What are the differences between buttons and links?

Question: What are the differences between buttons and links?
Comment: what do you mean?
Answer: Rule of thumb: a link takes you to other place, a button does something.
That said, things can be flexible in this regard. Links are sometimes seen as low priority buttons, and buttons, almost always take you to other place.
[edit 2013]
Things have changed a bit since I wrote this answer. I now use big buttons as clear "call to action" and try to avoid using more than two of them on any screen. Then I use smallish, tag-like buttons or links as low priority options.
The different meaning of buttons and links is not in their nature, but in its visual weight and its place in the hierarchy of the screen/design.
Comment: Two years ago, I would have agreed with this answer, but the convention has changed. Things styled as links now routinely act as buttons.
Comment: I would say a button _does_ something, rather than make something. But otherwise, yeah.
Comment: I try to follow this rule mostly. However, these days to most people, both are simply "things I can click on that make something happen" and that's fine too. The distinction is pretty conceptual anyway, I don't believe many people actually have expectations more precise than that.
Comment: This answer was written 3 years ago. I agree that today expectations have changed. I am editing the answer to reflect it.
Comment: Can you show some examples of big buttons vs. smallish, tag-like buttons vs. links?
Comment: http://www.lightcms.com/ Shows a big call to action, the menu (links) and many secondary buttons after the fold.
Comment: On the web, links and buttons work differently. You cannot arbitrarily choose one over the other. Generally, links change the URL. They can be Ctrl+click'ed to open in a new tab or window. Users can right click and copy the URL to paste to others. The result of clicking a link can be reversed by using the back button. Traditionally, buttons were always used to submit and control forms. With this distinction, we should continue to use links for navigation and buttons for entering data and submitting forms.
Answer: In general, users expect links to link and command buttons to command. That is, links navigate, presenting new content without changing the underlying data objects or their relations or positions. Buttons change these things, performing creation, deletion, association, conversion, duplication, etc. An easy rule-of-thumb is if the most terse caption for the control is a noun (e.g., Home, Products, Site Map), then use a link. If the caption is a verb (e.g., Update, Submit, Delete, Purchase), then use a button.
However, in thick-client desktop apps, buttons may navigate, especially in older apps that originated before the web (and links) was commonly used. Furthermore, more recently links have been used in place of command buttons in various web sites and even some style guides endorse this. In fact, links have been used in place of just about every other control (e.g., radio buttons, tabs, checkboxes).
I believe all this confuses users and we really should use distinct-looking controls for distinct functions. Both web apps and desktop apps should clearly distinguish between navigation and commands by using link and buttons respectively. Navigating is significantly distinct than commands because:

Users don't have to save after navigating. Saving is frequently necessary after a command.
Users easily revert navigation by clicking Back or closing the window. It's always a "safe" action. Commands frequently cannot be reverted in a web app. If commands can be reverted, it's through an Undo feature, which involves a different user response than Back or Close.
Commands provide different feedback that is often more subtle than navigation. It's generally apparent when the user is presented with new content. Commands may show the change in the content, but often no change is apparent (e.g., for Copy or Save). Web apps often resort to confirmation pages (which doesn't count as navigation in my book).

For these reasons, it helps the user to have distinct controls for navigation and commands, and fortunately user expectations for buttons and links make this easy. However, continued use of links for commands (and buttons for navigation) undermine these expectations, and soon we'll lose this opportunity.
Graphically distinguishing navigation and commands afford us powerful ways to communicate with our users. For example if Contact Us is a link, then it displays a list of addresses and phone numbers (I'd label it "Contact Us" rather than the more terse "Contacts" since "Contact Us" is such a common convention, users scan for it specifically in menus). In contrast, if Contact Us is a button, then it takes users to a form where they can directly submit questions or comments (the button caption should have an ellipsis to indicate more information is required for the command).
I agree there is a need for light-weight controls for secondary actions, especially for typical web apps that lack an object-selection-action interface. However, the solution is to develop lightweight version of the appropriate controls, not recruit another control with a totally different user expectations. Such lightweight controls may technically be links, but they should look like the control they're imitating. For example, a lightweight "button" can be a linked image of a small shaded rectangle with a center-aligned caption.
There is a gray area in navigation/command distinction which we should sort out. I recommend the following until the appropriate research can be conducted:
Use links for:

Loading a page of content
Loading dynamically generated content.
Loading content to part of a page if no other option is tenable (e.g., a tab).
Navigating between pages of a wizard (in contrast to traditional desktop wizards that use buttons).

Use command buttons for:

Actions that change or apply the underlying content or data objects.
Actions that affect the view of the content if no other option is tenable.
Execution of a dialog's commands, including the Finish action of a wizard.
Canceling of a dialog, assuming canceling resets the dialogs parameters to the default or previous values.

Use a command button with an ellipsis at the end of the caption to access a dialog.
Gory details at http://www.zuschlogin.com/?p=18.
Comment: Long answer, gets my vote for the rule of thumb in the first paragraph.
Comment: By far the best and most clear answer.
Answer: Links convey relationship, whereas buttons stress action.
This reasoning is based on the premiss that buttons actually mimic physical buttons, and the symbolic meaning of links stems from chaining.
If you think what a real button or trigger on a machine does, it is easier to see what kind of actions a digital button can use. I.e. on, off, fire, and so on. The same goes for thinking of hyperlinks as index cards in a library - book abc on shelf a1 section b - they are used to identify a way to an item.
Both are interchangeable in different scenarios, but the implied functionality is slightly different.
Answer: Links are text—if you can only click the text, it's a link.
Buttons tend to look like physical controls or icons (although many are disguised as links)—if you can click the area around the text, it's a button.
Links tend to navigate to different pages, while buttons tend to stand for actions, but those actions often include navigation. Links tend to provide a lighter visual impact because they are text-based. Buttons tend to emphasize a functional use. For example, a big SAVE button has more impact than an inline "Save" link.
Buttons represent the mental model of physical controls, while links are a purely hypertext entity with no physical analog. As web design has evolved, the UX distinction between buttons and links has blurred: many buttons are styled to look like just text; CSS-styled text takes on the look of buttons.
Answer: Semantically speaking, any action which modifies server state should be done using a POST request from a <form> and therefore use a button, rather than a link.
That's not to say the two can't be styled up to look and behave identically, but the markup should be different.
Comment: Sorry, I don't agree. I don't think server state should be reflected in design "per se". I always design from the user's viewpoint, and she couldn't care less for server state. Technicals details should be transparent to user.
Comment: Yes, that's what I was saying in my second paragraph - you can make a link and a button look and behave exactly the same. The user would never know one is a button and one is a link.

Though whether or not you should depends entirely on the context of their use. Buttons and links have different accordances and user expectations, which you may wish to leverage.
Comment: Unfortunately, buttons can't be styled *entirely* like links, but you can get close.
Comment: There are buttons which trigger no direct action and thus should use Post. The most common of these is "Search"
Answer: In the good old days when you could easily change the 'read / unread' period in the browser, which show read links in a different colour - the advantage of links would be that you could easily see where you'd already been.
(Footnote - you may still be able to change the periods - but I've long since given up trying to find the control which does this...)
Answer: Links have been around for a long time and have a higher population than buttons on the web.  When used in the context of navigating content they are effective.
Buttons are a much stronger affordance when you use them in the contexts when he user makes a form of commitment or investment to the website. (ie. saving, sharing, subscribing, joining, etc.)
I explain this in detail in the article I wrote:
the-link-vs-button-debate
I hope this clears up the question of when to use the two once and for all.
Comment: Buttons have been around much longer in UI design than links.
Answer: One very important thing to note in the differences between links and buttons is that crawlers (both for search sites like Google and many site-level search engines) will not go to the target of a button; they only follow links.
Beyond that, luna, Michael and Pete all have valid points that cover just about everything else that I could think of.
Answer: I agree with the above, and I am against using hyperlinks for commands, particularly in non-web apps (e.g. WinForms).
In non-web apps a hyperlink says to the user "ignore me unless to want to navigate away to some different information" and a button says "I'm going to change something or show a dialog if you click me".
The problem comes when the two are used interchangeably and a new user is scanning the form looking for a particular command. After a while they realise that they need to look at all of the hyperlinks too and invariably it takes the user twice as long to find what they are looking for because UI metaphors are not consistent. If the metaphors are not consistent the user loses trust and begins to hate the software. Trying to use software like this drives users up the wall (I think Hotmail had the "attach" command as a hyperlink for a while and certainly for a while they had it in a combo box).
The Microsoft Windows Interaction Guidelines are a little fuzzy on the issue:

Guidelines: Command Buttons, which includes a comparison to links
Guidelines: Links, which includes a comparison to command buttons

They suggest that links are acceptable for secondary commands. The link posted by Michael Zushlag above makes an excellent point about this and the need for lightweight buttons.
The problem I see with lightweight buttons for secondary commands is knowing which commands these are. If you can come up with a consistent logic behind these (that is apparent to the user) and you can differentiate between primary and secondary commands with ease, then this is the best option.
Answer: Michael Zuschlag's answer is great, I would only precise that a link is different than a simple reference (an anchor).
Many people make a confusion between user experiences/interactions and HTML markup because they do not view the difference between a link and an anchor:
- a link has a direction (forward or reverse link) and can be identify with a relation but can not be used by users with their user-agents to access to the hypertext reference (href attribute in HTML) because they can not be activated (except on Opera with the navigation toolbar).
- an anchor only refers to something. It is only a reference to another resource even if it can be activated (with a click or with your keyboard) because user-agents defines this behavior.
And I think it help us to understand differences between an anchor and a button:
- use a button when you call to action (as Michael said with "Update, Submit, Delete, Purchase" but also "read more", "download", etc.)
- use a anchor when you just refers to another resource with an anchor text identifying the resource. If you require your user to read it, that means it is a "call-to-action" and not just a reference, so implement it with a button.
Answer: My experience show that often links are recognized easier as clickable and therefore clicked better taht for us sometimes leads to decisions to use links instead of buttons. But I agree that that shouldn't be done deep inside a process where the user is triggering an action. I also would like to add that the verb/noun differentiation can be difficult in other languages than english.
Answer: Whilst it is true that buttons and links are used interchangeably on the modern web, there is one fundamental browser feature that sets them apart:
Users can open a link in a new window or tab.  A <button> or <input type='button'> cannot.
(As an example, try right-clicking on the "add comment" link and the (Add Comment) button below - only the first allows "Open Link In New Tab".)
Although  links can be styled to look like buttons, users will generally only expect the open-in-tab functionality to work on things that look like links.
Comment: This isn't all that true anymore given that both buttons and links can be set up to do anything you want client-side.
Comment: @DA01 I had not made it clear that I was talking about `` elements, which do not have this functionality.  I have now updated the answer!
Comment: yes, that is a good point. I'd maybe be a bit clearly and state that a 'link can be opened *by the user* in a new window or tab' whereas a button element can not (the code would have to open the new browser for you).
Answer: I come from an accessibility stand point and for non-visual or low vision users there are separate methods of selecting a link vs a button.   The problem happens when a user cannot navigate the page in the same speed and manner as a visual person then you have a lawsuit on your hands for title III discrimination.  If it looks like a link then it should be a link
If it quacks like a duck, and looks like a duck, therefor it is a duck....
Answer: The easiest way to distinguish the two is that a link navigates the user whereas a button triggers an action.
To give you a better idea, here are some quotes from the design guidelines of Microsoft, Google and Apple.
Links:

Hyperlinks navigate the user to another part of the app, to another app, or launch a specific uniform resource identifier (URI) using a separate browser app -- Microsoft Design Guidelines

Buttons:

A button gives the user a way to trigger an immediate action -- Microsoft Design Guidelines
Buttons allow users to take actions, and make choices, with a single tap -- Material Design Guidelines
Buttons initiate app-specific actions, have customizable backgrounds, and can include a title or an icon -- Apple Design Guidelines

As you go through the design guidelines, you'd realise that the use of buttons is more versatile and differs with the platform (e.g. Android or iOS) you are designing under.
When in doubt, especially on the types of buttons, I'd lean towards looking at what the best practices are at the current state of time and pick the one that best fits your context.
Answer: Links >> Navigate you to some pages and it doesn't affect the page.
Button >> On click the action happens on the same page and it affects the frontend or backend of the page.


Responsive design - setting a single breakpoint?

Question: As our UXD group does more responsive projects, we're running into an extremely high QA cost due to the complexity of our site compounded by testing multiple device and multiple breakpoints. To combat this we're considering setting a single breakpoint so that there are only 2 ranges for dev to QA. Has anyone else explored this option to manage costs? If so, what breakpoint did you choose? We're considering 760 but would other thoughts.
Comment: Compromising UX to accommodate QA is likely not the best UX strategy. I'd question the need to check so many devices, though. The point of responsive is that it's device agnostic.
Answer: I would strongly recommend a minimum of three breakpoints.
Desktop screen resolutions are getting higher and higher. When desktop resolutions are now commonly at 2560px, and with 4k on the way, how could one breakpoint possibly best serve all resolutions from 760px to 2560px?
For this reason, I would set at minimum three breakpoints, loosely set for mobile/tablet/desktop, and invest in a QA service like BrowserStack or something similar to help keep QA costs down.
Answer: Well the obvious answer is - it completely depends on your content. When does your site look like it needs a breakpoint? I would also second the recommendation of at least 3. If you plan to only use two I'd go lower than 760. You might consider looking at foundation as a starting point with 0-640 as the smallest breakpoint.
Answer: It's impossible to state how many breakpoints are good and only one is most likely not enough. The number of breakpoints is best defined by Stephen Hay who said to expand the browser until your layout looks ... "bad" ... and that's where a breakpoint is set. That could mean one might just work for you. But that also means you might need nine.
Answer: I would agree that one breakpoint is probably too little.
At times I have used 2 breakpoints for simplicity's sake (one at 1024px and down for iPads and other tablets, and one at 600px and down for mobile phones/phablets) - but I would agree that a minimum of 3 is probably best practice.


What's the significance of Shireen's stag?

Question: In Game of Thrones S6E9, Ser Davos went for a walk just before the battle and found a stag (assuming that will be the one he gifted to Shireen). So what is the significance of this scene and what does it actually say?
Answer: The significance is where he found it.
He found it at the charred remains of a pyre used to burn people at the stake.

Which means he knows now that she was sacrificed to the Lord of Light, and surely that's a set up to some sort of a later confrontation between him and Melisandre.
Comment: This is confirmed in the season finale, which aired last night. Ser Davos enters during a discussion between Melisandre and Jon, and tosses the charred stag figure at her, insisting she tell Jon where it came from and why or else he will. Jon then tells Melisandre to ride south and to never return to the North again or she'll be hanged, with Davos adding he'll kill her himself should she ever return.
Answer: There is no assuming the stag was Shireen's, since it was made by Davos himself and he recognizes it.The fact that Shireen's stag lay in the pyre revealed to Davos the events from the end of S5, when Shireen was burned alive.
Melisandre tells Ser Davos in S5 that Shireen is dead, but leaves out the fact that it was her idea to burn Shireen alive. When Davos discovers Shireen's grave at the Winterfell battleground, he surmises that if Shireen died before the battle (since she got a proper burial), Melisandre must have sacrificed her as a prebattle good luck charm.
Just before the battle, Stannis sends Davos back to the Wall to gather supplies. When Davos sees the grave, he realizes that Stannis had never really wanted the supplies, but only wanted to get rid of him so that he was free to sacrifice Shireen. Davos had an enormous amount of faith in Stannis, and Shireen's death represents a massive betrayal.
Comment: Also, another significance is that It is the symbol of [House Baratheon](http://gameofthrones.wikia.com/wiki/House_Baratheon) ;)
Answer: From a plot standpoint, as in how it advances the story, madmada's answer is correct.
From the standpoint of what does it mean symbolically, it is clearly a symbol of the downfall of House Baratheon.
By the time Davos finds it charred in the ashes of the fire, the main line of the family has been extinguished. Shireen was in fact the only legitimate offspring of her generation, as Renly never produced heirs, and all of Robert's children are "natural" as in illegitimate.
Thus for Davos, it is both a memory of the beloved child of his liege lord and an indication of his new, masterless status.
Answer:
Melisandre must have sacrificed her as a pre-battle good luck charm.

Or more like a "magical snow-shovel" :)
More seriously, I've always wondered about the stag, not just as (obviously) the symbol of the House, but as a reference to the original Iphigenia myth.  In one version, Artemis accepts a stag in place of her.
Sources:
https://en.wikipedia.org/wiki/Iphigenia#Among_the_Taurians
Primaries:

(Proclus writes) "Artemis ... snatched her away and transported her to the Tauroi, making her immortal, and put a stag in place of the girl [Iphigenia] upon the altar."
[Epicorum Graecorum Fragmenta, ed. G. Kinkel, p. 19]
Homer, "Delphi Complete Works of Homer (Illustrated)" (Delphi Ancient Classics Book 2)


When should I take my protein shakes?

Question:
When should I take my protein shakes bearing in mind I only do crossfit twice a week? Should I also take it on rest days?
Comment: Could you please edit your question to be text rather than a picture of text?
Comment: That is a surprising change in behaviour.  A comment from a moderator on this https://meta.stackexchange.com/questions/320162/cant-paste-data-to-question-get-prompted-for-image suggests that pasting with Ctrl-Shift-V rather than the usual Ctrl-V will grab the plaintext version from Microsoft Word rather than an image.  I don't have the means to test this, so you will have to experiment.  I hope they find a better mechanism for users to choose between the two options.
Comment: I'd love to. Unfortunately I've just started using Stack Exchange and I'm having trouble understanding how it works - I basically copied/pasted the text from Word into the 'body' box on SE and it automatically turned it into an image. Any advice would be welcome.
Answer: You already mentioned that you know protein shakes are not magic, and you should eat a balanced meal.
So don't think of protein shakes as anything more than another food. It's just a food with a really skewed macro ratio.
The general advice is to get 2.2g per 1kg. (1g per 1 lb.) of lean body mass a day, regardless of whether or not you worked out that day. So that means that the foods you eat in that day should contain that much protein.
So when should you take it?  Whenever is convenient for you. You're meal is lacking a protein? Take the protein shake. You can't have lunch (because life)? Take the protein shake.  Hungry and looking for a snack? Take the protein shake.
For macro counters, they're another tool that helps them keep within their dietary limits. For everyone else, they're a food that's very easy to transport and doesn't require cooking (though can be expensive).

When should I take my protein shakes?


Bracha on Coconut Wraps

Question:
What bracha would these be? The first ingredient is coconut meat. These are all of the ingredients:  Organic Coconut Meat, Organic Coconut Water, Organic Extra Virgin Coconut Oil.
Comment: im litterly having them for supper right now, i wahsed on bread so there would be no sheila but asking for the future
Comment: Since it has the star K on it, you can call 410 484-4110 9AM to 5 PM to find out if the prodect has been processed in such a way as to make it shehakol or if it is ha-aitz.
Comment: Welcome to Mi Yodeya, user15604. Remember that you can edit your profile and make it a bit more personal. We hope to see you around!
Answer: Provided it is not eaten as secondary (tafel) to another, more significant food (in which case it would not merit its own blessing), and assuming the meat is broken up beyond recognition as coconut (as seems to be the case in, e.g., this recipe), it would seem that, according to at least most Ashkenazic authorities, the bracha should be shehakol.  For a similar ruling regarding applesauce, see, e.g. here:

Apple Sauce | Shehakol | Borei Nefashot | Shehakol is to be said if the apples are totally pureed. This applies mostly to commercially available canned or bottled apple sauce. However, Ha-aytz applies for homemade apple sauce where the applesauce is chunky.

However, according to many rabbinic opinions the correct blessing is actually haeitz or even ha'adama.  See, e.g., Halachipedia's article on the topic:

If one grinds a vegetable or fruit, whether or not one cooks it, if the vegetable is still recognizable in the product then the Bracha is the same the vegetable, however if it's ground and unrecognizable then the Bracha is shehakol. According to Sephardic practice, the Bracha does not change, even if the fruit is unrecognizable. Some Ashkenazi poskim maintain that the Bracha for tree-fruits becomes Ha'adama, but the Bracha for vegetables remains the same...
The Gemara Brachot 38a concludes that the Bracha for Tarima (processed dates) is HaEtz because the actual fruit remains. Rashi (D"H Tarima) explains that Tarima is dates which were crushed but not pulverized. However, Rambam (Brachot 8:4) explains that even if one removed the pits and crushed it and kneaded it into a dough the Bracha would still be HaEtz. The S"A 202:7 rules like the Rambam and the Rama rules like Rashi. Yalkut Yosef 202:22 and Halacha Brurah 202:25 rule like Shulchan Aruch, that even if the fruit or vegetable is completely pulverized, the Bracha does not change.
The Mishna Brurah 208:42 concludes that whenever the fruit is recognizable (because of the form and texture) the Bracha would be like the fruit, however, when it's so processed that it's not recognizable the bracha is Shehakol. Vezot HaBracha (pg 100, chapter 12) and Veten Bracha (Halachos of Brochos by Rabbi Bodner pg 403-4, chapter 22) agree.
However, the Laws of Brachos (Rabbi Forst, pg 303-5) explains the Mishna Brurah as saying that even for an unrecognizable pulp one should make the bracha of the original fruit. Only something which completely lost it's solid form is shehakol. He therefore writes that apple sauce is HaEtz, and mashed potatoes and peanut butter are HaAdama.
Rabbi Hershel Schachter in Brachot Ha'nehenin (31:15) quotes an alternative approach from Rabbi Soloveitchik; Rosh (Brachot 6:18) writes that for the Bracha of Ha'adama, it is unnecessary for the vegetable to be recognizable. For example, the Bracha for a vegetable broth would be Ha'adama, even though the vegetables were strained out. However, he is unsure if the same rule applies to strained fruit soup. Therefore, Rabbi Soloveitchik felt that it would be preferable to recite Ha'adama on mashed fruits - like applesauce - since Ha'adama is more specific than Shehakol, and Ha'adama doesn't require tzurat ha'pri. Likewise, the Bracha for mashed vegetables would remain Ha'adama. Rabbi Schachter personally follows this opinion (See OU Document X-18 and HalachaDoc LG-A9).

According to all authorities, the blessing after eating an olive-sized amount in the requisite time would be borei nefashot.
Comment: note, this answer assumes coconuts are edible
Answer: Since the ingredients to these coconut wraps are:

Organic Coconut Meat, Organic Coconut Water, Organic Extra Virgin Coconut Oil

I believe the bracha would be ha'eitz which would make the bracha afterwards borei nefashos.
See here where you can see that the bracha on coconut meat including shredded coconut is ha'eitz.
Comment: @ezra coconuts are fruits, so its ha'etz, right? Is the right thing if its ground to pulp or is oil then shehakol? Also, I do ha'etz on fruit jam and jelly, is that wrong then?

Bracha on Coconut Wraps


How realize such concentric rings with increase of dots on path?

Question: I want to understand what is way to realize such concentric rings in illustrator more simply?
Comment: Wow, trying to figure this one out took me down a rabbit hole. So much for work this morning. I did find this link that seems to explain why we can't replicate this in Illustrator without some scripting or some sort... https://en.wikipedia.org/wiki/File:SunflowerModel.svg
Comment: Further down the rabbit hole.... https://en.wikipedia.org/wiki/Fermat's_spiral
Comment: There is a similar question here http://graphicdesign.stackexchange.com/questions/56200/programmatically-creating-radiating-rows-of-dots/
Answer: For a graphic like this I prefer to use the Polar Grid Tool, which is located in the sub-menu of the Line Segment Tool:

Set the stroke to black with no fill and make it 3pt in
thickness for the purposes of this explanation:

Select the Polar Grid Tool and click on the artboard to bring up
the Polar Grid Tool Options Menu:

For this instance, let's use the settings in the image above. Click OK to apply settings. The results should be as follows:

Use the Selection Tool to select the shape. Open the Stroke
Panel  and tick the Dashed Line, Round Caps and the Align
Dashes to corners and path ends options. Additionally, set the Dash to 0pt and the Gap to 6pt:

Add the center dot. Create a 3px by 3px circle with the Ellipse
Tool and center it in the resulting space:

As with many things in Illustrator, there are many ways to perform the same task. I find this option to be the most forgiving when it comes to making revisions since you only need to edit a few settings in easily accessible places. Hope it helps!
Answer: This is not quite the same, but it should get you moving in the right direction...
First, create a circle with a dashed stroke, using settings that are something like those in the following screens shot:

Next, duplicate the circle and then enlarge the duplicate, keeping the circles on the same centre point. Then use the blend tool to create a blend between the inner and outer circles. I used a fixed distance blend, but you might prefer a specified number of steps. The result will look something like this:

You can adjust the density of the dots and the circles by tweaking the gap setting of the dashed stroke and the spacing of the blend. To adjust the size of the dots, just change the Weight of the strokes. If you want to fill in the centre, just reduce the size of the inner circle.
Like I said, not exactly the same as your example, but not bad for 5 minutes!
Comment: You could also create a dotted, wavy line, then use the Effect > Distort & Transform > Transform Effect panel to Rotate the line and specify the amount of steps you'd like. Creates a similar effect, and is fun to play with too!
Comment: @GoofyMonkey: Wouldn't that produce a pattern with a high density of dots in the middle and relatively spaced out dots around the outside?
Comment: Possibly. I was playing around with this and got varying results. If you make sure you are rotating the line from one end (Bottom or Top) you get some interesting results. This method doesn't give you the result the question is asking for, which is why I didn't submit it as an answer, but may lead someone in a direction that will work.


Where a database of different z values of redshift can be found?

Question: I was working on reshift details for various galaxies but do not know any database to find the z values given to redshift galaxies. Can anyone help?
Answer: There are some great databases with a lot of information in them, when you found the galaxy you looked for, somewhere on the page there should be redshift information if it is has been measured at some point.
The NED/ipac database is quite nice for galaxies (https://ned.ipac.caltech.edu/).
Or SIMBAD is also great (http://simbad.u-strasbg.fr/simbad/).


Is there a way to change the call screen in lumia 535?

Question: Can I change the call screen in Lumia? Lumia 535 has a touch issue and therefore I miss many call trying to swipe up before saying "answer or ignore". Is there a way that I can avoid this swipe up screen and straight away go to "answer or ignore screen"? Please advice.
Comment: Do you have all the latest updates installed?
Answer: Unfortunately you cannot change the way calls are being displayed. The swipe issue you are describing is a known bug for some Lumias. A quick fix should be to turn the screen off and back on before swiping up.
Comment: That works when my fingers are dry. But when there is moisture, that doesn't work as well!!!! I have the latest updates for lumia denim.Will installing windows 10 help?
Answer: as I can't comment...
this touch issue can be fully solved only by hardware fix, they erleased few "final" fixes, every one helped a bit and upgrading to update 2 not released officialy made touch almost fine, but never solved problems completely.
For me touch sometimes just declines to work if device gets too hot due to stress and/or charging, moisture also breaks a lot
and unfortunately cold too


What is wrong with my gas furnace?

Question: Note: the below was solved. It was a loose wire between the controller and the gas valve (the white wire on the diagram)
This is about an old UltraMax Olsen HCS2 81AD gas furnace

it looks like this

and it sounds like this :-) when it is having problems
Here is what happened this morning. I waked up hearing the a noise that was coming from the furnace. I wend downstairs to the furnace room and it was making a sound like this (click to download a small mp3).
I switched the furnace off and I went upstairs to get my phone to take pictures and record the sound. When I returned I tried to start the furnace one more time and it started. It worked for a little while and it stopped again making the same sound
I switched the furnace off again and went upstairs to read a little bit about it (we bought the house this summer and I don't know much about it) and when I returned I started the furnace again. I think it worked again till it reached the temperature set on the thermostat and it stopped again making the same sound.
I am now waiting for it "to rest" :-) and I will start it again but with an increased temperature. It was set to 21.5 before, now it is set to 23 ..I want to see what it is going to do this time
Now the questions for you guys:
-can you say by the little info provided here what is going on?
-can anybody tell me what would be the cost to replace the furnace (I live in Toronto) and if it is worth replacing it? I would be curious to hear what are the main advantages that the newer models have over this ancient model (1988)
Y9u can listen to the sound it makes online here
Answer: Note: the below was solved. It was a loose wire between the controller and the gas valve (the white wire on the diagram)
Comment: Loose where? At the screws we can see on the controller?
Comment: Yes, at that end

What is wrong with my gas furnace?


Is there a notion of RMSD for two different molecules?

Question: The (least) Root Mean Square Deviation is used for comparing different conformations of the same molecule. However one may be interested in comparing the conformations of two different molecules e.g. two proteins of different backbone lengths. So is there any method for comparing conformations different molecules such as a generalized RMDS?
Answer: PyMOL ("align molecule1, molecule2" returns aligned structures and RMSD). TM-align (returns aligned structures and TM-score; tmalign.py is a python module for running TM-align using PyMOL).


How can I disable Kies in Samsung Galaxy S2?

Question: Whenever I connect my S2 to the power outlet (not to a computer), the Kies application pops up. Where do I disable this auto-activation?
Comment: Samsung Kies is one of the worst pieces of software I think I've ever come across. I had to install it to upgrade my mother's SGS, I was astonished by how much it clogged up my system (3 separate autorun entries, 2 services), and how unbearably slow it was.
Comment: @fredley Kies Mini is a lot better, just a small standalone app.
Answer: Go to Settings > Applications > Development > and check USB debugging
After that if you connect your S2 to a PC it will connect in USB mode and you won't get the KIES application popup.
Answer: Sounds like there's something funny with either your USB cable, the charger or the socket on your phone that's causing it to detect it as a full PC connection, rather than just a dumb charger.
You should be able to get rid of that prompt for the moment by going into Settings -> Wireless and Network -> USB Settings and selecting the Mass Storage mode rather than the Samsung Kies mode.
However you really ought to try with another charger and cable to see if that fixes the actual problem, pure-charger cables shouldn't be detected as a PC, the signal on the cable is different and the phone should detect that.
Comment: I don't have USB Settings under Wireless and Network.
Comment: @ripper sorry you must be running a different update then, I know Samsung have moved that setting around at times. Have a look under the other headings in Settings to see if you can see the USB settings, I think it might have been under the SD Card and phone settings in the past too?
Comment: haven't found it.


How was Shoto Todoroki able to resist One for All?

Question: Something that I dont understand from My Hero Academia it's something characters which supposedly have average resistance (because their quirks arent about resistance) are able to resist One for All. For example, Shoto in it's battle with Midoriya (and wasnt this One for All 100%?) How was Shoto Todoroki able to resist One for All?
Answer: The answer is basically given in chapter 22 of the manga. When Midoria tells All Might that he managed to hit Nomu without breaking his arm, they come to the conclusion that Midoria subconsciously limited his power output to avoid causing lethal harm to other humans. Mostly possible, that during his fight with Todoroki, he has limited his power in the same way.
Answer: The power level of that punch or others are not specifically stated in the manga or somewhere else.

We know that Izuku's current limit of %20. More than that harms him. This is also valid if he is using Full Cowl.
In many fights Izuku exaggerates the power output of his quirk. Muscular fight is the best example for this. He never uses %100 output nor that he can stand that kind of harm.

So since he is not using Full Cowl here we can assume his power output is noting more than %10. Because his power output is only %5-6 without Full Cowl.
Comment: hmmm I thought that everytime he was hurting himself it was because he was using 100%, before he learnt how to use 5% only.
Comment: One for All materialises in a different way for every user. For All Might it changes his body. For Izuku it changes the colour of his vein. Also there is that greenish lightning effect when he uses Full Cowl. We cant know when he will able to use %100 since Izuku will not enhance his body when it happens but for now we are far from it.
Comment: Please take into account that tournament was happening prior to internship, therefore Mydoria was unable to use Full Cowl (neither 5% nor 20%) at that time.
Answer: My theory is that because Endeavor has pushed todoroki so far, that todoroki learned to cope with painful attacks. Or Midoriya wasn't using 100%.
Comment: Welcome to Anime & Manga! We appreciate your contribution, but pure opinion/speculation answer is discouraged. Instead, please [edit] and try to back up the answer by providing supporting sources/references. Thank you.
Answer: Its either Midoriya wasn't using 100% OR Endeavor pushed Todoroki so far that he could resist painful attacks, that's all I think lmao
Comment: Welcome to Anime & Manga! We appreciate your contribution, but pure opinion/speculation answer is discouraged. Instead, please [edit] and try to back up the answer by providing supporting sources/references. Thank you.
Answer: I think there are multiple answers like endevor training shoto through painful ways so now shoto is immune to some painful attacks and that we probly know that deku can roughly control the power he uses on someone so as he did not want to severely injure shoto he used 1 or 3 something percent i think both.
Comment: Hi @AditeyaSharma, welcome to Anime & Manga SE. Do go through our [tour]! We discourage purely speculative answers here, so please try and [edit] your answer to include relevant sources or citations to support your statements. Thanks!


How do I transfer from HTC SENSE to the computer?

Question: I want to transfer contacts, photos and videos from my HTC SENSE to my computer. Does anyone know how to do this?
Thanks
Comment: Why don't you try that with HTC Sync?
Comment: I assume you're on Windows?
Comment: As your phone is an HTC, I agree with Abhishek above about HTC Sync Manager, however you havent specified which HTC model you are using because it doesnt work with all HTC devices eg I have a HTC Desire S and cannot use HTC Sync Manager however see this link for HTC Sync http://www.htc.com/www/software/htc-sync-manager/
Answer: One way would be to use WebSharing Lite available at Google Play/Android market. Once installed, you can navigate to an address set up by WebSharing via your computer and transfer any files you need.
EDIT:
There are many applications to do this as pointed out by @richard-borcsik below. This is just one off the top of my head. If you establish a Google Account for your android device and then log into Gmail for that Google Account, the contacts that you have on the phone/device automatically show up in your Gmail Contacts list. At least, that has been my experience. So you may not really need a separate application to transfer/update contacts.
Comment: That only partially explains the question. It does not support contacts. And there're better apps for the task than the one you recommend.
Comment: @richard-borcsik Please do post your answer so I can check out those applications as well! It would be very handy to future Android users who have the same question.
Answer: If your computer is a Windows PC, I recommend using Snap Pea described as "Android's Best Friend". Theres a short video tutorial, as well as explanation on the main front page of its functions. (Having never used it myself i'm not sure if it transfer videos, but as its free you have nothing to lose)
http://www.snappea.com/
If you are using an Apple Mac and your phone is incompatible with HTC Sync Manager, then I recommend using Air Droid which is browser based.
http://www.airdroid.com/


Where did those over 300k first questions go?

Question: There is a First Posts beta review task now. That one has currently about 34K posts. What stumps me a bit is that the old First Questions queue had over 300k posts in it yesterday. So what happend to the difference?
Comment: Maybe high-voted first questions are not included too, since they are considered "good" already
Comment: Either a lot of people did a *lot* of reviewing or they set a cut-off limit to get rid of some of the *really, really old* first posts that just never got reviewed and probably don't need reviewed.
Comment: Right now the old link still works on direct call: http://stackoverflow.com/review/first-questions?s=1&pagesize=15&filter=all
Answer: The old /review page was based on reputation, and could actually contain multiple posts from the same person. At the same time, it excluded true first posts from folks who passed the reputation threshold by some other means. IIRC, it was actually based on a 10K tool that existed previously, the more accurately named, "New Posts by New Users".
The new queue focuses specifically on the very first post made by a member of the site. The only exception right now is that posts older than 30 days are excluded - otherwise, everything else is fair game. If you show up and post a dozen answers on your first day, the first of these will still be in the queue - but the rest won't be.
The up-side of this is that it should be much more useful as a means of introducing new users to the site: rather than being clogged with posts from prolific but mediocre writers, everyone signing up gets one shot at fame.
The down-side is probably that it's less useful for highlighting crap. But at this point, we have better ways of handling that.


Squat for over weight people

Question: I'm trying to do dumbbell squats but not possible. I feel unbalanced hence no confidence to put my weight on heels . Could anyone help me to find out how I could progress to there ? Is there way I can do some sort of variation, like beginner level to get there
Comment: Start light to get the right feel, that start going heavier if you feel more comfortable, really nothing else you can do. I guess you aren't doing with the barbell because you can not reach that far yet. Do some stretches to get there. In my opinion, squats with barbell are much better.
Answer: You could try goblet squats, where you hold a single weight in front of you.
Or you could just to bodyweight squats, and work on getting low (ideally, you want to have your upper legs parallel to the ground or slightly lower. )
Comment: goblet squats worked ! , I managed to do two :) but I had to move weight some what away from the chest . Could this have negative effects ?
Comment: I think that is the point of the goblet squat. Your center of gravity should be directly above your feet. When you move the weight forward, you are "allowed" to move your body a bit backwards without falling.
Answer: Beginner level is to start at a railing or counter that you can rest your fingers on as you squat to get comfortable with the maneuver. Stand close to a railing, begin with a slight hip hinge to get your hips behind you then begin to lower down. Start slowly lowering only slightly, feel your weight move into your heels, then push through your heels to stand. Get comfortable there then begin to go lower. When you are confident that you no longer need to hold on or be near support then step back and squat away from support. Then begin adding weights and just holding them at your sides. Progress from here. Have fun!

Squat for over weight people


How can i create virtual desktops for cross platform testing?

Question: I have heard of ways by which one can perform cross-browser testing by setting up virtual desktops. I want to know the various ways by which this virtual desktop can be set up.
Answer: For cross platform testing, you have two options:

You create virtual machines (which any operating systems, including Windows, any Linux distributions (such as Debian, Ubuntu, Fedora and so on) by using a software like VMWare Workstation1 ($), Oracle VirtualBox[2] (free). Setup such environment is relatively easy (i.e. you create a virtual machine by providing required specifications (i.e. how much CPU cores, RAM, disk space and so on), then you install wanted operating systems and software). This kind of infrastructure is perfect for restricted environments where you are not allowed use cloud-based solutions (like in financial corporations). Disadvantages of testing infrastructure based on virtual machines are the cost of operation and maintenance.
Or you can use cloud-based solutions such as SauceLabs[3] or BrowserStack[4], which provide access to multiple browsers versions on different operating systems. Cloud-based solutions will provide a better return on investment than having a testing infrastructure based on virtual machines.

Credits : Copy-pasted from the top voted answer from here. Also please do a little bit of research before asking here and If you have already done so, please provide what's your research led to.
Answer: The tool Browseemall can be used fot that. The tool is to be installed on peremisis, so the website does niot have to be accesible from the internet. This is not a free/open source tool. One of the things it does is offer you the possibility to enter a url and pick a browser and version you want to test it on. If it is needed te tools downloads a virtual image for you. The tool also has an integrated Selenium Grid.


How Can I Fix This Gap In My Fluid Domain?

Question:
Just to start off and explain things, I've been having this problem whenever I try and create a fluid domain so I created the simplest example possible. The bounding box seen is not the domain but an exact copy to show the boundaries. I used to have great fluid simulations, now this happens and for some reason any objects set to obstacle are ignored by the fluid, any help would be appreciated
Also, if you're having trouble seeing the problem, download the blend file and if it's not my computer causing it locally, you should see that the fluid doesn't collide with the domain properly, there's gaps between all the sides.
Comment: Can you add the .blend file so we can take a look? Just the screenshot isn't much to go off
Comment: @m.ardito there's a gap between the fluid and the domain, the collisions aren't working properly
Answer: Increase the resolution to reduce the gap.
The "glitch" you are experiencing is indeed an artifact of the low-resolution simulation.
The fluid simulation is computed on a grid of N × N × N small cubes, N being your "Final" resolution setting. Every detail of the 3D world, like the boundary location or an obstacle, that is smaller than the diameter of these cubes may be ignored by the simulation. Therefore, you should always expect gaps that are as large as one N-th of the edge of the simulation box.
In your example, you are simulating at N = 65 and visualizing the "Preview" mode at N = 45. Since your gap is around 1/45-th of the box size, it shouldn't be considered a glitch.
Increase your "Final" simulation resolution to ~150 and switch the "Viewport display" to "Final" to see the difference it makes.

Your file simualted at Final = 300 and Viewport display = Final
Answer: I, like you, also remember perfect domain to simulation walls parity, but I think I just never noticed the small gap before.
I checked Blender 2.78, 2.79, 2.8, and 2.5, all exhibit the same behaviour.
So I'd say this is as it has always been.
Comment: I had it working perfectly and then in the same version this started happening (I was on like 2.3 or something) and then I updated and it stayed consistent, hopefully we can find an answer to if this changed in an update, I've also been having problems with fluids ignoring things designated as obstacles, any troubleshooting I can do that would work or should I be more specific?
Comment: best thing right now would be to ge 5+ people to notify if theyre getting the same bahaviour, I don't think anything external can break this, if I understand correctly this depends solely on cpu. I tried looking at a few other videos online and while it is difficult to tell I'd say that the gap is there.

kinda offtopic but why do you care about the gap? it's not something that I can see being a huge problem.


Is it ok to attempt to write in french?

Question: Is it ok to attempt to write in French my question, even though it probably contains some errors, and then hope a reviewer corrects them? In this way we could learn a lot more, by learning from our mistakes and by improving our French writing skills...
Comment: Check maybe http://meta.french.stackexchange.com/questions/547/ or http://meta.french.stackexchange.com/questions/445/ and included links.
Answer: Sure, it's even encouraged to write your question in French, as long as you can make yourself understood. People here expect that your French may not be perfect and will usually edit your question if they spot mistakes.
The one thing that could make you hesitate is that if you ask in French, people will usually answer in French. If you don't feel capable of understanding answers in French, it would be best to ask in English. But of course if someone answers in French and you have trouble understanding the answer, you're welcome to request clarifications.
Comment: @Anoldmaninthesea. No you didn't!
Comment: @An old man in the sea And you did not fall into the standard "merci de"/"merci pour" trap.
Comment: Time to use my limited french: Merci Gilles pour ta réponse.
(I bet I did a mistake there, lol)

Is it ok to attempt to write in french?


Where is the ball spotted on a quarterback slide

Question: When a quarterback slides feet first, is the ball spotted at the feet or where the ball is held in the hands, which could be 2 or 3 feet behind the feet?
Answer: As of 2018 the ball is spotted from the position at which the quarterback initiates the slide. This applies on any type slide or dive, for any ball carrier. So in this case, when the quarterback slides with the ball in his hands, the ball is spotted at the yardage it was when his body first contacts the ground, which is usually his thigh, shin or knee.
Here is an explanation by the NFL's competition committee regarding the ruling on ball carrier sliding:

(1) "If a runner (including a quarterback) gives himself up, then he is down where the first body part touches the ground. The runner should not benefit from additional yardage after the first body part touches. Defenders do not have to go down to initiate contact to stop a runner from gaining more yards after he contacts the ground."
(2) "Quarterbacks and all runners should be reminded that they must give themselves up early, and that if a defender has committed to a tackle, contact may occur. However, that contact cannot be late or to the head or neck area of the player who gave himself up."
(3) "A quarterback does not have to slide feet first to be considered to be giving himself up. Regardless whether the slide is feet first or head first, as long as he gives himself up, he should receive the protections afforded to him as a player in a defenceless posture."

This rule was added to give more protection to the ball handlers, make them treated the same when giving themselves up via feet first dive or head first dive.
Comment: This is a duplicate question and does not really answer the question - if you think it does your answer is wrong then.
Answer: Please see my comments in my answer here - When a QB slides, is it considered a dead ball?
For your specific question of a QB sliding feet first.   The ball should be spotted when he starts his slide where the ball was at that point.   Not when a shin or thigh or anything else hits.
The other answer is simply incorrect.   One could even go as far as saying that  whenever the QBs feet land for his slide that is the point where the ball is dead (where the QB has the ball being relative).
But that would also be wrong.   An athletic QB could easily slide high (think flying front kick) and gain at least 1-2 yards while in the air.   When the QB is in the "sliding" position he is not allowed to be hit so it would be completely inaccurate for a referee to mark the ball at the spot where the QB landed first when the defense wasn't allowed to hit him.
Rule is simple - start your slide and ball is dead...   Ball spotted right were it was when slide started.   That is why you see some smart QBs like Rodgers stick the ball out front on slides (this rule needs to be changed too as it is ridiculous near sidelines).


When is a limit cycle generated by a Hamiltonian oval stable?

Question: Consider a real polynomial $H$ of degree $n+1$ in the plane. A closed, connected component of a level curve $H=t$ is denoted by $\gamma(t)$ and called an oval of $H$. Let $\omega$ be a real 1-form with polynomial coefficients of degree at most $n$. We say that an oval $\gamma(t)$ generates a limit cycle of the perturbed system $dH + \epsilon \omega$ if there exists a family of closed curves $l(\epsilon)$ defined for small $\epsilon$ such that $l(\epsilon)$ is a limit cycle of $dH + \epsilon \omega$ when $\epsilon \neq 0$ and $l(0)=\gamma(t)$. Consider the abelian integral
\begin{equation*}
I(t) = \int_{\gamma(t)} \omega
\end{equation*}
The Pontryagin criterion says that if $\gamma(t)$ generates a limit cycle in the above sense then $I(t)=0$. Conversely, if $I(t)=0$ and $I'(t) \neq 0$ then the oval $\gamma(t)$ generates a limit cycle of the perturbed system. What can be said about the STABILITY of limit cycles generated in this way? Can we couple this result to Floquet theory or a related concept in a convenient way?
Comment: Higher  Melnikov  function  described in Perko books gives simillar results for the case of non simple roots of the corresponding abelian integral. I am also interested in these topics please see my question here :  In this  question the unperturbed system is  not  Hamiltonian: http://mathoverflow.net/questions/157966/a-question-on-the-weakened-hilbert-16th-problem
Answer: Well, it looks like this is simply a matter of a Poincare map. If you look at a proof of Pontryagin's criterion, it turns out that the integral $I(t)$ is the first derivative of the Poincare map with respect to the parameter $\varepsilon$, and then evaluated at $\varepsilon=0$. Indeed, assume you have a cross-section $\Sigma$ of the orbits of $\ker dH$ and parametrize this cross-section by $H|_{\Sigma} : \Sigma \to \mathbb{R}$. For small enough $\varepsilon$ the transverse arc $\Sigma$ is also a cross-section of the orbits of $\ker( dH + \varepsilon \omega)$. Fix a point $t$ on $\Sigma$. Then let $\gamma_{\varepsilon, t}$ be the orbit of $\ker( dH + \varepsilon \omega)$ starting from $t \in \Sigma$ and returning to $\Sigma$ again for the first time at the point $t_1 \in \Sigma$. This is the Poincare first-return map (guaranteed to exist for small enough $\varepsilon$) and we denote it by $P_{\varepsilon}(t):=t_1$, where the map $P_{\varepsilon} : \Sigma' \to \Sigma\,\,\,$ is defined on an open subset $\Sigma' \subseteq \Sigma$. Now, since $\gamma_{\varepsilon, t}$ is a an orbit of $\ker( dH + \varepsilon \omega)$, we can write this fact alternatively as  $( dH + \varepsilon \omega)_{{\gamma}_{\varepsilon, t}}(\dot{\gamma}_{\varepsilon, t}) = 0$. Therefore if we integrate the latter equality along   $\gamma_{\varepsilon, t}$ we obtain
$$0 = \int_{\gamma_{\varepsilon, t}}  dH + \varepsilon \omega =  \int_{\gamma_{\varepsilon, t}}  dH + \varepsilon \int_{\gamma_{\varepsilon, t}} \omega = H|_{t_1} - H|_{t} + \varepsilon \int_{\gamma_{\varepsilon, t}} \omega  = t_1 - t + \varepsilon \int_{\gamma_{\varepsilon, t}} \omega. $$ I have slightly abused notation, identifying the endpoints of $\gamma_{\varepsilon, t}$ on the cross-section $\Sigma$ with their coordinates $t$ and $t_1$. Now, by construction  $P_{\varepsilon}(t)=t_1$ so the result of the integration above yields $$0 = P_{\varepsilon}(t) - t + \varepsilon \int_{\gamma_{\varepsilon, t}} \omega$$ written also as $$P_{\varepsilon}(t) - t = - \varepsilon \int_{\gamma_{\varepsilon, t}} \omega.$$ Division by $\varepsilon$ takes us to
$$\frac{P_{\varepsilon}(t) - t}{\varepsilon} = - \int_{\gamma_{\varepsilon, t}} \omega.$$ If we let $\varepsilon \to 0$, by continuous dependence on parameters, $\gamma_{\varepsilon, t} \to \gamma(t)$, the latter being the oval orbit of $\ker dH$ through $t$. Therefore the last equality converges to
$$\frac{\partial P_{\varepsilon}(t) }{\partial \varepsilon}\Big{|}_{\varepsilon = 0} = - \int_{\gamma(t)} \omega = - I(t).$$ This last conclusion allows us to Taylor expand the Poincare map with respect to $\varepsilon$ near $0$:
$$P_{\varepsilon}(t) = t - \varepsilon I(t) + \varepsilon^2 R(t, \varepsilon).$$ Now, a fixed point of the Poincare map, $P_{\varepsilon}(t_{\varepsilon}) = t_{\varepsilon},$ gives rise to a periodic orbit of $\ker( dH + \varepsilon \omega)$ passing through $t_{\varepsilon} \in \Sigma$. So, in search of periodic orbits of $\ker( dH + \varepsilon \omega)$, we try to solve the fixed point equation
$$f_{\varepsilon}(t):=\frac{1}{ \varepsilon }(P_{\varepsilon}(t) - t) = - I(t) + \varepsilon R(t, \varepsilon) = 0.$$ The conditions for $I$ you mention are simply the conditions for the implicit function theorem applied to the latter equality, i.e. $f_{\varepsilon}(t) = 0$. Thus, if we find $t_0 \in \Sigma$ such that $I(t_0) = 0$ but $I'(t_0) \neq 0$, then we know that there is a one parameter continuous family of initial conditions $t_{\varepsilon}$ for which $f_{\varepsilon}(t_{\varepsilon}) = 0$, which in its own turn implies the existence of one parameter family of  cycles $l(\varepsilon)$ of $\ker( dH + \varepsilon \omega),$ passing through the points $t_{\varepsilon}$ so that $t_{\varepsilon}|_{\varepsilon = 0} = t_0$ and so $l(\varepsilon)$ continuously homotopes to $l(0) = \gamma(t_0)$.
Finally, we write the Poincare map as
$$P_{\varepsilon}(t) = t - \varepsilon I(t) + \varepsilon^2 R(t, \varepsilon)
 = t + \varepsilon \big( - I(t) + \varepsilon R(t, \varepsilon)\big) = t + \varepsilon f_{\varepsilon}(t),$$ and its first derivative with respect to $t$ is
$$P'_{\varepsilon}(t) = 1 - \varepsilon I'(t) + \varepsilon^2 \frac{\partial R}{\partial t}(t,\varepsilon)=1 + \varepsilon f'_{\varepsilon}(t).$$
Now, the first derivative of $f_{\varepsilon}(t)$ with respect to $t$ evaluated at $t_{\varepsilon}$ is
$$ g(\varepsilon) = f'_{\varepsilon}(t_{\varepsilon}) =
-  I'(t_{\varepsilon}) + \varepsilon \frac{\partial R}{\partial
t}(t_{\varepsilon},\varepsilon),$$ so we see that $g(\varepsilon)$
is a continuous function with respect to $\varepsilon.$ Assume for
instance that $I'(t_0) > 0$. For $\varepsilon = 0$ we obtain
$$g(0) = f'_0(t_0) = -I'(t_0) < 0.$$ By continuity,
$g(\varepsilon) = f'_{\varepsilon}(t_{\varepsilon}) < 0$ for small
enough values of $\varepsilon$. Therefore
$$0 < P'_{\varepsilon}(t_{\varepsilon}) =1 + \varepsilon
f'_{\varepsilon}(t_{\varepsilon}) < 1,$$ whenever $\varepsilon >
0$ and it is small enough. Analogously, $$
P'_{\varepsilon}(t_{\varepsilon}) =1 + \varepsilon
f'_{\varepsilon}(t_{\varepsilon}) > 1,$$ for $\varepsilon < 0$
near $0$. The former case implies that the limit cycle is stable,
while the latter one implies that the cycle is unstable. The
alternative assumption that $I'(t_0) < 0$ is handled in the same
way.
Notice that these arguments are more general and it is irrelevant whether  $H$ and $\omega$ have  polynomial nature.
Comment: Thank you for a very nice answer. If I understand correctly, the punchline is: Assume $\epsilon >0$. Then the limit cycle is stable if $I'(t_0)>0$ and unstable if $I'(t_0)<0$? This seems remarkably simple, but I'm left wondering if there is any notion of semi-stability? Moreover, do you have a good reference to confirm your proof of Pontryagin's criterion? I am a little unsure how much rigour is contained in the one you have provided. (and by $ker(a)=0$ do you just mean $ker(a)$?)
Comment: Yes, it is exactly as you say: for small enough $\varepsilon >0$ the limit cycle is stable if $I'(t_0)>0$ and unstable if $I'(t_0)<0$. The function $I(t)$ conveniently encodes a lot of information about the qualitative behavior of the dynamical system in the relevant neighborhood: existence of periodic orbits as well as stability of the latter. Otherwise, to hope for semi-stability, assuming the dynamical system is at least real analytic, or even polynomial, one probably needs to have $I(t_0)=0, \, I'(t_0) = 0$ but $I''(t_0) \neq 0$. BTW, I've already fixed the $\ker$ typo. Thanks.
Comment: In terms of literature, I am not too sure where exactly one can see the proof, although I have seen $I(t)$ used in all articles related to the topic of infinitesimal 16th Hilbert problem. But maybe in the books written by some of the experts in the field?


Acceptance of empty string by nondeterministic automaton

Question: Why is the input $\epsilon$ accepted by the nondeterministic finite automaton shown below?  Does it not leave $q_1$ and go to $q_3$?
Answer: You're confusing the concept of the empty string $\varepsilon$ with the concept of an $\varepsilon$-transition.
The empty string $\varepsilon$ is just the string with no characters.  The presence of a $b$-transition from $q_1$ to $q_2$ means that the automaton can move between those two states by reading character $b$ but the presence of an $\varepsilon$-transition from $q_1$ to $q_3$ doesn't mean that it moves by reading the character $\varepsilon$. Rather, it means that the automaton can (but is not forced to) move from $q_1$ to $q_3$ without reading any input at all.
So, when this automaton has no input, it can either remain in state $q_1$, which is accepting, or move to $q_3$, which isn't.  Since it can reach an accepting state, it accepts.
Answer: I think you are asking why the input string $\epsilon$ (the empty string) is accepted by the given NFA. If so, you need to create a set of all states reached by the given string (in this case it is $S=\{q_1, q_3\}$) and see if an accepting state belongs to this set (in this case - yes: $q_1 \in S$).
Answer: To expand on Denis's answer, the given automata is non-deterministic because it has $\epsilon$-transitions. Because it's non-deterministic, given an input of the empty string $\epsilon$, we don't have to follow the transition from $q_1$ to $q_3$; we can just stay in $q_1$, which accepts the string.


How do Dambadiva kings fit in Indian history?

Question: My question, I would like to know whether any space in Indian history to fit Dambadiva  kings in Indian history rather than keeping them only in Buddhist books? or it feels like they were foreign kings?
By leaving behind many number of books in original Mahavanshaya which were written in the past history by covering all 29th Lord Buddha's eras and the Great emperors in the great Island including King Maha Sammatha, King Ravana, King Shaka generation (King Shaka 1 to King Shaka 15) and many more Great emperors' eras, Mahavanshaya was rewritten by native foreigner, Monk Mahanama with influence of foreigner, Monk Buddhagosha in 05th Century.
As per the known history rewritten Mahavanshaya was not even  completed by those two foreigners based on protest which was arisen among the locals by leading Monk Upathissa, and also those two monks had left the island secretly by leaving incomplete rewritten Mahavanshaya in the Island.
Native foreigner, Monk Mahanama has taken the start in rewritten Mahavanshaya by giving all 29 Lord Buddhas' era with simple introduction by giving a clue of foreign arrivals, and  further stating there are many books of Mahavanshaya which ware already written in the past history by locals about the history of the island, however due to there are many errors in the written history, he rewrites the history of the Island by making short its long stories and dragging short stories to long stories by adding taste of art in to the history.
Here there is a BIG question?  How foreigner cut long stories to short stories in foreign country history? How he says there were many errors in the written history of the Island which was led to more than 20 thousand year's history by covering all 29 Lord Buddha's eras.
Native Foreigner,author of Mahavanshaya, has made many effort to convince readers to believe Dambadiva is a foreign  place in another country without mentioning the country. However in ancient written even in foreign countries, there are many evidence to proof it is the island of Jambudeepa, and also it was Heladeepa, Three Sinhale, Sinhale, Ceylon and SriLanka. Below are the few great examples to prove  Dambadiva is not a foreign place in another country, it is the Island of Ceylon.
First three  evidence ware taken from a great history book which was recently written in native language with heard research  under title "Land of Lord Buddha"   It was written by Mr H.S.Herath
1st Evidence - "General Account of the Encircling Ocean" this is also known as  "Ying-hwin-che-ke"
This book was written by yin Huwan -che-ke,  Lieutenant of Fue Kien reigon in 04th Century
In a chapter it says
"Seih-lan is situated in Southern India, and is a large island in the sea, on the south east ,coast,its circumference been about 1000 le (300 miles) having in the centre lofty mountains ;on the coast the land in low and marshy . The country is characterised by much rain and constant thunder. The hills and valleys are beautifully ornamented with flowers and trees of great variety and beauty, the cries of animals rejoicing together fill the air with gladness,and the landscape abounds with splendour.  In the forests are many elephants and the native use them instead of draught oxen or horses.  The people are all of the Buddhist religion ;it is said that Buddha was born here....
2nd Evidence-
Huu Newil book collection in London Museum-6607(2) - "Three Sinhale Kadaim saha Viththi " this book was written in native language in SriLanka, author A.J.W Marabe
"Magam paththuve Thissa maha veheraya pihita vadalau desiya dolahak magul lakunu athi saman deviyange aradanaven me jambuddeepaye senaga vadapuda gaththau samantha kuta parvathayada yana meki sthanada ruhunu ratata athulath vanneya"
English translation:
(This Island was also called "three Sinhale" one period of ancient time based on 03 monarchs in the Island)
Title of the book: "Three Sinhale boundaries and description" (ancient palm tree written book)
In a paragraph, author further explained quoting below information to indicate boundaries in the monarch of Ruhuna saying
"Thissa Dagaba in division of Magam, and Saman Mountain with 212 fortune symbols which is worshiped by here locals in Jambudeepa with an invitation of God Saman are also included to the Monarch of Ruhuna"
This ancient palm tree written book  is old nearly 700 years.
Mountain Saman  is also known as Sripada mountain which is situated in SriLanka, Buddhist worship this mountain based on Lord Buddha's footprint on it
03rd evidence:
In an ancient book under title "Wanni Rajavaliya" Author, A.V Suraweera
In  page 70, in a poem,  author explained incident which was occurred in SriLanka in native language saying
Ape muni varshayen lath hathsiya visithunaka
Ai  Baminisaya Dabadiva pamini warshayaka
Dakamin ekak Dabadiva rajakala warshayaka
Palabu thilovata mathu saka varshayaka
English translation:
In our Lord Buddha's calendar years, year, seven hundred and three
Year, Baminisaya Drought was in Dambadiva
Year, viewing one, being in crown
Shine Lord Buddha in future Shaka year
As a known history, Baminisaya Drought was a well-known drought in SriLanka in ancient time, and also Shaka warsha/shaka years were generated in one of the King Shaka era in king Shaka generation  in SriLanka, ancient time, as per the history which were read by Dr. Mirando Obesekara  in ancient palm written book, there were 15 kings in King Shaka generation as King Shaka 1 to King Shaka  15
Further There was a conflict between  Abayagiri Vihara monks & Maha vihara monks during the period of King Prakkamabahu 1, and this era(12th century CE), pure Theravada Buddhism was in threat,and Abayagiri Vihara was struggling to protect the pure Theravada Buddhism and the  Great history of the island which was bound  with Buddhism more than   20 thousand year's  history which was led to  29 Load Buddha's eras including Lord Buddha, Kakusada , Lord Buddha Konagama, Lord Buddha Kashshapa and Lord Buddha Gothama and finally as Abayagiri Vihara monks made a genuine  effort to protect the Island even forcing to king Prakkamabahu 1 to  give up his throne  to protect the pure Theravada Buddhism in the Island  from the King, who was no interest to hold his due responsibility  to protect  the Theravada Buddhism through his  crown; they were defeated by the Kind together with monks in  Maha vihara who influence foreign involvements to decline the pure Theravada Buddhism in the kingdom Not only that as per the known history, the history books which were stored   in  Abayagiri vihara library  about Great history of the Island with  more than 20 thousand year's history ware burned after Abayagiri Vihara was defeated by  the King and the Monks in Maha vihara, as per the known history the books were on the floor  up to the  height of seven elephants if they were on, one another when  books were caught  fire.
Monk Mahanama not only misled Dambadiva History, Island Ceylon, but also Indian History by dragging foreign country history, and mixing it in to their history, hence Dambadiva kings are in only in Buddhist books in Indian history.
Comment: Can you please name the "_Dambadiva kings_"? And it _seems_ to me you're particularly interested in _history of Theravada Buddhism_ - is this area of focus?
Answer: The word Dambadiva does not fit into Indian history because the reference is wrong. It does not refer to anything in India.
The word "Dambadiva" is the Sinhala translation of the Pali term Jambudipa. The name is wrongly used to refer to India/Nepal where Buddha lived. Check the Google search here -> https://www.google.com/search?q=dambadiva
Dambadiva is in fact the "Deva Area" shown here.

How the history got distorted is mentioned here -> https://jambudipa.quora.com


Vertex vs texture map

Question: I am trying to select a model vertex by the textures alpha trough the python.
But I cant figure out relationship between meshes vertex, uv-vertex and texture´s pixel rgba information. Can you help me with this please ?
Answer: So, after some time with the research i found the answers. It is for beginners like me, so pros please correct my mistakes if i have some. (From noob to noobs :D - for better understaning the fundamentals)
I am trying to made 2D puppet in blender, so mainly I created plane or grid and textures. Its not for a complex 3d puppet and materials.
A) Vertices + mesh
- Vertices have index and [0,0,0] is the pivot point. Default in the middle of object.
There are awesome addon for vizualize numbers of vertices for better control:
https://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/3D_interaction/Index_Visualiser
code to find coordinations of vertices:
import bpy
obj=bpy.context.active_object
x=obj.data.vertices[0].co[0] #X
y=obj.data.vertices[0].co[1] #Y
z=obj.data.vertices[0].co[2] #Z
print("X:"+repr(x) +" Y:"+repr(y) +" Z:"+repr(z))

If we want to use infromation from vertexes for image and pixels, we need recalculate ratio position of the vertices. (0-1 from dimensions * scale)
For separate dimension from scale I must applied scale. In that case dimensions are setting as you choose but scale is reset to default 1.
Next stage is to move axis of coordination system for vertexes to the left-down corner, because imaxe X,Y coords is the same.
import bpy
obj=bpy.context.active_object
dimension = obj.dimensions
for i in range(len(obj.data.vertices)):
    a = []
    axis = [-(dimension[0]/2),-(dimension[1]/2),0]
    a.append(obj.data.vertices[i].co[0] * obj.scale[0] - axis[0])     # X
    a.append(obj.data.vertices[i].co[1] * obj.scale[1] - axis[1])     # Y
    a.append(obj.data.vertices[i].co[2] * obj.scale[2] - axis[2])     # Z
    print(a)

Calculate the ratio is very easy now (everything is for the plane object):
    ratio_verts = []
    ratio_verts.append(a[0]/(dimension[0]))
    ratio_verts.append(a[1]/(dimension[1]))
    ratio_verts.append(0.0)

Challenge of this small research was to understang how is a PNG works it is the format which carry RGBA infromation. So at the begining I discovered that for 3x3 size of picture python give me 36 numbers. I was very confusing about that, because I though that every pixel have its own index and then under index are the information about RGBA.
import bpy
image = "Test.png"
print(bpy.data.images[image].pixels)
It was mistake, PNG RGBA infromation is saved like numbers in line. [1.0,1.0,1.0,1.0...] And how it works? Like this! [1R,1G,1B,1A,2R,2G,2B,2A,3R,3G,3B,3A...] 4 numbers next other for 1 pixel information. Yes, I know, I was dumb that I dont know it, but I never trying working with the pixels trough python.
So there are really nice maths about converting coordinates to this system :)
From coordination of pixel like X:3px Y:3px to number of the pixel in line.
like:
I created an function:
def sourxy(x,y,image_name,start):
    imgX = bpy.data.images[image_name].size[0]
    PXindex = (y*imgX)-(imgX-x)
    return PXindex-1+start

when X and Y os coordination for searhed pixel.
image_name > its name of my mum :D No, of course name of the image.
And start is number if the start index (0 or 1 often) for next maths.
For some reasons maybe you would like to use recalc for X and Y:
x = PXindex + imgX - (y*imgX)
y = PXindex/imgX)+((imgX-x)/imgX

Perfect, I though, i am almost done. Byt computer says : nooooooo !
I finded problem between recalc coordinaion of the vertexes and the pixels. Vertexes have coords like [0,0], [0,1], [0,2] and its not only 9 vertices it can be like 100*100 vertices for more dense planes.
So if i rounded ratio to integers. I had coords of pixels on image without any color. Its every border down and left vertex.
Solution was simple function:
def imground(n):
    if n==0.0:
        return 1
    else: return math.ceil(n)

From vertex coords to imagme coords by vertex ratio between position and dimensions is like:
imageX=imground(bpy.data.images[image].size[0]*ratio_verts[0])
imageY=imground(bpy.data.images[image].size[1]*ratio_verts[1])

That give me right coords without zero.
From that stage its pretty simply, we need alpha exact pixel. But every pixel have 4 numbers so it need to be miltiplied by 4. And then we know that 4th number is the Alpha we found.
VertexAlpha =bpy.data.images[image].pixels[sourxy(imageX,imageY,image,0)*4+3]

So every vertex which have alpha more than 0 assign to first vertex group:
if VertexAlpha > 0:
        vrx_grp.append(i)
obj.vertex_groups[0].add(vrx_grp,1.0,"REPLACE")
vrx_grp=[]

# get all the verts that belong to a certain vertex group index:
vg_idx = 0
vs = [ v for v in obj.data.vertices if vg_idx in [ vg.group for vg in v.groups ] ]
print("vertex_group inside: " + repr(vs))

last part of code is from: Python - Finding Vertices in a Vertex Group
And Last part of question was UV vertex. For me and the puppet project its not usable, because every vertex in uv can hold multiple coordinations. It is because Many parts of unwrapping. And trough the vertex can be created line of the seam.

Vertex vs texture map


Flag/close as "not a specific problem"?

Question: I'm looking at this question, a low-effort question asking us to do their work for them, where the problem given is really a series of small problems: Build the web interface, detect the clicks, validate, etc, any one of which could be an acceptable (though basic) question, but which together amount to "please write my code for me." I'd like to flag it as too broad, but the problems are each small enough that a complete answer would probably not actually be too long for this format, however it would not work well because it would be better to answer all of the problems individually so that people who have those problems in other contexts can find the solutions. "Unclear what you're asking" doesn't work because the question is clear enough; it's just not a good fit for Q&A. Therefore I'm proposing adding a flag/close reason to say that a question does not boil down to a specific problem, and that the asker should do as much as they can and then ask about the specific points at which they have trouble.
Comment: Close > Off-topic > Other > "Not a specific problem or whatever".
Comment: @Bjørn-RogerKringsjå I suppose the question is how often this is useful. I feel this could be applied to a good number of unhelpful "please write my code for me" questions.
Answer: "Unclear what they are asking" fits. Are they asking for the entire solution? Are they asking for help on pieces they have problems with, but merely did not show what they have already tried?
"Offtopic ... debugging" could be used as they have code that is not working but they have not show it or what they have tried. The possibility that they have not written any code is included here as Stackoverflow is about helping them with problems in their code, not providing all of it.
I am not sure that there is a "best" close reason for that question. Your suggestion of "Too broad" is also quite valid. We do not know whether they want detailed multi-paragraph answers on eachtopic, or whether they just wants some hints.
Comment: As written, it seems clear enough to me that they have not tried much and are asking for the entire solution.
Comment: @Saposhiente Maybe you are correct. There are numerous Q&A discussing close reasons and suggesting new ones. But the leaders of Stackoverflow seem reluctant to change the current ones. I think their argument is that the current reasons have evolved over time and they now work well as they have resolved problems with interpretation of other earlier attempts at close reasons.

Flag/close as "not a specific problem"?


Is anybody able to unaccept answers except the owner of the question?

Question: I noticed one thing a few times, after I edited my accepted answer after some time this answer is unmarked as accepted. In my experience, the user who asked the question is not even online in this time, and there's no reason for unaccepting the answer. When I edited my answers, it's in most cases grammar or better code formatting.
Comment: No, only the author of the question can accept/unaccept your answer.
Comment: An answer can be "unaccepted" if it gets deleted. Though I think it retains its "accepted" status so that it's accepted again if it's undeleted. Unless of course the OP accepts a different answer.
Answer: Only the author of the question can accept/unaccept your answer:

You may select any answer on questions you asked as the "accepted" answer. Only one answer at a time can be the 'accepted' answer.
  ...
You may change which answer is accepted, or simply un-accept the answer, at any time.

(from the FAQ, emphasis mine)
You can check if the author of the question has been online by looking at their profile, the block at the right contains a 'last seen' line:
Comment: Isn't 1024 the best ever round number ? :)
Comment: Don't forget to celebrate next day for very round number of "visited" days :)
Comment: @AlexeiLevenkov wait, I don't get it. In which base you're using is 92 a nice, round number? :P


Can single clamp measure total current from 3 wires?

Question: Single AC clamp can measure current flowing through a single wire in a non-invasive way. There are AVR/Arduino projects use such a clamp to measure house power usage. However, they use 3 clamps for 3 main wires that come into house breaker box. Unfortunately, I don't have access to separate wires in my breaker box. I can only access main power cable that comes to my house through the roof, and that cable has all the wires inside itself (is this a good assumption?) without possibility to separate them. If that is so, then the question is can I use a single clamp on that main cable for my own little power usage measurement AVR project, and if I can then is there some reason for it to be less reliable then 3 clamps solution?
Comment: Be especially careful when working on 3 phase, it is usually a higher voltage than single phase mains (eg 415V instead of 230V).
Answer: No, you cannot use a clamp meter on both the live and neutral wires at the same time. Current flowing back through the neutral wire will effectively cancel out current flowing through the live wire, and it will read 0 amps (assuming no current is leaking out anywhere).
One clamp around the live wire should give you the reading you want.
I don't know why you would need 3 clamps though, unless you have 3 phase coming into your building, in which case you'll need to sum the 3 separate currents to get the total current used.
Comment: In some parts of the world, such as Serbia, 3-phase power is standard even for small households. For single phase devices, load is distributed over 3 phases.
Comment: A single clamp meter around all three phase conductors at once is also no good, because they are seperated in phase so they won't be summed correctly. The question implied that a single clamp would be used around 3 phase plus neural, and that also won't work because the neutral field should cancel the live fields.
Comment: Yes Andreja, I live in Serbia ;-) Жив био и хвала на учешћу!
Comment: @AndrejaKo: Thanks... that would explain the need for 3 clamps then. I'm not as familiar with things like this outside my own country.
Answer: As said already, you cannot use a single ordinary CT clamp around both live and neutral wires. The total current it measures would be (close to) zero as the current in the neutral wire flows in the opposite direction.
However, for the sake of completeness, there are ways when putting multiple wires at once into a single CT clamp makes sense:

Wires of the same phase. If you made sure that all the wires you want to measure are live wires of the same phase, you can put them into the same CT clamp and it will correctly measure the total sum of the current in each of them (reference). Since they are of the same phase they have a combined sine wave current form, so this will also work with the cheaper CT clamp meters that "use a rectifier circuit which actually reads mean current, but is calibrated to display the RMS current corresponding to the measured mean, giving a correct RMS reading only if the current is a sine wave." (source).
Wires of different phases, with a true-RMS meter. In your case, if your grid electricity connection contains three live wires of different phase, you could route these (and these only) through one clamp. The total current will only be displayed correctly if you have a "true RMS" clamp meter, which means that it will read many current samples in one cycle and  average them. This works independent of the waveform, which in this case of combining different phases with potentially differing currents is not a sine wave (so the cheaper mean current measuring clamp meters cannot be used, and recalibrating them is also not possible as the different phases can have varying currents over time, resultingin different waveforms of the total current). The AVR / Arduino projects probably do not implement a true-RMS current meter, though (but they could).
(Important: While this part of the answer is logical to me, I did not test it. Please correct if required, I made this answer wiki for that reason.)
Live and neutral together, with a special CT clamp meter. As referred by Wikipedia:

A relatively recent development was a multi-conductor clamp meter with several sensor coils around the jaws of the clamp. This could be clamped around standard two- or three-conductor single-phase cables to provide a readout of the current flowing through the load, with no need to separate the conductors. (source)

An example of such a device is the Megger MMC850:

Unlike conventional clamp meters, the MMC850 has a complex
  array of Planer magnetic sensor coils to calculate the
  current flowing in the conductors of multicore cables with
  either 2 or 3 cores (source)

Still no match for your case of three phase wires, neutral and earth, and for sure not a feature in an Arduino project. But interesting.
Answer: Clamp meters measure the total current moving through them (i.e. currents moving in opposite directions cancel out). So if you were to put a single clamp around all of the conductors connected you house to the grid, you would only measure the difference between the current entering and leaving your house, this is often referred to as leakage current, and usually indicates a fault (if non-zero).
Note that just because you have 3 conductors doesn't mean that you have 3 phase power, for example in the US most houses are supplied with two phases (usually fed by a single phase in the distribution network), so the 3rd conductor is actually the neutral (not to be confused with ground). In fact in a residential environment, if you actually had 3 phases you would expect 4 conductors (3 phases plus neutral), this is known as a Wye (Y) configuration. While it is possible to have 3 phase system with only 3 conductors, that requires the load on each phase to be virtually identical, which isn't really possible in a residential system.
Answer: (yes i know this post is old, but still relevant since the Megger MMC850 has been discontinued and no alternative has presented itself)
Someone has been fiddling with hall sensors an made a sensor board. It might be a solution:
https://moderndevice.com/uncategorized/calibrating-current-sensor/
Comment: It might be a solution to the problem, but not really an answer to the question. To make it into an answer you could explain how that "someone" got this to work.
Answer: I would agree, curent coming back on the neutral conducter is esentially flowing in the oposite direction and nulling out the magnetic field produced by the load on the line conducter.  For example if you have 4.23a drawn through the line conducter and 4.22a back on the neutral, your clamp meter in theory would read 10ma which would be the leakage current. However this is all theoretical, in actual practice the chances are that the line and neutral fields would probabily not be perfectly canceled out due to positioning within the outer sheath and tolerance of your meter..


What is the formula for damage mitigation in Ingress?

Question: How does damage mitigation work on a portal? I heard that links and shields make it sturdier and harder to take down, but exactly what's the math behind this?
Comment: I've updated the answer with one important thing about old shields for people, who played at that time. Be sure to check it out!
Answer: The mitigation stacks additively and its damage reduction is hard-capped at 95%.
1 mitigation = 1% reduced damage. The mitigation can go over 95, but the extra damage reduction won't apply. Apart from mitigation, a shield has a mysterious property called Stickiness. It is said, that it might affect the destructibility of a deployed shield.
Shield Type         Mitigation  Stickiness
Common shield       30          0
Rare shield         40          150k
Very Rare shield    60          450k
Very Rare "AXA"     70          800k
Links*:
     *the Ultra Link mod increases mitigation from links by 50 %

A portal with 4 VR shields and with 10 links has 66 100 180 260 300 mitigation, BUT reduces only 95% damage. The extra shields have only the meaning of reserves, when some get destroyed.
It is wise to support shielded portal's defense with links.
The % damage reduction in action
An L8 burster with 2700 damage will do:
*Take a closer look at the defense effect of 80-95%
shield type  defense     damage
-            0%          2700
CS           30%         1890
RS           40%         1620
VRS          60%         1080
AXA          70%         810
RS + RS      80%         540
VRS + CS     90%         270   (same as 3x CS)
VRS + RS     95%         135   (same as 2x CS + RS)

I am leaving the following only for historical reasons
first version
# IMPORTANT! # for old players
If you are an old player and you don't use shields much or you didn't play long time for some reason, it may happen that you will have OLD + NEW shields in your inventory. Don't know why it works like that, but if you drop all the shields of same rarity and pick them up again, they will get renewed.
C: 6->10, R: 8->20, VR: 10->30
*do not bother yourself with common shields though, it is only worthy for R and VR S.
EDIT 1 (7 Mar 2014)
The shield strength changed once again, from 10,20,30 to 20,30,50. As far as I can tell, all old shields are renewed automatically without the need of dropping them. I am leaving the hint for historical reasons.
EDIT 2 (3 Jun 2014)
New shield strength :) - from 20,30,50 to 30,40,60. All shields are renewed automatically. Already deployed shields remain with old stats.
EDIT 3 (21 Dec 2014)  -  AXA shield
New shield type was introduced as a result of sponsorship deal with the international investment banking firm AXA. The so called AXA Shield is very rare and its mitigation is 70. More reading here...
EDIT 4 (4 Feb 2015)
Significantly increased values for stickiness started to show for newly placed shields in the JSON answer in intel. (Reddit: Shield stickiness gone mad in IITC.)
Shield Type         Old   New
Common shield       30    0
Rare shield         40    150000
Very Rare shield    60    450000
Very Rare "AXA"     70    800000

EDIT 5 (20 Jun 2015)  -  Ultra Link mod
New sponsored item SoftBank Ultra Link was introduced during the end of Persepolis anomaly. It is said to grant additional 50 % of mitigation from links. It's not known (yet) whether this effect stacks with multiple ULamps used.
# NUMBER OF LINKS
          1   ->  6   ->  40
# MITIGATION
without:  +18 ->  +50 ->  +66.8
with UL:  +27 ->  +75 ->  +100 (surpasses the 95 hardcap)

Apart from the mitigation, the UL mod increases the maximum of outgoing links by 8 to a total of 40 outgoing links when using 4x UL (stacks additively), and increases the linkable range 5 times (diminished stacking). (to compare: RLA 2x, VRLA 7x)
Comment: Just wanted to point out that this means that a single link is more powerful than a Common Portal Shield.  Adding two links is the same as a Very Rare Shield.  A couple of links is a very powerful mitigation strategy.
Comment: @womp: while links are still a powerful mitigation strategy (they won't pop off until there's less than 3 resonators remaining on the portal), the shield mitigation edits since your comment make it no longer true that a single link is more powerful than common shields or that two links are the same as a very rare.  As of the 3 Jun 2014 shield mitigation changes, a common is about equal to the first two links, and it takes 12+ links to reach the mitigation level of a very rare shield.
Comment: @jochen 1) the green line with red squares are the observed and measured values. The green and blue symbols are approximated equations. The red line is an old link mitigation. Incoming and outgoing links count the same. 2) the defense factor is both: a) how many times weaker the bursters are, b) how many xmp you need to use to deal the same damage as vs unshielded portal with single burster.
Comment: Thanks for the informative article.  Some follow-on questions: (1) is the green line in your link mitigation plot showing 400/9*atan(links/e)?  What are the other lines in this plot?  Are incoming and outgoing links counted the same for link mitigation?  (2) You have an image which plot "defense factor" against "mitigation".  What is the "defense factor" in this context?
Comment: @Qwerty just one think . In your table of shields/link mitigation and stickiness you didn't add the value of mitigation of the link. (Stickiness I suppose that will be "0" because it depends when de link goes down). Thanks for the answer. Is really complete.. Thanks!
Comment: @Shudy Yes, I didn't add the mitigation from links, because it's very easy to add (± between 18 & 50). The `stickiness` is a shield's attribute of how difficult it will be to pop. It has nothing to do with links or mitigation itself. Each shield has its own stickiness. Anyway, it's always good to reach max mitigation with shields only, disregarding the link mitigation as shields pop off often and this way you have reserves, also links can be taken down from other side.
Comment: @Qwerty Ok! perfect :D Thanks for the fast answer ^^
Answer: Shields mitigations are :

common shield : 30
rare shield : 40
very rare shield : 60
AXA shield : 70

The mitigation of the shields is a percentage of absorption of damages. A (common) shield with a mitigation of 10 will absorb 10% of the damages made by the buster. A second (common) shield with mitigation 10 will catch 10% of the remaining damages.
For example, let's imagine a burster making 100 of damages on a resonator. First common shield will absorb 10% so damages will be reduced to 90. A second common shield will absorb 10% of the 90 damages and will reduce damages to 81...
In the worst/better case with 4 very rare shields mitigation 30, a burster making 100 damages will be reduced to 24.
To compute the total mitigation of shields on a portal you have to just multiply the percentages. A very rare shield will eat 30%, to compute the effects you'll have to do X - (X * 30 / 100) that will reduce to X * 0.7.
So a very rare shield is equal to a 0.7 factor applied on the burster's damage, a rare shield is equal to 0.8 and a common to 0.9.
So the way of computing shield mitigation is :
SHIELDS_MITIGATION = SHIELD_1_FACTOR * SHIELD_2_FACTOR * SHIELD_3_FACTOR * SHIELD_4_FACTOR

To that, you have to add a defense mitigation made by links. The formula seems to be :
LINKS_MITIGATION = 4/9 * atan(NUMBER_OF_LINKS / e)

where e is the mathematical constant.
This will give you another mitigation to "add" (multiply) to the shield one to obtain final mitigation.
Then to compute the damages the formula is :
RESULTING_DAMAGES = BURSTER_DAMAGES * SHIELDS_MITIGATION * LINKS_MITIGATION

Comment: I don't believe that is true. I am very sure that mitigation is additive, not multiplicative. So four common shields give 40% mitigation. 4 rare 80%, and 4 very rare 120%. However, mitigation is capped a a certain level. Somewhere around 95% is the rumor.
Comment: Well, NianticOpsBernini confirmed the 95% cap, but noted that the exact formula is confidential:  https://groups.google.com/forum/m/#!msg/ingress-discuss/85ZfOoIsvnU/yGerMjD3mn0J
Comment: @JacobEggers the rumor [has been confirmed](https://groups.google.com/forum/m/#!msg/ingress-discuss/85ZfOoIsvnU/yGerMjD3mn0J) by NianticOpsBernini.
Comment: Thank you so much for this, I'm going to be trying to min-max portal defenses with my resources.
Comment: This answer doesn't make much sense, it correctly gives common shield as 30% mitigation but then does calculations as if they gave 10% and so on.


Is there a miner with a controllable hashrate?

Question: Sometimes people don't want to mine at a full load due to various reasons (computer noise, hardware concerns, etc). Are there any miners out there in which one can set a hashrate limit? I know one can use -f and -s flags, but the amount of control they give is quite limited.
Answer: I suggest you run the miner at full load but decrease GPU core clock speed (GPU mem clock speed should always be reduced) and even more important GPU voltage.
Reducing GPU core clock speed should reduce power linearly. Also it allows you to decrease voltage further which reduces power quadratically. Doing so you can reduce noise dramatically.
If you use cgminer you can underclock and undervolt from within the program itself. If you use another miner you can use a program supplied by your graphic card's manufacturer (e.g. MSI Afterburner, atifonfig on linux) or a third party software such as AMDOverdriveCtrl (Linux). There is also my very own windows command line tool clocktweak (not free).