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# Remote operation¶

The MagAO-X software is designed for use on Linux with CentOS 7, and the included provisioning script will automatically set up a fresh install on a computer running that OS. However, most of us don’t use CentOS 7 on our personal computers.

If you’re on a Mac or Windows machine, or if you just want to keep MagAO-X isolated from the rest of your OS, you should use a virtual machine (VM). A virtual machine is a simulated computer (running whatever “guest OS” you like) that runs as a program on your computer’s OS (which we call the “host OS”). This virtual machine can then be used to operate all the normal MagAO-X GUI and CLI tools and control the real instrument.

Conceptually, you just create a virtual CentOS computer and go through the normal installation process on it. To automate this process, and make certain customizations for speed and convenience, there’s Vagrant. Vagrant can start a virtual machine from a pre-made image, run your install script, and configure things like forwarding network ports from the VM to your host OS.

As it happens, MagAO-X has a Vagrantfile specifying the setup process to minimize the number of manual steps.

## Prerequisites¶

• git — Preinstalled on most Linuxes, install with xcode-select --install on macOS, see below for Windows

• Vagrant — Program to automate creation / provisioning of development VMs

• NFS — available preinstalled on macOS and most Linux hosts (ICC guest on macOS and Linux hosts only)

### Additional notes for Windows users¶

Windows use isn’t tested automatically, and things may break unexpectedly…

1. It’s probably easiest to get git from Anaconda if you’re already using it (use conda install git at the Anaconda command line)

2. git needs to be configured not to alter line endings. After installing git, you should do git config --global core.autocrlf false before cloning MagAOX. (However, if you use git for other things, you may not want this to be a global setting.)

3. The existence of a windows_host.txt advisory file is required for provisioning to succeed. (Its presence tells the scripts to work around functionality that is missing on Windows hosts.)

4. The section below on Using GUIs in the VM needs to be expanded with instructions for Windows. (Basically, we need to figure out which of the X11 servers for Windows works with vagrant ssh in the current configuration.) Until then, no GUIs in Windows.

## Setup¶

1. Ensure vagrant command is available:

$vagrant --help Usage: vagrant [options] <command> [<args>] ...  2. Clone magao-x/MagAOX (if necessary) and cd into MagAOX $ git clone https://github.com/magao-x/MagAOX.git
Cloning into 'MagAOX'...
...

$cd MagAOX  3. Windows only: Create a new blank file named windows_host.txt in the MagAOX folder. 4. Run vagrant up $ vagrant up

If prompted, enter your password to configure NFS exports. (See this doc for information on eliminating that prompt.)

Note: The vagrant up step is CPU and bandwidth intensive the first time, as it will download an OS image and all of the MagAO-X dependencies, then compile them. Subsequent vagrant ups will just boot the existing machine.

Don’t be alarmed by the output from vagrant up. Provisioning is very noisy, and messages in red aren’t necessarily errors. Successful provisioning will end with the message

Provisioning complete

### What to do if you don’t see Provisioning complete¶

Most likely that means an error occurred running the provisioning scripts and they did not finish. That can happen if a big download gets interrupted, for example. It’s always safe to run vagrant provision and it’ll re-run only necessary steps, which may be enough to get you to Provisioning complete.

If that doesn’t resolve the issue, you’ll need the complete provisioning output to get help. The following command will save it to a file provision.log, which you can then email or Slack to someone who can help.

$vagrant provision | tee provision.log  ## Usage¶ ### Connecting¶ To connect to the VM, use vagrant ssh. You’ll be logged in as user vagrant with no password, and the command prompt in your shell will change to something like this: [vagrant@centos7]$

The rest of the commands in this section are to be run in a vagrant ssh session, unless otherwise noted.

### Remotely controlling MagAO-X¶

Before you can remotely control MagAO-X, a little post-provisioning configuration is required. You must have a user account on MagAO-X with an SSH key file configured. (This will probably be called something like ~/.ssh/id_ecdsa on your host computer, with the corresponding file ~/.ssh/id_ecdsa.pub added to your authorized keys on the MagAO-X computers.)

With the username and key file handy, go to the folder where you cloned the MagAOX repository. There will be a subfolder called vm/ where the provisioning process placed a lot of files. In vm/ssh/ edit the config file. At the end you will see

Host *

which you should update with the username you use on MagAO-X computers. Notice the line at the top that says IdentityFile /vagrant/vm/ssh/magaox_ssh_key. This tells the VM to use the key file at vm/ssh/magaox_ssh_key from the host to authenticate you. Copy the key file you identified before and rename it to magaox_ssh_key and store it in the same directory as config.

#### Check connectivity¶

To ensure everything’s configured correctly, from a vagrant ssh session run ssh rtc, then exit:

[vagrant@centos7] $ssh rtc [you@exao2]$ exit
[vagrant@centos7] $ #### Start tunnels¶ The xctrl script is installed during provisioning, and a default set of apps is configured to run on xctrl startup. These apps launch SSH tunnels to the instrument. The proclist for VM usage is in magao-x/config/proclist_vm.txt. Running xctrl startup to start the tunnels should result in output like: [vagrant@centos7 ~]$ xctrl startup
Session vm_aoc_milkzmq does not exist
Session vm_aoc_indi does not exist
Created tmux session for vm_aoc_milkzmq
Created tmux session for vm_aoc_indi
Executed in vm_aoc_milkzmq session: '/opt/MagAOX/bin/sshDigger -n vm_aoc_milkzmq'
Executed in vm_aoc_indi session: '/opt/MagAOX/bin/sshDigger -n vm_aoc_indi'

And you can check their status with xctrl status or xctrl peek.

[vagrant@centos7 ~]$xctrl status vm_aoc_indi: running (pid: 6147) vm_aoc_milkzmq: running (pid: 6148)  ### Using GUIs in the VM¶ The VM is configured to be “headless”, meaning there’s no graphical display window. However, we can still build and run MagAO-X GUIs as long as your host OS has an X11 server (most Linux systems do by default, but you will need XQuartz on macOS). If you’re unfamiliar with SSH X forwarding, the short version is that the app runs on the VM but the window pops up like any other window on your own computer (the host). SSH (i.e. vagrant ssh) is the transport that moves information about the window back and forth to the GUI app, which is still running inside the VM. +------------------------------------------+ | +----------------------+| | Host OS | VM || | | || | [GUI window] <-SSH-> [MagAO-X GUI app] || | +----------------------+| +------------------------------------------+  So, to start the coronAlignGUI, you could do… host$ vagrant ssh
vm\$ coronAlignGUI

…and the coronagraph alignment GUI will come up like any other window on your host machine.

Be careful! Anything you do with these GUIs controls the real instrument (which is sort of the point, but it bears reiterating).

### Viewing camera outputs¶

The realtime image viewer rtimv is built during provisioning. To get up-to-date imagery from the instrument, we can use jaredmales/milkzmq, a set of programs that relay shared memory image buffers from one computer to another.

The AOC workstation runs a mzmqServer process that re-serves the images it replicates from the rest of the instrument using compression and a limit of 1 FPS. This ensures it doesn’t overwhelm your home internet connection.

(Napkin math: 1024 * 1024 * 16 bit, or one camsci1 frame, is ~2 MB. 2 MByte / second is 16 Mbit / second, more than compressed HD video streams. And that’s just one camera!)

The list of images re-served by AOC is kept in /opt/MagAOX/config/mzmqServerAOC.conf (view on GitHub).

After confirming the tunnel vm_aoc_milkzmq is running (xctrl status), start a milkzmqClient. For this example we’ll connect to camwfs and camwfs_dark:

milkzmqClient -p 9000 localhost camwfs camwfs_dark &

(We’ve used & at the end of the command to background the client, so just hit enter again to get a normal prompt back after its startup messages.)

The configuration in /opt/MagAOX/config includes rtimv config files named for the various cameras (see the shmim_name options in those files for hints about which images to replicate for a given camera).

Start the viewer with

rtimv -c rtimv_camwfs.conf

and it should pop up a window like this:

For instructions on rtimv, consult its user guide.


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# Which algorithm should I choose for lead scoring

I am a c# senior developer and I got a task to try and predict the potential in each new client, or maybe the worth of each customer. I don't have experience with machine learning, but I played with accord-framework.net and got some nice results on simple task.

My data model for training is:

GeoLocation, // the country of ip when registed. iso code string
Age, // number
DateRegistered, //date time
Email, //string can be broken to vendors as catergorial (gmail, yahoo, microsoft and such)
EmailValidated, //is the email really exists. bool
PhoneNumber, //string
PhoneNumberValidated, // is the phone number really exists
CampaignName, //string (may be categirial)
UserAgent, //string should I make it categorial? (has info about browser, device, verndor, operation system and such, long string)
LandedOnPage, //string first url the customer entered from
RegisteredFromPage, //string url of the page that the user registered from
RefererUrl, //string url the client came to our site from,
NumberOfPurchases, //the amount of times the customer puschase something on our site
CustomerValueUsd, //the total amount of USD the customer spent in our site

The output shoud be CustomerValueUsd

I have a lot of data in the history, so I can back test it.

My questions:

1. Does it make sense to do this task even though I don't have an experience with machine learning? How complicated is this task considering I'm using a well known framework?
2. Assuming that I'm taking the task, which algorithm should I choose to perform this kind of task?
3. How should I build the training data? see my comments, do you think my comments are ok to start with? or maybe I can break the data directly?
• I suggest you take an intro to ML course. Your coding background will help a lot understanding how to turn the concepts into code. You are missing the concepts themselves, but they can be learned. One suggestion: coursera.org/learn/machine-learning – Neil Slater Nov 27 '17 at 10:16

ML is a wide and deep topic to cover.

What you need is "classification" to predict an outcome. At first, you need to convert everything to numbers (check word2vec). Then, pre-process the data (Check what is a normalization for example). Train a classifier by using any ML techniques (i.e. linear classifier, SVM, deep learning, neural classifier). Then you can use that regression function to predict further values. If you need much more detailed way to do that, it is better to buy a 'thick' book that explains all other options.

Does it make sense to do this task even though I don't have an experience with machine learning? How complicated is this task considering I'm using a well known framework?

I think it does make sense, and using an established framework would get you up and running quickly.

Assuming that I'm taking the task, which algorithm should I choose to perform this kind of task?

This is a regression problem, so I would recommend that you don't treat it as a classification task (unless you want to have a binary output like "profitable" / "non-profitable"). In essence, you are trying to identify the correlation between your inputs (previous purchases, location, etc.) and a certain metric (dollar value of the customer). Neural networks are very good at that (Accord seems to support neural networks, so you should be able to use that; TensorFlow with Keras as the interface or Caffe might be other options to consider).

How should I build the training data? see my comments, do you think my comments are ok to start with? or maybe I can break the data directly?

In most cases, you'd want to normalise your data before feeding it to the algorithm (this is particularly important for neural networks). The other thing you should do is consider what features would be relevant to the task. For example, since you want the customer value as the predicted output, the customer's phone number and email address are most probably irrelevant, but number of previous purchases, age and geolocation might be very relevant. Maybe you have other features in your database - total dollar amount of previous purchases, frequency of purchase, number of returned items or refund requests, etc. Remember to keep your model in check by splitting your data into training, validation and test sets (as a rule of thumb, 70% training / 10% validation / 20% test, but that depends on how much data you have).

format: plain


text:
## Calculus, 10th Edition (Anton)

$\lim\limits_{x \to 4}\frac{3-x}{x²-2x-8}$ does not exist.
As $\lim\limits_{x \to 4^{-}}\frac{3-x}{x²-2x-8}$ = +$\infty$ $\ne$ $\lim\limits_{x \to 4^{+}}\frac{3-x}{x²-2x-8}$ = -$\infty$, we conclude that $\lim\limits_{x \to 4}\frac{3-x}{x²-2x-8}$ does not exist.


text: Wednesday's warmup felt on the cool side in Denver because of a pesky mountain wave cloud. In contrast, the phase propagation (or phase speed) of the waves points perpendicular to energy transmission (or group velocity).[6][7]. On the ground, they can result in very strong gusty winds in one place, with still air only a few hundred metres away. These wave fronts represent extrema in the perturbed pressure field (i.e., lines of lowest and highest pressure), while the areas between wave fronts represent extrema in the perturbed buoyancy field (i.e., areas most rapidly gaining or losing buoyancy). The latest breakthroughs, research and news from the Met Office. mountain barriers where wave clouds are generated by flow over these barriers. θ N Although the clouds are over the mountains, these are NOT mountain wave clouds. Clouds associated with mountain waves: Photo taken south of Walsenburg, Colorado on May 20, 2003 Photo by: Mark J. Madigan. Recognize special clouds (e.g. A lenticular cloud produced by a mountain wave. there are several terms for mountain wave:- The vertical airflow component of a standing wave may exceed 8,000 ft/min. 0 Mountain waves may extend into the stratosphere and become more pronounced as height increases. These include both natural features of the Earth, such as mountains or hills, and artificial structures, such as buildings and other structures. What weather is associated with lenticular clouds? At the wave dip, no clouds,” said Wind. The photo shared on social media captured clouds that look like ocean waves in the sky. The moving air hits the still mountain in the same way the prow of a moving boat hits still water.” As air funneled around the islands in February, its temperature and humidity was just right for the crests of the lee waves to rise and cool the air and form clouds. Mountain Wave and Rotor Clouds over the Colorado Front Range. Shape: Curved layers, like flying saucers, Latin: Altocumulus lenticularis = “like a lens”. Watch Queue Queue will occur at a lower frequency of = Buoyancy restoring forces therefore act to excite vertical oscillation of the perturbed air parcels at the Brunt-Väisäla frequency, which for the atmosphere is: N Skilled (and brave) glider pilots, on the other hand, like them, because they can tell from the shape of the clouds where the air will be rising. Both lee waves and the rotor may be indicated by specific wave cloud formations if there is sufficient moisture in the atmosphere, and sufficient vertical displacement to cool the air to the dew point. . Lee waves are a form of internal gravity waves produced when stably stratified flow is forced over an obstacle. 0 [5] Usually a turbulent vortex, with its axis of rotation parallel to the mountain range, is generated around the first trough; this is called a rotor. ) d. nacreous. … This is because the presence of the mountain wave results in severe turbulence of the aircraft’s rotor systems. … Virga. Lenticular clouds have a lens-shaped or almond-shaped cross section. The crests of the waves may be identified by the formation of lenticular clouds (lens-shaped), if the air is sufficiently moist. 0 Otherwise, when these clouds cannot form in the absence of enough moisture in the air, the presence of a mountain wave is hard to identify, and this can be potentially dangerous to the airplane. c. cumulonimbus. Pilot have come to accept all these names for wave activity regardless of where the lenticular clouds are positioned. In a way, Lenticular clouds warn pilots of the presence of mountain waves. Disk shaped, mountain-wave clouds are known as *a. altocumulus lenticularis. Waves may also form in dry air without cloud markers. It can even be a hazard for large aircraft; the phenomenon is believed responsible for many aviation accidents and incidents, including the in-flight breakup of BOAC Flight 911, a Boeing 707, near Mount Fuji, Japan in 1966, and the in-flight separation of an engine on an Evergreen International Airlines Boeing 747 cargo jet near Anchorage, Alaska in 1993.[14]. The air cools as it rises, and if there is moisture in the air, the water condenses into clouds. Wave cloud pattern in Tadrart region. A wave cloud is a cloud form created by atmospheric internal waves. [1][2][3] d Weather fronts mark the boundary or transition zone between two air masses and have an important impact up…, The classification of clouds into types was first proposed by Luke Howard in 1802 and we largely use the s…, Contrails are frequently seen criss-crossing the sky and are created from water vapour coming out of an ai…. When the air hit the edge of the mountains and began to pass over, it began to oscillate—much like the suspension of a car bounces after it goes over a speed bump. The conditions favoring strong lee waves suitable for soaring are: The rotor turbulence may be harmful for other small aircraft such as balloons, hang gliders and paragliders. Lenticular clouds are a visible sign of mountain waves in the air. They are also known as billow clouds, shear-gravity clouds, KHI clouds, or Kelvin-Helmholtz billows. {\displaystyle N\cos {\phi }} [9][10] The Mountain Wave Project of the Organisation Scientifique et Technique du Vol à Voile focusses on analysis and classification of lee waves and associated rotors.[11][12][13]. The waves or clouds downwind from the mountain are the mountain are the "standing wave" or "lee wave." 'Fluctus' is the Latin word for "billow" or "wave" and this may also be used to describe the cloud formation, though that most often occurs in scientific journals. Unusual wave clouds over the Aral Sea, seen from NASA's Water satellite on March 12, 2009. The rising air of the wave, which allows gliders to climb to great heights, can also result in high altitude upset in jet aircraft trying to maintain level cruising flight in lee waves. By Caitlin O'Kane June 19, 2019 / 8:31 AM / CBS News Seven weird weather phenomenons . Some decent mountain wave cloud/sunset time-lapses from a couple different days along the Colorado front range near Boulder, CO. However, these waves can be present beyond the clouds, and may exist even when no clouds are formed. mountain-wave cloud A cloud that forms in the rising branches of mountain waves and occupies the crests of the waves. A stable air mass will continue to rise and dip for a little while as it travels away from the mountain, setting up an invisible "standing wave". In a way, Lenticular clouds warn pilots of the presence of mountain waves. There are a variety of distinctive types of waves which form under different atmospheric conditions. Explore similar videos at Adobe Stock These were discovered in 1933 by two German glider pilots, Hans Deutschmann and Wolf Hirth, above the Krkonoše. Lee waves provide a possibility for gliders to gain altitude or fly long distances when soaring. 2019-12-01 12:30:13, 117 frames. cos Lenticular clouds are a visible sign of mountain waves in the air. The most distinctive are the sharp-edged, lens-, or almond-shaped lenticular clouds, but a variety of stratocumulus , altocumulus , and cirrocumulus forms appear in both the main, vertically propagating waves and in the lee waves. Cap clouds indicate that there is a strong … In meteorology, lee waves are atmospheric stationary waves. Provided that there is a steady increase in wind strength with altitude without a significant change in direction, standing waves may be created. castellanus, billow, lenticular, rotor, banner, fractus, etc.) The event was observed, and correctly interpreted, by German engineer and glider pilot Wolf Hirth (1900–1959), who wrote about it in: Wolf Hirth, Organisation Scientifique et Technique du Vol à Voile, "An Unexpectedly Heavy and Complex Snowfall Event across the Southern Appalachian Region", Observations of Mountain-Induced Rotors and Related Hypotheses: a Review, Chronological collection of meteorological data, satellite pics and cloud images of mountain waves in Bariloche, Argentina (in Spanish), On High Winds and Foehn Warming associated with Mountain-Wave Events in the Western Foothills of the Southern Appalachian Mountains, An Examination of the Areal Extent of High Winds due to Mountain Waves along the Western Foothills of the Southern Appalachian Mountains, https://en.wikipedia.org/w/index.php?title=Lee_wave&oldid=994069508, Creative Commons Attribution-ShareAlike License, A gradual increase in windspeed with altitude, Wind direction within 30° of perpendicular to the mountain ridgeline, Strong low-altitude winds in a stable atmosphere, This page was last edited on 13 December 2020, at 23:27. If you look further south you can see cirrus clouds coming off the mountains of Southern North Carolina the upstate of South Carolina into NE Georgia. Mountain wave clouds are created by the interaction of wind patterns with the terrain. Intense waves can present a significant hazard to aviation by producing severe or even extreme clear air turbulence. The large cloud had mostly dissipated by mid-morning. 23. Like giant breakers in the ocean surf, magnificent cloud waves in the sky crested and crashed above Virginia’s Smith Mountain Lake on Tuesday evening. This video is unavailable. If an aircraft were to fly at the altitude of this KH cloud, it would likely experience very strong turbulence. , where b. stratus. Moisture at high levels & mid-levels along with cold dry surface air make for some cool cloud formations. World record wave flight performances for speed, distance or altitude have been made in the lee of the Sierra Nevada, Alps, Patagonic Andes, and Southern Alps mountain ranges. These strange, unnatural looking clouds sometimes form downwind of hills or mountains. Not an official cloud classification but rather a "supplementary feature", virga form when rain … A lenticular cloud is a lens-shaped cloud that normally develops on the downwind side of a mountain or mountain range. Some decent mountain wave cloud/sunset time-lapses from a couple different days along the Colorado front range near Boulder, CO. They can also be caused by the surface wind blowing over an escarpment or plateau,[4] or even by upper winds deflected over a thermal updraft or cloud street. “At the wave crest, you get clouds. If there's enough moisture in the air, and the air at the top of the crest of the wave reaches the dew point, a cloud will form. When sufficient moisture is present in the upstream flow, vertically propagating mountain waves produce interesting cloud forms, including altocumulus standing lenticular (ACSL) and other foehn clouds. Mesmerizing wave-like clouds spotted over mountain in Virginia. Oscillations tilted off the vertical axis at an angle of Thermal (Convective) Turbulence. The development of a large mountain wave cloud along the foothills and adjacent plains overnight helped create the fiery scene as the rising sun lit the bottom of the clouds. By Caitlin O'Kane June 19, 2019 / 8:31 AM / CBS News Seven weird weather phenomenons ... the clouds will whip up into wave … They were discovered by a glider pilot, Wolf Hirth, in 1933. A fairly stable lenticular {\displaystyle N={\sqrt {{g \over \theta _{0}}{d\theta _{0} \over dz}}}} What's really interesting is that even though lenticular clouds appear to stay in a stationary position, the air … Roll clouds. *e. All of the above are correct.  mountain-wave cloud A cloud that forms in the rising branches of mountain waves and occupies the crests of the waves. These lens-shaped orographic wave clouds form when the air is stable and winds blow across hills and mountains from the same or similar direction at different heights through the troposphere. ϕ Photographs of prominent diffraction displays through mountain wave clouds downstream of Colorado’s northern Front Range communities of Boulder and Nederland (locations shown in Fig. Lee waves occur when a wind of 25 knots (46 km/h) blows over a mountain. Mountain wave clouds, a subset of “lee waves” can form in an otherwise stable atmosphere when unsaturated air is forced up by changing terrain beyond the lifting condensation level where the resulting adiabatic expansion causes it to cool below its dew point. {\displaystyle \theta _{0}(z)} Who we are, what we do and organisational news. ϕ Everything you need to know about the forecast, and making the most of the weather. {\displaystyle \phi } Support your business with world-leading science and technology. z Sometimes, mountain waves can help to enhance precipitation amounts downwind of mountain ranges. The wave that forms over the mountain is more properly called the "mountain wave." COMING UP CBSN Denver will air Colorado governor's news conference on … d ( If there is enough moisture in the air, the rising motion of the wave will cause water vapour to condense, forming the unique appearance of lenticular clouds. Wave clouds form when air flows over a raised landform. Rising, descending or turbulent air in or above the lee waves can cause overspeed or stall, resulting in mach tuck and loss of control, especially when the aircraft is operated near the "coffin corner". [8] The Perlan Project is working to demonstrate the viability of climbing above the tropopause in an unpowered glider using lee waves, making the transition into stratospheric standing waves. Once the air has gone over the obstacle, it sinks again. Mountain wave clouds typically contain liquid water drops at temperatures down to approximately 36 °C.14,15However, when the temperature falls below a threshold near this value, the water particles in these wave clouds freeze rapidly, forming small, quasispherical ice particles with diameters that ap- … is the vertical profile of potential temperature. The most distinctive are the sharp-edged, lens-, or almond-shaped lenticular clouds, but a variety of stratocumulus , altocumulus , and cirrocumulus forms appear in both the main, vertically propagating waves and in the lee waves. Some pilots have reported mountain waves at 60,000 feet. [4] Wave clouds do not move downwind as clouds usually do, but remain fixed in position relative to the obstruction that forms them. c. may produce altocumulus lenticularis clouds. You may see a cap cloud directly over the mountain, as pictured above. d. are standing waves. This is a "signpost of the sky" indicating that mountain wave activity is present. When air blows across a mountain range, in certain circumstances, it can set up a train of large standing waves in the air downstream, rather like ripples forming in a river when water flows over an obstruction. The air warms as it drops, and the cloud dissipates. (CNN) — A rare formation of clouds wowed onlookers at Virginia's Smith Mountain Lake on Tuesday. On the ground, they can result in very strong gusty winds in one place, with still air only a few hundred metres away. These strange, unnatural looking clouds sometimes form downwind of hills or mountains. They always occur in groups on the lee side of the terrain that triggers them. θ The strongest lee waves are produced when the lapse rate shows a stable layer above the obstruction, with an unstable layer above and below.[4]. There are three main types of lenticular clouds: altocumulus standing lenticular (ACSL), stratocumulus standing lenticular (SCSL), and cirrocumulus standing lenticular (CCSL), varying in altitude above the ground. If you look closely you see 2 types of cloud formations. A Virginia woman captured a stunning cloud formation above Smith Mountain, resembling a famous painting by Van Gogh. And it forms a lenticular cloud, to be specific. Time lapse video of clouds near the Mesa Lab in Boulder, Colorado in 1988. z Wave cloud pattern in Germany August 2020. In fact, a mountain wave action and turbulence can affect aircraft at altitudes into the lower stratosphere, which typically begins around 30,000 to 35,000 feet above sea level! They are periodic changes of atmospheric pressure, temperature and orthometric height in a current of air caused by vertical displacement, for example orographic lift when the wind blows over a mountain or mountain range. 22. These disrupt the flow of air into "eddies", or areas of turbulence influenced by these obstructions. However, these waves can be present beyond the clouds, and may exist even when no clouds are formed. A frequent wintertime weather phenomenon along the Colorado Front Range, the mountain lee wave sets up downwind of the Continental Divide (the snow-capped mountains on the horizon in this video) when winds aloft are westerly and increasing with altitude. At the wave dip, no clouds,” said Wind. The moving air hits the still mountain in the same way the prow of a moving boat hits still water.” As air funneled around the islands in February, its temperature and humidity was just right for the crests of the lee waves to rise and cool the air and form clouds. Oscillations occur in groups on the downwind side of a standing wave may 8,000! Groups on the downwind side of the aircraft ’ s rotor systems mass of air into eddies... Is that even though lenticular clouds because of the waves of constant phase ) altitude or fly long distances soaring. Latest breakthroughs, research and news from the mountain, as pictured above do., lee waves occur when a mountain that forms over the mountain wave in. 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# Can this be the solution for composites?

Propositions:

It is well known by the standard Riemann Zeta function that

$\zeta (s) = \displaystyle \sum_{n=1}^{\infty} \dfrac{1}{n^s}$

For $$\mathfrak{R} (s) > 1$$.

Also, the Prime Zeta function gives us

$P(s) = \displaystyle \sum_{p} \dfrac{1}{p^s}$

For $$p \in \{ \text{primes} \}$$ and $$\mathfrak{R} (s) > 1$$.

Conclusion:

This means that the sum of $$s^{\text{th}}$$ powers of the reciprocals of all composite numbers can be given by the formula

\begin{align} P'(s) &= \displaystyle \sum_{p'} \dfrac{1}{{p'}^s} \\ &= \sum_{n=1}^{\infty} \dfrac{1}{n^s} - \sum_{p} \dfrac{1}{p^s} - 1 \\ &= \zeta (s) - P(s) - 1 \end{align}

For $$p' \in \{ \text{composite numbers} \}$$ and $$\mathfrak{R} (s) > 1$$.

Knowing that infinite sums are risky to handle. I would like your opinions on whether the conclusion drawn from the two given true propositions made above are correct or not.

Note by Tapas Mazumdar
4 months, 3 weeks ago

Sort by:

if $$u_n,v_n$$ are convergent sequences then so is their difference. Provided $$\zeta(s),P(s)$$ converges which is obvious ,your conclusions are true enough · 4 months, 1 week ago


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# A Little Riak Book for LFE

## Clusters

Up to this point you've conceptually read about "clusters" and the "Ring" in nebulous summations. What exactly do we mean, and what are the practical implications of these details for Riak developers and operators?

A cluster in Riak is a managed collection of nodes that share a common Ring.

### The Ring

The Ring in Riak is actually a two-fold concept.

Firstly, the Ring represents the consistent hash partitions (the partitions managed by vnodes). This partition range is treated as circular, from 0 to 2^160-1 back to 0 again. (If you're wondering, yes this means that we are limited to 2^160 nodes, which is a limit of a 1.46 quindecillion, or 1.46 x 10^48, node cluster. For comparison, there are only 1.92 x 10^49 silicon atoms on Earth.)

When we consider replication, the N value defines how many nodes an object is replicated to. Riak makes a best attempt at spreading that value to as many nodes as it can, so it copies to the next N adjacent nodes, starting with the primary partition and counting around the Ring, if it reaches the last partition, it loops around back to the first one.

Secondly, the Ring is also used as a shorthand for describing the state of the circular hash ring I just mentioned. This Ring (aka Ring State) is a data structure that gets passed around between nodes, so each knows the state of the entire cluster. Which node manages which vnodes? If a node gets a request for an object managed by other nodes, it consults the Ring and forwards the request to the proper nodes. It's a local copy of a contract that all of the nodes agree to follow.

Obviously, this contract needs to stay in sync between all of the nodes. If a node is permanently taken offline or a new one added, the other nodes need to readjust, balancing the partitions around the cluster, then updating the Ring with this new structure. This Ring state gets passed between the nodes by means of a gossip protocol.

### Gossip and CMD

Riak has two methods of keeping nodes current on the state of the Ring. The first, and oldest, is the gossip protocol. If a node's state in the cluster is altered, information is propagated to other nodes. Periodically, nodes will also send their status to a random peer for added consistency.

A newer method of information exchange in Riak is cluster metadata (CMD), which uses a more sophisticated method (plum-tree, DVV consistent state) to pass large amounts of metadata between nodes. The superiority of CMD is one of the benefits of using bucket types in Riak 2.0, discussed below.

In both cases, propagating changes in Ring is an asynchronous operation, and can take a couple minutes depending on Ring size.

### How Replication Uses the Ring

Even if you are not a programmer, it's worth taking a look at this Ring example. It's also worth remembering that partitions are managed by vnodes, and in conversation are sometimes interchanged, though I'll try to be more precise here.

Let's start with Riak configured to have 8 partitions, which are set via ring_creation_size in the etc/riak.conf file (we'll dig deeper into this file later).

## Number of partitions in the cluster (only valid when first
## creating the cluster). Must be a power of 2, minimum 8 and maximum
## 1024.
##
## Default: 64
##
## Acceptable values:
##   - an integer
ring_size = 8

In this example, I have a total of 4 Riak nodes running on [email protected], [email protected], [email protected], and [email protected], each with two partitions (and thus vnodes)

Riak has the amazing, and dangerous, attach command that attaches an Erlang console to a live Riak node, with access to all of the Riak modules.

The riak_core_ring:chash(Ring) function extracts the total count of partitions (8), with an array of numbers representing the start of the partition, some fraction of the 2^160 number, and the node name that represents a particular Riak server in the cluster.

\$ bin/riak attach
([email protected])1> {ok,Ring} = riak_core_ring_manager:get_my_ring().
([email protected])2> riak_core_ring:chash(Ring).
{8,
[{0,'[email protected]'},
{182687704666362864775460604089535377456991567872, '[email protected]'},
{365375409332725729550921208179070754913983135744, '[email protected]'},
{548063113999088594326381812268606132370974703616, '[email protected]'},
{730750818665451459101842416358141509827966271488, '[email protected]'},
{913438523331814323877303020447676887284957839360, '[email protected]'},
{1096126227998177188652763624537212264741949407232, '[email protected]'},
{1278813932664540053428224228626747642198940975104, '[email protected]'}]}

To discover which partition the bucket/key food/favorite object would be stored in, for example, we execute riak_core_util:chash_key( {<<"food">>, <<"favorite">>} ) and get a wacky 160 bit Erlang number we named DocIdx (document index).

Just to illustrate that Erlang binary value is a real number, the next line makes it a more readable format, similar to the ring partition numbers.

([email protected])3> DocIdx =
([email protected])3> riak_core_util:chash_key({<<"food">>,<<"favorite">>}).
<<80,250,1,193,88,87,95,235,103,144,152,2,21,102,201,9,156,102,128,3>>

([email protected])4> <<I:160/integer>> = DocIdx. I.
462294600869748304160752958594990128818752487427

With this DocIdx number, we can order the partitions, starting with first number greater than DocIdx. The remaining partitions are in numerical order, until we reach zero, then we loop around and continue to exhaust the list.

([email protected])5> Preflist = riak_core_ring:preflist(DocIdx, Ring).
[{548063113999088594326381812268606132370974703616, '[email protected]'},
{730750818665451459101842416358141509827966271488, '[email protected]'},
{913438523331814323877303020447676887284957839360, '[email protected]'},
{1096126227998177188652763624537212264741949407232, '[email protected]'},
{1278813932664540053428224228626747642198940975104, '[email protected]'},
{0,'[email protected]'},
{182687704666362864775460604089535377456991567872, '[email protected]'},
{365375409332725729550921208179070754913983135744, '[email protected]'}]

So what does all this have to do with replication? With the above list, we simply replicate a write down the list N times. If we set N=3, then the food/favorite object will be written to the [email protected] node's partition 5480631... (I truncated the number here), [email protected] partition 7307508..., and [email protected] partition 9134385....

If something has happened to one of those nodes, like a network split (confusingly also called a partition---the "P" in "CAP"), the remaining active nodes in the list become candidates to hold the data.

So if the node coordinating the write could not reach node [email protected] to write to partition 7307508..., it would then attempt to write that partition 7307508... to [email protected] as a fallback (it's the next node in the list preflist after the 3 primaries).

The way that the Ring is structured allows Riak to ensure data is always written to the appropriate number of physical nodes, even in cases where one or more physical nodes are unavailable. It does this by simply trying the next available node in the preflist.

### Hinted Handoff

When a node goes down, data is replicated to a backup node. This is not permanent; Riak will periodically examine whether each vnode resides on the correct physical node and hands them off to the proper node when possible.

As long as the temporary node cannot connect to the primary, it will continue to accept write and read requests on behalf of its incapacitated brethren.

Hinted handoff not only helps Riak achieve high availability, it also facilitates data migration when physical nodes are added or removed from the Ring.


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# DE solve?

1. Nov 10, 2007

### dionysian

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

Solve the euqation $$dP/dt = k(M - P)P$$ to show that it equals: $$P(t) = (MP_{0}) /( P_{0} + (M - P_{0})e^{-kMt})$$

2. Relevant equations

3. The attempt at a solution
$$$\int \frac {dP} {P(M - P)}$ = k \int dt \$$

$$\frac {1} {M}\ \ln( \frac {P} {M - P}) + C = Kt + C$$

I combine the constants of integration... i can do this right?
Then i get rid of the log by taking the exponent of both sides.

$$P/(M - P) = e^{mkt + c}$$

I then turn $$e^{c}$$ into $$P_{0}$$

Next i divide through by $$(M - P)$$

$$P = (M - P)P_{0}e^{mkt}$$

next i combine the $$P$$ then divide through by the remainder.

$$P = (mP_{0}e^{mkt})/(1 + P_{0}e^{mkt})$$

and i end up with:
$$P = (mP_{0})/(e^{-mkt} + P_{0})$$

In the equation i am suppose to get i dont see how there could possibly be three terms in the denominator.

Last edited: Nov 11, 2007
2. Nov 10, 2007

### cristo

Staff Emeritus
You could just differentiate P and substitute it into the differential equation.

3. Nov 10, 2007

### dionysian

I was in the process of editing my post (i am still getting use to LaTex) when you replied. i could do that but my teacher want us to just solve it. Also this has been bugging me for a while, i have been working on it for the past few hours and cannot get it. My teacher... well a grad student TA for my DE lab couldn't solve it either.

I also would like to know what is wrong with my method... it seems like it should work but... its not.

one thing think might be wrong with my method is the $$P_{0}$$ initial condition.

4. Nov 11, 2007

### HallsofIvy

HOW did you "turn $e^{c}[/tex] into [itex]P_0$"?

When t= 0, You have $P_0/(M-P_0)= e^c$

5. Nov 11, 2007

### dionysian

Thanks a million. works out fine after that.