these goals in the mean time). It is about making sense of the results that your theory gives.
Like, for example, you would want to give a particle interpretation to your theory, with an $S$-matrix corresponding to particle scattering. What do you require to give your theory a particle interpretation? One of the requirements is that the 2-point function has a pole when $p^2 = M^2$ with residue 1. This follows directly from normalization of states, and it allows you to talk about interacting particles of mass $M$ which your theory is supposed to describe.
If you calculate this 2-point function to some loop order you will find that both the location and the value of the pole are not $m$ and $1$ as you would've expect naively, but depend on $\Lambda$. But what's it mean? It means that your particles are of mass $M = M(m, \lambda, \Lambda)$ and are generated by a Fock-space operator associated to the physical observable $Z(m, \lambda, \Lambda) \cdot \phi$, not just the field operator $\phi$.
Again, renormalization is about reinterpreting predictions in terms of interacting particles.
2. If yes, then instead of saying $\boldsymbol{\phi^6}$ to be a non-renormalizable theory, shouldn't we say that (i) it is renormalizable at low energy but (ii) non-renormalizable at high energies?
What happens is: the higher-valency correlation functions become highly dependent on $\Lambda$ even in the $\Lambda \gg p$ regime. Physically, your theory becomes pathologically sensible to short-scale fluctuations.
With renormalizable theories we can say that $\Lambda$ is very large and corresponds to the boundary of the domain of applicability of our theory. But the exact details of this boundary aren't relevant for the long-range physics: we can just adopt the limiting value for the higher-valency correlations.
In case of $\phi^6$ in $4d$ though, this is not the case. Instead, we have the following nonrenormalizable behaviour:
The long-range properties of your theory depend explicitly on the details of the cut-off procedure. It can be the value of $\Lambda$, the way you resolve the cutoff ambiguity in the loop momenta integration variables, masses of the Pauli-Villars regularizer fields, etc. The key fact is that - your results depend on something for which you can't really say how it works and if it is physical or not. That's what is bad about nonrenormalizability.
With nonrenormalizable theories you can tweak the theory to give whatever predictions you want by simply changing the cut-off mechanism a bit. Not a lot of predictive power there.
UPDATE: allright, I admit that it is not 100% true. I was trying to make a point in the context of HEP, but once you let go of your ambitions to describe arbitrary high-energy processes, you can actually do something useful with nonrenormalizable theories as well.
For instance, you can fix the perturbation theory order $k$ prior to renormalization, and then simply determine the values of counterterms from experiments. With renormalizable theories this could be done once, i.e. using a fixed finite number of counterterms independent of the perturbation theory order. But nonrenormalizable theories require more and more tweaking and adjustment with increasing order.
Of course one can claim that this is fine, since perturbation expansion is only an assymptoitic series and thus even renormalizable theories can't be solved with an a-priori arbitrary precision using perturbation theory. And it is probably true.
There's another property of nonrenormalizable theories which has to do with Wilsonian renormalization group flow. Effective couplings used in perturbation theory blow up in the ultraviolet regime thus rendering the whole concept of perturbation theory meaningless. Thus we end up with phase transitions in the high-energy regime which we can't describe with perturbation theory.
It is also worth mentioning that such phase transitions aren't specific to nonrenormalizable theories. As a useful example, QED (Quantum Electrodynamics), though renormalizable, has an ultraviolet phase transition (the Landau Pole problem). Renormalizable theories without these phase transition are called asymptotically free.
And asymptotic freedom, together with renormalizability, is enough to ascertain that a HEP theory can be used to make sensible predictions up to whatever energy is associated with the boundary of its domain of validity. This is because the further into the UV you go, the less becomes the coupling, making the asymptotic expansion a better approximation for an even further order in perturbation theory (remember how the closer the coupling is to zero – the more orders of perturbation theory we can trust without worrying about asymptotic expansion blowing up?). | {
"domain": "physics.stackexchange",
"id": 40857,
"tags": "quantum-field-theory, condensed-matter, renormalization, effective-field-theory"
} |
motion model for forward movement | Question: I thought this is a simple and well known problem and therefore there is a lot of literature. But I'm not able to find the correct keywords to google the answer. Maybe instead of answering the whole question you can already help me by telling me the correct keywords.
My problem is the following:
For a given parametrisation of a robot, for example the simple two dimensional $(\varphi,p_1,p_2)$, where $\varphi$ describes the orientation and $p$ the 2D position, I want to find a trajectory
$c:[0,1]\rightarrow S^1\times R^2$
from one given pose $(\varphi_0,(p_1)_0,(p_2)_0)$ to another given pose $(\varphi_1,(p_1)_1,(p_2)_1)$. This trajectory should also be optimal with respect to an energy functional for example
$\int_0^1 \varphi^2+p^2_1+p^2_2 \;dt$
and I want two constraints to be fulfilled in order to make sure that the robot moves only forward. These constraints are:
$\dot{p_1}=\cos(\varphi)$
$\dot{p_2}=\sin(\varphi)$
With Euler-Langrange I get the ODE system:
$\ddot{\varphi}=\varphi^2$
$\ddot{p_1}=-sin(\varphi)\dot{p_1}$
$\ddot{p_2}=cos(\varphi)\dot{p_2}$
Now I'm wondering if this equation system is solvable with my boundary conditions.
My questions are
1) Are there any theorems that I can use to make statements about the existence of solutions? Whenever I tried to solve this ODE in Matlab the second boundary condition was not reached.
2) Would it be easier to proof the existence if I would use another model for example with an orientation independent stearing wheel?
3) How can I solve this equation system?
4) In literature I only found very complicated models with a lot more parameters or the paper was not about reaching a specific goal pose can you advise me more basic literature with approches similar to what I derived here?
One step back to the onedimensional model
My parameters are $(p,v)\in R^2$, where $p$ indicates the onedimensional position and $v$ the velocity.
I used the energyfuctional $\int v^2 dt$ and the constraint $\dot{p}=v$.
The resulting ODE system is
$\ddot{x}_1=\dot{v}$
$\ddot{x}_2=0$
I didn't find a solution for the boundary values $(0,1)$ and $(1,1)$.
And a new question araised. Maybe I should not assume that I get a continuous solustion for all my model parameters?
Answer: Let me start by saying I haven't done trajectory optimization or anything, but I've done quite a bit of differential equations for controls. I think your equations might not be solvable because of the way you've defined your constraint conditions:
$$
\dot{p}_1=\cos{\phi} \\
\dot{p}_2=\sin{\phi} \\
$$
If you want your heading/orientation to remain steady, how do you change the translational speeds? In your ODE system,
$$
\ddot{\phi} = \phi^2
$$
What if your starting heading $\phi(0) = 0$? It would look like $\ddot{\phi}$ is "trapped" to be always zero, and your translational accelerations are always stuck at $\ddot{p}_1=−\sin(0)\dot{p}_1 = 0$ and $\ddot{p}_2=\cos(0)\dot{p}_2 = \dot{p}_2$.
Given your constraint conditions $\dot{p_1} = \cos(0) = 1$ and $\dot{p_2} = \sin(0) = 0$. The constraints and accelerations seem to match, but it's a trivial solution that doesn't get you anywhere; $\dot{p}_1$ is a constant speed of $1$ and $\dot{p}_2$ is a constant speed of $0$, so again it looks like you're not able to change speed (e.g., stop) and you're not able to change position at all on the $p_2$ axis.
You haven't provided a diagram of your system, so I'm not sure why you have that "forward motion" is defined by the sine/cosine of the heading. If I had to guess, I would think maybe you're looking at a steered vehicle, but in that instance you'd have an extra term - the vehicle's linear speed - and this would be reflected in your constraints:
$$
\dot{p}_1 = \dot{x}\left(\cos{\phi}\right) \\
\dot{p}_2 = \dot{x}\left(\sin{\phi}\right) \\
$$
This might be what's missing from your equations that's precluding you from obtaining a solution. Again, I haven't done anything with trajectory optimization, but in looking around I found the following paper that might be of use:
Guidelines in Nonholonomic Motion Planning for Mobile Robots
J.P. Laumond S. Sekhavat F. Lamiraux
This is the first chapter of the book:
Robot Motion Planning and Control
Jean-Paul Laumond (Editor)
You had asked too about terms to search, and I found this paper by looking for "nonholonomic trajectory control." | {
"domain": "robotics.stackexchange",
"id": 2141,
"tags": "mobile-robot, kinematics, motion-planning"
} |
Does the independent variable need to be a specific quantifiable physical quantity? | Question: I was writing a paper for my school submission and I am not sure what the independent variable could be since there seems to be no trend for the original independent variable I chose. I will explain what I mean through an example.
Let's say we talk about the young's modulus of a material, so can I call the 'material used' the independent variable for this example and the young's modulus as a dependent variable? Or will I have to use a quantifiable physical quantity as an independent variable?
I did try searching up the meaning of an independent variable for better clarity but it seems my question is a little arbitrary for Google to answer.
$$$$
Thank you in advance!
Answer: The Young's modulus is a physical property of a given material, and each given material will have a different Young's modulus. To determine the value of the Young's modulus, you must construct a material with a known cross-sectional area, put a known tension on that material, and measure how much the material stretches under that known tension. Thus, the variable that you would manipulate in such an experiment, also known as the independent variable, is tension (for the selected cross-sectional area). The dependent variable is the amount of stretch that occurs due to that tension.
Regarding your confusion of whether or not a material can be declared as an independent variable, physical properties are determined via scientific experiments. Scientific experiments MUST rely on measurements. If you can't measure a particular variable, it is not a valid independent variable. In other words, where would you find a "material meter", such that you would make some adjustment that allowed you to change your measured material from copper to brass to steel (as an example) by turning some knob on some device? In effect, if you don't have the ability to directly manipulate a variable, it cannot be an independent variable. | {
"domain": "physics.stackexchange",
"id": 83462,
"tags": "homework-and-exercises"
} |
MD5 shuffling with a defined pattern of numbers | Question: I've created a MD5 shuffler with a defined number pattern. Does this make sense? Will this make storing passwords more secure? Is it efficient?
<?php
echo "<pre>";
$md5 = "e2fc714c4727ee9395f324cd2e7f331f";
echo "Old hash: " . $md5 . "<br />";
$hash = str_split($md5, 1);
$shuffle = explode(",", "24,29,21,23,2,30,10,22,6,28,26,11,8,19,9,20,16,3,0,14,18,15,12,25,5,4,31,1,7,27,13,17");
$newhash = "";
for ($i = 0; $i < 32; $i++) {
$s = $shuffle[$i];
$newhash .= $hash[$s];
}
echo "New Hash: " . $newhash . "<br />";
$newhash = str_split($newhash, 1);
$reverse = "";
for ($i = 0; $i < 32; $i++) {
$s = $shuffle[$i];
$reverse[$s]= $newhash[$i];
}
ksort($reverse);
$reversehash = "";
foreach ($reverse as $value) {
$reversehash .= $value;
}
echo"Reversed hash: " . $reversehash . "<br />";
echo "</pre>";
?>
Answer: Security
In addition to what @Kid Diamond said (don't use md5, don't write your own hashing):
You also shouldn't 'improve' existing hashing functions yourself (in this case, shuffling doesn't make it more unsecure, but in general, it's not a good idea to change this kind of stuff yourself).
Shuffling doesn't really add that much security, as an attacker only has to look at your script to know how to shuffle themselves (it's security through obscurity). See also this discussion at security.stackechange.
Performance
Why are you doing this:
$shuffle = explode(",", "24,29,21,23,2,30,10,22,6,28,26,11,8,19,9,20,16,3,0,14,18,15,12,25,5,4,31,1,7,27,13,17");
instead of this:
$shuffle = [24,29,21,23,2,30,10,22,6,28,26,11,8,19,9,20,16,3,0,14,18,15,12,25,5,4,31,1,7,27,13,17];
The second one will definitely perform better.
You might also try to change
$reversehash = "";
foreach ($reverse as $value) {
$reversehash .= $value;
}
to
$reversehash = implode("", $reverse);
It is definitely easier to read, and it might perform better.
Other
please use correct indentation. Your code is hard to read if you don't.
naming: $reversehash sounds like you are reversing the hash (eg 123 -> 321), but it is in fact the original hash, so use something like $originalHash.
magic numbers: why hardcode 32 if you can just use the length of the string? If you do this, nobody will wonder if 32 is correct, and you can reuse your code for different hash functions.
functions: I know that this is just a proof of concept, but still functions would be nice (like shuffle() and unshuffle() or similar). | {
"domain": "codereview.stackexchange",
"id": 9365,
"tags": "php, cryptography"
} |
Is ROS2 going to support Python 3 and C++14? | Question:
My main question is in the title.
If these languages versions are not going to be supported, what are there the main reasons that prevent it from happening? What would be the libraries that are only supported for Python 2.7 and <=C++11 but not for the new versions of the programming languages, that the ROS team would like to include anyway in the system?
Originally posted by nbro on ROS Answers with karma: 372 on 2017-04-28
Post score: 0
Original comments
Comment by lakehanne on 2017-04-28:
Probably yes. See this github wiki: https://github.com/ros2/ros2/wiki
Answer:
This page currently says the following:
C++ standard
The core of ROS 1 is targeting C++03
and doesn’t make use of C++11 features
in its API. ROS 2 uses C++11
extensively and uses some parts from
C++14. In the future ROS 2 might start
using C++17 as long as it is supported
on all major platforms.
Python
ROS 1 is targeting Python 2. ROS 2
requires at least Python version 3.5.
Originally posted by jarvisschultz with karma: 9031 on 2017-04-28
This answer was ACCEPTED on the original site
Post score: 5 | {
"domain": "robotics.stackexchange",
"id": 27746,
"tags": "python, ros2, c++"
} |
Confusion on symmetry and basis transformation | Question: Let {$|a_n\rangle$} and {$|b_n\rangle$} be two basis related by: $|b_n\rangle = \hat{U}|a_n\rangle \forall n$.
From my understanding then the unitary operator $\hat{U}$ only transforms the basis {$|a_n\rangle$} into {$|b_n\rangle$} (just like in 2D geometry having a rotation operator which changes the basis $\hat{x},\hat{y}$ to $\hat{r},\hat{\theta}$).
If there is an operator $\hat{\Omega}$, then its representation in basis {$|b_n\rangle$}:
$$
\langle b_n|\Omega|b_m\rangle = \langle a_n| \hat{U}^\dagger\Omega\hat{U}|a_m\rangle
$$
$$\Omega \to \hat{U}^\dagger\Omega\hat{U}$$
On the other hand, consider the following unitary transformation:
$$|\psi\rangle = \Omega|\phi\rangle$$
$$\hat{U}|\psi\rangle = \hat{U}\Omega\hat{U}^\dagger\hat{U}|\phi\rangle$$
$$\Omega \to \hat{U}\Omega\hat{U}^\dagger$$
1)I am getting very confused by the difference between these, shouldn't the operator $\Omega$ transform in the same way?What is the difference between the two things I am doing?
Answer: I suppose I'll formally write this up since there seems to still be some confusion. Let's firmly establish that our $U$ is a transformation from $a$ to $b$, that has it's representation in the $a$ basis as
$$\langle a_i |U|a_j\rangle = \langle a_i|b_j\rangle$$
Let's look at how the representation of $|\psi\rangle$ in the $a$ basis transforms when we go to the $b$ basis:
$$|\psi\rangle = \sum_{j}|b_j\rangle\langle b_j|\psi\rangle=\sum_{j}\sum_{i}|b_j\rangle\langle b_j|a_i\rangle\langle a_i|\psi\rangle$$
Now pick out the $k$'th component of $b$
$$\langle b_k|\psi\rangle = \sum_{j}\sum_{i}\delta_{kj}\langle b_j|a_i\rangle\langle a_i|\psi\rangle = \sum_{i}\langle b_k|a_i\rangle\langle a_i|\psi\rangle \\ = \sum_{i}(\langle a_i|b_k\rangle)^{\dagger}\langle a_i|\psi\rangle = \sum_{i}(\langle a_i|U|a_k\rangle)^{\dagger}\langle a_i|\psi\rangle.$$
Letting subscripts denote the basis (i.e. $|\psi\rangle_a \equiv \langle\vec{a}|\psi\rangle$, and likewise for $b$), we see that this is telling us $|\psi\rangle_b = U^{\dagger}|\psi\rangle_a$. Now, from $U|a_i\rangle=|b_i\rangle$ we know that $\Omega_b = U^{\dagger}\Omega_a U$, so lets check that everything is consistent with your $|\psi\rangle = \Omega|\phi\rangle$ when we hit it with $U^{\dagger}$. Keeping subscripts to denote the basis for absolute clarity:
$$|\psi\rangle_a = \Omega_a|\phi\rangle_a \to U^{\dagger}|\psi\rangle_a = U^{\dagger}\Omega_a|\phi\rangle_a$$
Looking at each side individually, we have
$$U^{\dagger}|\psi\rangle_a = |\psi\rangle_b \\ U^{\dagger}\Omega_a|\phi\rangle_a =U^{\dagger}\Omega_a U U^{\dagger}|\phi\rangle_a = \Omega_b |\phi\rangle_b,$$
which shows us that everything is nice and consistent:
$$ |\psi\rangle_a = \Omega_a|\phi\rangle_a \xrightarrow{U^{\dagger}} |\psi\rangle_b = \Omega_b|\phi\rangle_b $$ | {
"domain": "physics.stackexchange",
"id": 56790,
"tags": "quantum-mechanics, symmetry"
} |
jQuery hide and show option value from a dropdown | Question: I have form with an "add field" button that does an Ajax call to add a new field.
Each field contains a list of options to choose from. When is public is Yes, I need to remove option value = "contacts" and "file upload" from the drop and when the "Add field" button is clicked. If the is public is no, I need to show the option value "contacts" and "file upload".
My code works, but I feel I can improve it.
publicFormValidation = function(){
$('#public').change(function(){
if(checkForm()){
$('.field_type option[value="file_upload"]').hide();
$('.field_type option[value="contacts"]').hide();
$('.add_many_fields').on('click',function(){
setTimeout(function(){
$('.field_type option[value="file_upload"]').hide();
$('.field_type option[value="contacts"]').hide();
}, 500);
});
}else {
var $contacts = $('.field_type option[value="contacts"]');
var $file_uploads = $('.field_type option[value="file_upload"]');
$contacts.show();
$file_uploads.show();
$('.add_many_fields').on('click',function(){
setTimeout(function(){
var $contacts = $('.field_type option[value="contacts"]');
var $file_uploads = $('.field_type option[value="file_upload"]');
$contacts.show();
$file_uploads.show();
}, 500);
});
};
});
}
checkForm = function(){
var public_val = $('#public').val();
return (public_val == "true");
}
The reason I have a setTimeout function is because when I needed to create a delay from when click to hide onto the DOM.
Answer: The primary things I would recommend here are
avoid polluting the global namespace
avoid unintentionally creating globals
cache your DOM element lookups to increase performance and also decrease filesize
Here is the code reflecting these considerations:
// Wrap this in a self-executing, anonymous scope, or in a document.ready
// this way you can avoid polluting the global (window) namespace
(function(){
// Cache this DOM element in the main scope because you look it up in both of your functions.
var $public = $('#public');
/* use "var" or publicFormValidation becomes a wild global */
var publicFormValidation = function(){
// Cache DOM elements that you're going to call multiple times, like ".add_many_fields"
// DOM lookups are very expensive operations (depending on the size of the DOM)
var $addManyFields = $('.add_many_fields'),
$fileUpload = $('.field_type option[value="file_upload"]'),
$contacts = $('.field_type option[value="contacts"]');
$public.change(function(){
if(checkForm()){
$fileUpload.hide();
$contacts.hide();
$addManyFields.on('click',function(){
setTimeout(function(){
$fileUpload.hide();
$contacts.hide();
}, 500);
});
}else {
$contacts.show();
$file_uploads.show();
$addManyFields.on('click',function(){
setTimeout(function(){
/* You definitely don't want to do this:
var $contacts = $('.field_type option[value="contacts"]');
var $file_uploads = $('.field_type option[value="file_upload"]');
you're actually overwriting variables you've already defined in the parent scope - you
already have these references, so no need to do another DOM lookup.
*/
$contacts.show();
$file_uploads.show();
}, 500);
});
};
});
}
/* Use var here as well to get rid of globals */
var checkForm = function(){
var public_val = $public.val();
return (public_val == "true");
}
}()); | {
"domain": "codereview.stackexchange",
"id": 10142,
"tags": "javascript, jquery"
} |
Control architecture survey | Question:
Dear all,
I am wondering what hardware tech is most used to interface with ROS. I have drawn a little diagram which I believe is typical of most ROS control architectures and I am wondering which particular technology you use for the items shown in white. The idea is to understand if there is a typical "kind of standard" control architecture. I guess this will be interesting for many among us.
Specifically:
The communication between the ROS PC and the controller
I expect most people use Ethernet, or I2C, SPI... But is it really the case?
The motor controller
I expect hobbyist use custom-made controllers or cheap ones from the internet and professionals use proprietary ones such as EPOS from Maxon... What do you use?
The communication between the encoders and the ROS PC
You also use Ethernet, or I2C, SPI?
I believe it would be great to indicate your skills level as well: whether you are a hobbyist, a researcher, or someone working in the industry...
Thanks,
Antoine.
Originally posted by arennuit on ROS Answers with karma: 955 on 2014-06-05
Post score: 3
Original comments
Comment by dornhege on 2014-06-05:
From my point of view there is no clear answer besides: Whatever the hardware dictates. The one thing I'd change in your diagram: Encoders are usually not directly connected to the PC.
Comment by arennuit on 2014-06-05:
Yep you are right, I have updated the diagram accordingly. Thanks.
Comment by AxisRobotics on 2018-09-19:
In our model, our encoders don't even directly connect to the motor controller. Point being, it's up to the designer of the robot and there are a lot of variables. When we first got started with ROS, it was the high level of abstraction that was difficult to digest. Start small!
Answer:
Interesting question indeed.
As for my own experience (academia): within ROS-Industrial we have a somewhat different setup:
image description http://wiki.ros.org/Industrial?action=AttachFile&do=get&target=ros_industrial_architecture.png
The driver part of ROS-Industrial (which lives in the ROS-I Controller layer in the above diagram) provides abstracted access to the sensors and actuators that the controller supports. On a hardware level this means that we use the facilities of the industrial controller built by the manufacturer, which provides us the blocks Motor Controller/Power and Motor/Encoders in your diagram.
The industrial controller runs a manufacturer specific program (most of the times in their proprietary language). The ROS side (the drivers) communicates with those programs using a simple TCP/UDP based protocol (simple_message). ROS-Industrial provided nodes (industrial_robot_client) implement the necessary interfaces (FollowJointTrajectoryAction, JointState, etc) needed for higher level ROS capabilities (eg MoveIt) to close the loop.
There are some drivers within ROS-Industrial though that are implemented on top of ros_control: the universal_robot C-API driver being one of them.
As for communication: many industrial controllers provide Ethernet connectivity, which is most often used. Some older controllers only support serial connections, but those aren't used in any released packages.
Originally posted by gvdhoorn with karma: 86574 on 2014-06-05
This answer was ACCEPTED on the original site
Post score: 4
Original comments
Comment by arennuit on 2014-06-05:
This is an interesting approach, I like the fact it is rather standardized (so much as ROS-I can be considered a standard ;)). Thanks ;) | {
"domain": "robotics.stackexchange",
"id": 18173,
"tags": "control, ros"
} |
Deriving Maxwell-Boltzmann momentum distribution | Question: I am studying statistical mechanics and I saw the following statement in my notes:
$$\frac{d\rho}{\rho} = \frac{e^{-\beta p^2/2m}}{(2\pi m k_B T)^{3/2}} 4\pi p^2 dp \quad \ldots (1)$$
where $\rho = \langle N \rangle /V$, the particle density and $p$ is momentum, $\beta = 1/k_B T$ where $T$ is the temperature, $k_B$ is Boltzmann's constant, $m$ is mass of the particle. We can see that the above equation denotes the momentum distribution function for an ideal gas.
I want to derive this equation from the Fermi distribution for particle density:
$$\rho = \frac{g}{h^3} \int \frac{1}{e^{\beta(p^2/2m - \mu)}+1} d\mathbf{p} \quad \ldots (2)$$
in the limit as $e^{\beta(p^2/2m - \mu)} \gg 1$, where $g=2$ for a Fermi gas.
My question is, how do I get equation $(1)$ from the above relation?
My attempt: Since we know that $e^{\beta(p^2/2m - \mu)} \gg 1$, equation $(2)$ becomes,
$$\rho = \frac{2}{h^3} \int_{0}^{\infty} \int_{0}^{\infty} \int_{0}^{\infty} e^{-\beta(p^2/2m - \mu)} dp_xdp_ydp_z \\
=\frac{2e^{\beta \mu}}{h^3} \int_{0}^{\infty} \int_{0}^{\infty} \int_{0}^{\infty} e^{-\beta(p^2/2m)} dp_xdp_ydp_z \\
=\frac{e^{\beta \mu}}{\sqrt{2}h^3} \cdot (2\pi m k_B T)^{3/2} $$
However, I don't see a way to make it to equation $(1)$.
I would appreciate any advice you have for me.
Answer: First, let's rewrite this in polar coordinates
\begin{equation}
\rho = \frac{2}{h^3} \int dp \; 4\pi p^2 e^{-\beta (\frac{p^2}{2m} - \mu)}.
\end{equation}
Thus we see that the particle densitiy in the intervall $[p, p+dp]$ is
\begin{equation}
d\rho = \frac{8\pi}{h^3} p^2 e^{-\beta(p^2/2m - \mu)} dp.
\end{equation}
Next we calculate $\rho$. This you have already done (But I think you have made a small mistake) $\rho = e^{\beta \mu} \frac{2}{h^3} (2\pi m k_B T )^{3/2}$. Deviding $d\rho$ by $\rho$ yields the desired result. | {
"domain": "physics.stackexchange",
"id": 71996,
"tags": "thermodynamics, statistical-mechanics"
} |
Why does a helium balloon rise? | Question: This may be silly question, but why does a helium ballon rise? I know it rises because helium is less dense than air. But what about the material of the ballon. It is made up of rubber/latex which is quite denser than air. An empty ballon with no air in it falls, so why does a helium filled balloon rise?
Answer: The buoyant force* depends on the volume of the object (or at least the volume of the object submerged in the fluid) and the density of the fluid that object is in, not necessarily/directly on the density of the object. Indeed, you will usually see the buoyant force written as
$$F_B=\rho_{\text{fluid}}V_{\text{sub}}g=w_{\text{disp}}$$
which just shows that the buoyant force is equal to the weight of the displaced fluid.
We usually talk about more dense objects sinking and less dense objects floating because for homogeneous objects of mass $m$ we can write the volume as $V=m/\rho$, so that when we compare the buoyant force to the object's weight (for example, wanting the object to float) we get
$$m_{\text{obj}}g<F_B=\frac{\rho_{\text{fluid}}m_{\text{obj}}g}{\rho_{\text{obj}}}$$
i.e.
$$\rho_{\text{obj}}<\rho_{\text{fluid}}$$
This is what we are familiar with, but keep in mind that this emerges from the buoyant force's dependency on the object's volume (not density) after we assumed that we had a homogeneous object.
If our object is not homogeneous (like the balloon), then you have to be more careful. You do not just "plug in" the density of the rubber, since it is not purely the volume of the rubber material that is displacing the surrounding air. You have to differentiate between the entire balloon and the rubber material. So, the buoyant force would be given by
$$F_B=\rho_{\text{fluid}}V_{\text{balloon}}g$$
whereas the weight is given by
$$w_{\text{balloon}}=(m_{\text{rubber}}+m_{\text{He}})g=(\rho_{\text{rubber}}V_{\text{rubber}}+\rho_{\text{He}}V_{\text{He}})g$$
So, if we want floating, we want
$$w_{\text{balloon}}<F_B$$
$$(\rho_{\text{rubber}}V_{\text{rubber}}+\rho_{\text{He}}V_{\text{He}})g<\rho_{\text{fluid}}V_{\text{balloon}}g$$
i.e.
$$\frac{\rho_{\text{rubber}}V_{\text{rubber}}+\rho_{\text{He}}V_{\text{He}}}{V_{\text{balloon}}}<\rho_{\text{fluid}}$$
We end up with something a little more complicated, but if we treat the balloon as a single object then we get a similar result to the homogeneous case. Just define the density of the balloon as
$$\rho_{\text{balloon}}=\frac{m_{\text{rubber}}+m_{\text{He}}}{V_{\text{balloon}}}$$
and so we end up with
$$\rho_{\text{balloon}}<\rho_{\text{fluid}}$$
It should be noted that it's not just the fact that helium is in the balloon that causes it to rise then. You still need the volume of the balloon to be large enough to displace enough of the surrounding air. However, helium is used because it's density is so low that as we add more helium to make the balloon (buoyant force) larger, we are not making the balloon weigh too much more such that the buoyant force can eventually overcome the balloon's weight.
To qualitatively summarize this, the density of the object only matters when we look at the object's weight. The volume of the object (more specifically, the volume the object takes up in the fluid) is what matters for the buoyant force. The relation of these two forces is what determines if something sinks or floats. If your object isn't homogeneous then you should look at the overall density of the object which is the total mass of the object divided by the volume the object takes up in the fluid.
* If you want to know about where the buoyant force comes from, then Accumulation's answer is a great explanation. I did not address it here, because your question is not asking about where the buoyant force comes from. It seems like you are just interested in how comparisons of densities can determine whether something floats or sinks, so my answer focuses on this. | {
"domain": "physics.stackexchange",
"id": 58819,
"tags": "newtonian-mechanics, density, air, fluid-statics, buoyancy"
} |
Potential vs Kinetic Energy of Particles in Gas | Question: "In the gas phase, the molecules are freely moving particles traveling through space, where the kinetic energy associated with each particle is greater than the potential energy of intermolecular forces."
Qualitatively, this makes perfect sense. The particles have are moving very quickly which trumps any attractive forces.
However, I don't quite understand the energetics of such a situation. This motion is where the kinetic energy term comes from. On the other hand, the tendency for the particles to attract is represented by a potential energy term. Two particles that are attracted to one another in close proximity would have a positive potential energy, right? How do we know that the kinetic energy term has to be greater than the potential energy term?
EDIT IN RESPONSE TO ANSWER
Thought I would post this in case anyone else was confused. This is my rationalization of the answer.
This has cleared up a lot for me. This also has to be why solids vibrate in place. For the following, assume two particles in one dimension. Assume the particles are at some finite distance from each other, each with no KE. Call this distance d. We can define the PE to be 0 at this distance, d. Since they attract each other, they fall towards one another. The attractive force is applied across the distance between them, hence work. The amount of work (or force * dist) to bring the particle to a certain velocity is its kinetic energy. In other words, all of the PE is converted to KE. Assuming the particles then “collide,” elastically of course, the particles reverse directions. They are now moving away, each with some KE. They still attract one another, however. The attractive force will apply itself across some distance. Well the amount of work to stop them will be equal to their KEs. This will happen at a distance at the distance d. At this point, there will not be enough KE to keep moving away from one another. They fall back towards one another and the process repeats. This is the vibration. In a gas, there is not enough attraction to stop the moving away from one another. In other words, the KE outweighs the PE.
Answer: A correction, the potential describing the inter-molecular force is negative. Have a look at http://en.wikipedia.org/wiki/Lennard-Jones_potential. If both molecules have a separation distance that puts them between 1 and 2 on the horizontal axis of the attached figure ,that means their potential energy is negative. Hence their total energy is
:
Total energy = kinetic energy (positive by definition) + potential energy (sign depends on the sign of the potential)
So if they are between 1 and 2 on the horizontal axis in the attached figure, the previous addition will become subtraction. In order to make the molecules free their total energy has to be positive which means their kinetic energy has to exceed their potential energy. | {
"domain": "physics.stackexchange",
"id": 9558,
"tags": "energy, inert-gases"
} |
Will there be change in electronegativity difference in C-O and C=O? | Question: Is there any change in EN difference in C-O and C=O. If yes, why?
Does EN difference change if its bond is changed to single, double, or triple?
Answer: I think that you didn't understand the answer to this question.
A dipole is created when two equal (only in magnitude) and opposite charges are separated by some distance. The dipole moment depends on the magnitude of the charges and the distance between them. Electronegativity is just a concept that helps us to get an idea of the magnitude of the charges. So, in order to find the dipole moment, you should focus on the magnitude of the two charges rather than the electronegativity difference.
Look at the hybridization of the atoms in the single and double bond. That will tell you that both the atoms should be more electronegative after forming a double bond, but won't help you comment on the electronegativity difference. | {
"domain": "chemistry.stackexchange",
"id": 10337,
"tags": "bond, electronegativity, dipole"
} |
Sorting 10,000 unique randomly-generated numbers | Question: I have to write this program in java.
Write a program name sorting.java that will use an array to store 10,000 randomly generated numbers (ranging from 1 to 10,000 no repeat number).
Here is what I have so far:
public class Sort
{
public static void main(String[] args)
{
Random rgen = new Random(); // Random number generator
int[] nums = new int[10,000]; //array to store 10000 random integers (1-10,000)
//--- Initialize the array to the ints 1-10,000
for (int i=0; i<nums.length; i++) {
nums[i] = i;
}
//--- Shuffle by exchanging each element randomly
for (int i=0; i<nums.length; i++) {
int randomPosition = rgen.nextInt(nums.length);
int temp = nums[i];
nums[i] = nums[randomPosition];
nums[randomPosition] = temp;
}
//Print results
for (int i = 0; i < nums.length; i++){
System.out.println(nums[i]);
System.out.println("\n");
}
}
Answer: Apart from the compiler errors, implementation issues and code style suggestions others have pointed out, your shuffling algorithm is fundamentally flawed.
Wikipedia explains it nicely:
Similarly, always selecting i from the entire range of valid array
indices on every iteration also produces a result which is biased,
albeit less obviously so. This can be seen from the fact that doing so
yields nn distinct possible sequences of swaps, whereas there are only
n! possible permutations of an n-element array. Since nn can never be
evenly divisible by n! when n > 2 (as the latter is divisible by n−1,
which shares no prime factors with n), some permutations must be
produced by more of the nn sequences of swaps than others. As a
concrete example of this bias, observe the distribution of possible
outcomes of shuffling a three-element array [1, 2, 3]. There are 6
possible permutations of this array (3! = 6), but the algorithm
produces 27 possible shuffles (33 = 27). In this case, [1, 2, 3], [3,
1, 2], and [3, 2, 1] each result from 4 of the 27 shuffles, while each
of the remaining 3 permutations occurs in 5 of the 27 shuffles.
To demonstrate this bias, I changed your code to only create three elements per array and ran it sixty million times. Here are the results:
Permutation Occurences
[1, 2, 3]: 8884128
[2, 3, 1]: 11111352
[3, 1, 2]: 8895318
[3, 2, 1]: 8891062
[2, 1, 3]: 11107744
[1, 3, 2]: 11110396
If your shuffling algorithm were correct, one would expect a relatively uniform distribution. However, the standard deviation is huge at about 1215764 (or ~2%) which should ring alarm bells. For comparison, here are the results of using the proven Fisher–Yates shuffle:
Permutation Occurences
[1, 2, 3]: 10000566
[2, 3, 1]: 9998971
[3, 1, 2]: 10000640
[3, 2, 1]: 10000873
[2, 1, 3]: 9998249
[1, 3, 2]: 10000701
As one would expect from a correct implementation, the standard deviation is low at about 1105 (or ~0.002%).
Here's the correct implementation for reference:
for (int i = numbers.length - 1; i > 0; i--)
{
int swapIndex = random.nextInt(i + 1);
int temp = numbers[i];
numbers[i] = numbers[swapIndex];
numbers[swapIndex] = temp;
}
However, another problem presents itself even with a correct shuffling algorithm:
A pseudo-random number generator is limited by its period, i.e. it can only produce a certain number of unique shuffles:
[...] a shuffle driven by such a generator cannot possibly produce more distinct permutations than the generator has distinct possible states.
java.util.Random has a period no larger than 248 which is unable to produce an overwhelming majority of the 10000! (approximately 2.85 × 1035659) possible permutations of your array. The default implementation of SecureRandom isn't much better at no more than 2160.
In the case of such a long array, the Mersenne Twister is a more adequate choice with a period of 219937-1 and excellently uniform distribution (although still not enough to produce all the possible permutations. At some point, it makes more sense to look into true random number generators that are based on physical phenomena).
So, in my opinion, the real moral of the story is this:
Take special care when working with randomness or pseudorandomness as the consequences of tiny mistakes can be hard to detect but devastating. Use Collections.shuffle instead of reinventing the wheel. For your (presumably) casual use, you might not need to worry about these inadequacies at all. On the other hand, it doesn't hurt to be aware of them. | {
"domain": "codereview.stackexchange",
"id": 3610,
"tags": "java, sorting, random"
} |
Prove that 2-Colourability is in L from Undir-Reachability is in L | Question: Let Undir-Reachability be the following problem:
given an undirected graph G and two specified vertices s and t in G, is there a path from s to t in G?
I need to prove that the 2-Colourability is in L, by knowing that Undir-Reachability belongs to the complexity class L.
I don't know how to start.
Answer: Hint: a graph is not bipartite if there is a walk of odd length from a vertex to itself. | {
"domain": "cs.stackexchange",
"id": 1083,
"tags": "complexity-theory, graphs, space-complexity, colorings"
} |
Is it possible to show simply using the Lagrangian that a body in free fall (& $v_i=0$) follows the most " efficient" path ( i.e. a vertical line)? | Question: In this video lecture by M. van Biezen ( Loyola Marymount Uni) https://www.youtube.com/watch?v=uFnTRJ2be7I&list=PLX2gX-ftPVXWK0GOFDi7FcmIMMhY_7fU9&index=2
it is shown how to apply the equation
$$\frac{d}{dt}(\frac{\partial L}{\partial x'})- \frac{\partial L}{\partial x}=0.$$
to an object in free fall ( with initial velocity $= 0$)
with $L = KE - PE$ , $x=$ height of an object in free fall and $x'$ = the derivative of $x$ with respect to time.
The lecturer shows one can derive the equation $F = ma$ from the previous one.
He also says in another lecture that one can show using the equation involving the lagrangian that the object in free fall follows the most " efficient" trajectory, that is, the vertical straight line.
Is it possible to do this not using too complicated mathematical methods?
The equation is an " equals zero" one. Maybe it means that the derivative of something ( that I cannot identify) is zero and therefore that this something is constant.
What is this unidentified quantity and how does it relate to the path of the object?
Answer: For each path, we can assign the following quantity known as action:
$$ S[\vec{r}]= \int_{t_1}^{t_2} dt( L)$$
Where,
$$ L = \text{ total kinetic energy} - \text{total potential energy}$$
The quantity 'S' is called a functional. A functional can be stated loosely as a function of functions. A concrete example of such objects being used to solve problems can be found in this post I made on MSE.
Anyhow, the great discovery was that the path which makes the action stationary (i.e: extremum of S) would be the path which the object follows. It turns out that the condition that the action is minimized/maxed is given as:
$$ \frac{d}{dt} \frac{ \partial L}{\partial q} = \frac{\partial L}{\partial \dot{q} }$$
This similar to how if we have a function then $ \frac{df}{dx}=0$ gives us the condition of $x$ such that it is maximized, the above is the condition that should be satisfied by $L$ for the action to be minimized/maxed. Turns out this condition is same as newton's second law.
The real rigorous details of all the above are quite complicated but I've heard Leonard Susskind's book gives a good take on this in a simple way. Btw the condition for action being optimized comes another mathematical result known as Euler Lagrange equations (there are too many videos deriving this one equation onyoutube, so check there) | {
"domain": "physics.stackexchange",
"id": 78260,
"tags": "homework-and-exercises, lagrangian-formalism, variational-principle, action, free-fall"
} |
How is the wire in this problem in pure bending? | Question: Problem:
A beam is said to be in pure bending if the bending moment in it remains constant throughout the length.
The problem asks to determine the bending moment in the wire. In the solution of the problem, the textbook uses the formulas which were derived for a beam in pure bending. So I believe the wire is in pure bending, but I don't understand how it is in pure bending.
How the wire is in pure bending?
Answer: The bending moment is there because the wire "bends" around the cylindrical drum. If there is bending of the wire there has to be a bending moment.
Regarding the pure bending moment first of all its an approximation (it is not accurate but its pretty good if you assume a very small d and neglect frictional forces).
The reason you can t happens because of the support conditions. e.g. if the applied force is the F like in the image below
then there is a bending and a shear force up to the point that the wire contacts the drum. Beyond that point the wire is resting on the cylinder (pretty much like a beam on elastic foundations). Therefore any shear forces are counteracted by the drum and therefore the wire is in pure bending. | {
"domain": "engineering.stackexchange",
"id": 4575,
"tags": "mechanical-engineering, structural-engineering, beam, homework"
} |
Raspian / armhf package repository plans? | Question:
Are there any plans for building and providing a standard repository for armhf packages compatible with the likes of Rasbian?
Raspberry Pi seem like a great gateway drug for getting into ROS given how cheap, relatively powerful and well supported platform it is. Seem like a very sensible/obvious first choice when upgrading a robot to include a computer capable of running a full blown OS. The rather convoluted, shaky and time consuming process of building the environment and trying to get different packages is pretty intimidating if your not already a ROS veteran and a competent linux buff. I can claim neither.
I have come across a willow garage effort by Paul Mathieu in mid 2013 for groovy (including buildfarm instructions) which looks great but I don't see any indication that it was ever taken further or updated since.
Having prowled through the ROS tutorials (via ROS in a VM) and being thoroughly impressed by it's capabilities I only imagine the satisfaction of being able to start operating ROS on a fresh $40 RPi with in minutes of powering it on for the first time.
I myself am one of those amateur robot builder trying to upgrade from a arduino based arbotix include a RPi and I know it has all the tools I need but getting them to work remains a pretty convoluted process still.
Originally posted by Freyr on ROS Answers with karma: 17 on 2015-01-21
Post score: 0
Original comments
Comment by ahendrix on 2015-01-26:
Spend the extra $10-15 for a better board with an ARMv7 processor. You'll get something significantly more powerful and better supported by Ubuntu and ROS. I have no plans to support the Raspberry Pi.
Comment by Freyr on 2015-02-02:
Raspberry Pi 2 is being announced these days with a quad 900Mhz ARMv7 and 1GB RAM so maybe I will have the entire cake and eat it in the end. I'll be looking for your packages when I get my hands on one :)
Answer:
The current build farm does not build ARM packages on a regular base.
@ahendrix built ARMhf packages some time ago and they are being imported into the official repositories in the next days (?). But they are already several months old.
The upcoming build farm will be able to build ARMhf at the same time as the other architectures. If you would like to try these packages (which are still in a temporary apt repository) you can get them from http://54.183.65.232/ubuntu/main/
Hopefully the new build farm can replace the current one (for Indigo and Jade) in the near future.
Originally posted by Dirk Thomas with karma: 16276 on 2015-01-26
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by ahendrix on 2015-01-26:
Note that these packages (old and new) won't work on the Raspberry Pi; it's a ARMv6 instruction set, while all of the builds are done for the ARMv7 instruction set.
Comment by TommyP on 2015-02-07:
Will they work on the new Raspberry Pi 2 B? I am playing around with one now but there was some problem following the Raspbian instructions. I suppose the Raspbian instructions when refrencing binary debs will give you the wrong kind (for ARMv6).
Comment by ahendrix on 2015-02-08:
The UbuntuARM debs probably won't work on Raspbian. They might work if you install Ubuntu. See also: http://answers.ros.org/question/202661/raspberry-pi-2b-and-indigo/ | {
"domain": "robotics.stackexchange",
"id": 20647,
"tags": "ros, buildfarm, packages, raspbian"
} |
What is an object detection problem with only one class called? | Question: Object detection is defined as the problem in which a model needs to figure out the bounding boxes and the class for each object. A lot of ML solutions for object detection base around having "two passes" - one for creating the bounding box of the region and another for classifying it.
I was wondering if there is a name for a subset of this problem where $n_{classes} = 1$. I feel like there is an interesting opportunity here as the whole classification part of the model can (basically) be ignored. Obviously, I can just train a typical object detection model with one class, but was just interested to see if there are any more specialized methods.
Answer: If you are talking about "two-stage" obejct detectors like Faster R-CNN, note that the second phase is not only for classification, but to obtain more accurate results (https://stackoverflow.com/a/61965140/4762996).
in addition, I guess training a detector with many classes acts like a regularizer, which results in much better accuracies.
The only benefit of explicitly training with one class could be the reduzed model size (and a corresponding speedup).
Note also that there are one stage object detectors (CornerNet: https://arxiv.org/abs/1808.01244, YOLOv3: https://pjreddie.com/media/files/papers/YOLOv3.pdf, DETR: https://arxiv.org/abs/2005.12872, and many more). I just wanted to stress that just because you only have one class, it does not make sense to take a two-stage detection architecture and skip the second stage.
Finally, have a look at: https://stats.stackexchange.com/q/351079
An interesting direction would be to incorporate one-class classification approaches, e.g. as mentioned here: https://stackoverflow.com/a/61965358/4762996. | {
"domain": "datascience.stackexchange",
"id": 7647,
"tags": "machine-learning, deep-learning, computer-vision, object-detection, theory"
} |
Does the Coriolis force apply to an object moving weightlessly in a tunnel around the center of Earth? | Question: I just want to be sure I understand correctly.
They ask us to find the speed at which an object moves weightlessly in a tunnel around the center of the Earth. Assume Earth is homogeneous, and the part of Earth beyond the tunnel does not contribute to gravity.
I suppose the gravity and centrifugal force need to cancel each other. But I was wondering if we also need to take the Coriolis force (or any other force by the way) into account?
If the object moves weightlessly in the tunnel, is it as if the object was moving in orbit around Earth? Because it doesn't touch the walls of the tunnel, shouldn't the Coriolis force apply?
The Coriolis force only applies to an object that was in contact with Earth, and then not any more. But in this case, if the object doesn't touch the wall, this doesn't apply, do I understand this correctly?
Answer:
But I was wondering if we also need to take the Coriolis Force (or any other force by the way) into account ?
If the object moves weightlessly in the tunnel, it's as if the object was moving in orbit around Earth ? Because it doesn't touch the walls of the tunnel, the Coriolis Force shoudn't apply ?
The Coriolis force is a fictitious force, meaning that it appears whenever we are doing our analysis of physics using a rotating reference frame. In that rotating reference frame it applies for all objects, regardless of whether they are in contact with the Earth or not.
This force is not due to contact with the Earth, it is due to the fact that we are using a non-inertial coordinate system to do our analysis. So everything in that analysis is affected. As a hint for your specific problem, it may be that you can build your tunnels in a specific location which will eliminate or simplify the Coriolis force. | {
"domain": "physics.stackexchange",
"id": 91308,
"tags": "newtonian-mechanics, newtonian-gravity, reference-frames, centrifugal-force, coriolis-effect"
} |
How to compute the eigenvector of this complex matrix in Grover's algorithm? | Question: We know that SO(3) matrix stands for the proper rotation in 3D space. But when I read this paper, there is a SO(3) matrix stands for the general query matrix of Grover's algorithm in SO(3) form:
$$
\left(\begin{array}{ccc}
R_{11} & R_{12} & R_{13} \\
R_{21} & R_{22} & R_{23} \\
R_{31} & R_{32} & R_{33}
\end{array}\right),
$$
where $$R_{11}=\cos \phi\left(\cos ^{2} 2 \beta \cos \theta+\sin ^{2} 2 \beta\right)+\cos 2 \beta \sin \theta \sin \phi\\R_{12}=\cos 2 \beta \cos \phi \sin \theta-
\cos \theta \sin \phi\\R_{13}=-\cos \phi \sin 4 \beta \sin ^{2} \frac{\theta}{2}+\sin 2 \beta \sin \theta \sin \phi\\R_{21}=-\cos (2 \beta) \cos \phi \sin \theta+
\left(\cos ^{2} \frac{\theta}{2}-\cos 4 \beta \sin ^{2} \frac{\theta}{2}\right) \sin \phi\\R_{22}=\cos \theta \cos \phi+\cos 2 \beta \sin \theta \sin \phi\\ R_{23}=-\cos \phi \sin 2 \beta \sin \theta-
\sin 4 \beta \sin ^{2} \frac{\theta}{2} \sin \phi\\R_{31}=-\sin 4 \beta \sin ^{2} \frac{\theta}{2}\\R_{32}=\sin 2 \beta \sin \theta\\R_{33}=\cos ^{2} 2 \beta+\cos \theta \sin ^{2} 2 \beta.$$
The paper says that the eigenvector of this matrix is $\mathbf{l}=\left(\cot \frac{\phi}{2},1,-\cot 2 \beta \cot \frac{\phi}{2}+\cot \frac{\theta}{2} \csc 2 \beta\right)^{T}$.
I know this question is very basic and I've tried to use Matlab to calculate it. But I just can't figure out how can the author got the eigenvector of such a simple form? Can it be manually calculated? Is there a better way to compute the eigenvector of this kind of parameterized matrix?
Answer: If I were you, I'd ignore the matrix $R$ and instead work with the matrix $Q$. They give you a conversion between vectors in the two different representations.
First, I'm going to simplify things a bit by working with
$$
\tilde Q=\left(\begin{array}{cc} e^{i\phi/2} & 0 \\ 0 & e^{-i\phi/2} \end{array}\right)Q.
$$
You'll have to compensate for this in the final analysis. Now, if I want to find the eigenvectors of $\tilde Q$, note that I can remove any amount of the identity and the eigenvectors don't change. So, remove $-\cos\frac{\theta}{2}I$. You're left with
$$
-\sin\frac{\theta}{2}\left(\begin{array}{cc}
\cos2\beta & \sin2\beta \\ \sin2\beta & -\cos2\beta
\end{array}\right)
$$
Again, for the sake of the eigenvector, you can ignore the overall multiplicative factor ($-\sin\frac{\theta}{2}$). Your eigenvector will be for the form
$$
\left(\begin{array}{c}
\cos\beta \\ \sin\beta
\end{array}\right)
$$
I believe that, ultimately, when you incorporate the adjustment between $\tilde Q$ and $Q$, you'll find the eigenvector is
$$
\left(\begin{array}{c}
\sqrt{1-\sin^2\frac{\phi}{2}\cos^22\beta}+\cos\frac{\phi}{2}\cos2\beta \\ \sin2\beta e^{-i\phi/2}
\end{array}\right).
$$
However, if you want to analyse the $R$ matrix directly, there must be an equivalent to each of my steps. | {
"domain": "quantumcomputing.stackexchange",
"id": 2805,
"tags": "quantum-algorithms, mathematics, grovers-algorithm, foundations"
} |
Relation between eccentric and true anomalies | Question: If $v$ is the true anomaly and $E$ the eccentric anomaly, how can I show that
$$\frac{dv}{dE}=\frac{b}{r}=\frac{\sin v}{\sin E}~?$$
Answer: Here is the proof: Please refer to the wikipedia page on eccentric anomaly for a diagram and a couple of intermediate formulae.
For an ellipse with the usual formula $x^2/a^2 + y^2/b^2=1$, it is the case that $\sin E = y/b$, and also by studying the figure on the wiki page you can see that $\sin (\pi-\nu) = \sin \nu = y/r$. Thus the two results you wish to derive follow from one another.
The relationship between the eccentric anomaly and true anomaly is
$$ \tan \left(\frac{\nu}{2}\right) = \left(\frac{1+e}{1-e}\right)^{1/2} \tan \left(\frac{E}{2}\right) \tag{1}$$
Differentiating (1):
$$\sec^2 \left(\frac{\nu}{2}\right) \frac{d\nu}{dE} = \left(\frac{1+e}{1-e}\right)^{1/2}\sec^2 \left(\frac{E}{2}\right)\tag{2}$$
But using (1) to replace the eccentricity term in (2)
$$ \frac{d\nu}{dE} = \frac{\sec^2 (E/2) \tan (\nu/2)}{\sec^2 (\nu/2) \tan (E/2)}$$
$$ \frac{d\nu}{dE} = \frac{\sin (\nu/2) \cos (\nu/2)}{\sin (E/2) \cos (E/2)} = \frac{\sin \nu}{\sin E} = \frac{y/r}{y/b} = \frac{b}{r}$$ | {
"domain": "physics.stackexchange",
"id": 28190,
"tags": "homework-and-exercises, newtonian-mechanics, newtonian-gravity, orbital-motion, celestial-mechanics"
} |
Are black hole event horizons hotter than our Sun? | Question: The outside (not inside) of black holes, the event horizon, are apparently extremely hot, and get even hotter the smaller in size and mass they are. Being completely black, are they generally more hotter than normal stars? Are black holes hotter than our sun?
An in-detail comparison of their heat and the heat of the sun would be appreciated, if not only temperature but electromagnetic radiation measurements.
Answer: Heat in black holes is due to Hawking radiation, which means in particular that the temperature you measure will depend on the observer you are considering. For an observer at infinity, the temperature is given by the Hawking temperature,
$$T_H = \frac{\hbar c^3}{8\pi k_B G M}.$$
Or, in units with $\hbar = c = G = k_B = 1$,
$$T_H = \frac{1}{8\pi M}.$$
However, this is the temperature measured by static observers at infinity. In other words, it is the temperature that observers at a fixed, infinite "radial distance" to the center of the black hole measure. Other observers measure other temperatures. If you are free falling, you won't measure any temperature at all: it is $T = 0 \text{K}$. If you are at a fixed, finite radial distance $r$, then the temperature is
$$T_H = \frac{1}{8\pi M \sqrt{1 - \frac{2 M}{r}}}.$$
Notice that $r \to +\infty$ recovers the previous formula. Furthermore, for $r \to 2M$ (i.e., close to the horizon), the temperature gets arbitrarily large. Hence, yes, the black hole will be hotter than the Sun if you are hovering sufficiently close to it. Furthermore, there is no limit on the black hole's mass: this will be true for a black hole of any size, as long as you are close enough.
Notice an important point: the temperature depends on the observer measuring it. A free falling observer will be freezing with the cold, but a hovering observer will be burning with the heat.
As for a more detailed comparison on heat spectrum, black holes are black bodies (okay, there are some caveats), while the Sun is not, and its emission is altered by its composition. | {
"domain": "physics.stackexchange",
"id": 91759,
"tags": "general-relativity, black-holes, temperature, event-horizon, hawking-radiation"
} |
Where does the number "380,000 years for electrons to be trapped in orbits around nuclei" come from? | Question: How does this number get calculated?
About 380,000 years after the Big Bang the temperature of the universe fell to the point where nuclei could combine with electrons to create neutral atoms.
http://en.wikipedia.org/wiki/Photon_epoch
I've seen it in many places (or something close to that), but there is never a citation or any explanation.
Answer: The calculation is described in detail in the Wikipedia article on recombination.
If you consider the ionisation of hydrogen as a reaction:
$$ p + e \rightarrow H + \gamma $$
Then you can write down an expression for the equilibrium constant as a function of temperature using the Saha equation:
$$ \frac{n_pn_e}{n_H} = \left( \frac{m_ek_BT}{2\pi\hbar^2} \right)^{3/2} \exp \left( \frac{-E_I}{k_BT} \right) $$
If you take 50% ionisation you can work out the corresponding temperature and it turns out to be about 4,000K. So now it's just a matter of relating the temperature of the universe to the time after the Big Bang. Once we're past the various phase transitions that happened in the first few instants after the Big Bang the temperature is inversely proportional to the scale factor. Sadly there isn't a simple equation to give the scale factor as a function of time, however it's a straightforward numerical calculation, and the result is that the temperature was 4,000K about 380,000 years after the Big Bang.
That's how the figure of 380,000 years is calculated. | {
"domain": "physics.stackexchange",
"id": 15406,
"tags": "quantum-mechanics, particle-physics, big-bang"
} |
Torsional Pendulum: Deriving an expression with time Period, Suspension Length, Moment of Inertia and Rigidy Modulus Constant | Question: I have been looking for the derivation/place where I can quote the formula $T=\frac{2\pi}{r^2}\sqrt{\frac{2IL}{\eta\pi}}$ from as I remember seeing in class but can't seem to find it online to quote/derive it for my self.
Clarification:
For
$$T=\frac{2\pi}{r^2}\sqrt{\frac{2IL}{\eta\pi}}$$
$I$ is the moment of inertia, $L$ is suspension length, $\eta$ is the rigidity modulus of the material and $T$ is the time period.
Any help would be greatly appreciated.
Answer: For relatively small (see Note) angular twists of the wire, the torque $\tau$ which restores the wire to its untwisted position is proportional to the angle $\theta$ through which the end of the wire is rotated : $$\tau=-\kappa \theta$$
$\kappa$ is called the torsion constant of the wire. The minus sign indicates that the direction of the torque is opposite to the direction in which angle $\theta$ is increasing.
The torque causes rotational acceleration $\ddot\theta$ of mass at the end of the wire. Newton's 2nd Law for this acceleration is $$\tau=I\ddot\theta$$ where $I$ is the moment of inertia of the mass. This is the rotational equivalent of $F=ma$.
Combining the above two equations, the equation of motion for the torsional pendulum is $$\ddot\theta+\frac{\kappa}{I}\theta=0$$
This has the form $\ddot x+\omega^2 x=0$ which describes Simple Harmonic Motion. Here $\omega=2\pi f$ is the angular frequency of the periodic motion (radians per second) and $f$ is frequency (cycles per second; one cycle is $2\pi$ radians). Period and frequency are related by $f=\frac{1}{T}$ and $\omega=\sqrt{\frac{\kappa}{I}}$ therefore $$T=\frac{2\pi}{\omega}=2\pi\sqrt{\frac{I}{\kappa}}$$
This can be compared with the period of a mass on a spring : $$T=2\pi\sqrt{\frac{m}{k}}$$ The moment of inertia $I$ is equivalent to mass $m$ and the torsion constant $\kappa$ is equivalent to the force constant $k$ or stiffness of the spring.
The final difficult step is to relate torsion constant $\kappa$ to the dimensions of the wire and its shear modulus $\eta$. This calculation is done in Deriving the Shear Modulus S From the Torsion Constant κ. The result is $$\kappa=\frac{\eta \pi r^4}{2L}$$ in which $r$ is the radius of the wire and $L$ its length. Substituting into the equation for the period we get $$T=2\pi\sqrt{\frac{2LI}{\eta \pi r^4}}$$ which is the formula you were given.
Note
The angle $\theta$ through which the end of the wire is rotated is not the same as the angle of twist $\psi$ along the length of the wire. Whereas $\theta$ is measured by the rotation of a radius in the base of the wire, $\psi$ is measured by the twist of a line parallel to the axis. The two are related by $$L\psi=r\theta$$
To ensure that the elastic limit of the wire is not exceeded $\psi$ should be small, typically no more than $10^{\circ}$. However since $L\gg r$ the angle $\theta$ can be quite large. The base can be rotated a whole circle without exceeding the elastic limit. | {
"domain": "physics.stackexchange",
"id": 64677,
"tags": "harmonic-oscillator, oscillators"
} |
Namespace and Remapping | Question:
Hello all,
I have been reading the documentation and running test examples on namespaces and remaps but I still cannot achieve what I am trying to do. My attempts have also spawned new questions which I could not find answers to.
First Problem: My node publishes topics in the following manner:
/mynode/[robot_name]/sim/twist
/mynode/[robot_name]/sim/odom
/mynode/[robot_name]/sim/base_scan
I would like to remap the sim/* commands to other commands:
/mynode/[robot_name]/sim/twist -> /[robot_name]/cmd_vel
/mynode/[robot_name]/sim/odom -> /[robot_name]/odom
/mynode/[robot_name]/sim/base_scan -> /[robot_name]/base_scan
Note, that [robot_name] is dynamic, based on an input file. (Just like stage's robot_0, robot_1, robot_2, etc).
Removing the node name was simple, but the sim/* -> new_name did not work.
In the launch file:
<remap from="/mynode" to ="/" /> --- This works
<remap from="sim/twist" to ="cmd_vel" /> --- These don't
<remap from="sim/odom" to ="odom" /> --- These don't
<remap from="sim/base_scan" to ="base_scan" /> --- These don't
Could anyone offer any suggestions on a fix?
Second Problem: When I remap "/mynode" to "/", parameters I pass into my node aren't found anymore. NodeHandle.searchParam does not find them, but they still exist. For example:
namespace of node = "/" (this is because of the remap above)
parameters = "/mynode/PARAM1" , "/mynode/PARAM2" (parameters are not remapped!!)
As stated, searchParams does not find them, but getParam("/mynode/Param1") works (and of course getParam("Param1") fails since the node's namespace changed. Does anyone have any thoughts? Thank you for your time!
Originally posted by Constantin S on ROS Answers with karma: 296 on 2011-10-28
Post score: 6
Answer:
I think your problem arises from the difference between a NodeHandle (constructed as NodeHandle nh;) and a private NodeHandle (Nodehandle nh("~");) that you probably use.
I suspect you only use the second, which will put everything in the node's namespace (mynode). This is what you want for parameters, but not necessarily for topics, etc.
So: Use the private NodeHandle for getting parameters and a "normal" NodeHandle for creating topics/services. That should clean up a lot of your problems.
Originally posted by dornhege with karma: 31395 on 2011-10-28
This answer was ACCEPTED on the original site
Post score: 13
Original comments
Comment by Constantin S on 2011-10-29:
This, sir, is beautifully elegant. Thank you. | {
"domain": "robotics.stackexchange",
"id": 7125,
"tags": "ros, remap, parameter"
} |
How to flatten the image of a label on a food jar? | Question: I'd like to take pictures of labels on a jar of food, and be able to transform them so the label is flat, with the right and left side resized to be even with the center of the image.
Ideally, I'd like to use the contrast between the label and the background in order to find the edges and apply the correction. Otherwise, I can ask the user to somehow identify the corners and sides of the image.
I'm looking for general techniques and algorithms to take an image that is skewed spherically (cylindrically in my case) and can flatten the image. Currently the image of a label that is wrapped around a jar or bottle, will have features and text that shrinks as it recedes to the right or left of the image. Also the lines that denote the edge of the label, will only be parallel in the center of the image, and will skew towards each-other on the right and left extreme of the label.
After manipulating the image, I would like to be left with an almost perfect rectangle where the text and features are uniformly sized, as if I took a picture of the label when it was not on the jar or bottle.
Also, I would like it if the technique could automatically detect the edges of the label, in order to apply the suitable correction. Otherwise I would have to ask my user to indicate the label boundaries.
I've already Googled and found articles like this one: flattening curved documents, but I am looking for something a bit simpler, as my needs are for labels with a simple curve.
Answer: A similar question was asked on Mathematica.Stackexchange. My answer over there evolved and got quite long in the end, so I'll summarize the algorithm here.
Abstract
The basic idea is:
Find the label.
Find the borders of the label
Find a mapping that maps image coordinates to cylinder coordinates so that it maps the pixels along the top border of the label to ([anything] / 0), the pixels along the right border to (1 / [anything]) and so on.
Transform the image using this mapping
The algorithm only works for images where:
the label is brighter than the background (this is needed for the label detection)
the label is rectangular (this is used to measure the quality of a mapping)
the jar is (almost) vertical (this is used to keep the mapping function simple)
the jar is cylindrical (this is used to keep the mapping function simple)
However, the algorithm is modular. At least in principle, you could write your own label detection that does not require a dark background, or you could write your own quality measurement function that can cope with elliptical or octagonal labels.
Results
These images were processed fully automatically, i.e. the algorithm takes the source image, works for a few seconds, then shows the mapping (left) and the un-distorted image (right):
The next images were processed with a modified version of the algorithm, were the user selects the left and right borders of the jar (not the label), because the curvature of the label cannot be estimated from the image in a frontal shot (i.e. the fully automatic algorithm would return images that are slightly distorted):
Implementation:
1. Find the label
The label is bright in front of a dark background, so I can find it easily using binarization:
src = Import["https://i.stack.imgur.com/rfNu7.png"];
binary = FillingTransform[DeleteBorderComponents[Binarize[src]]]
I simply pick the largest connected component and assume that's the label:
labelMask = Image[SortBy[ComponentMeasurements[binary, {"Area", "Mask"}][[All, 2]], First][[-1, 2]]]
2. Find the borders of the label
Next step: find the top/bottom/left/right borders using simple derivative convolution masks:
topBorder = DeleteSmallComponents[ImageConvolve[labelMask, {{1}, {-1}}]];
bottomBorder = DeleteSmallComponents[ImageConvolve[labelMask, {{-1}, {1}}]];
leftBorder = DeleteSmallComponents[ImageConvolve[labelMask, {{1, -1}}]];
rightBorder = DeleteSmallComponents[ImageConvolve[labelMask, {{-1, 1}}]];
This is a little helper function that finds all white pixels in one of these four images and converts the indices to coordinates (Position returns indices, and indices are 1-based {y,x}-tuples, where y=1 is at the top of the image. But all the image processing functions expect coordinates, which are 0-based {x,y}-tuples, where y=0 is the bottom of the image):
{w, h} = ImageDimensions[topBorder];
maskToPoints = Function[mask, {#[[2]]-1, h - #[[1]]+1} & /@ Position[ImageData[mask], 1.]];
3. Find a mapping from image to cylinder coordinates
Now I have four separate lists of coordinates of the top, bottom, left, right borders of the label. I define a mapping from image coordinates to cylinder coordinates:
arcSinSeries = Normal[Series[ArcSin[\[Alpha]], {\[Alpha], 0, 10}]]
Clear[mapping];
mapping[{x_, y_}] :=
{
c1 + c2*(arcSinSeries /. \[Alpha] -> (x - cx)/r) + c3*y + c4*x*y,
top + y*height + tilt1*Sqrt[Clip[r^2 - (x - cx)^2, {0.01, \[Infinity]}]] + tilt2*y*Sqrt[Clip[r^2 - (x - cx)^2, {0.01, \[Infinity]}]]
}
This is a cylindrical mapping, that maps X/Y-coordinates in the source image to cylindrical coordinates. The mapping has 10 degrees of freedom for height/radius/center/perspective/tilt. I used the Taylor series to approximate the arc sine, because I couldn't get the optimization working with ArcSin directly. The Clip calls are my ad-hoc attempt to prevent complex numbers during the optimization. There's a trade-off here: On the one hand, the function should be as close to an exact cylindrical mapping as possible, to give the lowest possible distortion. On the other hand, if it's to complicated, it gets much harder to find optimal values for the degrees of freedom automatically. (The nice thing about doing image processing with Mathematica is that you can play around with mathematical models like this very easily, introduce additional terms for different distortions and use the same optimization functions to get final results. I've never been able to do anything like that using OpenCV or Matlab. But I never tried the symbolic toolbox for Matlab, maybe that makes it more useful.)
Next I define an "error function" that measures the quality of a image -> cylinder coordinate mapping. It's just the sum of squared errors for the border pixels:
errorFunction =
Flatten[{
(mapping[#][[1]])^2 & /@ maskToPoints[leftBorder],
(mapping[#][[1]] - 1)^2 & /@ maskToPoints[rightBorder],
(mapping[#][[2]] - 1)^2 & /@ maskToPoints[topBorder],
(mapping[#][[2]])^2 & /@ maskToPoints[bottomBorder]
}];
This error function measures the "quality" of a mapping: It's lowest if the points on the left border are mapped to (0 / [anything]), pixels on the top border are mapped to ([anything] / 0) and so on.
Now I can tell Mathematica to find coefficients that minimize this error function. I can make "educated guesses" about some of the coefficients (e.g. the radius and center of the jar in the image). I use these as starting points of the optimization:
leftMean = Mean[maskToPoints[leftBorder]][[1]];
rightMean = Mean[maskToPoints[rightBorder]][[1]];
topMean = Mean[maskToPoints[topBorder]][[2]];
bottomMean = Mean[maskToPoints[bottomBorder]][[2]];
solution =
FindMinimum[
Total[errorFunction],
{{c1, 0}, {c2, rightMean - leftMean}, {c3, 0}, {c4, 0},
{cx, (leftMean + rightMean)/2},
{top, topMean},
{r, rightMean - leftMean},
{height, bottomMean - topMean},
{tilt1, 0}, {tilt2, 0}}][[2]]
FindMinimum finds values for the 10 degrees of freedom of my mapping function that minimize the error function. Combine the generic mapping and this solution and I get a mapping from X/Y image coordinates, that fits the label area. I can visualize this mapping using Mathematica's ContourPlot function:
Show[src,
ContourPlot[mapping[{x, y}][[1]] /. solution, {x, 0, w}, {y, 0, h},
ContourShading -> None, ContourStyle -> Red,
Contours -> Range[0, 1, 0.1],
RegionFunction -> Function[{x, y}, 0 <= (mapping[{x, y}][[2]] /. solution) <= 1]],
ContourPlot[mapping[{x, y}][[2]] /. solution, {x, 0, w}, {y, 0, h},
ContourShading -> None, ContourStyle -> Red,
Contours -> Range[0, 1, 0.2],
RegionFunction -> Function[{x, y}, 0 <= (mapping[{x, y}][[1]] /. solution) <= 1]]]
4. Transform the image
Finally, I use Mathematica's ImageForwardTransform function to distort the image according to this mapping:
ImageForwardTransformation[src, mapping[#] /. solution &, {400, 300}, DataRange -> Full, PlotRange -> {{0, 1}, {0, 1}}]
That gives the results as shown above.
Manually assisted version
The algorithm above is full-automatic. No adjustments required. It works reasonably well as long as the picture is taken from above or below. But if it's a frontal shot, the radius of the jar can not be estimated from the shape of the label. In these cases, I get much better results if I let the user enter the left/right borders of the jar manually, and set the corresponding degrees of freedom in the mapping explicitly.
This code lets the user select the left/right borders:
LocatorPane[Dynamic[{{xLeft, y1}, {xRight, y2}}],
Dynamic[Show[src,
Graphics[{Red, Line[{{xLeft, 0}, {xLeft, h}}],
Line[{{xRight, 0}, {xRight, h}}]}]]]]
This is the alternative optimization code, where the center&radius are given explicitly.
manualAdjustments = {cx -> (xLeft + xRight)/2, r -> (xRight - xLeft)/2};
solution =
FindMinimum[
Total[minimize /. manualAdjustments],
{{c1, 0}, {c2, rightMean - leftMean}, {c3, 0}, {c4, 0},
{top, topMean},
{height, bottomMean - topMean},
{tilt1, 0}, {tilt2, 0}}][[2]]
solution = Join[solution, manualAdjustments] | {
"domain": "dsp.stackexchange",
"id": 306,
"tags": "image-processing, computer-vision"
} |
What is the meaning of this wave function? | Question: In these notes here the tight binding model for graphene is worked out.
The tight Binding Hamiltonian is the usual:
$$H=-t\sum_{\langle i,j\rangle}(a_{i}^{\dagger}b_{j}+h.c.)$$
where two different sets of creation/annihilation operators are used because there are 2 different sub lattices in graphene (indicated with A and B).
Then it says at the bottom of page 3 that
It is convenient to write the TB eigenfunctions in the form of a spinor, whose components correspond to the amplitudes on the A and B atoms respectively
So if I understand correctly the wave function is a two component spinor with the first component corresponding to sub lattice A and the second to sub lattice B:
$$\psi=\begin{bmatrix}\psi_{A}(x) \\ \psi_{B}(x)\end{bmatrix} \quad .$$
The problem is that I don't understand the meaning of a wave function like that. In the case of spin for me it makes sense to have a two component wave function:
$$\psi=\begin{bmatrix}\psi_{up}(x) \\ \psi_{down}(x)\end{bmatrix} \quad ,$$ where for example $|\psi_{up}(x)|^2$ gives the probability density of finding the electron at position x with spin up.
But in the previous case what does it mean? Is $|\psi_{A}(x)|^2$ the probability density of finding the electron at x on sub lattice A? I can't make sense of this statement.
Any suggestions on how to interpret that?
Answer: The basis here consist of all the lattice sites, which can be label by the position of a unit cell, $x_i$ and the atom in this cell (A or B):
$$
\phi_{i,A}(x), \phi_{i,B}(x)\leftrightarrow \phi_{i,\alpha} (i=A,B).
$$
The arbitrary wave function than can be written es an expansion in this basis:
$$
\psi(x)=\sum_{i,\alpha}c_{i,\alpha}\phi_{i,\alpha} =
\sum_{i}c_{i,A}\phi_{i,A}(x) + \sum_{i}c_{i,B}\phi_{i,B}(x)=\psi_A(x) + \psi_B(x)
$$
Since the orbitals $\phi_{i,\alpha}$ are localized on the sites, some matrix elements will be non-zero only between $A$ and $B$, while others only between $A$ and $A$ or $B$ and $B$, which makes it convenient to use the matrix notation.
As an instructive example, one could solve a problem of a one-dimensional chain with two identical masses in a unit cell. | {
"domain": "physics.stackexchange",
"id": 87980,
"tags": "quantum-mechanics, wavefunction, solid-state-physics, graphene, tight-binding"
} |
Find the number of iterations for Amplitude Amplification to get the correct states amplified | Question: I'm trying to use Grover operator in Qiskit (more precisely to perform Amplitude Amplification) but I'm facing some problems. I'm experimenting the Quantum Amplitude Amplification in order to amplify some states of an arbitrary quantum input states providing more than one solutions (sometimes more than half of the total states). In particular, I'm struggling with the right number of iterations that I have to provide in order to get the best results.
I have seen that Qiskit already provides a method to compute this optimal number, but in my case it doesn't work as expected. Indeed, I have as input state a quantum circuit of 5 qubits and as solutions the following states: '11111' and '11110'. Following the theory and the Qiskit's method, the optimal number of iterations is 3 but providing this number I obtain the opposite result that I expect.
Indeed, I see that the procedure amplifies all the states except the last two that correspond to my solutions. However, with 1 iteration the procedure amplifies the correct states. The problem is that it seems not possible to estimate the correct number of iterations to get the correct results when I choose a custom circuit as StatePreparation.
I also provide the example code that I'm using to generate the solution.
Hope someone can help me,
Thank you.
Answer: Taking the problem generally, we have an operator $O$ defined such that $O|k\rangle = (-1)^{f(k)}|k\rangle$ for all computational basis states $|k\rangle$ where $f(k) \in \{0, 1\}$ for all $k$, and a unitary state preparation $U$ and its inverse. Defining $G = U(2|0\rangle\langle0| - I)U^{\dagger}O$, we want to know the value $q$ such that the probability that $G^q U|0\rangle$ will be measured on the computational basis as a -1 eigenvector of $O$ is maximized.
$|\psi\rangle = U|0\rangle$ can be written in the form $\cos(\theta) |\psi_b\rangle + \sin(\theta)|\psi_g\rangle$ where $0 \leq \theta \leq \pi/2$ for two $|\psi_b\rangle$ and $|\psi_g\rangle$ that are unit eigenvectors of $O$ corresponding to 1 and -1 eigenvalues respectively. Treating this geometrically as just a unit vector on a 2D real plane, applying $O$ will reflect the vector across $|\psi_b\rangle$, and applying $2|\psi\rangle\langle\psi| - I$ will reflect the new vector across $|\psi\rangle$. Applying them in order will result in $\cos(3\theta)|\psi_b\rangle + \sin(3 \theta)|\psi_g\rangle$, and then $G^q |\psi\rangle = \cos((2q + 1)\theta)|\psi_b\rangle + \sin((2q + 1)\theta)|\psi_g\rangle$. Since the probability of measuring a good state is best if $(2q + 1)\theta = \frac{\pi}{2}$, we get what can be rounded to the nearest integer as the number of iterations, independent of any more details of $U$, $O$, and $|\psi\rangle$ other than $\theta$.
Qiskit's built-in optimal_num_iterations (source https://qiskit.org/documentation/_modules/qiskit/algorithms/amplitude_amplifiers/grover.html#Grover.optimal_num_iterations) calculates $a = \sin(\theta)$ ("amplitude") as $\sqrt{s/2^n}$ where $s$ is the number of solutions and $n$ the number of qubits, and then solves for $q = \frac{\pi}{4\theta} - \frac{1}{2} = \frac{\pi}{4 \sin^{-1}(a)} - \frac{1}{2} = \frac{\cos^{-1}(a)}{2\sin^{-1}(a)}$. The amplitude of $|\psi_g\rangle$ is guaranteed as $\sqrt{s/2^n}$ only in the uniform superposition case, so this built-in function won't work if the state preparation is different.
In the more general case, you'll need to know the value of $\theta$ beforehand, or have a procedure classically or quantum to derive it, to know the number of iterations to do. The value of $\theta$ can be worked out in general using a separate quantum phase estimation circuit to measure the period of $G$ applied to $|\psi\rangle$ with a number of additional qubits corresponding to the desired level of precision: in very small cases, this will take sufficient effort so as to invalidate the potential advantage, but asymptotically the phase estimation circuit will remain only about as large as the Grover circuit run afterwards armed with knowledge of $\theta$. | {
"domain": "quantumcomputing.stackexchange",
"id": 4921,
"tags": "qiskit, grovers-algorithm, amplitude-amplification"
} |
What direction does the angular velocity of an object lie on if linear velocity is in XY axis? | Question: So,I was watching the solution of a question of rotational motion. The object's rotational motion was in XY plane. And the direction of angular velocity of the object was given to be along Z-axis in the solution. Now, I cannot understand how the angular velocity can possibly be along that direction. I expected it to be either along clockwise or anticlockwise direction, but on the XY plane either way.
So, please tell me where I am going wrong here. Also,I am a total beginner at this subject, so please frame your answers bearing thing in mind.
Answer: Consider a particle that moves instantaneously in a circle of radius R about an axis perpendicular to the plane of motion. If the origin is a point on the axis, then the time rate of change of the position vector is its linear velocity, whose magnitude is $$v = R \omega$$
The directions of the vectors $\vec \omega, \vec r$ and $\vec v$ are orthonormal, and the direction of $\vec \omega$ is defined (by convention) such that
its positive direction is normal to the plane and corresponds to the direction of advance of a right-hand screw when turned in the same sense as the rotation of the particle (the right hand screw rule). It can even be defined this way:
Simply put, a counter-clockwise rotation corresponds to $\vec \omega$ being along the positive z - axis, and a clockwise rotation corresponds to $\vec \omega$ being along the negative z - axis.
Also, by doing so we can formuate the vector form of the previous equation:
$$\vec v = \vec \omega \times \vec r$$
which satisfies both, the equation relating their magnitudes, and the direction of the vector $\vec \omega$.
Hope this helps
Image source | {
"domain": "physics.stackexchange",
"id": 90359,
"tags": "rotational-kinematics"
} |
Calculating the enthalpy of polymerisation of ethylene given the bond strengths | Question:
Given the average bond dissociation enthalpies of a $\ce{C-C}$ bond (say $x$) and a $\ce{C=C}$ bond (say $y$), find the enthalpy of the following polymerisation reaction (per mole of ethylene):
$$\ce{nCH_2=CH_2 -> [-CH2-CH2 -]_n}$$
where $n$ is a large integer and $x, y$ are in $\pu{kJ/mol}$.
According to me, this should simply be $y-x$ as for every double bond broken, a single bond is formed. But the source book of this problem states the answer to be $y-2x$ claiming that for every double bond broken, 2 single bonds are formed.
How is this possible?
Answer: The mistake I was making was not noticing that every time a double bond is broken, i.e.; completely broken, 2 single bonds are formed in its place.
One bond between the 2 carbons of the same molecule and another between two molecules, the former of which I forgot to consider.
Thus, the enthalpy is in fact $y-2x$ | {
"domain": "chemistry.stackexchange",
"id": 10184,
"tags": "thermodynamics, polymers, enthalpy"
} |
File parser convert to node data and neighbouring relational data | Question: I have been working on a file parser that takes a very specific file format and parses it into a list that is arranged into node data and the neighbors that it relates to. I am new to Python (this is my very first program in this language), so I am not familiar with more advanced methods of solving the problem using Python.
The program runs very quickly: I get an average of about Elapsed time: 0.0006923562137193841 with a test file, but think it could be even better, especially if I task it with a significantly larger file.
Seeking from question:
Optimization in the form of cleaner methods
Decrease the overall runtime
Verification of estimated runtime: \$O(N * E)\$. I got this because there are N nodes, which each contain E edges. However, this may or may not be incorrect.
General style comments for Python coding
Input file example:
The following would be 1 line of data in the file. This file could contain thousands of lines, each line identifying a node and the neighbors that it has.
100 Alpha 123 321 ((101,Beta,123,321)(101,Gamma,123,321)(102,Alpha,123,321)(103,Alpha,123,321)(104,Beta,123,321)(105,Alpha,123,321)(099,Gamma,123,321)(098,Beta,123,321)(097,Beta,123,321)(222,Gamma,123,321)(223,Beta,123,321)(234,Gamma,123,321)(451,Beta,123,321)(999,Beta,123,321)(879,Gamma,123,321)(369,Gamma,123,321)(741,Beta,123,321)(753,Beta,123,321)(357,Beta,123,321)(159,Alpha,123,321))
The parsing would end with the line containing only "At the last row".
import os
import timeit
__author__ = 'Evan Bechtol'
"""
Parses through a file given the appropriate filepath. Once a filepath
has been received, the Parser instance opens and begins parsing out the
individual nodes and their neighbor node relationships. Each node is an
index of the nodeList, which contains a sub-list of the nodes that are neighbors
of that node.
The structure is created as follows:
nodeList: A list that is 'n' nodes long. The sub-list containing neighbors is of
length 'e', where 'e' is the number of neighbor-edges.
numNeighbors: A list that contains the number of neighbors for each node from 0 to (n-1)
Resulting runtime of class: O(N*E)
"""
class Parser:
# Constructor accepting filepath for file to read
# as am argument. The constructor also calls readFile with
# the filepath to begin parsing the specific file.
def __init__(self, filePath):
self.nodeList = []
self.numNeighbors = []
self.readFile(filePath)
# Add nodes the the nodeList in order that they appear
def setNodeData(self, id, sector, freq, band, neighborList):
tmpData = ((id), (sector), (freq), (band), (neighborList))
return tmpData
# Add neighbors to the neighborList in the order that they appear
def setNeighborData(self, id, sector, freq, band):
tmpData = ((id), (sector), (freq), (band))
return tmpData
# Returns the entire nodeList as a string
def getNodeList(self):
return str(self.nodeList)
# Return a specific node of the nodeList with all of its' neighbors
def getNodeListIndex(self, index):
return str(self.nodeList[index])
# Return a specific neighbor for a given node
def getNodeNeighbor(self, node, neighbor):
return str(self.nodeList[node][4][neighbor])
# Retrieves the location of the line to begin retrieving node and
# neighbor data in the file. This eliminates any data above the actual
# data required to build node and neighbor relationships.
def searchForStartLine(self, data):
startLine = "-default- - - - - "
numLines = 0
for line in data:
numLines += 1
if startLine in line:
return numLines
# Removes parenthesis from the line so that neighbors can be parsed.
# Returns the line with all parenthesis removed and individual neighbors
# are separated by spaces.
def removeParens(self, line):
# First, remove all parenthesis
line = line.strip("((")
line = line.strip("))")
line = line.replace(")(", " ")
return line
# Splits the provided line into the required sections for
# placement into the appropriate lists.
# The reference node is parsed first and stored into the nodeList
#
# Once the nodeList is updated, the neighbor data is then parsed from
# the line and stored in the neighborList for the reference node.
def splitLine(self, line):
# Separate into individual reference nodes
splitLine = line.split()
line = self.extractNode(line, splitLine)
# Get each individual node from the specific line. This is referred to as the
# "reference node", which represents the node that we will be creating a specific
# list of neighbors for.
# Each reference node is unique and contains a unique neighborList.
def extractNode(self, line, splitLine):
# Get all of the node data first and store in the nodeList
nodeId = splitLine[0]
sector = splitLine[1]
freq = splitLine[2]
band = splitLine[3]
line = self.removeParens(splitLine[4])
# Separate into individual neighbors
neighbor = line.split()
# Contains the number of neighbors for each reference node
self.numNeighbors.append(len(neighbor))
# Place each neighbor tuple into the neighborList
neighborList = self.extractNeighbors(neighbor)
self.nodeList.append(self.setNodeData(nodeId, sector, freq, band, neighborList))
return line
# Get the parsed list of neighbors for all nodes, then append
# them to the neighborList in order that they are read.
def extractNeighbors(self, neighbor):
# Create a temporary storage for the neighbors of the reference node
neighborList = []
# Separate each neighbor string into individual neighbor components
for i in range(len(neighbor)):
neighbor[i] = neighbor[i].replace(",", " ")
neighbor[i] = neighbor[i].split()
nodeId = neighbor[i][0]
sector = neighbor[i][1]
freq = neighbor[i][2]
band = neighbor[i][3]
# Append the components to the neighborList
neighborList.append(self.setNeighborData(nodeId, sector, freq, band))
return neighborList
# Read the file and remove junk data, leaving only the node and neighbor
# data behind for storage in the data structure
def readFile(self, fileName):
# Check if the file exists at the specified path
if not os.path.isfile(fileName):
print ('File does not exist.')
# File exists, will attempt parsing
else:
with open(str(fileName)) as file:
data = file.readlines()
# Look for the first sign of data that we can use, read from that location
currentLine = self.searchForStartLine(data)
# Read from file until we find the last line of data that we need
lastLine = "At the last row"
for line in data:
if lastLine in data[currentLine + 1]:
break
else:
nodeId = data[0]
self.splitLine(data[currentLine])
currentLine += 1
return file.read()
# Read file, given the exact file path
startTime = timeit.timeit()
parse = Parser("<file_path>")
#print(parse.getNodeNeighbor(1, 0))
print (parse.nodeList[0][4][0])
endTime = timeit.timeit()
print ("Elapsed time: " + str(endTime - startTime))
Answer: Style
Use snake_case for functions and variables.
Leave 1 line between methods.
Don't overwrite keywords, id, file. Use synonyms or id_, the former is preferred.
Keep lines to a maximum of 79. (Comments should be a maximum of 72 however.)
Avoid excessive white-space.
Use one space between both sides of the assignment operator. E.G. a = 1, not a = 1.
As @Quill said docstrings are good.
And you should write them instead of some of your comments in your code.
Algorithms
setNodeData Can be shortened to just:
def setNodeData(self, id_, sector, freq, band, neighborList):
return ((id_), (sector), (freq), (band), (neighborList))
searchForStartLine should use the builtin enumerate.
def searchForStartLine(self, data):
start_line = "-default- - - - - "
for line_num, line in enumerate(data):
if start_line in line:
return line_num
splitLine is only used once. Also you overwrite line and don't use it after the overwrite.
Consider removing it.
extractNeighbors can be simplified to a list comprehension, and could be simpler that way.
It is also faster than appending to an existing list.
I first used the * operator on the slice [:4]. This way you don't have to define sector, etc.
I then removed the need for i, there is no need for it, as everything uses neighbor[i].
def extractNeighbors(self, neighbors):
return [
self.setNeighborData(
*(neighbor.replace(",", " ").split()[:4])
)
for neighbor in neighbors
]
We can do roughly the same thing above to extractNode, to minimise code.
First remove all the noise of sector etc. We will use *(splitLine[:5]).
You only make changes to splitLine[4], and the other informaton just clutters that.
def extractNode(self, splitLine):
splitLine[4] = self.extractNeighbors(
self.removeParens(splitLine[4]).split()
)
self.numNeighbors.append(len(splitLine[4]))
self.nodeList.append(self.setNodeData(*(splitLine[:5])))
In readFile you should change the for loop.
for line in data:
You don't use line, and you do currentLine += 1.
for line_num, _ in enumerate(data, currentLine):
if lastLine in data[line_num + 1]:
break
else:
nodeId = data[0]
self.splitLine(data[line_num])
It may be better to use range however.
Overall, this will have no effect on the speed.
But it highlights that str.split and str.replace are probably the reasons that it is slow.
This is as they are, if I recall correctly, linear time.
You could try using the optional argument of str.split, maxsplit, to not go through the entire string.
And you wouldn't need to use [:4] and [:5].
The only other way I can see speeding this up would be to use a different algorithm to handle each line in roughly O(n).
I know that we aren't allowed to write compleat rewrites so here is an example I wrote.
There are no speed optimisations.
Same as 1. But try str.split's maxsplit.
I can't comment.
It's throughout. | {
"domain": "codereview.stackexchange",
"id": 14578,
"tags": "python, beginner, parsing"
} |
Explanation of binding energy in decays | Question: Everyone knows that the mass of a system is less than the mass of its components, with the equation:
$M = \sum_i m_i - BE(M) $
Now, if we consider a general decay, lets say
$A \rightarrow \sum_i B_i$
then, for the conservation of the first component of the four-vector momentum we obtain a necessary condition for the decay:
$ M(A) \ge \sum_i M(B_i) $
Isn't this last condition in contradiction with the first one?
The only answer I get is a particle that can decay is not an eigenstate of the system. For this reason it shouldn't have a defined binding energy. So, for example, Tritium, that can decay, hasn't a BE? This appears so illogical if we think about nuclei with an half-life of years or more. Moreover I know this energy is experimentally defined and is bigger that 3He's BE.
Answer: The thing here is that when a particle decays (NB here I talk about point-like decays, I'll address decaying compound systems later), the products were not "in" the original particle in the first place.
That is
$$A \to b + c + d$$
does not imply that $A$ was made up of $b$ and $c$ and $d$. It implies the combination of two facts
That $A$ and $b+c+d$ have compatible quantum numbers.
That $M_A$ is sufficiently larger than $M_b + M_c + M_d$ to allow for the products to escape from each other.
In other words a neutron is a particle distinct from the collection of a proton, an electron and a electron anti-neutrino, but those of the neutron's quantum numbers that are respected by the charged-current weak interaction are the same as the collection of lighter particles and the neutrons mass is high enough to produce them.
Compound systems with tree-level decays
Now consider beta decay of a non-trivial nucleus. Let's take tritium for the sake keeping the writing simple. The fact that the system is bound means
$$M_T < M_p + 2M_n \,.$$
But it is still true that
$$M_{^3\mathrm{He}^{+2}} + e^- + \bar{\nu}_e < M_T\,$$
and the quantum number of the resulting system are compatible with those of a Triton
Alpha-decay
Alpha decay is a little different. There is no tree-level transformation there, instead there are multiple masses to think about. I'm going to use $m$ to label the mother isotope, $d$ for the daughter isotope and $\alpha$ for the alpha particle.
Here we have a hierarchy of masses. The mother isotope is bound, so we know that
$$ M_m < Z_m M_p + (A_m - Z_m) M_n \,.$$
(Here $Z_m$ and $A_m$ are the charge number and mass number of the mother isotope.)
But, because the decay is energetically allowed we also know that
$$M_d + M_\alpha < M_m \,,$$
which is to say that the combined system of the daughter and an alpha is more bound than the mother isotope. | {
"domain": "physics.stackexchange",
"id": 14403,
"tags": "energy-conservation, radiation, binding-energy"
} |
Embedding Values in word2vec | Question: Are the embedding values for a particular word using word2vec Skipgram model the weights of the first layer or the softmax output of the function?
Does the embedding value change according to the training corpus?
Answer: The word embeddings are the weights of the first layer i.e. the embedding layer and not the softmax output of the function. The embedding values represent a vector which gives the location of the word with respect to other words in a high dimensional vector space. And yes, the embedding values change according to the training corpus. However, if you are using a given language (for example English) and have a large amount of training data the final values of the vectors will turn out to be pretty close even with training corpus of different contexts. | {
"domain": "datascience.stackexchange",
"id": 7041,
"tags": "machine-learning, nlp, word2vec, machine-translation"
} |
Pion $SU(2)$ representation with two light flavors of quark | Question: I am working through Srednicki's Quantum Field Theory. I'm in chapter 94 and, perhaps I missed something, but I'm wondering how he arrived at a result.
He has the pion fields in his Lagrangian written as
$$\pi^aT^a\qquad(1)$$
This would be in $SU(2)$ and so when Srednicki later explains that $T^a=\frac{1}{2}\sigma^a$. I took that to mean the $\sigma^a$ here refers to the Pauli matrices.
Later in the chapter, however, Srednicki shows:
$$\pi^a\sigma^a=\begin{pmatrix}
\pi^0 & \sqrt{2}\pi^+\\
\sqrt{2}\pi^- & -\pi^0\\
\end{pmatrix}\qquad(2),$$
which is not what I'd expect if I did that sum over the index $a$ (which I presume runs from $1,2,3$ in order of the Pauli matrices).
Did I miss a detail? Am I wrong in assuming $\sigma^a$ here refers to the Pauli matrices? Is it that the $\pi^{\pm}$ here are actually combinations of two other fields?
Answer: This is just the same thing rewritten in a different basis—the basis of charge eigenstates, rather than the $SU(2)$ eigenstates. The physical charged pion fields are complex linear combinations of the $a=1,2$ components of the isotriplet, $\pi^{\pm}=\frac{1}{\sqrt{2}}(\pi^{1}\mp i\pi^{2})$. The other physical pion state, the neutral state, is $\pi^{0}=\pi^{3}$. Thus the expansion $\pi^{a}\sigma^{a}$ may be written
$$\pi^{a}\sigma^{a}=\pi^{1}\left[
\begin{array}{cc}
0 & 1 \\
1 & 0
\end{array}\right]+\pi^{2}\left[
\begin{array}{cc}
0 & -i \\
i & 0
\end{array}\right]+\pi^{3}\left[
\begin{array}{cc}
1 & 0 \\
0 & -1
\end{array}\right]\\
=\left[
\begin{array}{cc}
\pi^{3} & \pi^{1}-i\pi^{2} \\
\pi^{1}+i\pi^{2} & -\pi^{3}
\end{array}\right]=\left[
\begin{array}{cc}
\pi^{0} & \sqrt{2}\pi^{+} \\
\sqrt{2}\pi^{-} & -\pi^{0}
\end{array}\right].$$
This is similar to the decomposition of the Pauli matrices in terms of $\sigma^{3}$ and the raising and lowering matrices $\sigma^{\pm}=\frac{1}{2}\left(\sigma^{1}\pm i\sigma^{2}\right)$, which are
$$\sigma^{+}=\left[
\begin{array}{cc}
0 & 1 \\
0 & 0
\end{array}\right],\quad \sigma^{-}=\left[
\begin{array}{cc}
0 & 0 \\
1 & 0
\end{array}\right].$$ | {
"domain": "physics.stackexchange",
"id": 93258,
"tags": "quantum-field-theory, particle-physics, pions"
} |
Point2D.Double wrapper | Question: I have made a Point2D.Double wrapper so I can add my own functionality (like a dominate method) and alter some (like toString) and control some (like not having public access to x and y).
Point class:
public class Point implements Serializable {
private final Point2D.Double point2D;
public Point(double x, double y) {
this.point2D = new Point2D.Double(x, y);
}
public Point(String line, String delimiter) {
line = line.trim();
String[] lineArray = line.split(delimiter);
double x = Double.parseDouble(lineArray[0]);
double y = Double.parseDouble(lineArray[1]);
this.point2D = new Point2D.Double(x, y);
}
public boolean dominates(Point point) {
return (this.getX() <= point.getX() && this.getY() < point.getY())
|| (this.getY() <= point.getY() && this.getX() < point.getX());
}
public double getX() {
return point2D.getX();
}
public double getY() {
return point2D.getY();
}
@Override
public boolean equals(Object o) {
return point2D.equals(o);
}
@Override
public int hashCode() {
return point2D.hashCode();
}
@Override
public String toString() {
StringBuilder builder = new StringBuilder();
builder.append('(').append(point2D.getX()).append(", ").append(point2D.getY()).append(')');
return builder.toString();
}
}
Answer: I took a look and came up with a couple of suggestions:
Extend rather than wrap
I think it will be more useful if you extend the Point2D.Double class, instead of writing a wrapper around it. This way you will be able to use your custom point class everywhere that a normal Point2D.Double is expected. It also spares you from implementing and overriding many of the Double's methods like getX() and the hashCode() and toString() methods.
Use static method for construction from line
When subclassing Double it is not possible to have a constructor that takes a line, does some calculations and then calls super(), as super has to be the first call in the constructor. Therefor we need to add a static utility class to create a Point from a line. See the fromLine() method below.
I think this is not a problem, as it leads to very readable line:
Point start = Point.fromLine(line);
Documentation
Your code does not include any documentation in form of comments, so that for example the input format for the fromLine() function is not entirely clear. Also it only uses one point from a line (which should be two points?), so maybe it should be called fromLineStart() or fromLineEnd() depending on which you mean.
Class Naming
The current name Point doesn't tell us a lot about what the class does. Maybe use something a little more descriptive like PointDouble2D? Maybe add some indication as that it does more than the normal Point2D.Double, by naming it: PointDouble2DAdvanced or something like that, not totally sure myself :)
Final Result
Here is the entire code example, without documentation comments:
import java.awt.geom.Point2D;
public class PointDouble2D extends Point2D.Double {
public Point(double x, double y) {
super(x, y);
}
public boolean dominates(Point2D.Double point) {
return (getX() <= point.getX() && getY() < point.getY())
|| (getY() <= point.getY() && getX() < point.getX());
}
@Override
public String toString() {
StringBuilder builder = new StringBuilder();
builder.append('(').append(getX()).append(", ").append(getY())
.append(')');
return builder.toString();
}
public static PointDouble2D fromLineStart(String line, String delimiter) {
line = line.trim();
String[] lineArray = line.split(delimiter);
double x = java.lang.Double.parseDouble(lineArray[0]);
double y = java.lang.Double.parseDouble(lineArray[1]);
return new PointDouble2D(x, y);
}
}
What do you think? | {
"domain": "codereview.stackexchange",
"id": 10803,
"tags": "java, wrapper"
} |
How pure is the tone produced by a typical tuning fork in air? | Question: When a musical instrument plays a note that note is usually just the highest amplitude contribution to the sound wave. That peak is known as the fundamental harmonic, and the Fourier transform of the sound wave also has peaks at higher frequency harmonics, known as overtones, and possibly at lower frequencies, called undertones. These peaks have finite width, and there's frequently some kind of overlap.
How pure is the tone produced by a typical tuning fork? Specifically, ignoring questions of the bandwidth of the peak, how much do overtones and undertones contribute to the sound of a tuning fork? The answer, of course, will be, "It depends on the tuning fork," but it is still interesting to ponder what is produced by typical tuning forks.
Answer: One way to see answers to this question is to enter "tuning fork spectrogram" (without quotes) into a search engine. The answer, qualitatively, is fairly pure, after the initial high pitch transients from striking it die out.
In the spectrograms presented in this work (Douglas Lyon, “The Discrete Fourier Transform, Part 5: Spectrogram”, Journal of Object Technology, Volume 9, no. 1 (January 2010),pp. 15-24), Figures 4 and 5, the tuning fork clearly has both overtones and undertones present in the spectrogram. Qualitatively, though, Figure 4 (the one with a linear stretch) makes it appear that the fundamental is very dominant, probably at least a factor of 2 louder than the nearest harmonic (a difference of about 3 decibels). The downside is that this kind of quantitative statement based on the presented information could be wildly inaccurate (the numbers are guessed).
This video presents a spectrum for a recording of a tuning fork, but the horizontal axes are difficult to read.
The followup video shows animations of the different modes from a finite element analysis. This video is interesting primarily for it's demonstration of how many of the higher frequency modes are unbalanced, producing motion at the part of the tuning for that is held/mounted, leading to their increased damping speed.
Downloading the audio from the first YouTube video and feeding part of it (roughly time code 2:21.75 to 2:25.6) into Audacity gives me a spectral analysis of the tuning fork recording (Hamming window).
As you can see from the plot, the next highest peaks are about $46\operatorname{dB}$ down from the fundamental. | {
"domain": "physics.stackexchange",
"id": 39350,
"tags": "acoustics, fourier-transform"
} |
Python Console App | Is there a better way to go back a page? | Question: I have a system for going back to a previously-visited page in a Python console application; it works well enough, but I feel that there could be a prettier way of doing it. Does anyone have any suggestions to improve what I have below?
def main():
try:
while True:
print('Main Menu\n')
option = input('page 1, page 2, quit\n')
if option in ['1', 'one']:
menu_stack.append(0)
page_one()
elif option in ['2', 'two']:
menu_stack.append(0)
page_two()
elif option in ['q', 'quit']:
quit()
else:
print('Invalid input, please try again\n')
sleep(1)
except KeyboardInterrupt:
quit()
Very similar to the main menu page, below is page 1:
def page_one():
while True:
clear_terminal()
print('Page One\n')
option = input('Page 2, back\n')
if option in ['2', 'two']:
menu_stack.append(1)
page_two()
elif option in ['b', 'back']:
menu_checker()
else:
print('Invalid input, please try again\n')
sleep(1)
menu_checker() calls the other pages based on what pops from the stack:
def menu_checker():
page = menu_stack.pop()
if page == 1:
page_one()
elif page == 2:
page_two()
elif page == 0:
main()
else:
print('Error')
Does anyone have any better ideas/solutions? Even though it doesn't cause any issues (as far as I am aware), I feel what I have is kind of clunky and could be improved.
Answer: I'm thinking there are a few different approaches you could take here.
The stack was inside you all along
It may not be the most flexible of approaches, but the way things are right now, your pages are just functions. And guess what? Your program already has a stack of functions -- you navigate it by calling functions and returning from them! You don't get a whole lot of information about where you'll end up if you return, but if that's not a problem, you might be able to just get rid of menu_checker and menu_stack altogether -- if the user wants to go back, you just return.
For example, your page_one could simply look like
def page_one():
while True:
clear_terminal()
print('Page One\n')
option = input('Page 2, back\n')
if option in ['2', 'two']:
page_two()
elif option in ['b', 'back']:
return
else:
print('Invalid input, please try again\n')
sleep(1)
It's not the fanciest-looking perhaps, but it's easy to implement, easy to understand and does the job just fine.
Where do you want to go?
But maybe that isn't good enough. It might be nice if the "back" option could say something like "Back (to page 1)" depending on what the stack looks like, for example. Or maybe you'd like to also have a "forward" option in case the user accidentally presses "back" too many times. Or maybe there's another reason you don't want to use the call stack for this. That's fine too.
Another option could be to move the navigation logic from the individual menus into a single core loop. Each menu then returns which menu it thinks you should go to next.
For example, we might be looking at something like this:
def main():
menu_stack = [main_menu]
while menu_stack:
current_menu = menu_stack[-1]
next = current_menu(option)
if next:
menu_stack.append(next)
else:
menu_stack.pop()
With menus looking a lot like the previous ones, but instead of calling the next menu like page_two() they return it like return page_two. Or perhaps return None if we should go back.
Classy
Personally, though, I think there are some tasks (like asking for input) that should be the responsiblity of the app itself rather than the menus. The menu can know what it looks like and how to navigate based on input, but the core loop asks it for help and then handles those things on its own terms.
def main():
menu_stack = [main_menu]
while menu_stack:
current_menu = menu_stack[-1]
clear_terminal()
print(current_menu.text)
option = input(current_menu.prompt)
try:
next = current_menu.get_next_menu(option)
if next:
menu_stack.append(next)
else:
menu_stack.pop()
except ValueError as e:
print("Invalid input, please try again")
sleep(1)
Defining a nice Menu class is left as an exercise for the reader. | {
"domain": "codereview.stackexchange",
"id": 40673,
"tags": "python, stack"
} |
Question about the Bernouilli equation | Question: There are some things I encountered, studying the Bernouilly equation, that I don't understand. I was studying in the following book: http://www.unimasr.net/ums/upload/files/2012/Sep/UniMasr.com_919e27ecea47b46d74dd7e268097b653.pdf. At page 72-73 they derive the Bernouilli equation for the first time, from energy considerations. They state that it can be applied if the flow is steady, incompressible, inviscid, when there is no change in internal energy and no heat transfer is done (p.72 at the bottom). I understand this derivation, my problems arise when they derive the equation again at page 110-111, this time from the Navier-Stokes equation.
I don't quite understand the derivation yet, but I am more confused about the outcome. It seems that the Bernouilli equation can now be applied under the four conditions they state (inviscid flow, steady flow, incompressible flow and the equation applies along a streamline) while it seems that there are no limitations to the internal energy of the flow and the heat transfer done. If I understand the last paragraph right, they state that the requirement that the flow is inviscid already comprises the claim that there is no change in internal energy ("the constant internal energy assumption and the inviscid flow assumption must be equivalent, as the other assumptions were the same", I don't really understand this reasoning, because the "inviscid flow assumption" was also already made in the previous derivation).
Furthermore, if I follow the reasoning (so if I assume that inviscid flow indeed implies that there is no change in internal energy or if I assume that the Bernouilli equation can also be applied, without the assumption of "no change in internal energy") then example 4 at page 74 seems strange to me. It shows that in this situation the Bernouilli equation can't be applied directly (because headloss has to be included in the equation). However I think that we can easily repeat the derivation, assuming that the flow is inviscid (and assuming that the other conditions are satisfied), but this example shows that the internal energy increases, so inviscid flow can't imply "no change in internal energy". And the example also shows that the Bernouilli equation can't be applied, because head loss has to be considered (so this example seems to contradict the result at page 110-111).
I hope someone can explain where my understanding is lacking, because this really confuses me about the conditions under which the Bernouilli equation can be applied.
It would also be helpful, if someone could explain the derivation at p.110: what I don't understand is the definition of "streamline coordinates". Do they just take a random point on the streamline, where they place a cartesian coordinate system?
Answer: Yes, they look at how the point (on the streamline) moves as a result of the defined quantities (pressure, density, velocity, etc).
Since Bernoulli's equation results from an equation of conservation of energy, you are assuming no loss of energy, which means no friction, which for fluids means no viscosity, which means inviscid flow.
So the equation is $v^2/2+gy+P/\rho = const$, which has no change in internal energy (i.e. $U_1=U_2$).
Example on pg74, however, has a change in internal energy, but that's because here the fluid is not inviscid.
OK was going to leave this for you to puzzle through, but just for completeness: because of the immediate area change of the pipe, with the constant steady pressure $P_1>0$, there is turbulent flow (high Reynolds number, depicted in the picture by the swirls), corresponding to viscosity and hence not inviscid. | {
"domain": "physics.stackexchange",
"id": 9094,
"tags": "fluid-dynamics, bernoulli-equation"
} |
UWSim install problem, Ubuntu 12.04,ROS Groovy | Question:
Hi,
I have some problems on using command "rosrun uwsim uwsim" to run uwsim following errors are showing:
Jack@Jack:~$ rosrun uwsim uwsim
Starting UWSim...
. Setting localized world: 6.1e-05s
Loading URDF robot...
· robot/GIRONA500/g500_March11.osg: 2.67438s
· robot/ARM5E/ARM5E_part0.osg: 0.082435s
· robot/ARM5E/ARM5E_part1.osg: 0.119529s
· robot/ARM5E/ARM5E_part2.osg: 0.127205s
· robot/ARM5E/ARM5E_part3.osg: 0.439133s
· robot/ARM5E/ARM5E_part4_base.osg: 0.420119s
· robot/ARM5E/ARM5E_part4_jaw1.osg: 0.065359s
· robot/ARM5E/ARM5E_part4_jaw2.osg: 0.058875s
· Linking links.../opt/ros/groovy/lib/uwsim/uwsim: line 20: 25729 Segmentation fault (core dumped) rosrun uwsim uwsim_binary --dataPath ~/.uwsim/data $@
Thank you for your help!
Originally posted by Cong Wang on ROS Answers with karma: 1 on 2014-09-12
Post score: 0
Answer:
I will answer this one as it seems the only one "legit", I mean try to post your question in a new question rather than copy-paste it in every single uwsim tagged question please this just causes confusion.
As Miquel answered in other post do you have 3d support in your computer?, and have you tried starting it with --disableShaders option?. Segmentation fault at loading usually means a problem with graphic card/drivers so check if 3d is working.
Originally posted by Javier Perez with karma: 486 on 2014-09-16
This answer was ACCEPTED on the original site
Post score: 1 | {
"domain": "robotics.stackexchange",
"id": 19394,
"tags": "ros, ubuntu, uwsim"
} |
Efficient representation of set of partial order | Question: I guess that notions I describe are already well known, may be by combinatorician, but I do not know their name or any book/article about them. So if you have a link/title I would love to read it.
Let $r$ be an integer, let $P_r$ be the set of partial (pre)order over $[1,r]$ and $T_r$ the set of total (pre)order. I say that $P\in P_r$ is included in $T\in T_r$ if it is included as subset of $[1,r]^2$, or to state it another way, if for all $i,j$ with $i$ less than $j$ for $P$ then it is also less for $T$. Finally I say that $P$ and $P'$ are incompatible if there is $i,j$ with $i<j$ for $P$ and $i>j$ for $P'$ (or if $i=j$ for $P$ and $i<j$ for $P'$).
Let $P\in P_r$ with $i<j$ and no $k$ such that $i<k<j$, then $P_{i,j}$ is the same partial (pre)order, except that $i$ and $j$ are incomparable.
I would like to find an efficient data structure to store a subset of $P_r$. I can't imagine something better than a trie of depth $r(r-1)/2$, with one level for every pair $(i,j)$ with $i<j$. If possible I would want to be able to efficiently add and remove elements from the set, or at least to easily transform $P$ into $P_{i,j}$ as defined above.
I need to know if for a given subset $S$ of $P_r$ and $P\in P_r$, $P$ is incompatible with every $P'\in S$. Or an equivalent problem would be to figure out if a set $S$ is such that its element are one to one incomparable. I also need to know if for every total (pre)order $T$ it is a superset of a partial order $P\in S$.
Intuitively, to each $P\in P_r$ is associate its set $T_P=\{T\in T_r\mid T\supseteq P\}$ and I need to know if $(T_P)_{P\in S}$ form a partition of $T_r$.
Then let $T_S=\bigcup_{P\in S} T_P$, then I would also be interested by having a way to efficiently describe $T_S$. (That is, efficiently checking for a given $T\in T_r$ if $T\in T_S$.
Finally, I will introduce the real structure I'm interested in, which is more complicated and probably less usual.
A partial preorder $P$ can be seen as partial function from $[1,r]^2$ to $\{<,>,=\}$, where $i=_P j$ if $i<j$ and $j<i$ in $P$ and $f(i,j)$ is undefined if neither $i<j$ nor $i>j$ in $P$. We can associate to $P$ a subset of $\mathbb N^r$ called $\mathbb N_P$ defined by $(x_1,\dots,x_r)\in \mathbb N_P$ if for all $i<_Pj$ $x_i<x_j$ and for all $i=_Pj$, $x_i=x_j$.
The real data structure I must study is the structure of partial function from $[1,r]^2$ to $\{<,\le,>,\ge,=,\not=\}$. I will call this structure "extended preorder". Let $P$ be an extended preorder, where $(x_1,\dots,x_r)\in \mathbb N_P$ if for all $i<_Pj$ $x_i<x_j$ and for all $i=_Pj$, $x_i=x_j$, for all $i\le j$, $x_i\le x_j$, and for all $i\not_P=j$, $x_i\not=x_j$.
I say that a total preorder $T$ is included in an extended preorder $P$ if $i\le_Pj$ implies $i<_Tj$ or $i=_Tj$, and $i\not=_Pj$ imply $i<_Tj$ or $j<_Ti$.
The operation I must have are still the same, having a set $S$ of extended preorder, verify if an extended preorder is incompatible with every extended preorder of the set, and verify that every total preorder is included in an extended preorder of the set. Or to say it another way, $(\mathbb N_P)_{P\in S}$ is a partition of $\mathbb N^r$.
Answer: Restrictions on pre-orders
You've described that you would like to assert restrictions on a given pre-order: for instance, that specifically $a < b$ rather than merely $a \leqslant b$, so that it would not be compatible with a pre-order in which $a \cong b$ (that is $a \leqslant b$ and $b \leqslant a$). We can achieve this by supplementing the pre-order with a list of forbidden relationships: that is, we specify $a < b$ using a pre-order which specifies $a \leqslant b$ along with many other relationships, and by separately specifying that $b \leqslant a$ is forbidden.
We may similarly represent $a \not\cong b$ by having any pre-order in which at least one of $a \leqslant b$ or $b \leqslant a$ fails to hold. (I got this confused in a previous edit.)
So: we will consider how to represent pre-orders, and presume that we have a list of further restrictions representing relations of the type $\leqslant$, $\geqslant$, and $\cong$ which we forbid between certain pairs. (For each pair $(a,b)$, there are then four possibilities for forbidden relations, including the the case of no forbidden relation.) The forbidden relations I would represent as a list, which we will later iterate through exactly once; however, in order to be able easily to remove restrictions when computing the order $P_{a,b}$ from a pre-order $P$, you might want to combine this list structure with an $r \times r$ array $F$ which stores for each $1 \leqslant a < b \leqslant r$ what sort of relation (if any) is forbidden between $a$ and $b$.
Representing pre-orders
You can easily represent a partial order by a transitive reduction: a minimal relation (naturally represented as a directed graph, via adjacency lists for immediate predecessors and immediate successors) subject to the constraint of having the partial order as its transitive closure. For a pre-order, you can instead use a relation $R$ which would be the transitive reduction if you "collapsed" all sets of equivalent elements to a single item each; where for all $i \leqslant j$, we have $(i,j) \in R$ if and only if $\exists k: i \leqslant k \leqslant j$ implies that $j \leqslant i$. That is, $(i,j) \in R$ only if one of the following holds:
$i < j$ and $\neg\exists k: i < k < j$;
$i \leqslant j$ and $j \leqslant i$.
Such a relation can be easily computed by reduction to computing the transitive reduction of the partial order obtained, as I described, by collapsing equivalence classes (using only one representative node for each equivalence class, and then copying relations across the class). This can be done in time $O(r^3)$ or better.
Given such a representation of pre-orders $P$ by reductions $R$, one may decide $(i,j) \in P$ by testing $(i,j)$-connectivity in $R$, e.g. by breadth-first search. This, of course, takes time $O(n)$. However, one can quite efficiently compute the reduction $R_{i,j}$ of the pre-order $P_{i,j}$ for $i<j$, by
copying the immediate successors of $j$ and sharing them with $i$,
copying the immediate predecessors of $i$ and sharing them with $j$,
removing the relation $(i,j)$ from $R$.
The complexity of this is essentially the sum of the in-degree of $i$ and the out-degree of $j$. I imagine that you would also like to remove the prohibition on $i \leqslant j$ and/or $j \leqslant i$ at the same time; we can achieve this simply by removing any restrictions which are stored at $F[i,j]$ or $F[j,i]$ as appropriate.
Representing subsets of $S \subseteq P_r$
Assuming that all you want to use the subsets $S \subseteq P_r$ for is to check compatibility of individual pre-orders with the elements of $S$, I think the best approach is to store an $r \times r$ array where each element $(i,j)$ contains a collection which indicates the labels of all pre-orders $P \in S$ such that $(i,j) \in P$. (That is: you do not need to store any forbidden relationships.)
The collection may as well be a simple list, for small sets $S$ or if the orders which it contains don't have too many common relations (e.g. minimal and maximal elements in common); otherwise use your set-implementation of choice (e.g. balanced search trees) instead. This can be updated simply by adding a new relation $P'$ to the entries for all pairs $(i,j)$ which are contained in $P'$. If $P'$ is represented by a reduction $R'$, one may do this by a depth-first search from its minimal elements (which one may store a list of in the representation), and performing depth-first search to find all descendants of each element.
If one maintains a list of traversed nodes along each path of the traversal, one may add each newly traversed node to the descendants of each of those already on the list; after finishing a traversal, pop the node off the list and mark it as visited.
For each visited node, we copy its descendants to any nodes on the traversal-list, rather than re-traversing it.
This is also a good thing to do, to compute a more explicit representation of $P'$ from $R'$, once your interest in $P'$ becomes dominated by testing $(i,j) \mathbin{\in?} P'$. This will take time $O(r^2)$, as there is essentially unit cost to reverse each edge $(i,j) \in R$, and to record each of the descendants of any $i \in [1,r]$ throughout the traversal. If $s = |S|$ and you use trees for collections at each index $(i,j)$, constructing the representation for $S$ takes time $O(r^2 s \log s)$, with the $\log s$ factor being saturated in the case where many elements of $S$ share many pairs $(i,j)$ in common. This works best for partial orders which are sparse and essentially unrelated, which would reduce both the expected overlap for pairs $(i,j)$ and the number of entries $(i,j)$ for which any relationship is recorded in the traversal of its reduction.
Having this representation of $S$, you can test incompatibility of $P$ with $S$ (where $P$ is given by a reduction $R$) as follows.
Initialise a list of all of the elements of $S$, representing those which are potentially compatible with $P$.
Iterate through your forbidden relations, and remove from the list of potentially compatible relations, any element of $S$ which violates any of the constraints. (That is, if $a \leqslant b$ is forbidden, remove any element of $S$ for which that relation holds; and similarly for any element of $S$ fo which $a \cong b$, if that relation is forbidden.)
Perform a breadth-first search of $R$: and at each link $(i,j) \in R$ traversed, remove from the list of potentially-compatible orders any order $P$ for which $j < i$, by checking for each order on the list whether this is the case.
If the list of potentially-compatible orders ever becomes empty, then $P$ is incompatible with $S$. Otherwise, the list contains at least one partial order in $S$ with which $P$ is compatible.
We can bound each index search $(i,j)$ for a potentially-compatible order by $O(\log s)$, for $s =|S|$; this will happen for each "reduced" relation in $P$, that is for every ordered pair in $R$. If $m = |R|$, then the worst case is $O(ms \log s) \subseteq O(r^2 s \log s)$, in the case that every element of $S$ is compatible with $P$. If you have $f = |F|$ forbidden relationships, then iterating through these and eliminating potentially compatible relations takes time $O(f \log s)$; this is also dominated by $O(r^2 \log s)$, though the larger $f$ is the faster the subsequent compatibility-checking becomes. | {
"domain": "cstheory.stackexchange",
"id": 1994,
"tags": "ds.algorithms, partial-order, order-theory, total-ordering"
} |
On the singularity of Biot-Savart's law inside a current-carrying conductor | Question: When using Biot-Savart's law to compute magnetic flux density on a field point away from a current source point, the integrand is finite; however when using it to compute the field inside the source where "R" the distance between field and source is zero the integrand is singular.
All three versions, i.e. for linear currents, surface and volume currents this problem arises.
$$ B = \frac{\mu_0}{4\pi}\int_V \frac{J_v \times a_R}{R^2}dv $$
$$ B = \frac{\mu_0}{4\pi}\int_S \frac{J_s \times a_R}{R^2}ds $$
$$ B = \frac{\mu_0}{4\pi}\int_C \frac{Idl \times a_R}{R^2} $$
where $J_v$ and $J_s$ are the volume and surface current densities. $a_R$ is the unit vector pointing from source to field point.
Does the formula states that the magnetic flux density is infinitely large inside the source? Because this seems impossible.
I encountered this problem when I was trying to find the flux density on a surface current. The same issue happens when calculating the self-inductance using Neumann's formula.
Answer:
Does the formula states that the magnetic flux density is infinitely large inside the source? Because this seems impossible.
This situation occurs only when the current distribution is curve-like, with zero thickness (or point-like, due to moving charged point-like particle). Then magnetic field diverges at the line (or the point). This does not necessarily mean it is "infinitely large" at that line or point.
It is "infinitely large" in the sense its magnitude diverges to infinity when one approaches to the current line or point from any direction. But there is no single limit, because direction of magnetic field always depends on the direction of approach. This is a mathematical fact. It is not correct to say this is impossible in mathematics.
This means that we have a discontinuous magnetic field, not infinite magnetic field. In fact, magnetic field definition can be sometimes completed even in that point of singularity. For example, if there is other source of magnetic field, this acts on the line/point, and we can define total magnetic field at the line/point as the external magnetic field due to the other source.
If the current distribution is planar, i.e. current is running in a plane, then there may not be a divergence at all. If finite line element in the plane, perpendicular to the current, is associated with finite current passing through it, then even infinite plane with net infinite current will create finite magnetic field in both half-spaces. This follows from Ampere's law; magnetic intensity times length of a line segment equals net current intensity associated with that length. | {
"domain": "physics.stackexchange",
"id": 89168,
"tags": "singularities, magnetostatics"
} |
Transmission and track chain | Question:
I added a "transmission" block in the URDF to describe the model of the tracks of my robot...
My tracks are triangular, with an active sprocket and two passive sprockets. The active sprocket is rotated according to joint state message in my "control node".
I expected that this kind of description resulted in a automatic joint state update of the passive sprockets in Rviz, but I think to have not understood very well how "transmission" works.
Does transmission work only in Gazebo?
Originally posted by Myzhar on ROS Answers with karma: 541 on 2015-02-12
Post score: 1
Answer:
If you mean ros_control's transmissions, only simple reducers are supported in Gazebo.
It sounds like you need to implement a custom transmission type. Is this what you are trying to do?. If so, what is exactly the behavior you want to produce: That the active sprocket triggers motion of the two passive ones, or do you also want to move some sort of track geometries?.
Originally posted by Adolfo Rodriguez T with karma: 3907 on 2015-02-12
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by Myzhar on 2015-02-14:
I would like to move the passive sprockets according to the angular position of the active respecting the radius ratio propagated by the track chain.
I was going to create a subscriber to the joint_state message submitted by the "active" sprockets, but it does not seems a good solution to me.
Comment by Adolfo Rodriguez T on 2015-02-17:
If you just want the passive sprockets to move as a linear function of the active one, consider using mimic joints (look for <mimic> element documentation).
Comment by Myzhar on 2015-02-17:
Great!!! It is just what I was searching for!!!
Thank you very much
Comment by Adolfo Rodriguez T on 2015-02-17:
Glad to hear!. Please mark the question as answered if it is indeed the case.
Comment by Adolfo Rodriguez T on 2015-02-19:
Hey, for the record. To mark a question as answered, you don't need to close it and provide a reason. There's a checkmark icon to the left of every answer. Once you click on it, it becomes green, and the question is considered answered. You can only accept one answer (when there are more than one).
Comment by Myzhar on 2015-02-19:
Done... I thought that closing it was the most complete way. Thank you again | {
"domain": "robotics.stackexchange",
"id": 20859,
"tags": "ros, rviz, urdf, transmission"
} |
No debugging symbols found in base_local_planner library | Question:
Hey everyone,
I'm new to ROS. At the moment I'm using Eclipse CDT to debug the move_base node, more specifically the default local planner (base_local_planner/TrajectoryPlannerROS). When I start the move_base node, Eclipse can apparently find the debugging symbols for all the necessary packages (navfn, costmap_2d, etc) except for base_local_planner (libbase_local_planner.so). Indeed when I run the command "file libbase_local_planner.so" inside gdb, it tells me there's no debug symbol for that library.
I've tried to make sure the "-g" option was actually used to link the library, but I admit I got lost in the cmake files.
However I don't remember changing any linking option anywhere... anyone's got a clue to what may cause the problem? (and are the debugging symbols for this library present in your setup?)
Thanks,
Simon C
Originally posted by SimonC on ROS Answers with karma: 13 on 2011-10-10
Post score: 1
Answer:
The base_local_planner has the build type set to "Release" in the CMakeLists.txt which does not include debug symbols. Change it to RelWithDebug and recompile to get debugging symbols. Usually the release type should be commented out in released code to allow the system builder to change the build type for the whole system. You might want to open a ticket about this for the base_local_planner package.
Originally posted by tfoote with karma: 58457 on 2011-10-10
This answer was ACCEPTED on the original site
Post score: 3
Original comments
Comment by SimonC on 2011-10-11:
Thanks that was it! Not sure why I didn't spot the option...! | {
"domain": "robotics.stackexchange",
"id": 6922,
"tags": "navigation, ros-diamondback, eclipse, base-local-planner"
} |
Recording Audio Continuously in C | Question: As an ongoing little side project of mine, I've been working on recording audio in c. You can the code's progression by looking at past versions (V1.0, V2.0).
I've found that my past versions were too limited. They required a certain time frame for which they would record, and then stop. This isn't very practical for many real-world applications, so I rewrote everything so the computer would always be listening, and only record necessary data.
Here is what I would like reviewed:
Memory consumption: Obviously a huge potential problem is lots of space being consumed in recording and saving the audio to file. Am I wasting space at all? Every little bit counts. Note: file storage container must be FLAC.
Speed: I have to be processing the data in real time. I can't hang for anything or I might lose precious audio data. Is there anywhere I could speed up processing?
Syntax/Styling: How does my code look? What about it could make it look better? Anything I'm doing wrong syntax-wise?
Feel free to review other stuff as well, I would just like reviews to be focused on the above. Keep in mind I've been away from the C language for a bit now, so I may have forgotten some of the more simple things ;)
main.c:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <time.h>
#include <portaudio.h>
#include <sndfile.h>
#define FRAMES_PER_BUFFER 1024
typedef struct
{
uint16_t formatType;
uint8_t numberOfChannels;
uint32_t sampleRate;
size_t size;
float *recordedSamples;
} AudioData;
typedef struct
{
float *snippet;
size_t size;
} AudioSnippet;
AudioData initAudioData(uint32_t sampleRate, uint16_t channels, int type)
{
AudioData data;
data.formatType = type;
data.numberOfChannels = channels;
data.sampleRate = sampleRate;
data.size = 0;
data.recordedSamples = NULL;
return data;
}
float avg(float *data, size_t length)
{
float sum = 0;
for (size_t i = 0; i < length; i++)
{
sum += fabs(*(data + i));
}
return (float) sum / length;
}
long storeFLAC(AudioData *data, const char *fileName)
{
uint8_t err = SF_ERR_NO_ERROR;
SF_INFO sfinfo =
{
.channels = data->numberOfChannels,
.samplerate = data->sampleRate,
.format = SF_FORMAT_FLAC | SF_FORMAT_PCM_16
};
SNDFILE *outfile = sf_open(fileName, SFM_WRITE, &sfinfo);
if (!outfile) return -1;
// Write the entire buffer to the file
long wr = sf_writef_float(outfile, data->recordedSamples, data->size / sizeof(float));
err = data->size - wr;
// Force write to disk and close file
sf_write_sync(outfile);
sf_close(outfile);
puts("Wrote to file!!!!");
return err;
}
int main(void)
{
PaError err = paNoError;
if((err = Pa_Initialize())) goto done;
const PaDeviceInfo *info = Pa_GetDeviceInfo(Pa_GetDefaultInputDevice());
AudioData data = initAudioData(44100, info->maxInputChannels, paFloat32);
AudioSnippet sampleBlock =
{
.snippet = NULL,
.size = FRAMES_PER_BUFFER * sizeof(float) * data.numberOfChannels
};
PaStream *stream = NULL;
sampleBlock.snippet = malloc(sampleBlock.size);
time_t talking = 0;
time_t silence = 0;
PaStreamParameters inputParameters =
{
.device = Pa_GetDefaultInputDevice(),
.channelCount = data.numberOfChannels,
.sampleFormat = data.formatType,
.suggestedLatency = info->defaultHighInputLatency,
.hostApiSpecificStreamInfo = NULL
};
if((err = Pa_OpenStream(&stream, &inputParameters, NULL, data.sampleRate, FRAMES_PER_BUFFER, paClipOff, NULL, NULL))) goto done;
if((err = Pa_StartStream(stream))) goto done;
for(int i = 0;;)
{
err = Pa_ReadStream(stream, sampleBlock.snippet, FRAMES_PER_BUFFER);
if (err) goto done;
else if(avg(sampleBlock.snippet, FRAMES_PER_BUFFER) > 0.000550) // talking
{
printf("You're talking! %d\n", i);
i++;
time(&talking);
data.recordedSamples = realloc(data.recordedSamples, sampleBlock.size * i);
data.size = sampleBlock.size * i;
if (data.recordedSamples) memcpy((char*)data.recordedSamples + ((i - 1) * sampleBlock.size), sampleBlock.snippet, sampleBlock.size);
else
{
free(data.recordedSamples);
data.recordedSamples = NULL;
data.size = 0;
}
}
else //silence
{
double test = difftime(time(&silence), talking);
if (test >= 1.5 && test <= 10)
{
char buffer[100];
snprintf(buffer, 100, "file:%d.flac", i);
storeFLAC(&data, buffer);
talking = 0;
free(data.recordedSamples);
data.recordedSamples = NULL;
data.size = 0;
}
}
}
done:
free(sampleBlock.snippet);
Pa_Terminate();
return err;
}
Compile with: gcc main.c -lsndfile -lportaudio (assuming you have those libraries installed)
Answer: Indeed you must have been working on this project for a while, since I answered a question on SO related to one of your old versions a while back. At least some of the feedback I had is still pertinent even now.
Code and style comments
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <time.h>
#include <portaudio.h>
#include <sndfile.h>
The problem starts already here. You make heavy use of uint32_t and other such types, without #include <stdint.h>. I assume this works because you're probably still on Mac OS X, and this would also explain why your GCC doesn't complain about C99 loop initial declarations without -std=gnu99.
As mentioned previously, you make unnecessary use of pointer arithmetic, which makes the code hard to read. I definitely prefer @nhgrif's version of your average; I find sum += fabs(data[i]); eminently easier on the eye.
The avg() function has at least a few other issues. First, if you want to compute when someone is talking, I wouldn't do a straight average, even with a gimmick like fabs(). I'd do an RMS (Root-Mean-Square) instead and then subtract the regular average (without fabs()) from the RMS value; this computes the audio "power" in the buffer while ignoring any DC bias (non-zero average), which your code isn't robust against. This is directly connected to the number of decibels in your sample by the same power law used to "compand" the input from the microphone (It could be A-law or u-law, or maybe something else).
Second, and related; At 1024 frames and a sample rate of 44100Hz, your buffers cover a period of just 23 milliseconds; In other words, only one complete cycle of a sound with frequency 43 Hz. I don't know how low @rob0t's voice goes, but you may want to increase that amount if you will be dealing with low-frequency content. When computing the RMS and DC (average), you can only get an accurate result if you capture precisely an integer number of cycles for the frequencies of interest to you; But if your buffer spans enough cycles of all frequencies of interest to you, any inaccuracy introduced by partial cycles is drowned out by the complete ones in the average.
Thirdly, your buffer has 1024 frames, but the accumulator is float. I suspect you don't care about precision much here, but you may be interested in knowing that because IEEE floating-point arithmetic isn't exactly like real math, the order in which floating-point values are added may make a small difference. In particular, if you were to add up 1024 identical values, you'll loose about 10 out of 24 bits of precision on your last accumulations. This is because the accumulator will have grown to 2^10 times the size of the accumulands, and additions into the accumulator will only use the 14 MSBs while rounding off the 10 LSBs. I'd use double here unless it were proven to me that avg() is a performance bottleneck and that vectorization has already done all it can.
Fourthly and lastly,
return (float) sum / length;
is entirely redundant: sum is already a float, and you're casting it to float again. If you wanted to carry out this division using floating-point math, this is already guaranteed; In C, floating-point values outrank any integer in the implicit conversions. Remember, casts don't apply to the operation (/), but to their operand (here, sum).
storeFLAC() has no logging in case of errors, so I have no immediate explanations as to why your code, built on Linux, succeeds only in creating zero-length files. The error code it returns is completely ignored.
SNDFILE *outfile = sf_open(fileName, SFM_WRITE, &sfinfo);
if (!outfile) return -1;
// Write the entire buffer to the file
And due to lack of braces around early return statements, it's harder for reviewers to add their own debugging code, because it's that much more of a chore to add braces on top of a debug printf(). It's nice to be considerate to your reviewers, including your future self.
main() is in sore need of refactoring, specifically extraction of a few functions for each major step. The code you wrote does not "speak" to me; I must invest some effort to understand what it does. At least it is approximately a screenful, which is in my opinion a good size for a function.
This is gross misuse of goto:
int main(void)
{
PaError err = paNoError;
if((err = Pa_Initialize())) goto done;
const PaDeviceInfo *info = Pa_GetDeviceInfo(Pa_GetDefaultInputDevice());
AudioData data = initAudioData(44100, info->maxInputChannels, paFloat32);
AudioSnippet sampleBlock =
{
.snippet = NULL,
.size = FRAMES_PER_BUFFER * sizeof(float) * data.numberOfChannels
};
...
done:
free(sampleBlock.snippet);
Pa_Terminate();
return err;
}
While I do approve of goto for error handling, you've here committed the sin of jumping over the initialization of local variables, then bothering to use them. Nothing guarantees that sampleBlock.snippet is initialized when you attempt to free() it: You haven't even done sampleBlock's initialization if PortAudio failed to initialize!
This is an error you would have discovered had you used GCC's and Clang's -Wall -Wextra flags to ask for many, many useful diagnostics. This error was reported as
portaudio.c: In function ‘main’:
portaudio.c:135:6: warning: ‘sampleBlock.snippet’ may be used uninitialized in this function [-Wmaybe-uninitialized]
free(sampleBlock.snippet);
^
. Note however that this warning only appears when optimizations are enabled; This is because the analysis passes GCC requires to discover such uninitialized uses are only run at -O1 and up. It may thus be worthwhile for you to build regularly at high optimization levels, where GCC puts more effort into analysis and can as a side-effect discover potential bugs.
This line:
if((err = Pa_OpenStream(&stream, &inputParameters, NULL, data.sampleRate, FRAMES_PER_BUFFER, paClipOff, NULL, NULL))) goto done;
It's pretty obvious that if you need to scroll that far right, you have greatly exceeded my 80-column soft limit. You've also not put braces around your statement, and here a nice debug printf would have been helpful. I certainly want to know if my stream failed to open.
For functions with a large number of arguments with long names, I tend to put them down one per line. Don't be afraid to spend several lines on them.
Congratulations on your use of difftime() to portably and safely determine time differences. I've learned something. However, time_t is commonly defined as an integer number of seconds since the Epoch. Since you will be calling time() around 43 times per second, many consecutive calls will give the same time, and thus a difference of 0 s, while some calls will give a difference of 1 s, despite only really being separated by 23 ms.
Better here would have been to use a higher-resolution wall-clock timer. For this type of timing I advise gettimeofday(); For extreme resolutions I advise clock_gettime() on Linux, or the much easier-to-use and lower-overhead mach_absolute_time() on Mac OS X.
This is madness:
data.recordedSamples = realloc(data.recordedSamples, sampleBlock.size * i);
data.size = sampleBlock.size * i;
if (data.recordedSamples) memcpy((char*)data.recordedSamples + ((i - 1) * sampleBlock.size), sampleBlock.snippet, sampleBlock.size);
else
{
free(data.recordedSamples);
data.recordedSamples = NULL;
data.size = 0;
}
Firstly, one of your lines here is excessively long again. You've here used the infamous x = realloc(x, ...) idiom, which is awful since if realloc() fails, you will leak memory.
Moreover, you're memcpy()'ing a new block of data into your homebrew resizable vector, on top of any memcpy()'s inside realloc(). Leaving aside the fact that every 23 ms of speech you'll potentially realloc() and copy the entire array of data gathered so far, I seriously query the need for even moving any data at all. It should be possible for you to craft yourself either a double buffer or, more generally, a circular buffer, and avoid any copying at all.
And then on top of that, look at your conditional statement again. If data.recordedSamples is indeed NULL (and thus, you've already leaked memory by loosing your last reference to that block of memory), why are you free()'ing said NULL pointer, then setting said NULL pointer to NULL again? It is completely ineffectual.
Design comments
There is a general lack of documentation in your code. It would be helpful to know the finer points of certain things. For instance, I can quickly take it that you only record in float format, since your undocumented structures use only float*; But what precisely is a sample, snippet or frame, according to either you or PortAudio? What's the interleaving scheme for channels, if any? What is the fundamental difference between an AudioSnippet and AudioData that compelled you to make a different structure for both of them?
Given that you put emphasis on not dropping any audio data at all, I advise that you make this application threaded. One thread would drive the reading of data into a circular buffer, and would perform tasks with negligible computational complexity (presumably, an RMS will take sufficiently little time as to never be the bottleneck). If this thread detects speech, it can message a worker thread to start reading this buffer at the given offset and encode it into a FLAC file. Of course, if the worker thread is too slow, eventually the reading thread will exhaust the circular buffer and will have to block, possibly dropping frames. | {
"domain": "codereview.stackexchange",
"id": 12686,
"tags": "performance, c, audio, memory-optimization"
} |
Why not space out memory allocations? | Question: In ext4 file system, the files are spaced out as far apart as reasonably possible to allow for efficient reallocation. Why do we not do this in memory?
Why not allocate one memory as page 20, and the next large allocation as page 100 to allow for excess expansion before and after the current allocation? I feel that makes sense for large frequently changing-in-size buffers. For smaller buffers, doing so would probably be a drain on memory because we have to allocate each page for a small amount of bytes(but perhaps do it within a block too in the malloc impl). This would also provide greater memory corruption prevention, allowing segfaults(or windows equivalent) to happen quicker(specifically for larger buffers).
Why don't we do this? I get it on modern 32-bit systems because of limited address space, but why not on 64-bit?
Answer: Why is memory different from a hard disk?
Because hard disks have different performance characteristics than RAM.
With hard disks, seeking is extremely slow. Sequential reads are much faster than random-access reads. In other words, it's much faster to read data that is stored consecutively than to store data that's scattered all around the disk. Therefore, there are benefits to making sure your files are contiguous, as much as possible.
RAM doesn't have the same property. With RAM, there is no penalty for "seeking". You can pick any page and read from it, and the cost will be the same, no matter where the page is located. For instance, reading page X and then page Y will have the same cost regardless of whether X and Y are adjacent or not.
So, you end up with different algorithms that are optimized for hardware with different performance characteristics.
Why do hard disks have this strange property? Because they are based on a rotating piece of iron. If you read block X on the hard disk, and next want to read block Y, but Y is on the other side of the platter, then you'll have to wait for the platter to finish rotating far enough for Y to be under the read head. That takes time. RAM doesn't have this property.
Interestingly, the differences are becoming less these days. Today, SSD (solid state storage devices, based on Flash storage) are becoming a popular replacement for hard disks. SSD's have their own performance characteristics, but they're more like RAM than like magnetic hard disks. This means that the filesystem optimizations you'd do for a SSD-oriented filesystem are different from the ones you'd do for a hard-drive-oriented filesystem. Many of today's filesystems were designed decades ago when magnetic hard disks were dominant, and optimize for the performance characteristics of magnetic hard disks.
Why not harden software by deliberately leaving space between buffers?
You are implicitly proposing a scheme for making software more robust against out-of-bounds errors and buffer overruns: leave plenty of unallocated space between each pair of buffers allocated on the heap.
That's not a bad idea. It's been proposed before and studied in considerable depth. It does add some robustness against bugs. It can also make buffer overrun attacks harder, especially if you randomize the location of all heap buffers. It's also relatively easy to deploy in a way that is compatible with legacy software. So it does have some quite attractive advantages.
However, it also has some disadvantages. It imposes some performance overhead -- not a huge amount, but enough to be a bit painful. Why does it impose performance overhead? Largely because it reduces spatial locality. Consider two 16-byte allocations. Current allocators try to pack them together into a single page. In your scheme, we'd have to put each allocation onto its own page. That means we have a lot more pages, which means that we get a lower TLB hit rate.
There are different variants on this scheme, with different performance implications, but they all run up against the challenge: in exchange for the robustness and security benefits, there is some non-zero performance overhead. So that's one reason why people might not adopt it.
The other big reason is: we're using platforms and allocators that were designed decades ago. At the time, security wasn't as critical as it is today, so this sounded like a pretty unattractive proposal: I get to implement something more complicated and fiddly, and it'll make my entire system slower? No thanks.
Today given the magnitude of security problems we're facing, there's gradually increasing interest in these alternatives. But they still face an uphill battle, because of the non-zero performance implications.
To learn more about academic research on this subject, read research papers on the Diehard, Dieharder, and Archipelago systems. They discuss the design in a very accessible way and measure the performance and other costs of such a scheme. If you're still intrigued, you can explore the literature where other researchers have explored other points in the design space to understand their implications.
Bottom line: you're not the first to think of this, and it is a pretty attractive idea, but it also comes with some significant costs. | {
"domain": "cs.stackexchange",
"id": 7091,
"tags": "memory-management, virtual-memory, memory-allocation"
} |
Controllers for interacting with a vacation service | Question: I have a controller called VacationController; in this controller, I retrieve a list of vacations which will be displayed in a grid.
In the grid, I have the option to create a new vacation through a popup window. Should I create a new controller for this popup, considering that the model is represented by one row of the vacation list?
Those are my controllers:
app.controller('app.VacationController', ['$scope', 'vacationService', function ($scope, vacationService) {
var vm = this;
vm.model = {
hasError: false,
errorMessage: '',
hasData:false,
data: []
}
vacationService.get().success(function (vacations) {
vm.model.hasData = vacations.length !== 0;
vm.model.data = vacations;
}).error(function() {
vm.model.hasError = true;
vm.model.errorMessage = 'Error';
});
}]);
app.controller('app.NewVacationController', ['$scope', 'vacationService', function ($scope, vacationService) {
var vm = this;
vm.hasError = false;
vm.error = '';
vm.data = null;
vacationService.getById(0).success(function (vacation) {
vm.data = vacation;
});
vm.createNewVacation = function (viewModel) {
vacationService.post(viewModel.data).success(function () {
alert('success');
});
}
}]);
Answer:
Should I create a new Controller for Insert?
Yes, and here's why. From a maintenance perspective, this is nightmare waiting to happen. The problem will start to appear when you want your popup used somewhere else independent of the list. However, if you bound your popup to the list controller, you can't move it out because you potentially bound the UI of the popup to some variable in the list controller.
The state of the popup should be independent of the list, thus you need to have a controller (or should I call it "view-model") for it.
As for your code:
I suggest you use the more standard then for promises instead of success and error. This makes it easier to swap out your promise libs/native promises when the time comes.
Use breakpoints to debug code instead of alert (or console or debugger). This prevents you from potentially leaving behind debugging code when you push to production. | {
"domain": "codereview.stackexchange",
"id": 16682,
"tags": "javascript, angular.js, controller"
} |
Rosserial_arduino use on an arduino uno with IMU (I2C/Wire library) | Question:
Hey!
I have been testing the rosserial_arduino (http://wiki.ros.org/rosserial) in order to run a ROS node on arduino. I tested some of the examples and thought I had the hang of it. (In case it's useful: I'm running Ubuntu 14.04 on a macbook pro).
However I'm unable to get the arduino node to publish information from the IMU connected to the arduino UNO.
The IMU is the MPU9150 and I'm using an implementation of the I2Cdev library found here: https://github.com/richards-tech/MPU9150Lib (I have tried a different library, in order to understand if the problem was related to this specific library, but ended up with the same problem). If I only use the MPU9150 library, that is, if I don't try to use resserial, I'm able to get the IMU data on the arduino and print it on the serial monitor. However, if I try to use rosserial I'm unable to make the node work.
When I run the serial_node from rosserial I get the following output:
nmirod@nmirod:/$ rosrun rosserial_python serial_node.py _port:=/dev/ttyACM1 _baud:=57600
[INFO] [WallTime: 1422735802.267338] ROS Serial Python Node
[INFO] [WallTime: 1422735802.270908] Connecting to /dev/ttyACM1 at 57600 baud
/home/nmirod/catkin_ws/src/rosserial/rosserial_python/src/rosserial_python/SerialClient.py:336: SyntaxWarning: The publisher should be created with an explicit keyword argument 'queue_size'. Please see http://wiki.ros.org/rospy/Overview/Publishers%20and%20Subscribers for more information.
self.pub_diagnostics = rospy.Publisher('/diagnostics', diagnostic_msgs.msg.DiagnosticArray)
[ERROR] [WallTime: 1422735819.375623] Unable to sync with device; possible link problem or link software version mismatch such as hydro rosserial_python with groovy Arduino
Notice that the SyntaxWarning appears even in the tutorial examples. After some testing it seems that this problem is related to the use of the Wire library. Commenting the functions that perform the initialization and reading of the IMU, I' able to get a msg on the desired topic (although constant). However, if I try to run the node as it is, I get the "Unable to sync with device" error.
Is this problem associated with the "Wire library"/I2C communication? Can you help me out?
EDIT:
Is it possible to use Serial.print()'s in combination with rosserial?
When I wrote this sketch I had the caution to remove all debug prints, to be sure it wouldn't scramble the communication with ros. However, when I was out of options I decided to try to use some Serial.print()'s for debugging and it seems that using Serial.begin(57600) solved the problem (same baud rate as the node).
Althought the problem seems to be solved I still would like to understand what's going on so that if something similar happens down the road I know what to do.
EDIT2:
Here is the code:
#include "ros.h"
#include "rospy_tutorials/Floats.h"
#include "freeram.h"
#include "mpu.h"
#include "I2Cdev.h"
ros::NodeHandle nh;
float aux[] = {9, 9, 9, 9};
rospy_tutorials::Floats msg;
ros::Publisher IMUdata("IMUdata", &msg);
int ret;
void setup()
{
Serial.begin(57600);
Fastwire::setup(400,0);
ret = mympu_open(200);
msg.data_length = 4;
nh.initNode();
nh.advertise(IMUdata);
}
void loop()
{
ret = mympu_update();
if(ret == 0){
aux[0] = mympu.ypr[0];
aux[1] = mympu.ypr[1];
aux[2] = mympu.ypr[2];
}
aux[3] = ret;
msg.data = aux;
IMUdata.publish( &msg );
nh.spinOnce();
}
I still want to add a subscriber to this code, but even thought he works correctly (after the addition of the Serial.begin()), once I have both the subscriber and publisher working I can't get correct data from the IMU, that is, the parameter ret comes equal to -1, what means there was some problem reading the IMU data.
The subscriber will receive an array of floats and control 2 motors throught the use of a H-bridge.
EDIT3:
First, since the previously stated library was really big I switched to the other one I had tried: https://github.com/rpicopter/ArduinoMotionSensorExample
From what I can tell it seems that there is some problem when trying to update the data from the dmp of the MPU9150. the mympu_update() is returning "-1" and from what I see it seems that this happens if the dmp has any problem with it's initialization.
And that problem only happens when I add the publisher.
Another strange thing I noticed is that even if I don't subscribe to the topic I want (that is if I don't do nh.subscribe(sub)), but I still instantiate the subscriber, the same error happens. However if I comment/delete both the subscription to the topic and the instantiation of the subscriber, I'm able to get the data.
The code I'm using right now is:
#include <ros.h>
#include <rospy_tutorials/Floats.h>
#include <std_msgs/Empty.h>
#include "freeram.h"
#include "mpu.h"
#include "I2Cdev.h"
//#include "Wire.h"
//PORTS ASSIGNING
const int motor11 = 8;
const int motor12 = 7;
const int motor21 = 5;
const int motor22 = 4;
const int motorcontrol1 = 6;
const int motorcontrol2 = 11;
//MOTOR CONTROL VARIABLES
int motorflag = 0;
float motor1output = 0;
float motor2output = 0;
ros::NodeHandle nh;
float aux[] = {9, 9, 9, 9};
rospy_tutorials::Floats msg;
ros::Publisher IMUdata("IMUdata", &msg);
int ret;
void receiveMotorControl(const rospy_tutorials::Floats& controlarray){
motor1output = controlarray.data[0];
motor2output = controlarray.data[1];
motorflag = 1;
}
ros::Subscriber<rospy_tutorials::Floats> sub("motorControl", &receiveMotorControl);
void setup()
{
nh.getHardware()->setBaud(57600);
nh.initNode();
nh.advertise(IMUdata);
nh.subscribe(sub);
//Wire.begin();
Fastwire::setup(400,0);
ret = mympu_open(200);
msg.data_length = 4;
//PORT SETUP
pinMode(motor11, OUTPUT);
pinMode(motor12, OUTPUT);
pinMode(motor21, OUTPUT);
pinMode(motor22, OUTPUT);
}
void loop()
{
// if(motorflag == 1){
// motorControl();
// }
ret = mympu_update();
if(ret == 0){
aux[0] = mympu.ypr[0];
aux[1] = mympu.ypr[1];
aux[2] = mympu.ypr[2];
}
aux[3] = ret;
msg.data = aux;
IMUdata.publish( &msg );
nh.spinOnce();
delay(100);
}
void motorControl(){
if(motorflag){
if(motor1output >= 0){
digitalWrite(motor11, HIGH);
digitalWrite(motor12, LOW);
analogWrite(motorcontrol1, motor1output);
}
else{
digitalWrite(motor11, LOW);
digitalWrite(motor12, HIGH);
analogWrite(motorcontrol1, abs(motor1output));
}
if(motor2output >= 0){
digitalWrite(motor21, HIGH);
digitalWrite(motor22, LOW);
analogWrite(motorcontrol2, motor2output);
}
else{
digitalWrite(motor21, LOW);
digitalWrite(motor22, HIGH);
analogWrite(motorcontrol2, abs(motor2output));
}
motorflag = 0;
}
}
And the output I get on the terminal is:
nmirod@nmirod:~$ rosrun rosserial_python serial_node.py _port:=/dev/ttyACM2
[INFO] [WallTime: 1422913940.904599] ROS Serial Python Node
[INFO] [WallTime: 1422913940.912298] Connecting to /dev/ttyACM2 at 57600 baud
/home/nmirod/catkin_ws/src/rosserial/rosserial_python/src/rosserial_python/SerialClient.py:336: SyntaxWarning: The publisher should be created with an explicit keyword argument 'queue_size'. Please see http://wiki.ros.org/rospy/Overview/Publishers%20and%20Subscribers for more information.
self.pub_diagnostics = rospy.Publisher('/diagnostics', diagnostic_msgs.msg.DiagnosticArray, queue_size=None)
/home/nmirod/catkin_ws/src/rosserial/rosserial_python/src/rosserial_python/SerialClient.py:101: SyntaxWarning: The publisher should be created with an explicit keyword argument 'queue_size'. Please see http://wiki.ros.org/rospy/Overview/Publishers%20and%20Subscribers for more information.
self.publisher = rospy.Publisher(self.topic, self.message)
[INFO] [WallTime: 1422913943.242449] Note: publish buffer size is 280 bytes
[INFO] [WallTime: 1422913943.242726] Setup publisher on IMUdata [rospy_tutorials/Floats]
[INFO] [WallTime: 1422913943.251476] Note: subscribe buffer size is 280 bytes
[INFO] [WallTime: 1422913943.251721] Setup subscriber on motorControl [rospy_tutorials/Floats]
Originally posted by nvoltex on ROS Answers with karma: 131 on 2015-01-31
Post score: 3
Original comments
Comment by tonybaltovski on 2015-01-31:
I've used the i2c library without any isseus. Try publishing slower on the arduino.
Comment by nvoltex on 2015-02-01:
Could you check my edit? I still don't understand what's happening.
Comment by tonybaltovski on 2015-02-01:
Can you post your code? Did you try slowing down the publishing rate?
Comment by nvoltex on 2015-02-02:
I have added the code, but note that it's the code before adding the subscriber. By slowing down the publishing rate are you talking about the baudrate used on the node? (thanks for helping!)
Comment by tonybaltovski on 2015-02-02:
I meant adding delay(15); or publishing at a certain rate. You maybe overfilling the serial buffer.
Comment by nvoltex on 2015-02-02:
At the time I tried using different delays however it didn't help. With the addition of Serial.begin() it started working, althought I don't know why that would help. However when I try to add a subscriber to the node, the IMU stops responding (I think he fails to initialize).
Comment by tonybaltovski on 2015-02-02:
Try initializing the node before you start the i2c comm. Also, try manually setting the baud nh.getHardware()->setBaud(BAUD); before the node initializes.
Comment by nvoltex on 2015-02-02:
I tried your suggestions and still got the same problem. I made an edit with some new information and the code I'm using right now.
Comment by tonybaltovski on 2015-02-02:
Did you create the ros_lib machine that is connecting to the Arduino?
Comment by nvoltex on 2015-02-02:
I didn't understand your question. The arduino is connected to a computer running ubuntu 14.04 and I installed the ros library on the arduino IDE following the tutorial: http://wiki.ros.org/rosserial_arduino/Tutorials/Arduino%20IDE%20Setup.
Comment by tonybaltovski on 2015-02-02:
After updates, you may need to remake your ros_lib. Can you run any example sketches currently?
Comment by nvoltex on 2015-02-02:
Yes I can. In fact if I simply comment the parts related to the subscriber, I'm able to get the desired information on the topic /IMUdata (as expected). What seems to be the problem is that once I instantiate the subscriber and subscribe to the desired topic I'm unable to retrieve data from the IMU.
Comment by nvoltex on 2015-02-02:
That is, the output of mympu_update() is '-1' what seems to be related to some problem with the initializaion of the MPU9150's dmp. I added the output I get on the terminal to the last edit. btw, which i2c library did you use? Wire?
Comment by tonybaltovski on 2015-02-02:
I used wire here. That output is normal for it working. Which Arduino are you using? If leonardo, add #define USE_USBCON before #include <ros.h>.
Comment by nvoltex on 2015-02-02:
I'm using an usb uno. The library i'm using for the MPU9150 was using fast-wire and since I was having problems on the configuration of the dmp I decided to switch to wire in hope of better performance. However with wire I'm unable to even connect to the node (like in the original problem).
Comment by tonybaltovski on 2015-02-03:
I think your are just trying to publish to much data at once. I increased the serial buffer on an example here but worked but there were many errors during the connection.
Comment by nvoltex on 2015-02-03:
Thanks for your repository. Thanks to it I added confirmations to the rosserial connection before starting I2C configuration. Although I wasn't able to solve the problem with your help I'm definitely closer to a solution.
Comment by tonybaltovski on 2015-02-03:
Try asking on Github. It maybe that the I2C communication is indeed interfering since it is taking too long.
Comment by nvoltex on 2015-02-04:
Already did that ;) I'm now waiting for a response from the creator. Once I solve the problem will post an answer.
Answer:
In the original problem I was trying to use the DMP of the MPU9150 in order to do the calculations to obtain the Yaw, Pitch and Roll directly from the MPU. However it seemed like the rosserial communication was messing up the DMP configuration and I wasn't able to make the DMP configuration to work once I tried to add both a subscriber and a publisher to the node.
The work-around I ended up using is to simply get the raw data from the IMU (magnetometer, gyro and accelerometer) and publish it to the desired topic. Then I could add a subscriber and I would still be able to get the raw data from the IMU.
This raw data is then processed by a node on the PC and outputs the desired information to another topic.
Note: I would like to thanks tonybaltovski for all the help and I leave here the link to his repository where he uses rosserial in combination with I2C communication with a IMU:
https://github.com/tonybaltovski/ros_arduino
Originally posted by nvoltex with karma: 131 on 2015-02-06
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by tonybaltovski on 2015-02-09:
Try declaring your node handle before you include wire.
Comment by nvoltex on 2015-02-11:
I already tried that and it didn't solve the problem.
Unfortunately I wasn't able to receive an answer from the developers of the library. Tried to contact the developers of rosserial, but no response either. | {
"domain": "robotics.stackexchange",
"id": 20746,
"tags": "arduino, imu, rosserial"
} |
Problem Using Roscore and Roslaunch in Groovy | Question:
I am relatively new to ROS. Recently I installed Groovy on my Linux machine and some new packages only to be given the error:
WARNING: unable to configure logging. No log files will be generated
Checking log directory for disk usage. This may take awhile.
Press Ctrl-C to interrupt
Done checking log file disk usage. Usage is <1GB.
Cannot locate [roslaunch]Invalid tag: Cannot load command parameter [rosversion]: command [rosversion roslaunch] returned with code [1].
Param xml is param command="rosversion roslaunch" name="rosversion"/
Furthermore, I get the same error message when trying to use roscore.
I have seen this error in other threads; however, I have already followed the instructions given and gotten no results.
Is there a way to direct rosversion to the location of roslaunch to get rid of this error?
Originally posted by Jacob Guerra on ROS Answers with karma: 1 on 2013-02-07
Post score: 0
Answer:
We've seen this error when roslaunch is not in your ROS_PACKAGE_PATH. Make sure that it is in your ROS_PACKAGE_PATH. For more information see the wiki page for envionrment variables and filesystem tutorials
Originally posted by tfoote with karma: 58457 on 2013-05-06
This answer was ACCEPTED on the original site
Post score: 0 | {
"domain": "robotics.stackexchange",
"id": 12799,
"tags": "roslaunch, roscore"
} |
erratic simulation does not work after ubuntu updates | Question:
I have been successfully using the erratic robot simulation in Gazebo (fuerte on ubuntu 12.04). I know this is not the recommended way to use Gazebo now, but I have been using simulator_gazebo 1.6.16 (I have just installed Gazebo 1.3).
I installed the erratic robot for simulation using:
sudo apt-get install ros-fuerte-erratic-robot
After some updates were installed (including python-rospkg, ros-fuerte-pr2-controllers, and ros-fuerte-pr2-mechanism) using the ubuntu update manager, I have not been able to launch Gazebo with the erratic robot.
For example, the output of
roslaunch erratic_navigation_apps demo_2dnav_slam.launch
(from (http://www.ros.org/wiki/simulator_gazebo/Tutorials/TeleopErraticSimulation)) is:
This code block was moved to the following github gist:
https://gist.github.com/answers-se-migration-openrobotics/0de983bba3c735ff03db3220ebd89dce
I'm not sure how much of the log files to post, but here is part of the master.log that contains an error (this error also occurs again later in the log file):
...
[rosmaster.master][INFO] 2013-01-15 11:44:10,003: +PUB [/base_scan/scan] /gazebo http://scott-ub:34652/
[rosmaster.master][ERROR] 2013-01-15 11:44:10,004: Traceback (most recent call last):
File "/opt/ros/fuerte/lib/python2.7/dist-packages/rosmaster/master_api.py", line 161, in validated_f
code, msg, val = f(*newArgs, **kwds)
File "/opt/ros/fuerte/lib/python2.7/dist-packages/rosmaster/master_api.py", line 406, in searchParam
search_key = self.param_server.search_param(caller_id, key)
File "/opt/ros/fuerte/lib/python2.7/dist-packages/rosmaster/paramserver.py", line 116, in search_param
raise ValueError("namespace must be global")
ValueError: namespace must be global
And this is the full text of the spawn_robot-4.log:
[rospy.client][INFO] 2013-01-15 11:44:08,337: init_node, name[/spawn_robot], pid[14482]
[xmlrpc][INFO] 2013-01-15 11:44:08,337: XML-RPC server binding to 0.0.0.0
[xmlrpc][INFO] 2013-01-15 11:44:08,338: Started XML-RPC server [http://scott-ub:45884/]
[rospy.init][INFO] 2013-01-15 11:44:08,338: ROS Slave URI: [http://scott-ub:45884/]
[rospy.impl.masterslave][INFO] 2013-01-15 11:44:08,338: _ready: http://scott-ub:45884/
[rospy.registration][INFO] 2013-01-15 11:44:08,338: Registering with master node http://localhost:11311
[xmlrpc][INFO] 2013-01-15 11:44:08,339: xml rpc node: starting XML-RPC server
[rospy.init][INFO] 2013-01-15 11:44:08,438: registered with master
[rospy.rosout][INFO] 2013-01-15 11:44:08,438: initializing /rosout core topic
[rospy.rosout][INFO] 2013-01-15 11:44:08,440: connected to core topic /rosout
[rospy.simtime][INFO] 2013-01-15 11:44:08,442: initializing /clock core topic
[rospy.simtime][INFO] 2013-01-15 11:44:08,445: connected to core topic /clock
[rosout][INFO] 2013-01-15 11:44:08,449: waiting for service /gazebo/spawn_urdf_model
[rospy.internal][INFO] 2013-01-15 11:44:08,453: topic[/clock] adding connection to [http://scott-ub:34652/], count 0
[rospy.internal][INFO] 2013-01-15 11:44:08,708: topic[/rosout] adding connection to [/rosout], count 0
[rospy.core][INFO] 2013-01-15 11:44:10,328: signal_shutdown [atexit]
[rospy.internal][WARNING] 2013-01-15 11:44:10,329: Unknown error initiating TCP/IP socket to scott-ub:32926 (http://scott-ub:34652/): Traceback (most recent call last):
File "/opt/ros/fuerte/lib/python2.7/dist-packages/rospy/impl/tcpros_base.py", line 511, in connect
self.socket.connect((dest_addr, dest_port))
File "/usr/lib/python2.7/socket.py", line 224, in meth
return getattr(self._sock,name)(*args)
error: [Errno 111] Connection refused
[rospy.internal][INFO] 2013-01-15 11:44:10,330: topic[/rosout] removing connection to /rosout
[rospy.impl.masterslave][INFO] 2013-01-15 11:44:10,330: atexit
None of the other log files have errors in them. Thanks in advance for any suggestions.
EDIT: I tried in groovy (there is not a debian for erratic in groovy, so I downloaded and compiled the source).
When using simulator_gazebo (1.2.5), executing
roslaunch erratic_navigation_apps demo_2dnav_slam.launch
results in
... logging to /home/scott/.ros/log/b7ffc898-6980-11e2-bc25-782bcbb7d7cd/roslaunch-scott-ub-8096.log
Checking log directory for disk usage. This may take awhile.
Press Ctrl-C to interrupt
Done checking log file disk usage. Usage is <1GB.
started roslaunch server http://scott-ub:36638/
SUMMARY
========
PARAMETERS
* /base_laser_self_filter/min_sensor_dist
* /base_laser_self_filter/self_see_default_padding
* /base_laser_self_filter/self_see_default_scale
* /base_laser_self_filter/self_see_links
* /base_laser_self_filter/sensor_frame
* /base_shadow_filter/high_fidelity
* /base_shadow_filter/scan_filter_chain
* /base_shadow_filter/target_frame
* /move_base_node/NavfnROS/allow_unknown
* /move_base_node/TrajectoryPlannerROS/acc_lim_th
* /move_base_node/TrajectoryPlannerROS/acc_lim_x
* /move_base_node/TrajectoryPlannerROS/acc_lim_y
* /move_base_node/TrajectoryPlannerROS/dwa
* /move_base_node/TrajectoryPlannerROS/escape_vel
* /move_base_node/TrajectoryPlannerROS/goal_distance_bias
* /move_base_node/TrajectoryPlannerROS/heading_lookahead
* /move_base_node/TrajectoryPlannerROS/holonomic_robot
* /move_base_node/TrajectoryPlannerROS/max_rotational_vel
* /move_base_node/TrajectoryPlannerROS/max_vel_x
* /move_base_node/TrajectoryPlannerROS/min_in_place_rotational_vel
* /move_base_node/TrajectoryPlannerROS/min_vel_x
* /move_base_node/TrajectoryPlannerROS/occdist_scale
* /move_base_node/TrajectoryPlannerROS/oscillation_reset_dist
* /move_base_node/TrajectoryPlannerROS/path_distance_bias
* /move_base_node/TrajectoryPlannerROS/sim_granularity
* /move_base_node/TrajectoryPlannerROS/sim_time
* /move_base_node/TrajectoryPlannerROS/vtheta_samples
* /move_base_node/TrajectoryPlannerROS/vx_samples
* /move_base_node/TrajectoryPlannerROS/xy_goal_tolerance
* /move_base_node/TrajectoryPlannerROS/yaw_goal_tolerance
* /move_base_node/aggressive_clear/reset_distance
* /move_base_node/clearing_radius
* /move_base_node/conservative_clear/reset_distance
* /move_base_node/controller_frequency
* /move_base_node/controller_patience
* /move_base_node/footprint
* /move_base_node/footprint_padding
* /move_base_node/global_costmap/base_scan/clearing
* /move_base_node/global_costmap/base_scan/data_type
* /move_base_node/global_costmap/base_scan/expected_update_rate
* /move_base_node/global_costmap/base_scan/marking
* /move_base_node/global_costmap/base_scan/max_obstacle_height
* /move_base_node/global_costmap/base_scan/min_obstacle_height
* /move_base_node/global_costmap/base_scan/observation_persistence
* /move_base_node/global_costmap/base_scan/sensor_frame
* /move_base_node/global_costmap/base_scan/topic
* /move_base_node/global_costmap/base_scan_marking/clearing
* /move_base_node/global_costmap/base_scan_marking/data_type
* /move_base_node/global_costmap/base_scan_marking/expected_update_rate
* /move_base_node/global_costmap/base_scan_marking/marking
* /move_base_node/global_costmap/base_scan_marking/max_obstacle_height
* /move_base_node/global_costmap/base_scan_marking/min_obstacle_height
* /move_base_node/global_costmap/base_scan_marking/observation_persistence
* /move_base_node/global_costmap/base_scan_marking/sensor_frame
* /move_base_node/global_costmap/base_scan_marking/topic
* /move_base_node/global_costmap/global_frame
* /move_base_node/global_costmap/inflation_radius
* /move_base_node/global_costmap/map_type
* /move_base_node/global_costmap/observation_sources
* /move_base_node/global_costmap/obstacle_range
* /move_base_node/global_costmap/publish_frequency
* /move_base_node/global_costmap/raytrace_range
* /move_base_node/global_costmap/robot_base_frame
* /move_base_node/global_costmap/rolling_window
* /move_base_node/global_costmap/static_map
* /move_base_node/global_costmap/transform_tolerance
* /move_base_node/global_costmap/unknown_cost_value
* /move_base_node/global_costmap/update_frequency
* /move_base_node/local_costmap/base_scan/clearing
* /move_base_node/local_costmap/base_scan/data_type
* /move_base_node/local_costmap/base_scan/expected_update_rate
* /move_base_node/local_costmap/base_scan/marking
* /move_base_node/local_costmap/base_scan/max_obstacle_height
* /move_base_node/local_costmap/base_scan/min_obstacle_height
* /move_base_node/local_costmap/base_scan/observation_persistence
* /move_base_node/local_costmap/base_scan/sensor_frame
* /move_base_node/local_costmap/base_scan/topic
* /move_base_node/local_costmap/base_scan_marking/clearing
* /move_base_node/local_costmap/base_scan_marking/data_type
* /move_base_node/local_costmap/base_scan_marking/expected_update_rate
* /move_base_node/local_costmap/base_scan_marking/marking
* /move_base_node/local_costmap/base_scan_marking/max_obstacle_height
* /move_base_node/local_costmap/base_scan_marking/min_obstacle_height
* /move_base_node/local_costmap/base_scan_marking/observation_persistence
* /move_base_node/local_costmap/base_scan_marking/sensor_frame
* /move_base_node/local_costmap/base_scan_marking/topic
* /move_base_node/local_costmap/global_frame
* /move_base_node/local_costmap/height
* /move_base_node/local_costmap/inflation_radius
* /move_base_node/local_costmap/map_type
* /move_base_node/local_costmap/observation_sources
* /move_base_node/local_costmap/obstacle_range
* /move_base_node/local_costmap/origin_x
* /move_base_node/local_costmap/origin_y
* /move_base_node/local_costmap/publish_frequency
* /move_base_node/local_costmap/publish_voxel_map
* /move_base_node/local_costmap/raytrace_range
* /move_base_node/local_costmap/resolution
* /move_base_node/local_costmap/robot_base_frame
* /move_base_node/local_costmap/rolling_window
* /move_base_node/local_costmap/static_map
* /move_base_node/local_costmap/transform_tolerance
* /move_base_node/local_costmap/update_frequency
* /move_base_node/local_costmap/width
* /move_base_node/recovery_behaviors
* /robot_description
* /robot_state_publisher/publish_frequency
* /robot_state_publisher/tf_prefix
* /rosdistro
* /rosversion
* /slam_gmapping/angularUpdate
* /slam_gmapping/astep
* /slam_gmapping/base_frame
* /slam_gmapping/delta
* /slam_gmapping/iterations
* /slam_gmapping/kernelSize
* /slam_gmapping/lasamplerange
* /slam_gmapping/lasamplestep
* /slam_gmapping/linearUpdate
* /slam_gmapping/llsamplerange
* /slam_gmapping/llsamplestep
* /slam_gmapping/lsigma
* /slam_gmapping/lskip
* /slam_gmapping/lstep
* /slam_gmapping/map_update_interval
* /slam_gmapping/maxUrange
* /slam_gmapping/odom_frame
* /slam_gmapping/ogain
* /slam_gmapping/particles
* /slam_gmapping/resampleThreshold
* /slam_gmapping/sigma
* /slam_gmapping/srr
* /slam_gmapping/srt
* /slam_gmapping/str
* /slam_gmapping/stt
* /slam_gmapping/temporalUpdate
* /slam_gmapping/xmax
* /slam_gmapping/xmin
* /slam_gmapping/ymax
* /slam_gmapping/ymin
* /use_sim_time
NODES
/move_base_node/local_costmap/
voxel_grid_throttle (topic_tools/throttle)
/
base_laser_self_filter (robot_self_filter/self_filter)
base_shadow_filter (laser_filters/scan_to_cloud_filter_chain)
gazebo (gazebo/gazebo)
gazebo_gui (gazebo/gui)
move_base_node (move_base/move_base)
robot_state_publisher (robot_state_publisher/state_publisher)
slam_gmapping (gmapping/slam_gmapping)
spawn_robot (gazebo/spawn_model)
voxel_visualizer (costmap_2d/costmap_2d_markers)
auto-starting new master
process[master]: started with pid [8120]
ROS_MASTER_URI=http://localhost:11311
setting /run_id to b7ffc898-6980-11e2-bc25-782bcbb7d7cd
process[rosout-1]: started with pid [8133]
started core service [/rosout]
process[gazebo-2]: started with pid [8147]
Gazebo multi-robot simulator, version 1.2.5
Copyright (C) 2012 Nate Koenig, John Hsu, and contributors.
Released under the Apache 2 License.
http://gazebosim.org
process[gazebo_gui-3]: started with pid [8170]
Warning [parser.cc:358] Converting a deprecatd SDF source[/opt/ros/groovy/stacks/simulator_gazebo/gazebo_worlds/worlds/wg_collada.world].
Version[1.0] to Version[1.2]
Please use the gzsdf tool to update your SDF files.
$ gzsdf convert [sdf_file]
Warning [Converter.cc:191] Deprecated SDF Values in original file:
<background rgba='0.5 0.5 0.5 1'
Warning [Converter.cc:191] Deprecated SDF Values in original file:
<background
Gazebo multi-robot simulator, version 1.2.5
Copyright (C) 2012 Nate Koenig, John Hsu, and contributors.
Released under the Apache 2 License.
http://gazebosim.org
Msg Waiting for master[ INFO] [1359401238.297721514]: waitForService: Service [/gazebo/set_physics_properties] has not been advertised, waiting...
Msg Connected to gazebo master @ http://localhost:11345
Msg Waiting for master
Msg Connected to gazebo master @ http://localhost:11345
process[spawn_robot-4]: started with pid [8208]
process[robot_state_publisher-5]: started with pid [8209]
/opt/ros/groovy/lib/robot_state_publisher/state_publisher
[ WARN] [1359401238.509989899]: The 'state_publisher' executable is deprecated. Please use 'robot_state_publisher' instead
[ERROR] [1359401238.512125486]: Material [Green] color has no rgba
[ERROR] [1359401238.512163917]: Material [Green] not defined in file
[ERROR] [1359401238.512226471]: Material [Blue] color has no rgba
[ERROR] [1359401238.512240719]: Material [Blue] not defined in file
[ERROR] [1359401238.512312242]: Material [Black] color has no rgba
[ERROR] [1359401238.512326624]: Material [Black] not defined in file
[ERROR] [1359401238.512398933]: Material [Black] color has no rgba
[ERROR] [1359401238.512414554]: Material [Black] not defined in file
[ERROR] [1359401238.512454940]: Material [Black] color has no rgba
[ERROR] [1359401238.512467869]: Material [Black] not defined in file
[ WARN] [1359401238.512779639]: The root link base_footprint has an inertia specified in the URDF, but KDL does not support a root link with an inertia. As a workaround, you can add an extra dummy link to your URDF.
process[base_shadow_filter-6]: started with pid [8233]
process[base_laser_self_filter-7]: started with pid [8332]
process[slam_gmapping-8]: started with pid [8367]
process[move_base_node/local_costmap/voxel_grid_throttle-9]: started with pid [8368]
process[move_base_node-10]: started with pid [8442]
process[voxel_visualizer-11]: started with pid [8468]
[ INFO] [1359401239.481263489]: Subscribed to Topics: base_scan base_scan_marking
[ INFO] [1359401239.488517705]: Requesting the map...
[ INFO] [1359401239.489302008]: Still waiting on map...
loading model xml from ros parameter
[INFO] [WallTime: 1359401239.585223] [0.000000] waiting for service /gazebo/spawn_urdf_model
Error [TrimeshShape.cc:59] <mesh><filename>/opt/ros/groovy/stacks/simulator_gazebo/gazebo_worlds/Media/models/willowgarage2.stl</filename></mesh> is deprecated.
Error [TrimeshShape.cc:61] Use <mesh><uri>file:///opt/ros/groovy/stacks/simulator_gazebo/gazebo_worlds/Media/models/willowgarage2.stl</uri></mesh>
Warning [parser.cc:374] Gazebo SDF has no <gazebo> element in file[data-string]
Warning [parser_urdf.cc:437] do nothing with canonicalBody
Dbg [base_footprint] has no parent joint
Warning [parser.cc:313] parse from urdf.
[ INFO] [1359401240.463746266]: Laser plugin missing <hokuyoMinIntensity>, defaults to 101
[ INFO] [1359401240.463824837]: INFO: gazebo_ros_laser plugin should set minimum intensity to 101.000000 due to cutoff in hokuyo filters.
spawn status: SpawnModel: successfully spawned model
Dbg plugin parent sensor name: robot_description
[ INFO] [1359401240.545290761]: starting diffdrive plugin in ns:
[ INFO] [1359401240.608129322]: pluginlib WARNING: PLUGINLIB_DECLARE_CLASS is deprecated, please use PLUGINLIB_EXPORT_CLASS instead. You can run the script 'plugin_macro_update' provided with pluginlib in your package source folder to automatically and recursively update legacy macros.
[ INFO] [1359401240.608335488]: pluginlib WARNING: PLUGINLIB_DECLARE_CLASS is deprecated, please use PLUGINLIB_EXPORT_CLASS instead. You can run the script 'plugin_macro_update' provided with pluginlib in your package source folder to automatically and recursively update legacy macros.
[ INFO] [1359401240.608380390]: pluginlib WARNING: PLUGINLIB_DECLARE_CLASS is deprecated, please use PLUGINLIB_EXPORT_CLASS instead. You can run the script 'plugin_macro_update' provided with pluginlib in your package source folder to automatically and recursively update legacy macros.
[ INFO] [1359401240.608418552]: pluginlib WARNING: PLUGINLIB_DECLARE_CLASS is deprecated, please use PLUGINLIB_EXPORT_CLASS instead. You can run the script 'plugin_macro_update' provided with pluginlib in your package source folder to automatically and recursively update legacy macros.
Dbg plugin model name: robot_description
[ INFO] [1359401240.608567660]: starting gazebo_ros_controller_manager plugin in ns:
[ INFO] [1359401240.608693151]: Callback thread id=0x7f275c7ada00
[spawn_robot-4] process has finished cleanly
log file: /home/scott/.ros/log/b7ffc898-6980-11e2-bc25-782bcbb7d7cd/spawn_robot-4*.log
Dbg plugin parent sensor name: robot_description
[ INFO] [1359401266.210791346, 0.001000000]: starting diffdrive plugin in ns:
Dbg plugin model name: robot_description
[ INFO] [1359401266.213961598, 0.001000000]: starting gazebo_ros_controller_manager plugin in ns:
[ INFO] [1359401266.214127828, 0.001000000]: Callback thread id=0x7f275c81f820
[ERROR] [1359401266.436481894, 0.001000000]: Tried to advertise a service that is already advertised in this node [/pr2_controller_manager/list_controllers]
[ERROR] [1359401266.436593701, 0.001000000]: Tried to advertise a service that is already advertised in this node [/pr2_controller_manager/list_controller_types]
[ERROR] [1359401266.436684166, 0.001000000]: Tried to advertise a service that is already advertised in this node [/pr2_controller_manager/load_controller]
[ERROR] [1359401266.436768297, 0.001000000]: Tried to advertise a service that is already advertised in this node [/pr2_controller_manager/unload_controller]
[ERROR] [1359401266.436869158, 0.001000000]: Tried to advertise a service that is already advertised in this node [/pr2_controller_manager/switch_controller]
[ERROR] [1359401266.436943296, 0.001000000]: Tried to advertise a service that is already advertised in this node [/pr2_controller_manager/reload_controller_libraries]
[ INFO] [1359401266.457805476, 0.022000000]: waitForService: Service [/gazebo/set_physics_properties] is now available.
[ INFO] [1359401266.495811250, 0.056000000]: Starting to spin physics dynamic reconfigure node...
[ WARN] [1359401267.061316070, 0.601000000]: Message from [/base_shadow_filter] has a non-fully-qualified frame_id [base_footprint]. Resolved locally to [/base_footprint]. This is will likely not work in multi-robot systems. This message will only print once.
-maxUrange 4 -maxUrange 3.99 -sigma 0.05 -kernelSize 1 -lstep 0.05 -lobsGain 3 -astep 0.05
-srr 0.01 -srt 0.02 -str 0.01 -stt 0.02
-linearUpdate 0.5 -angularUpdate 0.436 -resampleThreshold 0.5
-xmin -10 -xmax 10 -ymin -10 -ymax 10 -delta 0.025 -particles 80
[ INFO] [1359401267.063221833, 0.601000000]: Initialization complete
update frame 0
update ld=0 ad=0
Laser Pose= 1.08887e-05 2.92677e-12 1.11502e-05
m_count 0
Registering First Scan
[ INFO] [1359401267.475379580, 1.005000000]: Still waiting on map...
[ INFO] [1359401268.490956284, 2.003000000]: Received a 800 X 800 map at 0.025000 m/pix
[ INFO] [1359401268.746005702, 2.234000000]: MAP SIZE: 800, 800
[ INFO] [1359401268.756695152, 2.245000000]: Subscribed to Topics: base_scan base_scan_marking
[ INFO] [1359401268.941572418, 2.424000000]: Sim period is set to 0.10
I can not see the walls of the environment and the robot's appearance is different than it was in fuerte, but topics such as /odom and /base_scan/scan are publishing and I can drive the robot around.
I also tried to use the run_gazebo script to use Gazebo 1.3.1, but the model does not spawn in Gazebo. This is the output:
This code block was moved to the following github gist:
https://gist.github.com/answers-se-migration-openrobotics/3c3c71350bec2a4a41e299a5b60de27e
Would updating ros-groovy-simulator-gazebo help improved on either one of these results? Thanks!
Originally posted by otto on Gazebo Answers with karma: 11 on 2013-01-17
Post score: 1
Answer:
You mentioned that you installed Gazebo 1.3, but your posted output says you're actually running Gazebo 1.0:
Gazebo multi-robot simulator, version 1.0.2
As a side note, the Gazebo tutorials on ros.org are only applicable to Gazebo 1.0.
Originally posted by nkoenig with karma: 7676 on 2013-01-19
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by otto on 2013-01-22:
Thanks for responding and sorry for the confusing post. I have both installed (Gazebo 1.0 with Ros Fuerte and Gazebo 1.3 as stand alone). After a lack of progress with the problem described above with 1.0, I installed 1.3 to look into how practical it would be to move to using that version.
Comment by hsu on 2013-01-24:
could you try to run things in groovy? If debbuild (http://www.ros.org/debbuild/groovy.html) finishes, simulator_gazebo 1.7.8 will have gazebo 1.3 in it. | {
"domain": "robotics.stackexchange",
"id": 2945,
"tags": "gazebo"
} |
Attach dynamic text to models | Question:
If I want to display different text contents in real time to different models, i.e. attaching dynamic text to models, how should I do?
Any help would be greatly appreciated!
Originally posted by winston on Gazebo Answers with karma: 449 on 2016-06-19
Post score: 0
Answer:
Check out this answer.
Take a look at this video of a plugin which displays floating model names. The source code is here. You can try to modify it to display the information you want.
Originally posted by chapulina with karma: 7504 on 2016-06-20
This answer was ACCEPTED on the original site
Post score: 0 | {
"domain": "robotics.stackexchange",
"id": 3939,
"tags": "gazebo"
} |
Could an Alcubierre Drive modify a gravitational field? | Question: I'm a high school student, so I have no clue if warping spacetime has any effect on gravitational fields, but the two seemed to be linked based on what I've watched and read. And if a warp drive is possible (not nessecarily for ftl travel) could it be used for artificial or antigravity applications?
Answer: You can't just randomly warp spacetime. The curvature of spacetime is related to the matter that is present. It's a bit more complicated than that because it's actually related to an object called the stress-energy tensor, but in most cases that just means the amount of matter present. Anyhow, the curvature of spacetime is what we call gravity.
The Earth warps spacetime in it's vicinity by having about $6 \times 10^{24}$ kg of (normal) matter in a ball. An Alcubierre drive warps spacetime by having a ring of exotic matter (views differ on the amount of exotic matter needed). In both cases the matter that is present curves spacetime and produces a gravitational field - the difference is in the shape of the matter and its type. For the record, as far as we know exotic matter doesn't exist, and if it did it would cause all sorts of problems with the stability of the universe.
So your question is really something along the lines of could exotic matter, as used by the Alcubierre drive, be used for artificial or antigravity applications?. And the answer is yes it could. If exotic matter existed and could be easily handled the physicists would be happier than a child in a toy shop. Sadly for the physicists, but luckily for the universe, exotic matter (probably) doesn't exist. | {
"domain": "physics.stackexchange",
"id": 25594,
"tags": "gravitational-waves, warp-drives"
} |
Groovy install in Ubuntu 14.04 | Question:
Is it possible to install Groovy in Ubuntu 14.04 using the ROS repository, instead of compiling from source? I ask since most all of our code is in Groovy (rosmake) but the device running ROS requires Ubuntu 14.04 due to hardware drivers/configuration, etc.?
Thanks for all the help!
Originally posted by dambrosio on ROS Answers with karma: 161 on 2014-07-15
Post score: 0
Original comments
Comment by ccapriotti on 2014-07-15:
Dambrosio, hello.
I do not have an answer for you, but this was one of my objectives; to test groovy on 14,04. It is not a matter of working or not, but rather of being supported or not. So far, it is an unsupported platform, but go for it. If you have the means, test on a VM with 14.04.
Answer:
Well what do you know... Same question a few minutes earlier.
http://answers.ros.org/question/186649/groovy-on-ubuntu-1404/
It helps to know what hardware/platform we are talking about. x86 installs and ARM have different statuses.
Originally posted by ccapriotti with karma: 255 on 2014-07-15
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by dambrosio on 2014-07-15:
This is a AMD64 platform.
Comment by dambrosio on 2014-07-16:
Would this be the link for installing from source: http://wiki.ros.org/groovy/Installation/Source? I will step through this today and let you know what the outcome is. Thanks for the responses.
Comment by dambrosio on 2014-07-16:
I got to step 2.1.2 Resolving Dependencies and ran into issues running: rosdep install --from-paths src --ignore-src --rosdistro groovy -y
I get errors stating: the following packages/stacks could not have their rosdep keys resolved to system dependencies. I tried to adding the --os. Any advice?
Comment by demmeln on 2014-07-18:
You probably ran into this issue? https://github.com/ros/rosdistro/issues/4792 | {
"domain": "robotics.stackexchange",
"id": 18623,
"tags": "ros-groovy, ubuntu, ubuntu-trusty"
} |
How to do Localization and Navigation in 3D using octomap from RGBD-SLAM? | Question:
I am using ROS- electric. Now, I am able to built a octomap with the help of RGBDSLAM package. The map is in format '.bt'. Is there any packages available for doing localization and navigation in 3D using this octomap?
Note:localization should be done without using laser.
Originally posted by Sudhan on ROS Answers with karma: 171 on 2012-08-10
Post score: 1
Answer:
We have a 6D localization running in an OctoMap for our humanoid robots. You can find details in the publication "Humanoid Robot Localization in Complex Indoor Environments". It's runnning MCL (particle filtering) and uses ray casting for the sensor model.
The code is now published at http://ros.org/wiki/humanoid_localization
It's mostly designated for humanoid robots and still being polished right now, but I'm sure you can use much of the sensor model code as example.
If you want to implement your own localization, you can use the function castRay in OctoMap.
In terms of map building, planning, and collision checking in an OctoMap look at the 3d_navigation stack and the publication "Navigation in Three-Dimensional Cluttered Environments
for Mobile Manipulation".
Originally posted by AHornung with karma: 5904 on 2012-08-10
This answer was ACCEPTED on the original site
Post score: 3
Original comments
Comment by Sudhan on 2012-08-10:
yes, I am interested and you can publish the codes. Is it possible to ray casting with kinect or LASER is necessary?
Comment by AHornung on 2012-08-10:
OctoMap doesn't care about your sensor. You can raycast with any distance sensor, all it needs is a direction and an origin. The sensor model may be a little harder to tweak though.
Comment by Sudhan on 2012-08-10:
I have a kinect but it can't measure the objects lesser than 1.2m. Is there any solutions for that? Also, I saw one more package(3d_navigation) just now which is maintained by you. Both are same?
Comment by AHornung on 2012-08-10:
The minimum range should be around 0.7m, but that is the general problem with such a sensor. I added 3d_navigation to my answer, they serve different purposes. You will have to read the papers for the details.
Comment by AHornung on 2012-09-25:
The code is now public, I edited my answer. It's still being polished and finalized for point clouds, but it may give you some idea.
Comment by Sudhan on 2012-09-26:
Thank you very much
Comment by AHornung on 2012-09-28:
If your question is answered, please mark the answer as correct (checkmark).
Comment by Sudhan on 2012-10-10:
I marked this as a correct answer long back, but for some reasons the checkmark is not working in my browser properly. | {
"domain": "robotics.stackexchange",
"id": 10564,
"tags": "slam, navigation, rgbd6dslam, octomap, octomap-mapping"
} |
Statistics mode function | Question: I will get straight to the point - I am a freshman at uni and I am currently working on my first bigger personal project - Statula is a terminal tool for data analysis which takes in dataset (as a file) and then spits out bunch of numbers about the numbers. I am quite satisfied with where it is going but I am not gonna lie - I have some concerns.
Here is the git repo.
I will say it beforehand in case someone goes for a lecture - I am aware that I did not check for returned errors in compute_dataset.
I have just reworked some of them and I am kind of busy this week - I will get onto it as soon as possible. Also, my tests suck - or rather a single one. I have just introduced new structure which basically broke all of my tests. I am also working on that.
So, back to the point.
My main focus is performance. I am satisfied with the fact that on my rig (i5-4670k) this program can finish it's job in under 240ms. However, that is not good enough for me. I believe that the main performance hog might be the mode function - and for a good reason.
Here is the code:
int mode(struct dataset *set)
{
assert(set->number_count>0);
double max_value=0;
int max_count=0,i,j,mode_count=1;
for(i=0;i<set->number_count;i++){
int count=0;
for(j=i+1;set->numbers[j]==set->numbers[i]&&j<set->number_count;j++);
count=j-i;
if(count>max_count){
mode_count=1;
max_count=count;
max_value=set->numbers[i];
} else if(count==max_count) {
mode_count++;
i=j-1;
}
}
if(mode_count==1){
*(set->mode)=max_value;
set->is_mode_present=1;
} else{
*(set->mode) = 0;
set->is_mode_present=0;
}
return mode_count==1?1:0;
}
Perhaps there is some room for improvement. For the record, the number set is qsorted before being passed to the function. That's the main premise. Can it get any faster than that?
I also wonder whether the struct itself is a good idea - I guess there is no going back. Do not get me wrong, I have put a lot of thought into this matter and I came to a conclusion that by using struct I can:
Analyse multiple sets by reading multiple datasets - each has it's own struct. Beforehand, all I had was a local variable.
Avoid some unneccessary function calls - for instance, I have needed mean to compute standard deviation. Sure, I could pass it as an argument to a function, but.. where is the fun?
Unfortunately, that means that you cannot just copy-paste the function out of the source code and expect it to work - it relies on dataset structure being present.
So that is more of a general question - do you prefer your code to be correct (in a very loose sense) or portable?
General code suggestions are also welcome!
Answer: Well, of course your code is too slow, it's O(n²) but should be O(n):
Unless you already found a run of the same length, you don't skip to the end of the run!
Your inner for-loop only tests whether you are beyond your list after already having read there. That's slightly too late, rearrange that.
A side-question: Why do you insist on the dataset not being empty?
Why do you call your mode max_value? That's strange.
Restrict the scope of your values to the minimum you need: If it's not in scope, there's nothing for you to keep track of, allowing you to concentrate on other issues.
Consider investing in a bit more whitespace, especially around binary operators.
You know that true is 1 and false is 0?
Never use ; as the empty statement: It always looks suspicious. Either put a comment before it /**/; or use a block {} instead. | {
"domain": "codereview.stackexchange",
"id": 25789,
"tags": "performance, c, statistics"
} |
Multithreaded search for solutions to an inequality | Question: This question is related to my previous question on the brute-force search
for a solution to an unsolved mathematical inequality:
$$3^{k}-2^{k}\left\lfloor \left({\tfrac {3}{2}}\right)^{k}\right\rfloor >2^{k}-\left\lfloor \left({\tfrac {3}{2}}\right)^{k}\right\rfloor -2$$
The following code, tested on Ubuntu 16.04, compiles with no warnings or errors using the flags -Wall -std=c++14 -pthread -Ofast using the g++ compiler. I'm using -Ofast because I am trying to squeeze every ounce of performance out of this code (more info here).
I am not 100% sure if this is the proper, fastest, implementation of multithreading. Since I'm new to multithreading, I used this SO question, this page, and this page for learning how to multithread.
For questions about other parts of the code, I explain it way more on my previous question (like why I have a completely separate if-else check).
Let me know how I can improve my use of multithreading in this program.
#include <boost/multiprecision/cpp_dec_float.hpp>
//#include <cmath> (already included from cpp_dec_float.hpp)
#include <iostream>
#include <future>
typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<2000>> arbFloat;
enum returnID {success = 0, precisionExceeded = 1};
arbFloat calcThreeK(const arbFloat & k){
return pow(3, k);
}
arbFloat calcTwoK(const arbFloat & k){
return pow(2, k);
}
int main(){
arbFloat k, threeK, twoK;
bool isSolution = false;
for(k = 6; !isSolution; ++k){
std::future<arbFloat> futureThreeK = std::async(std::launch::async, calcThreeK, k);
std::future<arbFloat> futureTwoK = std::async(std::launch::async, calcTwoK, k);
threeK = futureThreeK.get();
twoK = futureTwoK.get();
isSolution = threeK - twoK * floor(threeK / twoK) > twoK - floor(threeK / twoK) - 2;
}
if(pow(3, k) - (pow(2, k) * floor(pow(1.5, k))) <= pow(2, k) - floor(pow(1.5, k)) - 2){
std::cout << "Solution at k = " << k << ".\n";
return returnID::success;
} else {
std::cout << "Error: Precision exceeded at k = " << k << ".\n";
return returnID::precisionExceeded;
}
}
Answer: You are asynchronously calculating intermediate results that are not worth parallelizing. Instead of calculating \$2^k\$ and \$3^k\$ sequentially, you do those calculations in parallel. But then you have to wait for both of them to complete before proceeding. I would expect that the overhead of setting up the async calls would negate any performance benefit.
Suppose you had a dozen friends helping you. Would you ask one of them to go off and calculate \$2^6\$, the second friend to calculate \$3^6\$, and report the results back to you so that you can check whether 6 is a solution? No, that would be crazy. You would be better off asking the first friend to check whether 6 is a solution, the second friend to check 7, the third friend to try 8, etc. Then each of them has a chance to do some substantial work independently instead of waiting for each other's results.
Moreover, calculating \$3^k\$ would be a trivial multiplication if you already knew \$3^{k-1}\$. You should be able to avoid calling pow() altogether if you are trying increasing \$k\$. | {
"domain": "codereview.stackexchange",
"id": 24546,
"tags": "c++, performance, beginner, mathematics, asynchronous"
} |
Are the reaction rates of these equations equal? | Question: $$\ce{CH3CH2CH2Br + OH- -> CH3CH2CH2OH + Br-}$$
$$\mathrm{rate} = k[\ce{CH3CH2CH2Br}][\ce{OH-}]$$
If I change the $\ce{Br}$ with any element from halogens (without changing concentration, volume, mass etc.), does the rate of reaction change? If so, how does it change? What factors change it?
Answer: For the reaction kinetic rate constants, there is the well known Arrhenius equation:
$$k=A \cdot \exp{\left(-\frac{E_\mathrm{a}}{RT}\right)}$$
$A$ is sometimes called frequency factor, interpreted as the rate of collisions with the proper orientation of molecules.
It has 2 terms:
The rate of general collisions, that is function of temperature and molecular masses, which determine speed of molecular motion (close relation to the kinetic theory of gases). Note that the temperature dependence is much smaller than for the exponential Boltzmann term.
The probability of the proper orientation of molecules, what depends on the molecular geometry. For molecules of otherwise the same geometry, it depends on covalent atom radii.
The exponential term follows the Boltzmann statistical distribution, determining the probability molecules would have enough kinetic energy to overcome the reaction activation energy barrier.
All 3 terms (2 for $A$ and the exponential term) Are different for different halogen atoms.
The mass molecules increases fluorine < iodine, so collision frequency as the rate constant term is the lowest for iodine.
As the reaction mechanism I suppose SN2. The geometrical aspects of $\ce{-CH2X}$ is tricky to determine from basic principles. Bigger halogen is more sterically blocking, but is also farther from the central carbon. More polar bond of the smaller halogen should cause stronger repelling of the other 3 bonds, so the other side is more open for sn2 reaction.
Activation energy would decrease ( and the Boltzmann term for the rate constant increase) in order F ... I
That about the principles. To compare the particular rates, it is matter of experimental data. | {
"domain": "chemistry.stackexchange",
"id": 12962,
"tags": "reaction-mechanism, kinetics, halides, nucleophilic-substitution"
} |
What is a temperature inversion and can it trap smog/pollution? | Question: Just as the title says, I heard about this term but am not sure how it works.
Answer: Normally, temperature broadly decreases with altitude, and convection is effective: locally warmer air will rise, and cooler air will fall. A temperature inversion is where the air temperature rises with altitude. This means that convection is less effective because the air above is already warmer, and so there is less mixing of air between altitudes.
Since pollution is generally produced at ground level, temperature inversions can trap the pollution (e.g. smog) at ground level. | {
"domain": "earthscience.stackexchange",
"id": 518,
"tags": "meteorology, pollution, air-pollution"
} |
What does +60mm mean in MRI scans? | Question: What do the -30 to +60mm markings mean in this MRI scan image?
Answer: Short Answer
They are marking distance from a reference plane.
Longer Answer
In the images you provided, you are looking at horizontal slices through a brain. The legends are indicating that each plane has that vertical distance from a reference point (if the subject were standing); the positive numbers are dorsal to that reference and the negative numbers are ventral.
A common reference point for MRI images (to define as [0,0,0]) is the midpoint of a line through the pre-auricular point, though ultimately it is an arbitrary distinction.
If the actual reference point is important to you, you will need to verify the reference coordinate system used in the study you are looking at. It's also possible you are looking at coordinates transformed to some reference brain rather than real-life coordinates for that particular subject, but again, whether that matters or not depends on why you care. If you are doing research across subjects, you probably want to know reference coordinates; if you are doing brain surgery on a particular patient you want real-life coordinates. | {
"domain": "biology.stackexchange",
"id": 8628,
"tags": "human-biology, neuroscience, brain, mri"
} |
PHP page pagination | Question: I think my code is sloppy can anyone give me advice to do it better?
This is a page pagination that get rows from mysql db and calculate the number of pages.
<div class="row">
<div class="twelve columns tac">
<?php
//Check for the current page and select one of the two versions of "back" link.
if (isset($_GET["page_num"]) && $_GET["page_num"] >= 2): ?>
<a href="?page=blog&page_num=<?php echo($_GET["page_num"] - 1); ?>">Back</a>
<?php else : ?>
<span>Back</span>
<?php endif;
//looping through the number of pages and list page numbers.
for ($i = 1; $i <= $totalPages; $i++): ?>
<?php if ($i == $_GET["page_num"]) : ?>
<span><?php echo $i; ?></span>
<?php else : ?>
<a href="?page=blog&page_num=<?php echo $i; ?>"> <?php echo $i; ?></a>
<?php endif; ?>
<?php endfor;
//Check for the current page and select one of the two versions of "Next" link.
if ($_GET["page_num"] < $totalPages): ?>
<a href="?page=blog&page_num=<?php echo($_GET["page_num"] + 1); ?>">Next</a>
<?php else : ?>
<span>Next</span>
<?php endif; ?>
</div>
</div>
Answer: Checking if a variable is set
if (isset($_GET["page_num"]) && $_GET["page_num"] >= 2): ?>
Here you check if $_GET["page_num"] is set before using it, which is correct. However, you don't do so in any of the later tests. Consider starting with something the code block with something like
$currentPage = isset($_GET['page_num']) ? $_GET['page_num'] : 1;
Now you can just use $currentPage instead. And it will always be set. It defaults to 1, as that is the normal pagination behavior (no selected page means the first page).
I also changed the double quotes to single quotes. In PHP, double quotes means that a string is open to variable interpolation. You aren't using variable interpolation, so you might as well use single quotes instead.
Later you can change the original line of code to
if ($currentPage > 1) {
?>
Note that I also moved the closing ?> to its own line. This makes it much easier to tell when you switch from code to HTML.
I also switched from the non-standard : notation. Very little PHP code is written that way. The only time that I've actually seen it is in WordPress templates.
And I switched from >= 2 to > 1 because 2 is not a significant number here. What you are saying is that you don't want allow the back link on the first page, only on pages after the first. This translates to > 1 more directly.
Separating PHP and HTML
I'd tend to write this as
<?php
$currentPage = isset($_GET['page_num']) ? $_GET['page_num'] : 1;
?>
<div class="row">
<div class="twelve columns tac">
<?php
echo getPaginationLinks($currentPage, $totalPages);
?>
</div>
</div>
and define getPaginationLinks in a separate file with most of the original block. The getPaginationLinks function would build and return a string.
Note that I put the <?php> and ?> on separate lines and at the beginning of each line. This makes it easier to tell when you are switch from HTML to PHP code.
Don't switch context for no reason
You have
for ($i = 1; $i <= $totalPages; $i++): ?>
<?php if ($i == $_GET["page_num"]) : ?>
You could just as well write this
for ($i = 1; $i <= $totalPages; $i++):
if ($i == $_GET["page_num"]) :
?>
Then the compiler isn't switching from PHP context to HTML context just to print out some meaningless whitespace. As @tim said, in this case it would be even better to build the string in PHP code rather than mixing PHP and HTML. In other situations this construct would be more acceptable. But there's still no point in switching out of PHP context unless you want to display something before you switch back into it. | {
"domain": "codereview.stackexchange",
"id": 16440,
"tags": "php, html, php5, pagination"
} |
Complexity of finding the maximal number of pair-wise disjoint sets | Question: Assume that I have $P$ sets with elements taken from $r$ possible ones. Each set is of size $n$ ($n<r$), where the sets can overlap. I want to determine whether the following two problems are NP-complete or not:
Problem A. Are there $M$ ($1 \le M \le P$) distinct sets within the $P$ sets (i.e., their pair-wise intersection is empty)?
Problem B. Now $k$ ($k<n$) elements can be chosen from each set. Are there $L$ ($1 \le L \le P$) distinct sets of size $k$ each within the $P$ sets? Note that only one set of $k$ elements can be taken from each set of $n$ elements.
Remark: I am mainly interested in the case where $k,n$ are fixed ($n \ge 2, k \ge 2$).
I think that Problem A can be thought as an $n$-uniform $r$-partite hyper-graph matching problem. That is, we have the elements of $r$ as vertices, and each hyper-edge contains a subset of $n$ vertices of the graph.
In the $n$-uniform $r$-partite hyper-graph matching problem NP-complete?
I think that Problem B is equivalent to finding the number of distinct hyper-edges of cardinality $k$ taken from hyper-edges of cardinality $n$. Is this restricted version (in the sense that each $k$-cardinality set is taken from a pre-chosen set of $n$ elements rather than taken arbitrarily from $r$ elements) of Problem A NP-complete?
Example ($n=3,r=5, P=3$):
$A=\{1,2,3\}$, $B=\{2,3,4\}$, $C=\{3,4,5\}$
If $k=n=3$, there is only $M=1$ one distinct set, which is $A$ or $B$ or $C$, since each of the pairs $(A,B)$, $(A,C)$, $(B,C)$ has non-empty intersection.
If $k=2$, we have $L=2$ distinct sets: one solution is $\{1,2\}$, $\{3,4\}$ (subsets of $A$ and $B$).
Answer: This is a special case of the Maximum Set Packing Problem and both problem A and B are NP-Complete. Note that the problem is simply a matching problem if $n=2$ and is also easy if $n=1$. So I'll assume $n \ge 3$.
Instead of asking the question,
Are there $M$ disjoint sets among the $P$ sets?
Let's ask the following question
What is the maximum number of disjoint sets we can obtain from the $P$ sets?
It is clear that if the second question is answerable in polynomial time, then so is the first since all we have to do is compare this maximum value to $M$ and output YES if $M$ is less than or equal to this maximum and NO otherwise.
Also, if the first question is answerable in polynomial time, then the second is too since we can use binary search on $M$ and obtain the answer to the second question and only add a factor of $O(\log{M})$
So we can conclude that both questions are equivalent. i.e. Question 1 is polylomial time solvable if and only if Question 2 is too.
It is also clear that the problems are in NP since we can easily verify that the $M$ sets outputed are disjoint.
So the question now is how do we reduce a known NP-Hard problem to this? To do this we reduce from the maximum set packing problem. I'll simply focus on problem A since problem B can easily be shown to be hard by setting $k=n-1$
Consider an arbitrary instance of the maximum set packing problem $T$. Note that the only difference between problem A and the original maximum set packing problem is that in problem A, the size of the sets have to be equal. Let $t$ be the maximum cardinality among all sets in $T$. If every set in $T$ have the same cardinality, we are done and the set cover problem is exactlly problem A. Now suppose that for some set $S_i \in T$, we have $|S_i| < t$. We simply add $(t-|S_i|)$ elements to $S_i$ which are not elements of any set in $T$. We repeat this process until all sets $S_i \in T$ have the same size. It is clear that adding new elements in this way does not change the size of the maximum number of disjoint sets.
So, if we can solve problem $A$ in polynomial time, we can solve the maximum set packing problem in polynomial time since all we have to do is remove the extra elements that we have added, and doing this doesn't change the size of the maximum number of disjoint sets in $T$.
EDIT - Some Additional information about problem B
Suppose problem B has a polynomial time solution, now consider an arbitrary instance $T$ of problem A with $n$ elements per set. Now we add a dummy element $d$ to each set in $T$. We now ask the following question.
What is the maximum number of disjoint sets we can obtain by taking
$n$ elements from each set?
Now we know that among the sets in the maximum, at most one of them can contain the dummy element, hence if the answer we get as the maximum is $M$, then the actual maximum number of sets in instance $T$ (our original problem A) is either $M$ or $(M-1)$, but this gives a constant factor approximation for maximum set packing. And such an approximation is only possible if $P=NP$. So problem B is also hard. | {
"domain": "cstheory.stackexchange",
"id": 2524,
"tags": "graph-theory, np-hardness"
} |
Difference between sunrise and sunset? | Question: Other than knowing which direction is east and which direction is west, or observing for a sufficient timespan (to determine the direction of motion), is there any way of telling whether what one is seeing is a sunset or a sunrise? A priori it seems not but I was wondering if there are some subtler effects beyond Rayleigh.
Note. I just came across an article that mentions that the green flash can occur only at sunset, and provides additional references:
Broer, Henk W.
Near-horizon celestial phenomena, a study in geometric optics. Acta Appl. Math. 137 (2015), 17–39.
Answer: In real life: A sunset is "redder" than a sunrise which makes people feel more romantic.
It's mostly because the atmosphere is warmer in the evening (no pollution here, lemon, the Earth is warmer in the evening because it was naturally warmed up during the day). However, there's also a very small contribution of the Doppler shift, one that you could in principle measure accurately. When you're looking to the East, your point on the Earth is moving towards the Sun at speed up to 1,500 km/h or so (on the equator). This small velocity still exceeds the radial component of the velocity around the Earth, I think, so if you measure the Doppler shift accurately, you may learn something about the motion.
You may also watch where the Sun is moving. If it is setting (dropping, approaching the horizon), it is a sunset, and if it is rising, it is a sunrise. ;-) | {
"domain": "physics.stackexchange",
"id": 31250,
"tags": "visible-light, atmospheric-science, geophysics"
} |
Complexity of BST | Question: I have the following pseudo-code for printing all nodes of a BST :
traverse(x):
if x == nil:
return
else:
print x
traverse(x.left)
traverse(x.right)
I want to find its complexity. I have an idea, but I'm not sure if I am implementing it correctly.
$T(n) = 2T(n-1) + cn$
Where $T(n-1)$ for each recursive call and $cn$ for the return statement.
Is my solution correct?
Answer: What i said in previous reply was about finding a node. I excuse for misunderstanding your question. For worst case its the same but for printing in average case it's $T(n)=2T(n/2)+1$ which is $O(n)$. | {
"domain": "cs.stackexchange",
"id": 4036,
"tags": "time-complexity, asymptotics, search-algorithms, search-trees"
} |
Interference between 2 electrons | Question: If 2 electrons undergo destructive interference (as they show wave nature) will they disappear or will they have no wave nature left?
Answer: The mathematics of quantum mechanics predicts an unevenness of the observation, similar to wave equations in that there are points where high values of electron density/reaction and low (~zero) values occur. If you have places (~50% of the places) where "interference" has yielded zero electron density/reaction, then the other 50% of the places will have twice the expected (average) electron density/reaction.
The question should include the entire observation, the whole experiment. For example, it is easy to imagine a photon experiment where diffraction causes interference effects upon a photographic film: photons abandon their even spread by being diffracted, and don't go to certain places on the film, but do go (in twice the expected density) to other places. Two photons don't just cancel out in some places - they "cancel out" and also "add up" in other places. Oh, heck, just think of a sine wave (square its amplitude) plopped down on the film and where the high peaks are, the film turns dark and where the wave bottom is, nothing happens. Two photons, two sine waves; there has to be a slight difference in path so that when you superimpose them, they add up more in one place and subtract more in another.
That thought experiment was reasonably easy because we think of photons as sort of fuzzy, wavy, intangible things. We usually consider electrons to be touchable, therefore firm on some sort of basis, so how can they interfere and cancel out of existence? Well, the wave nature of electrons means that they have a spread in space which has some of the characteristics of a wave, and they can, under the right conditions, exhibit this effect strongly. Getting back to the photographic film experiment, electrons can be made to exhibit the same effects as diffraction does to photons. Where it becomes more difficult to understand is that while the photon (say, ~500 millimicrons wavelength) is much fuzzier than a silver ion (~0.25 millimicron diameter in AgCl), you would expect an electron to be, if anything, a bit smaller than an atom, since, after all, electrons (many of them!) will fit into an atom or ion.
So you can see that a photon with a spread of 500 millimicrons will smash down over close to a million Ag+ ions, but can only activate one, but you might expect a little electron to be like a bullet and just hit one silver ion. How could you miss? Consider the bullet to be wobbly (wavy) enough to hit either one Ag+ or its neighbor. The faster it goes, the wobblier (wavy) it gets. And these waves interfere so that some paths just don't happen, and others are travelled twice as frequently - this doesn't mean that two electrons cancel out of existence or form a bi-electron.
At least that's the way I look at it without the comfort and brevity of mathematical equations. But words only poorly describe the situation and it takes forever to try to explain. | {
"domain": "chemistry.stackexchange",
"id": 12496,
"tags": "physical-chemistry"
} |
Python calculate arrangements of sequence | Question: I have just started thinking about probabilities. A Problem that come up was how to calculate all the potential arrangements for a given sequence. By arrangement I mean unique permutation.
I initially used this method:
from itertools import permutations
sequence = '11223344'
len(set(permutations(sequence)))
# 2520
But for long sequences this can take a long time! (or run out of memory)
I came up with this function arrangements
from math import factorial
from functools import reduce
from operator import mul
def arrangements(sequence):
return factorial(len(sequence))/reduce(mul,
[factorial(sequence.count(i)) for i in set(sequence)])
# arrangements(sequence)
# 2520.0
My thinking is this:
For a given length sequence with all unique items there are factorial(len(sequence)) permutations.
For every repeated item in the sequence there will be factorial(#repeats) that will result in the same permutation.
My function calculates all permutations / all repeated permutations.
I'm sure I have reinvented an already existing standard python function somewhere. I'd like to know if my thinking is sound and the implementation makes sense.
Wouldn't itertools.arrangements be cool?
Answer: Notes
I'd expect arrangements to return the unique permutations of sequence, not just how many there are.
If it returns a number, it should be an integer.
You could use collections.Counter instead of counting the integers again and again.
You're right, it would be nice to have itertools.unique_permutations. In the meantime, I often come back to this SO answer.
Possible refactoring
from math import factorial
from functools import reduce
from collections import Counter
from operator import mul
def count_unique_permutations(sequence):
count_permutations = factorial(len(sequence))
repetitions = (factorial(v) for v in Counter(sequence).values())
return count_permutations // reduce(mul, repetitions) | {
"domain": "codereview.stackexchange",
"id": 29887,
"tags": "python, python-3.x, combinatorics"
} |
Drift velocity current electricity | Question: I have a question which I got stumbled upon between two different options (MCQ), as it required to have only one correct option. So the question goes like this:
In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor :
options are: (`Wherever potential is mentioned it is electric potential )
move in the straight line paths in the same direction.
drift from higher potential to lower potential.
move in the curved paths from lower potential to higher potential.
move with uniform velocity throughout from lower potential to higher potential.
I know that, generally electric field lines( by convention) starts from higher potential and goes towards lower potential which makes option 1 and 2 false. While option 3 is correct but I have doubt in option 4. wether option 4 is also correct.
option 4: according to me although there is an acceleration of free electrons inside the conductor due to electric field, the various forces like nuclear attraction, electron-electron repulsion, etc. makes it seems like the electrons are drifting with constant velocity from lower potential to higher potential.
Sir If have made any mistakes above please pardon me for my dull mind.
Answer: Replace your . . . . . drifting at constant velocity . . . . . with . . . . . drifting at constant average velocity . . . . . thus negating option $4$. | {
"domain": "physics.stackexchange",
"id": 94996,
"tags": "homework-and-exercises, electromagnetism, electric-current, velocity"
} |
How can I connect a cylinder and block in a way that can be detached multiple times? | Question: I have this assembly of a cylinder and a block, where the cylinder can rotate inside the block.
How can I connect the cylinder and the block in a way that is detachable, so that while the connection is close, the cylinder can not be moved, and while it is open, it can be moved? The cylinder is supposed to be able to be set in every rotary position.
One suggestion that I had was to connect them using a screw, as shown in the picture.
However, in this way, the area where they make contact is very small, so I thought maybe there was a better solution? Are there maybe any ressources where you can read about problems like this?
Thanks for any replies and ideas!
Answer:
Figure 1. A slot and clamp screw provide an even clamping friction around the surface of the mating surfaces and doesn't leave grub-screw marks.
If forced to use a grub screw then a groove can be cut in the cylinder to allow the grub screw to bite on an area that isn't a mating surface between the block and cylinder. This will prevent problems with burrs binding on the mating surfaces. | {
"domain": "engineering.stackexchange",
"id": 4846,
"tags": "mechanical-engineering"
} |
Large amount of Sigmoid outputs are ones and zeros | Question: I have Keras neural network for binary classification with final layer having one output with Sigmoid activation. I have noticed that large amount of output numbers are strictly one or zero (rather than between 0 and 1 as expected). What could be the reason for this?
At first I thought maybe network is 100% sure about accuracy of these numbers, but noticed that some of these predictions are actually incorrect.
Edit:
Model:
model = tf.keras.models.Sequential()
model.add(tf.keras.layers.Dense(32, activation = tf.nn.relu, input_shape=(X_train.shape[1],)))
model.add(tf.keras.layers.Dense(64, activation = tf.nn.relu))
model.add(tf.keras.layers.Dense(32, activation = tf.nn.relu))
model.add(tf.keras.layers.Dense(1, activation = tf.nn.sigmoid))
model.compile(optimizer = tf.keras.optimizers.Adam(), loss = 'binary_crossentropy', metrics = ['accuracy', roc_auc])
model.fit(X_train, y_train, epochs=10, validation_data=(X_test, y_test))
y_pred = model.predict(X_test)
yhat = []
for pred in y_pred:
if pred >= 0.7:
yhat.append(1)
else:
yhat.append(0)
Data consists of 8 columns (features) and 270 000 rows (9th column is 'y' column). Out of these 270,000 rows only 9% contained labels of class 1 (rest were zero), so I downsampled the data (just removed bunch of data with label 0), trained the model and then did the prediction on full data. I modified how ones and zeros were determined by Sigmoid though, I changed threshold from 0.5 to 0.7 (which was the ROC score I got on downsampled data)
Answer: Apparently the problem was that I forgot to normalize data. As I found out, sigmoid turns any input greater than 10 into 1 and inputs less than -10 into 0. Normalization solves this problem (as normalized values are between 0 and 1) | {
"domain": "datascience.stackexchange",
"id": 6383,
"tags": "deep-learning, classification, keras"
} |
Why are RNNs used in some computer vision problems? | Question: I am learning computer vision. When I was going through implementations of various computer vision projects, some OCR problems used GRU or LSTM, while some did not. I understand that RNNs are used only in problems where input data is a sequence, like audio or text.
So, in kernels of MNIST on kaggle almost no kernel has used RNNs and almost every repository for OCR on IAM dataset on GitHub has used GRU or LSTMs. Intuitively, written text in an image is a sequence, so RNNs were used. But, so is the written text in MNIST data. So, when exactly is it that RNNs(or GRUs or LSTMs) need to be used in computer vision and when don't?
Answer: RNNs and CNNs are not mutually exclusive! It might seem that they are used to handle different problems, but it is important to note that some types of data can be processed by either architecture. For instance, RNNs uses the sequences as the input. It should be mentioned that sequences are not just limited to text or music. Sequences can also be videos, which are a set of images.
RNNs, such as LSTM, are used for cases where the data includs temporal properties, e.g., time series, and also where the data is context-sensitive, e.g., in the case of sentence completion, the function of memory provided by the feedback loops is critical for adequate performance. In addition, RNNs have been successfully applied in the following areas of computer vision:
Image classification (one-to-one RNN): e.g., “Daytime picture” versus “Nighttime picture”.
Image captioning (One-to-many RNN): giving a caption to an image based on what is being shown. For example, “Fox jumping over dog”.
Handwriting recognition: Please read this [paper] (https://arxiv.org/pdf/1902.10525.pdf)
Regarding CNN, here are some of its applications:
Medical image analysis
Image recognition
Face detection
Recognition systems
Full-motion video analysis.
It is important to know that CNNs are not capable of handling a variable-length input.
Finally, using RNNs and CNNs together is possible and it could be the most advanced use of computer vision. For example, a hybrid RNN and CNN approach may be superior when the data is suitable for a CNN, but has temporal characteristics.
Ref | {
"domain": "datascience.stackexchange",
"id": 7857,
"tags": "deep-learning, cnn, rnn, computer-vision"
} |
Silly Question about Supersymmetric Gauge Theory | Question: In $\mathcal{N}=1$ super electrodynamics, one has the following vector superfield
$$V(x,\theta,\bar{\theta})=\bar{\theta}\bar{\sigma}^{\mu}\theta v_{\mu}(x)+\bar{\theta}^{2}\theta\lambda+\theta^{2}\bar{\theta}\bar{\lambda}+\theta^{2}\bar{\theta}^{2}D(x)$$
in Wess-Zumino gauge. One can define the following gauge invariant spinorial superfield
$$W_{\alpha}=-\frac{1}{4}\bar{D}^{2}D_{\alpha}V,$$
where $\bar{D}_{\dot{\alpha}}=\bar{\partial}_{\dot{\alpha}}-i(\bar{\sigma}^{\mu})_{\dot{\alpha}\beta}\theta^{\beta}\partial_{\mu}$, and $D_{\alpha}=\partial_{\alpha}-i(\sigma^{\mu})_{\alpha\dot{\beta}}\bar{\theta}^{\dot{\beta}}\partial_{\mu}$ are the supercovariant derivatives.
One can find that the gauge invariant spinorial superfield has the following component expansion:
$$W_{\alpha}(x,\theta,\bar{\theta})=\lambda_{\alpha}(x)+2\theta_{\alpha}D(x)+\frac{i}{2}\theta_{\beta}(\sigma^{\mu\nu})^{\beta}_{\,\,\,\alpha}f_{\mu\nu}(x)+i\theta^{2}(\bar{\sigma}^{\mu})_{\dot{\beta}\alpha}\partial_{\mu}\bar{\lambda}^{\dot{\beta}}(x)-i\theta\sigma^{\mu}\bar{\theta}\partial_{\mu}\lambda_{\alpha}(x)-2i\theta_{\alpha}\theta\sigma^{\mu}\bar{\theta}\partial_{\mu}D(x)+\frac{1}{2}\theta\sigma^{\mu}\bar{\theta}\theta_{\beta}(\sigma^{\mu\nu})^{\beta}_{\,\,\,\alpha}\partial_{\rho}f_{\mu\nu}(x)+\frac{1}{4}\theta^{2}\bar{\theta}^{2}\Box\lambda_{\alpha}(x),$$
where $f_{\mu\nu}=\partial_{\mu}v_{\nu}-\partial_{\nu}v_{\mu}$.
I am interested in the following integral
$$\int d^{2}\theta W^{\alpha}W_{\alpha}.$$
The relevant terms in the above product are
\begin{align}
&\epsilon^{\alpha\beta}W_{\beta}W_{\alpha} \\
=\epsilon^{\alpha\beta}&\left[\lambda_{\beta}+2\theta_{\beta}D+\frac{i}{2}\theta_{\gamma}(\sigma^{\mu\nu})^{\gamma}_{\,\,\,\beta}f_{\mu\nu}+i\theta^{2}(\bar{\sigma}^{\mu})_{\dot{\beta}\beta}\partial_{\mu}\bar{\lambda}^{\dot{\beta}}\right]\times \\
&\left[\lambda_{\alpha}+2\theta_{\alpha}D+\frac{i}{2}\theta_{\rho}(\sigma^{\mu\nu})^{\rho}_{\,\,\,\alpha}f_{\mu\nu}+i\theta^{2}(\bar{\sigma}^{\mu})_{\dot{\gamma}\alpha}\partial_{\mu}\bar{\lambda}^{\dot{\gamma}}\right].
\end{align}
My question comes from the following terms:
$$\epsilon^{\alpha\beta}(i\theta^{2}(\bar{\sigma}^{\mu})_{\dot{\gamma}\alpha}(\partial_{\mu}\bar{\lambda}^{\dot{\gamma}})\lambda_{\beta}+i\theta^{2}(\bar{\sigma}^{\mu})_{\dot{\beta}\beta}(\partial_{\mu}\bar{\lambda}^{\dot{\beta}})\lambda_{\alpha})$$
It seems that the above two terms cancel, which must be wrong. Where did I make the mistake?
Answer: In the first term of your last equation $\lambda_\beta$ should be on the left side of $\partial\bar{\lambda}^{\dot{\gamma}}$. Spinors anticommute. | {
"domain": "physics.stackexchange",
"id": 57427,
"tags": "homework-and-exercises, gauge-theory, supersymmetry"
} |
Time series binary classification probability smoothing | Question: Problem
Suppose we have trained binary classifier and want to predict value of [x1, ..., x5] with associated timestamps [t1, ..., t5]. We get the prediction as following: [0.25, 0.99, 0.1, 0.75, 0.79].
Assume that I have the domain knowledge to say that probability of positive class must not change abruptly. Jumps like from 0.99 at t2 to 0.1 at t3 cannot occur in real application.
Questions
Can I enforce smooth output constraint on (any/some) classifier?
Does applying moving average on the prediction probability to smooth it make sense?
Answer: You can use a total variation regularizer (https://en.wikipedia.org/wiki/Total_variation_denoising), it's a penalty for abrupt changes of neighbor values. It's usually used for images, that's why its TF version (https://www.tensorflow.org/api_docs/python/tf/image/total_variation) operates with 4D tensors, but if you're writing your model in pytorch for instance, it's easy to implement that regularizer yourself. Also possibly you don't need it if you've got enough data and target values there are already smooth. Your ML algorithm would just learn that smoothness from data, the only 2 cases you'd need it is when your dataset is small or when your training targets aren't smooth, but testing targets should be smooth. | {
"domain": "datascience.stackexchange",
"id": 8280,
"tags": "classification, time-series"
} |
Lime Explainer: ValueError: training data did not have the following fields | Question: I'm attempting to gather ID level drivers from my XGBoost classification model using LIME and I'm running into some odd errors. I'm using this link as a reference.
Here is the overall code that I'm using:
explainer = lime.lime_tabular.LimeTabularExplainer(Xs_train.values, class_names = [1.0, 0.0], kernel_width = 3)
predict_fn_xgb = lambda x: trained_model.predict_proba(x).astype(float)
data_point = Xs_val.values[5]
exp = explainer.explain_instance(data_point, predict_fn_xgb, num_features = 10)
exp.show_in_notebook(show_all = False)
Key:
trained_model: trained xgboost classification model
class names: This is a binary classification model
Xs_train: This is a (73548, 84) dimension training set. This was used to build the training_model
Xs_val: This is a (4910, 84) dimension training set. The columns are the same with the training and validation set.
data_point: one specific validation point
Now, when I run this code, I get the following error:
ValueError: expected res_time, email_views...training data did not have the following fields: f6, f49, f34, f21,...
I don't know where the f# column names are coming from. Seems really bizarre and I believe I'm following the example correctly.
Any help would be much appreciated. Let me know if any additional information is required.
Answer: It looks like a dataframe/nparray mismatch. Probably your model was trained on a dataframe; doing the training instead on an nparray may fix the problem.
I've seen such errors in working with xgboost; see e.g.
https://github.com/dmlc/xgboost/issues/2334 and
https://stackoverflow.com/a/52578211/10495893 | {
"domain": "datascience.stackexchange",
"id": 6429,
"tags": "machine-learning, classification, xgboost"
} |
How does one become a control systems engineer? | Question: From what I understand, a control systems engineering job is almost always a senior level position. What kind of entry level jobs do most engineers have before they are qualified to actually design control systems? Is a PE license necessary for this kind of work?
I am currently working on a masters degree in electrical and computer engineering. I am mostly interested in control theory and that is the subject of my thesis.
Answer: To a large extend the answer depends on the industry. For example if you work for a large aerospace company it might take a while before you can get chance to get involved in designing a control systems. In this case you will be most likely a team member design a control system. On the contrary if you happen to work for smaller company you will mostly get to design smaller control system early in your career. Your choice is, do you want be a large fish in a small pond or small fish in a big pond.
For either choice you might want to get practical experience in area such as
Measurement systems including sensor characteristics and technologies
including pressure, motion, flow, ultrasonic sensors etc
Signals, Transmission and networking including EMI/EMC, communication
protocols, cross talk, routers
Control elements such as motor controls, pressure relieving devices,
valves etc
Code Standards and Regulation such as ANSI, NEMA, and OSHA
Implementation methodologies including management of change (Scope,
ECN/ECO, Cost, Time)
You also might want to look at Control Systems Engineer (CSE) Licensure exam as well as some of the requirements for current control engineering entry level jobs.
Below are some engineering SE post that discuss some aspects of the above
References:
International Society of Automation
Is interference between aircraft an issue for fly-by-wireless technology?
How can I arrange my ECO system to enforce the principle of least privilege?
Sensors / processing algorithms to emulate a human's sense of smell | {
"domain": "engineering.stackexchange",
"id": 898,
"tags": "control-engineering, control-theory, employment"
} |
Determining axis of rotation from angular speeds about axes | Question: I think my pure-math head is messing with me on the question below: my physics and CS friends both seemed to think it was a simple computational thing, and my program says the method works, but now I've confused myself about rotations vs. angular velocities.
The problem: you have data from gyroscopes on a rigid body that give you the angular speeds of the object around three orthogonal axes through the body. These measured angular speeds are constant, call them $\omega_x$, $\omega_y$, and $\omega_z$.
Sine the angular speeds are constant, the axis of rotation of the object is also constant, and it's not too much trouble to find it by considering the combined angular velocity vector $\Omega$ = ($\omega_x$,$\omega_y$,$\omega_z$).
I am then confused when I think about this in terms of rotations. There's a unique axis of rotation because every composition of rotations is equivalent to a single rotation about some axis. It seems, then that you should be able to determine this axis by determining the eigenvectors of the combined matrix ABC, where A, B, C each represent the rotation about one of the axes.
But of course, rotations in general don't commute. I'm forced to conclude that what makes the unique determination of an axis work is that infinitesimal rotations commute.
So, if I'm right about this, my question is -- how can I see that infinitesimal rotations commute? My intuition fails me here.
If they don't - what's the link between the rotation and angular velocity vector way of looking at this that removes the usual problems dealing with rotations that don't commute?
Answer:
how can I see that infinitesimal rotations commute
See the Wolfram MathWorld article on Infinitesimal Rotation
UPDATE: I've recently been made aware that it's bad form to simply "answer" with a link sans summary so I will succinctly summarize the contents of the link.
Essentially, the infinitesimal rotation matrix is the Identity plus an infinitesimal matrix. In the product of two of these, the non-commutative part evaporates as the components are products of infinitesimals. Only the sum of the Identity (squared) and the two infinitesimal matrices remain regardless of the order in the product. | {
"domain": "physics.stackexchange",
"id": 3846,
"tags": "classical-mechanics, rotational-dynamics"
} |
training the face_recognition using kinect | Question:
Hi , I try to run this package ""https://github.com/procrob/procrob_functional"" but when i execute the commands in this page """http://wiki.ros.org/face_recognition""" No images are added to the data folder ???
I am using fuerte distribution on Ubuntu 12.04
Originally posted by smart engineer on ROS Answers with karma: 11 on 2014-05-08
Post score: 1
Answer:
A lot of Fuerte stuff is broken and it's not being updated. I would highly suggest looking into OpenCV or PCL for any sort of computer vision applications.
Originally posted by Athoesen with karma: 429 on 2014-05-08
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by smart engineer on 2014-05-30:
But ROS face _ Recognition package worked with other people using Fuerte distribution ??? and I am interesting in working with it ... | {
"domain": "robotics.stackexchange",
"id": 17882,
"tags": "ros, ros-fuerte, face-recognition"
} |
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