How Good Is A Recommendation Letter For MS in CS From A Workplace If It's Coming From A Mentor?

Question: I have 3 years of work experience in cloud computing and virtualization and am intending to illuminate this in my SOP. With what degree of credibility will the above mentioned work experience be accepted by admissions committees if I do not have any letter from my workplace at all? Also, since it is difficult for me to get a recommendation from my immediate manager at my workplace, if at all I do get one from my company, it may be from a colleague who was my mentor (no managerial role). How good will such a recommendation be? I already have two recommendations from my college professors, each of which highlight one of my two research publications. It is for the third recommendation that I have the choice between this letter from my mentor at my workplace and from an assistant professor at my college who had taught me in a number of courses and labs. Which recommendation should I go forward with? Please advise on these matters.
Answer: Unless the MS is very applied, I'd think that an additional academic recommendation would be better. That is especially true if they can speak to different aspects of your work.
But a letter from a mentor should, in general, be fine. It might even be better than one from a manager as the person likely has more knowledge of you and your contributions. The letter from a manager is likely to be a bit pro forma. The recommender should be clear about the relationship (i.e. mentor, not manager).
Comment: Thank you for your answer. One concern that I have is : if I don't get any LOR from my company, how credible will the work experience mentioned in my SOP be from an admission committee's perspective?
Answer: Speaking from UK institution experience, candidates who have "real world" experience in roles relevant to their Masters course tend to be favoured much more than students who are applying directly from undergradute, as it shows that you've put thought and consideration into your choice of course and so are more unlikely to drop out.
I would argue that your mentor, and so someone who likely interacts with you much more often than your manager probably does, would likely count more towards your recommendation anyway, as it is more bespoke. I would advise to go with the current choice of 2x academic and 1x professional, otherwise it may come across as a little peculiar that you have this 3 year work experience but no one to recommend you from that role/institution.
Answer: I review applications to our master's program, and it would seem strange to us if someone with years of work experience did not include a letter from their workplace. I don't think it would matter much to us whether it came from their mentor or their manager. It's useful to us to know that someone can show up for work every day and do what they're supposed to. Presumably your mentor can say that and more.


Does background video affect SEO?

Question:
Does the extra loading time that a background video has, affect SEO? Or that does not really affect it because the HTML already loaded and the video is just streaming after?
Does it make a difference  (in terms of SEO) if the video is embedded using the video tag, or a JavaScript or jQuery?
Answer:
Yes a video background does effect your SEO see
https://support.google.com/adsense/answer/6196932?hl=en and
http://searchengineland.com/mobilegeddon-beginning-not-ending-220512
The slower your site loads the farther Google pushes you down the
SERPs. The biggest concern for Google is mobile devices.
So what should you do instead of adding a video background? Research
Sales Copywriting, customers care about your website solving their
problem more than anything else. It's hard for a video that's a
background to solve any problem unless that customer is looking for
flash.
Maybe, but the main goal of your site should be to create something users love. Your website could look terrible and very plain and outdated however if users find it valuable you'll get backlinks and organic traffic. See http://craigslist.org for a shining example.
Comment: Both links in your answer do not answer the question in any way. They are  talking about mobile friendly sites, they do not even contain the word "video". To say "The slower your site loads the farther Google pushes you down the SERPs. " is kind of misleading also. Of course loading time is a factor, but the most important one?
The interesting part of this question is if there is a difference bewtween a sync and async load. Whats your opinion about this?
Comment: The question is about SEO. Google wants websites to load fast period. Speed is now a ranking factor. Good point on the second question, I'll edit my answer.
Comment: I had a video auto-playing on one of my pages.  It didn't seem to affect the page speed in Google Analytics but in July the page speed in Google Analytics shot up.  Google was making Page Speed updates in July so I suspect it was related.
Answer: Google measures the speed of your page using Googlebot.   If the page load event doesn't happen for 10 seconds, Google may directly penalize your page.
Google pays attention to user experience.   If users turn back to Google too look for something else, Google notices.   If your video is loading so slowly that it makes your site appear to load slower to users, then users will turn back.   In my experience, three seconds appears to be the magic number.   If your page can load in under three seconds, users won't turn back to Google enough to affect your rankings.
So for background video, make sure that your page is useable and that the page load event can happen even before the video loads.  If you do so, an unloaded video shouldn't change the user experience or SEO.
The technology you use for embedding the video doesn't matter unless some of them make it harder to allow the rest of the page to be useable when the video is loading.
Comment: Yeap, that is the general idea. The page already loaded, the video is a stream that loads after and it is an adition to the already loaded design.
Comment: Hi Stephen Can I know How much time Googlebot take to load specific webpage?
Comment: If you have your own question please use the ask question link

Does background video affect SEO?


What's the difference between demixing temperature and cloud point?

Question: I am learning something about polymer solution which has LCST phenomenon. But I met researchers used demixing temperature and cloud point to describe the transformation of this kind of solution from solutable into insolutable state. But for me, they seem the same. So I ask it here to learn what is the difference between these two concepts?
Answer: Cloud point typically refers to the LCST (or UCST) in solution. Demixing temperature usually refers to the LCST (or UCST) of a polymer mixture or copolymer in bulk.


Anonymizing bitcoins?

Question: Is there any way to anonymize bitcoins? It doesn't need to be AML-proof, or even completely anonymize their source, I'd just like to obfuscate the source of the bitcoins more effectively than sending them through a chain of addresses that would be easy to follow.
Answer: Yes. With Zerocoin. It completely and properly and mathematically anonymizes the source, it seems. http://zerocoin.org
Answer: 1) Shared send from blockchain.info is a mixing service which bundles together transactions. Consider to sending addresses, A1 and A2, and two receiving addresses, B1 and B2. A1 wants to send coins to B1 and A2 to B2. To obfuscate both of these transactions, the shared send service sends A1's coins to B2 and A2's to B1 (this is a simplified version of what actually happens but shows the main point).
2) Coins that go onto the Silk Road are "tumbled" - mixed with other coins - so if fund a Silk Road account then withdraw your funds you should have clean coins (although potentially tainted by having come from a Silk Road-associated account if that is a concern).
3) Other mixing and tumbling services are available, though with generally less history and the associated risk that either the service won't anonymise you effectively, or that your coins will just be stolen.
4) Cash sales via Local Bitcoins, or private sales could provide a useful cut-out in any money trail.
5) Generating a new address for all receiving transactions reduces the risk of traffic analysis being used to link your transactions together into a chain.
Edit Possible duplicate of this question - you might want to check for other answers there.

Anonymizing bitcoins?


Incorporating expanded crit-range into anydice?

Question: Not sure if this is a valid "tools" question, but here goes: I want to compare a build that can attack 5 times, with a 5% critical chance; to a build that can attack 3 times, but with a 15% critical chance. How can I do this in anydice? Assume each attack in the first case is 1d6 + 5, and 2d6 + 5 in the second case.
Comment: Sorry, that was my bad. Without the effect of a critical in the question the dnd-5e tag is still required.
Comment: There's no way to really compare the two without assuming to-hit numbers. E.g. if only natural 20 hits the former deals 67% more damage on average, while if 18 and up hit (and nothing else) it only deals 10% more.
Comment: @Hassassin While you're technically right, that's an extreme case--one that doesn't even exist. A Tarrasque, **designed for a Level 30 party,** has an AC of 25... so, **any L20 char** that maxed their main stat and uses a non-magical weapon with proficiency will hit on a 14 or more.
Comment: @Khashir, my point is that the relative damage output depends on the hit chance. Those were just two numbers I could calculate in my head. Real probability graphs look something like [this](http://anydice.com/program/4a88) (based on Miniman's answer).
Comment: @Hassassin: Fair enough, it's an interesting refinement, thank you. It seems like it doesn't affect the answer except when PC's have to roll >14 (which, right now, is a non-issue, per my comment above). But it's still good to keep in mind.
Answer: This was my first try at using anydice.
The results for the first build are here: http://anydice.com/program/4a60
The results for the second build are here: http://anydice.com/program/4a62
The comparison between the two is here: http://anydice.com/program/4a63
I'll include the comparison graph for the sake of having something other than a link in this answer:

(For those who don't want to zoom in, the black line is the first build, and the orange one is the second.)
Comment: The question doesn't take into account the possibility of missing, so neither did I.
Comment: You are assuming anything that isn't critical hit deals normal damage. At least a natural 1 will deal none, probably other low numbers.


Will cardano halving happen to increase the demand of it?

Question: Compared to ETH and BTC, Cardano's total supply is higher. Given this, how will ADA ever reach $1000. Will a Cardano halving happen and lead to increased demand of ADA?
Comment: I'm not sure if ADA will ever hit a thousand (less alone thousands of USD). Maybe at some point there won't be even USD? Cardano has a fixed supply of 45 billion, but it is still deflationary and just doesn't become more and more. The demand - hopefully - will be driven by utility.
Answer: Welcome to the community.
Rewards get reduced by up to 0.3% every epoch (5 days).
I'd suggest calculating your market cap projection. 1000 USD / current price (1.64 USD) would give us a 609.7x market cap (compared to our current market cap)
Cardano's value comes from the utility it provides, and the demand for ADA will increase with the applications built upon it, the identities managed with it, and the services governed by it. It is still, by nature, deflationary.
Answer: No. There will be no reduction of the supply of ADA in the future to increase its value or demand. Total supply is fixed and yes its greater than that of BTC and ETH. All this means is that the individual coins are worth less themselves. You should consider the total market cap.
Consider this, is there is more Satoshies than ADA? You can always use a bigger or smaller unit. You need to look at the market cap as a whole to do a comparison.
Comment: Supply, in the context of the question refers to the rewards given out to people staking and not to the total number of ADA. So, yes, the supply will decrease. As the other answer points out, the supply of ADA set aside for rewards decreases by .3 % per epoch. So Cardano does not have halvings like bitcoin where rewards get cut once every four years but rather there is a constant, gradual decrease in rewards which result in  staking rewards four years from now  being about one half what they are today.
Answer: There is no hidden pool of Ada, and the treasury should be used to back projects and support the growth of the ecosystem. Furthermore, to my knowledge, no new Ada are currently being minted.
Fees paid to stake-pool are charged at the point of transaction. As supply is currently constrained, it seems likely that as adoption increases and the demand for Ada increases, the price of Ada will also increase. As the cost of Ada increases, the value of the fees produced by staking will also become more valuable incentivizing more staking and a further reduction in supply, which should increase the value of Ada further. This will continue until fees are inhibiting the growth of the ecosystem and we have reached the Voltaire Era. Then, we will vote to lower fees, which will temporarily decrease the value of Ada as an appreciating asset but increase the value of Ada as a currency and Cardano as an ecosystem.


On playing the Agricola Bielefeld minor improvement called Bielefeld Playing Cards, does it include animals?

Question: We are playing with the Agricola Bielefeld card deck.  When playing the card called "Bielefeld Playing Cards", it says whenever you use an accumulation space, place all items on this card until you have accumulated 4 like items.  Then you can move the items to your playing board.  We are wondering if that would include animals... specifically cattle, since there aren't enough moves (with other players taking cattle) to ever get 4 cattle accumulated on the card.  Is this calculated into the points of the card since the card comes with 5 points on the card?
Answer: You are right, the chances of getting any cows on your farm are going to be limited.
There is a nice post about the deck that includes a discussion of this card.
You are getting a lot of points in exchange for a lot of extra management of resources, so that is all factored in.  You have to decide if it is worthwhile and it probably depends on what other cards you might have that could assist.


Lithium-ion vs SLA batteries for power inverter (1000W)?

Question: What are disadvantages/Advantages of each.
Is it possible to replace an SLA battery with a Lithium battery pack of equivalent capacity?
Comment: @immibis, yes. Typically if one lithium ion cell goes into thermal runaway, it will likely light up all the cells in the pack in a cascading fire event. Lead acid fires and explosions are less energetic and don't happen as often. But large lead acid banks are definitely hazardous. In either case, you have to take appropriate precautions to make sure that a fire does not result in loss of life or extensive loss of property.
Comment: Lead acid batteries are heavier and larger. Lithium ion batteries are smaller, lighter, more expensive and slightly more hazardous. If the inverter is just an inverter (not an inverter charger) then the battery type does not matter. Only the voltage. DO NOT charge lithium batteries with a charger designed for SLA batteries. For various reasons a lithium ion battery pack of equivalent capacity will actually provide longer run time than a lead acid battery. (Because it is OK to discharge a lithium battery to, say 20%, but lead acid should only be cycled to 50%).
Comment: @mkeith "Slightly" more hazardous?
Answer: Lead acid batteries are heavier and larger. Lithium ion batteries are smaller, lighter, more expensive and slightly more hazardous. If the inverter is just an inverter (not an inverter-charger) then the battery type probably does not matter. The only thing to watch out for is whether the inverter has a low-voltage cutoff point. If the low-voltage cutoff point is not suitable for your battery, that could be a problem. Typical 12V inverters are designed to shut off when the battery voltage drops to 10V. That would be OK for 3 lithium ion batteries in series (11.1V battery), but not for 4 lithium ion batteries in series (14.8V battery) unless the batteries have their own low-voltage cutoff.
DO NOT ever charge lithium batteries with a charger designed for SLA batteries. Some inverters have programmable low-voltage cutoff. Some inverter-chargers are so programmable that you can set them up to work OK with Lithium Ion batteries, but you have to know what you are doing. The two most important things are setting the CV voltage to be correct, and disabling the float stage of charging (don't float lithium ion batteries).
If you have a lithium ion battery pack that is rated for 100 Ah, and a lead acid battery with the same rating, the lithium ion battery pack will actually have quite a bit more useful capacity. Lead battery capacity is normally based on discharging to 10V at C/20. If you discharge faster, the capacity will be less. And if you discharge all the way to 10V, your battery capacity will fall very rapidly, and you will be lucky to even get 100 charge/discharge cycles from it without noticeable capacity loss. So in practice, most people plan to discharge their lead batteries only to 50%. So really, when comparing lead acid to lithium ion batteries, you should cut the capacity of the lead acid battery in half. You can subract 10% or 20% from the Lithium ion battery, because you may not want to cycle it to 100% either (but 80% or 90% is very reasonable).
So our 100 Ah lead acid battery is really only good for 50 Ah. And our 100 Ah Lithium ion battery is good for 80 or 90 Ah.
Hope that helps.
Answer: with good Panasonic high discharge nca cells, you can get 1000w of capacity for roughly 10 pounds of cells. one good example is 24 cells parallel for 81.6ah and 4 serial for 14.4 nominal. this pack would be about 11 pounds and 96 18650 cells. i have an lfp battery i use with a 1000w inverter its 84ah at 12.8v nominal and only weighs 30 pounds with inverter attached.


What does ardupilot do and how does it do it?

Question: I have been using ardupilot on drones for a while and I don't exactly know what it does. I know it keeps a drone leveled, lets us set way points and automatically fly through them, etc. Is that it? If so why is the pixhawk so expensive? don't you just need a cheap imu and gps with a $5 pi zero. I might be mixing up pixhawk's hardware and ardupilot. But yeah what do they do individually? and how do they do it? It it just hard coded to add more thrust to a few motors if its tilted, just use gps to go to a location, etc or is there more to it.
Answer: Quick answer:
Hardware wise the Ardupilot is based on the "Arduino", I can't remember what chip it actually uses, but it's Arduino  compatible.
Pixhawk uses a 32-bit chip, this chip is faster than the Ardu's chip.


Streaming video from Rpi3 through raspicam remote

Question: Help needed with Raspicam Remote.
I just set my Rpi3 up as a WiFi hot spot to stream to may Samsung tablet.  Tablet connects fine to Rpi3.
I loaded Raspicam report to my tablet and then updated the Rpi3 with VLC per the instructions.
I cannot get my connection to work.     I'm using the ae of Pi3-AP and the password of raspberry which is what I have setup.   The port is defaulting to 22.
I'm getting an error that it cannot Connor to 184.108.40.206 which is the IP for my Rpi3.
Does anyone have any suggestions or can help.
Answer: I found the solution.  SSH needed to be enabled.   I turned it on on my tablet via an app from Google play then enabled on my RPI3.


Use Lightroom catalog on windows and mac

Question: I have my photos saved on an external hard drive formatted in exFat (so I can read and write from mac and windows). I have my catalog also saved on this drive. Every time I open the catalog from windows the files are missing. I understand that mac and windows have different file systems but is there a way to get around that? I want to use my catalog on both systems without having to relocate my pictures every time.
Answer: You can create smart preview for the photos. And work on both platform with those previews. When it come time to export them you should do it from the platform you import the photos. Or update the library for particular OS.
Answer: Mac and PC use different file path naming schemes, so paths stored into the catalog from the Mac will be meaningless on the PC.
A possible workaround could be (untested) to use UNC (aka. network) paths. If you create a share on the photo location (eg. D:\photos) you can access them via \\localhost\photoshare. This should work the same on both systems.
You might need to activate the loopback adapter.


Can I hook up two monitors

Question: I have a wacom interactive tablet for my editing.  I hook it up to my laptop to use Photoshop.  My question is can I hook up another monitor?  I want to hook up a larger monitor.
Answer: If you mean can you attached an additional monitor to your laptop then yes, you can. Obviously it depends on the age of the laptop and what connector you have. For example I have a Dell Inspiron 1520 and I can use the normal blue VGA connector you find on the end of most monitors. I plug it in, press a combination of keys and the display can be shown in a variety of configurations - one desktop on each screen, stretch the display across both etc.
Some modern day laptops have an HDMI connector instead of the VGA connector so you'll have to take a look and see what you have and buy the monitor that will work for you.

Can I hook up two monitors


Add new outlet in pantry to one of the two existing 20 amp small appliance branch circuits

Question: I am doing some remodeling in my kitchen. I currently have the required two 20-amp small appliance branch circuits powering the kitchen counter outlets. I have a small pantry/closet directly off the kitchen area and I would like to add an outlet or two in there. Can I hang those additional outlets off one of the two existing small appliance branch circuits?
Comment: Yeah I was wondering about that because it just says no other outlets but I don't know if that means that a pantry is considered part of the kitchen or not because another area says "These circuits may also supply receptacle outlets in the pantry, dining room,
and breakfast room, as well as an electric clock receptacle and electric loads associated with gas-fired
appliances, but these circuits are to have no other outlets."
Answer:
National Electrical Code 2014
Chapter 2 Wiring and Protection
Article 210 Branch Circuits
III. Required Outlets
210.52 Dwelling Unit Receptacle Outlets.
(B) Small Appliances.
(1) Receptacle Outlets Served. In the kitchen, pantry, breakfast room, dining room, or similar area of a dwelling unit, the two or more 20-ampere small-appliance branch circuits required by 210.11(C)(1) shall serve all wall and floor receptacle outlets covered by 210.52(A), all countertop outlets covered by 210.52(C), and receptacle outlets for refrigeration equipment.
(2) No Other Outlets. The two or more small-appliance branch circuits specified in 210.52(B)(1) shall have no other outlets.
(3) Kitchen Receptacle Requirements. Receptacles installed in a kitchen to serve countertop surfaces shall be supplied by not fewer than two small-appliance branch circuits, either or both of which shall also be permitted to supply receptacle outlets in the same kitchen and in other rooms specified in 210.52(B)(1). Additional small-appliance branch circuits shall be permitted to supply receptacle outlets in the kitchen and other rooms specified in 210.52(B)(1). No small-appliance branch circuit shall serve more than one kitchen.

So if this is really a "pantry", and is considered a pantry by the AHJ (Authority Having Jurisdiction). Then yes, you can supply the receptacles in the pantry with the one or more small appliance circuits.
NOTE: There is no official definition for "pantry" in the NEC.


How can I create an effect of pictures like an album

Question: I am using Vegas Pro 10 and I can't find a (good) way to make pictures flying through the screen.
Well, it's a little bit difficult to describe but what I am thinking of is a screen, where you can see small pictures coming from the background and growing to the middle of the screen, these pictures come in sequence und after it reaches a certain size it fades away. (A little bit like a Picture Gallery). So there is also a little bit of an 3D-Effect included.
Maybe the best comparable situation is when you click [WIN] + [Tab] and then you go through the windows.
Sorry for the bad eyplanation, I hope anybody gets what I am talking about ;)
Answer: Vegas Pro 10 has two features that could help you out. Either using the Track Motion feature for the entire video track engaged with key frames, or the pan/crop feature for the shot itself engaged with key frames would allow for changes of size, shape, rotation, zooming, orientation (reverse, upside down) and such.
Here is a tutorial on Vegas (not sure of version but this will work in Pro 10) on
how to use the Track Motion feature:

Here is a tutorial on Vegas Pro 10 on how to use the Pan/Crop feature:

If you are using more than one clip or several still images, you should use the Track Motion with key frames as the Pan/Crop feature works only with the shot itself.
Hope this helps.
Answer: Not sure if this was possible in Vegas 10 already, but in Vegas Pro 13 there is a transition called "3D Fly In/Out" which you could use to achive that effect. It probably much simpler than having to deal with pan/crop. As any transition it also offers the option to store your settings and re-apply them to other events.
3D Fly In/Out let's you determine

the start position of your event in three coordinates (x, y and z, where z is the distance from the screen)
the number of rotations in three dimensions
an additional lighting effect

You can apply the effect to the event by

adding a normal fade transition to the event
right-clicking in the fade transition
selecting Transition-->Insert Other
The PlugIn-Chooser-Transition Window opens. Select "Sony 3D Fly In/Out"


How can I make totally sure that I don't have a keylogger/trojan/something uploading my personal files to the web?

Question: I got this Antivirus Soft installed. It was awfully annoying and my antiviruses (yes, I have more than one) just didn't do anything. So, now I am afraid they might be compromised or something. I am really worried about keyloggers or virus that upload any information/personal files to the web. Is there a way to relieve myself without having to format?
Comment: to make totally sure, disconnect any network cables from your computer and disable or remove any wireless cards.  to make absolutely, totally sure, turn your computer off.
Comment: a slightly paranoid solution is disconnect all cables and put it in some kind of  Faraday cage to screen the EM spectrum.
Answer: For a start, multiple anti virus engines is a VERY bad idea.
Next, you really can never be 100% sure your machine is malware free, the best you can do is simply to install legitimate software, install all updates and then a good antivirus (such as Microsoft Security Essentials on Windows).
lastly, don't download pirate or software that you don't trust - I cannot say this enough. Anything can be infected.
Now, just be careful when browsing the internet.
For good general virus help/information, take a look here.
Comment: +1 for multiple anti virus engines is a **VERY** bad idea
Comment: But *why* is it a bad idea, or even a *very* bad idea?
Comment: @Arjan van Bentem - Simple, multiple AV engines do not understand that there are other AV engines on the machine, if you have two "active" scanners, you can get in to endless loops of scanning files or other unforseen problems.
Answer: As @Wil commented, multiple AV engines running at the same time is counter-productive.
To verify nothing gets transmitted from your machine, use a sniffer (like Wireshark etc.) or download TcpView from SysInternals. It'll show you which applications are in contact with the outside world. If you stop all you regular browsing/streaming/download activity - the apps that are left are worth inspection (mind you, they might be innocent OS components, so don't just go hacking randomly :))


What is the song that plays when Clovis indirectly orders the Purebloods (Jermiah, Nu) to board their Knighmares in Episode 1?

Question: In ep 1, starting from  6:10 minute mark, when Clovis says "its all in the performance", a song that seem to be a duo of piano and violin plays and continues until beyond 7 minute mark while the Jeremiahs group board their Knightmares. I couldnt fidn it anywhere on youtube for some reason.
Answer: Edit/update: I found the song what is identical to the one I was looking for. It's titled Out of the Ordinary. The one below is somewhat similar to this track, though.
I found one that appears to be similar to the one I was looking for,  it's called Cold Nobility, I suppose it might even be supposed to be  the same song, despite some differences.


What's this noise? Is it from my crank?

Question: I have recently been riding bmx, racing to be more specific. I ride around my neighborhood a lot when im not at the track and have noticed this loud clanking noise. I didn't know where it was coming from at first. Thought it was maybe the pedal. But then I started paying more attention to it. It happens on my right foot when I pedal. This happens about every 10-15 minutes and sometimes I don't get it for an hour or two. When I was at the track I was standing up at the gate with my right foot forward. Then it happened. I was simply standing there and it made the loud clank noise, but then I found out where the problem is.(sort of). When it happened my right foot went down one crank. My foot went foward with out the tire or bike moving. What's the problem? Will it cause future damage? My guess is that the crank is slipping and not engaging. I have a 3 piece cliq crank. I'll try to discribe the sound a little better. It sounds like your hitting the bottom bracket with a rock or tapping it with your finger.
Comment: The symptoms you describe in the start gate suggest to me that your freewheel may need replacing. BMX racing is pretty tough on single speed freewheels.
Comment: It's a little hard to tell from your description, but it sounds like something to do with the chain -- slipping a tooth, a "frozen" link flattening out or some such.  But with the 3-piece crank it could be a crank arm loose on the shaft (which is a more serious problem).  To check for that, grab the crank arm and try to move it in and out.  Any motion at all relative to the shaft is not good.
Comment: Thanks for the reply, I checked the crank arms and they don't move so that's good. Now I just need to pay close attention to the chain. That might be the problem. I'm not sure if it would make that noise though. I don't have another chain to test it either. The only other chain I have is filled with grease from a 1970 mongoose :)
Comment: Well, I've heard of using goose grease in a pinch, but never mongoose grease.  (Thoroughly clean and oil the chain, and see if that helps.)
Comment: I meant mongoose, as in a 1974 mongoose m1 bike. It's a classic bmx bike :) Never heard of mongoose grease.
Answer: I've had similar problems (clicking on the right side down stroke) before, and it is probably the bottom bracket.  But the first thing to do is to check and make sure that you don't have a loose bolt/ nut somewhere.  This could be in your pedal, the crank, or somewhere else in your drivetrain.  If you make sure that everything is tight and it still doesn't go away it's time to try replacing your bottom bracket.  It's a pretty easy fix, but does require a special tool.  http://sheldonbrown.com/tooltips/cartridge.html
Comment: Thanks, I haven't been able to try anything yet because it's been poring rain all day. But i will make sure everything's tight, I've done everything but look at the chain. I won't know until I get to ride again.

What's this noise? Is it from my crank?


Multi-Stage digital FIR filter vs Single stage FIR filter. Which is better?

Question: Can anyone provide an insight to select a filter structure out of multi-stage and single stage FIR filter?(it will be great help if references are also provided) Let's say I have to make 50 tap filter. So, is it better to design it using two cascaded filters each with 25 tap then 50 tap single filter only or both are same ? Thank you.
Answer: First, two cascaded 24th-order (25-tap) filter will yield a 48th-order filter which is not identical to a 49th-order (50 tap). However, as I assume that this isn't really the answer you are looking for, but rather the difference between multi-stage and single stage.
Assuming infinite precision arithmetic they are the same. In practice, multi-stage filters have lower coefficient sensitivity, so using two (or more) filters would (statistically) allow shorter coefficients word lengths. However, multi-stage filters also require intermediate quantization, so for a complete comparison one should also consider that. And, as obvious from the first paragraph, multi-stage require more multiplications for a given filter order. I would say that unless you run into problems with coefficient quantization you should go with a single stage.
Another use case where multi-stage is relevant is when implementing interpolation and decimation. By using more than one stage some of the filtering can be performed at a lower sample rate and the total arithmetic complexity is reduced.
Comment: For multi-stage you will have to quantize (round) the result from the first filter as well as from the second filter, while for a single stage there is only one quantization. Hence, one can expect slightly higher round-off noise for the multi-stage (typically not "double" since the first noise source is filtered through the second filter). However, you could expect a better frequency response for the multi-stage filter if you simply round the coefficients (although this is only in a statistical sense so if you are unlucky it will be worse).
Comment: hi thanks for replying soon. please give more insight on the following lines from your answer which I did not get, "multi-stage filters have lower coefficient sensitivity, so using two (or more) filters would (statistically) allow shorter coefficients word lengths. However, multi-stage filters also require intermediate quantization."
Comment: @user2624915: How do you plan to implement the filter? The insights would depend on that (and may be more or less relevant depending on the implementation technique).
Comment: On FPGA, I have 8 bit registers for each coeff. output and input values are also 8 bit. I am using fixed point arithmetic for rounding and all.
Now I want to compare the performance of filter each multi-stage and single stage filter.


Can I go back to CiviCRM 4.5.8?

Question: We've recently installed CiviCRM 4.6.6 and we're on WordPress 4.3. I've got a major problem with CiviMail (see HERE. No one has responded in six days. Is there backwards compatibility? Would it be safe to install 4.5.8?? At this point, we're just using the Contact table. I'd rather not import all the data again, since I could only do 600 records at a time (the command line doesn't support groups or dup checking). I've got to get this fixed...someone please help me!! thanks...jim
Answer: I recommend you engage a professional to help you resolve the issue you experienced with 4.6.x, because then you'll have the bug fixed AND the security fixes which 4.5.x lacks.
Comment: We don't have the time or money to hire a php programmer to find this bug in CiviCRM/CiviMail. And we can't restore the old version (4.4) very easily, because we changed domain names and hosting services. It would be very helpful to know if this is a known bug in 4.6.6?? Has it been fixed in 4.6.8??
Answer: The recommended method for downgrading is to restore to the backups you made before upgrading.
For contact data modified between when you upgraded and now, you'd need to either export your changes and import them to the 4.5.x system, or keep the upgraded system running and copy the data over.
I would not expect downgrading the DB directly to work, and I would expect manually reversing the DB changes between versions to be more complex than fixing your mail issue.
Comment: Thanks very much for your reply. This is useful. Has this problem been fixed in 4.6.8?
Comment: If it has, it ought to be documented over on https://issues.civicrm.org somewhere. I couldn't see any obvious candidates there though ... You might have some luck by getting in touch with the author of [this related question](http://civicrm.stackexchange.com/questions/3581/civimail-mailing-unable-to-select-group-getting-error-of-no-recipients) and pooling resources to get the issue fixed?

Can I go back to CiviCRM 4.5.8?


Why is fiscal deficit always shown as a percentage of GDP?

Question: If the probable reason is because it must reflect the government's ability to pay back the deficit, wouldn't government income be a better indicator, rather than GDP?
Answer: In short: yes, it very well might be and this has been argued by some (see, for example: http://www.forbes.com/sites/jeffreydorfman/2014/07/12/forget-debt-as-a-percent-of-gdp-its-really-much-worse/#29b8530f6e0c).
The use of Debt/GDP is the current international norm, but Debt/Tax revenue might very well be a better, more concise option. Using Debt/GDP might be because it has been common to compare countries to each other with GDP or GDP/capita and having GDP as a factor relates the debt to these measures.
It can also be argued that in the end the whole population of a country is responsible for paying their country's debts, so in an extreme situation it's not just the government's income which might be used to pay off debts.


Bitlocker in Windows 7: how to change from USB key to PIN?

Question: I've just encrypted my drives using Bitlocker but since I don't have TPM, I went with USB key. Is it possible to switch that method to PIN or is it too late now and I have to re-encrypt the drives?
Answer: Well, apparently it's not possible.
Only four options are available:
TPM only
TPM and PIN
TPM and Startup Key
USB only
Therefore, USB it is for me ;)
Answer: If you later decide to add a TPM to your computer, you can initialise it by running tpm.msc and choosing "Initialize TPM" and "Turn TPM On...". This will prompt you to create an owner password for the TPM.
You can then configure Bitlocker to use the TPM at startup by running cmd.exe as Administrator and typing:
<code>manage-bde.exe -protectors -add TPMandPIN c:
</code>
This will prompt you to create a numerical PIN. On restart you will have to enter the PIN, then enter the recovery key. Once Windows is started you will need to suspend then resume Bitlocker to tell it the changes are valid. On future restarts you will only need to enter the PIN.
I could not find a way to tell Bitlocker to start using the TPM instead of the USB key using the GUI. It seems straightforward using manage-bde.exe. I used documentation from Microsoft Technet to figure it out. There does not seem to be a setting to tell Bitlocker which protector to use. I assume it tries all of them and once the USB key is removed it only finds the TPM one and uses that.
Answer: It is possible to change the protectors, but if you don't have TPM then only USB is available to you.
I have TPM and use TPM + PIN + USB as the protector.
The most important thing is for you to store your recovery key somewhere safe as without that you will NOT be able to access your data if you lose your key.
Comment: I have recently installed a TPM. How is it possible to change the protectors?


Why 1000 and 500 Indian rupee are not accepted in Nepal and Bhutan?

Question: Why all Indian rupee notes are accepted in Nepal and Bhutan, except 500 Rs and 1000 Rs? Why spare those two notes?
Comment: Maybe too many counterfiet notes in circulation?
Comment: Anyone coming here by random search: the 500 and 1000 rupee notes have been demonetized in India, so the question of using them in Nepal and Bhutan is moot. There is a new 500 rupee note. The 1000 is replaced by a 2000. Perhaps someone else can fill in the permanent rules for Nepal and Bhutan, once the new notes are in wide circulation.
Comment: Are you asking me?
Comment: Am in doubt, so I don't know the answer
Comment: Source for your claim that they're not accepted? Personal experience? Online information?
Comment: I read it in a travel mag
Comment: He's not wrong, that used to be the law, but it's now been lifted. See below.
Answer: India had tried to curb unauthorized trading between these countries by requesting they ban them.
However, as of 2013, Nepal and India have agreed to allow 500, 1000 notes again.
The Bhutan Monetary Authority also banned it for similar reasons.
However, as of January 2015, the RBI has also allowed travelers to take these notes to Bhutan.
So yes, that used to be the law, and it was to curb unauthorised trading, but that ban has now been lifted officially.
Comment: Oh, so it's been recent. Thanks, I didn't knew the change.
Answer: As Mark Mayo's answer states, these two denominations were "banned" (either officially or unofficially) in the two countries due to issues with counterfeit notes. Other denominations were not banned since most fraud on high value items / purchases would involve these two denominations.
While a lot of travel websites and guides state these are still banned, this is old advice. In practice, trading in these two denominations never really stopped. As of 2015, even government shops and agencies in Bhutan accept Rs 500 and 1000, for instance.
Having said that, there are very strict controls on export and import of Indian currency by non-Indian nationals (excluding those of a neighbouring SAARC countries). So you may find, depending on your nationality, that the point on whether those denominations are accepted is moot because you're not allowed to take Indian rupees anyway.
Comment: *"very strict controls"* -- in theory, yes, but in practice, these are not enforced (= you're not going to have Customs going through your wallet).  Standard disclaimers apply, and if you do get caught, you run the risk of losing the currency.
Comment: Related: [Is it really forbidden to cross the Indian border with Indian rupees?](http://travel.stackexchange.com/q/2720/108)
Comment: @jpatokal True. The "strict controls" are only on paper.
Answer: Both the governments(Nepal and India) have agreed to permit the use of INR500 and INR1000 notes. So it is totally legal to carry INR500, INR1000 notes to Nepal if you are going to Nepal.
Comment: Nice. But... can you perhaps include a source for your claim that both governments explicitly agreed to permit the use of these notes?


Is a father empowered to truly give ownership of something to his young child?

Question: I know that a child's things really belong to his father (although help with a source would be appreciated). However, the same is generally true of a wife's property/income belonging to her husband, yet, under certain circumstances, a wife can retain her property, and in other cases a husband can give property to his wife (more source help required!). My question is, can a father give something to his young child, or is ownership utterly meaningless until a certain age (and, if the latter, is that age majority, or sometime slightly before majority)?
Comment: Related: http://judaism.stackexchange.com/questions/17805/does-a-child-own-what-hes-implicitly-given-by-his-parents
Answer: It is certainly possible to transfer ownership of an object to a child. One place this is made clear is in the Gemara (Sukkah 46b) which says that one should not transfer possession of his lulav to a child on the first day of Sukkos. The reasoning is that the child is not of legal age to transfer it back, and therefore the adult will not be able to perform his own obligation, as the first day's obligation requires a lulav one owns. This represents normative Halacha as codified in Shulchan Aruch OC 658:6.
As for the age of the child - I cannot source this offhand but I believe it is possible to transfer ownership of an item to any just born child, through zechiya. This is the legal concept which says that anything which is a beneficial to a person can be done without the person's knowledge, since there is an assumed will of the person. Since the only real potential issue with a minor acquiring something is lack of the requisite awareness, one can effectively establish oneself as the minor's agent and make the acquisition on the minor's behalf even without the minor's saying so, using the mechanism of zechiya.
Furthermore, the aforementioned case about the lulav itself is clearly talking about a child who is even younger than the age of six - the age when a child presumably understands the basics of business dealings (see Shulchan Aruch CM 235:1), because for ages six and up the SA cites a view that maintains that the whole thing isn't relevant since such a child might legally be able to return the lulav. Clearly then, the blanket statement, "one should not transfer ownership of his lulav to a child," refers even to children under the age of six.
Comment: Do we Pasken this way? And what age?
Comment: @SethJ Yes - Shulchan Aruch OC 658:6. It is even talking about a child who under six years old, because above that age the SA cites a view that holds it is okay, as in Choshen Mishpat we rule that such a child can transfer ownership. Moreover, I cannot cite this offhand but I believe it is possible to transfer ownership of an item to a just born child, through zechiya (where someone acquires something on behalf of someone else), since when it is a benefit, one can do so for someone without the other's knowledge, as there is an assumed will.
Comment: @DovF, could you add that information to your answer?
Comment: @MonicaCellio Sure


Shir Hama'alos in "Barech"?

Question: Among the many hagada versions in use at the seder I attended this year, some of them included Shir Hama'alos before birkas hamazon in the "Barech" section and others did not. Is there any reason to deviate from the usual practice of saying it on holidays on the night of the seder?
Comment: I'll do you one better: one of my Haggadot (a reprint of a 1784 Haggadah) started Barech at "Nevarech SheAchalnu MiSheLo".
Comment: The practice of recite שיר המעלות בשוב may be tied to a fear that Torah might not be learned during the meal. As we have learned the Maggid prior to eating and (presumably) continued to discuss it over the שלחן עורך, the recitation of the מזמור shouldn't be necessary
Comment: @NoachMiFrankfurt interesting, sounds like answerable material...
Comment: @רבותמחשבות, I don't have reasonable mekorot on hand, or I would've answered as such
Comment: @DoubleAA I have never seen that, but it fits interestingly in since there is a discussion about how of all meals, this one's _b'racha acharona_ needs the least invitation/introduction.
Answer: This Hebrew article on Shir Hamaalos gives me some thoughts on this that may answer the question:
Firstly, while this is a very widespread Minhag nowadays, it isn't all that old. Perhaps some of the Haggados that you were using were based on versions that were written prior to this custom being accepted in many communities. This would mean that there is no reason not to say it.
Secondly, the article seems to understand that the purpose of Shir Hamaalos is to remind us of the destruction of the Beis Hamikdash, but in a more positive, redemption-focused attitude:

...אמירת 'שיר המעלות' נועדה להזכיר לסועדים את החורבן גם אם אמנם מתוך תחושת גאולה אופטימית...

If so, on a night where we celebrate such Ge'ulah, it may be less appropriate to say it...
Comment: Good point about the provenance. The earliest (of 2) source the article mentions is the _Sh'nei Luchos Hab'ris_, so any publication printed or descended from something printed before 1630(?) or outside the (often mystical) influence thereof - not just _hagados_ - would be expected to not have _Shir Hama'alos_.

Shir Hama'alos in "Barech"?


1 out of n oblivious transfer

Question: So I read some stuff about oblivious transfer and came a ross that 1 out of 2 OT can be used as a black box to build 1 out of n OT. At first it seemed trivial just feeding in 4 messages and 2 chooser bits but then I realized it's not that trivial since it doesn't guarantee security.
How is 1 out of 2 OT used to build 1 out of 4 OT if we can use 1 out of 2 OT as a black box?
Comment: see this paper: a nice trick for 1-oo-n OT https://eprint.iacr.org/2016/799.pdf
Answer: The sender chooses log n pairs of secret keys (say, for encryption). Then, each number between 1 and n is naturally associated with a subset of exactly log n keys. The protocol then works by running log n 1-out-of-2 OTs where the receiver asks for the keys that are associated with its input (number between 1 and n). Finally, the sender encrypts each of the n messages with the subset of keys associated with the number (using encryption so that without all keys nothing is learned).
It is not difficult to formally prove the security of this using simulation (as long as the OT is secure for malicious adversaries, this is also secure for malicious adversaries).
This solution goes back to a paper by Benny Pinkas [1].
[1] Moni Naor and Benny Pinkas. 1999. Oblivious transfer and polynomial evaluation. In Proceedings of the thirty-first annual ACM symposium on Theory of Computing (STOC '99). Association for Computing Machinery, New York, NY, USA, 245–254. DOI:https://doi.org/10.1145/301250.301312
Comment: Yes; the solution I gave is only computational. I don't know if there is an information-theoretic solution that is better than the naive you mentioned in the comment.
Comment: However, if L is the minimum length over the n messages, then it's significantly harder when the 1-out-of-2 OTs must be for strings of less than L$\cdot$n/2 bits.  (I don't know of any nice way of handling that restriction.)
Comment: @RickyDemer Sorry; I didn't understand what problem you are referring to. The 1-out-of-2 OTs I am referring to are for strings of length $n$ where $n$ is the security parameter (for transferring keys). If you are asking what can be done with lower communication complexity, then I agree; this is an interesting problem.
Comment: I was referring to preserving whatever information-theoretic security the original OTs have, when the 1-out-of-2 OTs can only be used to transfer not-too-long strings.  (In fact, my previous comment also applies to just preserving information-theoretic privacy for the sender, with the same limitation on the 1-out-of-2 OTs.)

1 out of n oblivious transfer


What's the difference between "Reaching For The Goal" and "Reaching To The Goal"?

Question: I'm asked to make a title for an article that's basically boiled down into either "Reaching For The Goal" or "Reaching To The Goal". I don't know what's the difference of them. I tried to google it, and "Reaching For The Goal" gets 5 million hits while "Reaching To The Goal" only gets 50 hits. So I guess "Reaching For The Goal" is more commonly used? But I still feel these two phrase interchangeably and both sounds right to me. Which one I should actually use?
Answer: You should definitely use "reach for the goal," as that's what native English speakers use. "For" here is used to indicate an intended goal, a function that "to" doesn't completely share in this context. "Reach to the goal" might work if the reaching isn't metaphorical -- that is, if there's actually a physical goal (like in sports) that the person is literally reaching towards -- but even in that case, "towards" would be more natural than "to," and "for" would still be appropriate. "For" is simply the preposition that native English speakers use with "reach" in the vast majority of cases.
Comment: Ah, "towards" is an interesting alternative in this case. But I think I'll still stick to "for" then. Thanks!!


Big hole in front of mailbox from mail truck how can I fill it?

Question: So we bought our home last July, we never noticed that right in front of the mailbox which is an area with a big patch of dirt and grass is where the mail truck swoops in and delivers the mail, we have tried to refill the hole from the tires with dirt, then with rocks, but each time the tires dig in so much that it's worse now, especially when it rains, two huge puddles.  It's now two holes from the tire going in and then out. We are happy and appreciative that we get our mail in a timely fashion but how can we best get that hole to be a flat surface? maybe more dirt? like a hill? help!
Answer: Not dirt, ideally. But you can use dirt if you can't get better material.
Better material would be crushed rock, ideally the sort that has all the fine dust from crushing still in it. Rock without fines can also work, but is less ideal.
Biggest problem with "filling a hole" most people have is the fact that you will lose (as you have seen) if you just put stuff in the hole you have. It will be saturated by any standing water, and it will be looser than the hole, and will get shoved back out of the hole easily with traffic.
So, let's look at what you could do differently for the poorest but most available fill - the dirt you have right there. You want to dig out the area of the hole you have to (at least) the full depth of the deepest part of the hole over the whole area of the hole, and somewhat beyond. Then you fill the hole with dirt - but not all at once. Put in an inch or two of dirt, and compact it throughly - don't use a large tamper (ie the common 10x10 square you probably don't own and would be wasting money to buy) - use something like a sledgehammer held head-down, handle vertical, and lifted and dropped over the whole area until it's all compacted. A 2x4 stud (inexpensive) is also effective used the same way (lift and drop on the end.) Then add another inch or two and repeat. In theory a high-heel dance party in high heels you don't mind getting dirty could also work, but it's not one I've tried. Physics says it should work, though.
If you "upgrade" to crushed rock or gravel, you'll want to add a layer of (ideally, but difficult to get in small quantities) geotextile to keep the dirt below from "eating" your rock fill. Probably the closest thing to geotextile commonly available in small amounts is weed-block fabric or filter fabric. The idea is that water should drain through but your rock is not pushed down into the dirt below. Otherwise the tamping is similar.
In both cases you do want to build up slightly, because tamping is good, but not perfect, and also because removing standing water greatly reduces the progression of holes from wheels, while allowing even a small puddle to develop quickly grows as water and dirt splash out. Running your own car smoothly back and forth over the patch (without stopping as the mail-truck does) will also help to compact it. If you do see it starting to puddle, fill it back in sooner rather than waiting for it to get worse (it won't get better by itself.)
Comment: I would like to try this first rather than try to move the mailbox. That mailbox is in there good and we are both not that great with these types of projects, I think we will try the first suggestion, It's either this works or we get a P.O. box. I'll get my high heels out just in case the sledgehammer trick fails.
Comment: This is the correct way to repair the pothole on a dirt road, which is effectively what you have, even if the vehicle is traveling much slower. Two things cause a pot hole, softer ground and a hammering affect by tires hitting it that increases once the hole starts to form. Pot hole fixes don't last because they are filled in with soil that won't compact well enough and often they do not even compact the soil that was put into the hole. So use a good fill, like 'pit run' and compact it well.
Comment: #2 or #3 crusher rock, use smaller stone on the bottom (compact). Do not use pea-gravel. Before finishing, sprinkle cement in the hole as you fill it up.
Answer: There are only a few solutions here.

Pave the area with asphalt or concrete. Gravel or other rabble will only work short-term.
Move your mailbox closer to the road and reseed or replant the area.

Option #2 is the way I would go.
Edit
Apparently there is a need to clarify option #2 with more detail.
The USPS has guidelines concerning height as well as setback from the road on mailboxes. Before moving the mailbox you should contact USPS to make sure you are in compliance.
Based on your description, "area with a big patch of dirt and grass" and your request for how to repair I assume the problem area is on your property. My suggestion is to move the mailbox closer to the road so that the mail truck can safely use the shoulder of the city/county/state road in compliance with USPS and local traffic regulations.
The other option is the suggestion from Ecnerwal to run a horizontal extension to move the box closer to the shoulder. You'll still need to make sure you are in compliance with USPS regs.
Comment: Depending on a number of factors that vary with locale, closer to the road may be a problem (due to snowplows, for instance.) If you want to move the box while leaving the post where it is, all that takes is a pole of some sort (my post is 10 feet back from the edge, with a 15 foot pole on it - 9 feet towards the road, 6 feet back to where it ties into the ground for support.) Proper mailbox height SHOULD permit a snowplow wing to slide under the box, and this way the post is way too far back for them to hit that. Paving makes no sense here, as the road isn't paved.
Comment: I knew someone was going to say that. :), we are so clueless, ok, so I will likely be on here again asking how to move the mailbox in a few weeks. Its in there pretty good with a wooden post.
Comment: You just dig it out. It takes some work - know any teenagers? If you pave you're going to have to lay in a good base to pave over - see Ecnerwal answer.
Comment: You need to check the local regulations and with your USPS before you move the box. If it's acceptable, then it's a good idea.
Comment: True. There are always setback and height requirements but not usually a problem.
Comment: Moving the mailbox would still have the same issue, creating new holes at the new location.  Moving the mailbox closer to the road could create a unsafe condition and might not be allowed.  It is away from the road to allow the mail vehicle to pull off the road to deliver the mail and not create a traffic hazard.


Do Mexico border towns near the U.S. accept USD as currency?

Question: Do merchants in the US border towns of Mexico accept USD as currency?
If not, where are the currency exchange facilities available while driving in to Mexico from the US? Another related question: Is one currency preferred over the other?
Comment: Isn't this default in all border towns worldwide? Except maybe for those currencies with hyperinflation.
Comment: @Andra: Default or not, it's a valid question, I think... many first-time international travelers wouldn't have any way of knowing this.
Comment: @flimzy that I why I added it as comment ;) I actually don't know if this is true, but I would expect so. I agree that it is a valid question.
Answer: Many do, but at a very poor exchange rate.  At the time of this post, there are 13.15 mexican pesos per US dollar.  But you'll usually get an exchange rate in the range of 10:1-11.5:1.  I saw several exchange rates in this range in Puerto Vallarta (which isn't a border town, but does cater to many US tourists) last weekend.
The best exchange rate will probably be from your local bank, but will likely require that you order your pesos at least a week or two in advance of your trip.
The next best bet is probably from an ATM, especially if your home bank doesn't charge a currency conversion fee. Most credit unions won't, and many larger banks will have deals with a local Mexican bank to avoid such fees.  Bank of America allows free cash withdraws from Santander ATMs, for instance.
You can also change your cash from U.S. to Mexican currency (or vice versa) at many locations on either side of the border, and are called "Casa de Cambio" (translation: Change House).  The exchange rates vary, and aren't as good as you'll get from a bank, but are better than you'll get from a vendor accepting U.S. dollars.
Comment: I don't know if the US has anything like this, but I was able to get Mexican pesos from my bank's ATM at Toronto's Pearson airport. The rate was virtually identical to making a withdrawal from an ATM in Mexico (I checked) and I avoided the charge for using a foreign ATM.


diffrent style for post single page

Question: We need to style a single page differently depending on what user journey you take. Currently we have event posts listed in WP, they are either under the "get involved > events" page or "urban innovation center > attend an event" some events are listed in both. If you come from "get involved > events" we need the single event page to have a light background and if you come from "urban innovation center > attend an event" we need the single event page to have a dark background. We dont want to have to duplicate the events in WP.
https://futurecities.catapult.org.uk/events/
Comment: @jdm2112 not really sure where to start with this?
Answer: You could listen for the $_SERVER['HTTP_REFERER'] and add a class to the body depending on that referer
add_filter( 'body_class','wpse_body_classes' );
function wpse_body_classes( $classes ) {

  if ( is_page( 'event' ) ){ // event is the page slug of the page we wish to add the class for

    if( wp_get_referer() == '/url/of/get_involved' ){

      $classes[] = 'my-light-bg';

    }

    elseif( wp_get_referer() == '/url/of/urban_innovation_center' ){

      $classes[] = 'my-dark-bg';

    }

    else {

      $classes[] = 'my-default-bg';

    }

  }

  return $classes;

}

EDIT
Updated the code to

make use of wp_get_referer
check if we are on the event page so the filter only runs on that page
add a default body class to that page if no referrer is set
Comment: WP has a function for this: [wp_get_referer](https://codex.wordpress.org/Function_Reference/wp_get_referer).
Comment: Also you'd need a default - in case someone is coming from a search engine or a bookmark.
Comment: @vancoder good comment, I wasn't aware of that function. updated the answer to reflect this
Comment: A problem you might have is that, as no useful referer will be available when someone visits from Google, your page will have to "guess" what colour to show in that case.
Comment: I think my update takes care of that now. I think a `switch/case` could also be used here and set a default case to take care of that issue.
Answer: Keeping in mind the issues with checking referers, I'd probably approach this differently.
I'd append a parameter to the permalink using add_query_arg. The param added would be different for each referring page - eg, get involved > events might add class=my-light-bg, whereas urban innovation center > attend an event might add class=my-dark-bg.
Your event page itself could then retrieve that parameter by looking at $_GET[ 'class' ].
The advantage here is that, even when coming from a bookmark or search engine result, the correct style will be presented.

diffrent style for post single page


Automatic weights are not being computed as intended (Topology issue?)

Question: I have the following model, and skeleton
I'd say the topology is good enough, so I wanted to use the auto-weights feature to get a quick "draft" for the weights. I know this feature can be a bit rough sometimes, but what I'm seeing in this case is way worse than what I'm used to:

As you can see here, after parenting with auto-weights, the arm deforms both the head and the upper body. You can also see the generated weights for the left leg, which seem to be even higher for the right side than the left side.
I'm thinking there may be something fundamentally wrong with either my topology or my approach. Is such a bad auto-weighting normal for Blender? I certainly remember it performing way better in my previous attempts.
I thought this may be due to a low poly count, so I've tried subdividing the mesh (2x) and applying the modifier. No luck so far.
Any ideas?
Answer: It turns out the normals were not correctly oriented. When showing the normals in the editor, I saw this:

After recalculating normals (Ctrl+Shift+N, and unticking the "Inside" checkbox), automatic weights worked much better.


Rational curves on varieties of general type

Question: Let $S$ be a complex surface of general type. Are there infinitely many smooth rational curves on $S$? And more general, what if $V$ is a variety of general type?
Comment: @J.C.: if you really can, you will be famous...
Comment: Actually, it seems that a general surface of general type over $\mathbb{C}$ should have at most finitely many rational curves, but I guess you could also make some example with infinitely many.
Answer: I am surprised nobody mentioned the result of Lu and Miyaoka (Math. Res. Letter 2, 663-676 (1995)) which implies indeed that there are only finitely many smooth rational curves on a surface of general type, thus answering the question of the OP.
Answer: I think that the best result in this direction is the following theorem due to Bogomolov:

Theorem. Let $S$ be a surface of general type with $c_1^2(S) > c_2(S)$. Then for any $g$ the curves of geometric genus $g$ on $S$ form a bounded family.

In particular, since a surface of general type cannot be covered by rational or elliptic curves, these curves cannot deform. So Bogomolov's result implies that if $c_1^2(S) > c_2(S)$ then $S$ contains only finitely many rational or elliptic curves.
In general, it is conjectured than rational curves are never Zariski dense on a variety $V$ of general type, and more precisely it is expected that they are contained in a proper subvariety (hyperbolicity conjecture).
If $\dim V \geq 3$, you can obviously have infinitely many of them: for instance, take $V= S\times C$, where $S$ is a surface of general type containing a smooth rational curve and $C$ is a curve of genus at least $2$.
Comment: ...So Bogomolov's theorem is really a non-trivial result. At any rate, if hyperbolicity conjecture is true for surfaces of general type, then one always has only finitely many rational curves (i.e. the numerical condition on $c_1^2$ and $c_2$ would be superflous).
Comment: Great answer! Thanks! Well, if only assuming that any of these smooth rational curve has negetive intersection number without the condition on $c_1$ and $c_2$, can I say that the number is finite using the finiteness of the rank of Neron Severi group?
Comment: I think it is. It is the Picard number.
Comment: If $C$ is a smooth rational curve on a minimal surface of general type, then $C^2 \leq -2$ by the genus formula.
The rank of NS(S) is always finite, but in order to prove finiteness  you should also prove that the rational curves are *independent* in the Neron Severi. This is easy if $C^2$b is bounded from below; but if you allows $C^2$ to vary, than a priori you could have countably many smooth rational curves...
Comment: I don't get this question. If $C^2<0$ then by the genus formula $C.K<-2$ and so C is a fixed component in $|K|$? Surely, there must be finitely many such curves (if any). What does this have to do with the Picard number?
Comment: I think you miscalculated. The genus formula actually yields $KC=-2-C^2 \geq 0$, so $C$ is not a component of $|K|$ in general.
Comment: For smooth rational $C$ on a minimal non-ruled complex surface $X$ the Bogomolov-Miyaoka-Yau inequality $c_1^2\le 3c_2$ for the logarithmic cotangent bundle $\Omega^1_X(\log C)$ gives $K_X^2-3c_2(X)+2\le C^2$, so there are only finitely many such $C$ on $X$. But this says nothing about their (in)dependence in the Neron-Severi group.
Comment: @inkspot: What you mean is that there ARE only finitely many smooth rational curve on surfaces of general type?
Comment: I have not read Bogomolov's paper, but assuming the condition on the chern numbers on surfaces of general type, can you find the finitely many rational curves explicitly? Is there any explicit description?
Answer: The conjecture Francesco is referring to as the "hyperbolicity conjecture" is actually the Green-Griffiths-Lang conjecture. It states that on any given smooth projective manifold of general type $X$ there should exist a proper subvariety $Y\subsetneq X$ such that for all non-constant holomorphic map $f\colon\mathbb C\to X$ one has $f(\mathbb C)\subset Y$.
This would imply in particular that the same proper subvariety should contain every rational or elliptic curve (or, more generally, every image of a complex torus).
Beside the result of Bogomolov (which treats "only" the algebraic part of this conjecture) one should cite also Mc Quillan's theorem, which prove this conjecture for surfaces under the same assumption on the second Segre number $c_1^2-c_2>0$.
This condition is a technical hypothesis which guarantees the existence of an algebraic (multi)foliation on the surface. The core of Mc Quillan's proof is then in showing that an algebraic (multi)foliation on a surface of general type does not admit any dense parabolic leaf.
In higher dimensions, very little is known even for the algebraic part of the conjecture, apart from the case of generic complete intersections of high (multi)degree (Clemens, Ein, Voisin, Pacienza...).
To finish with, thanks to very recent results of Cano about resolution of singularities of holomorphic foliations by curves on threefolds, probably Mc Quillan will be soon able to improve his previous result with the weaker assumption $13c_1^2-9c_2>0$.
Comment: The resolution of singularities of holomorphic foliations by curves on 3-folds is due to McQuillan-Panazzolo (preprint IHES). Cano proved the resolution for codimension one foliations on 3-folds
Comment: Definitely right Jorge! I meant adapting the strategy of Cano... And I forgot Panazzolo, because Michael Mc Quillan told me that personally quite long ago... Thanks for having given the precision!
Answer: Some related additional comments:
Siu-Yau showed that when the bisectional curvature of a compact K\"ahler variety is positive then there exists a rational curve.
Birkar, et al, showed that when $X$ is a Moishezon manifold which is not projective. Then $X$ contains a rational curve. Moreover we have the same result when $X$
is a normal Moishezon variety with analytic $\mathbb Q$-factorial singularities.
Existence of rational curve is related to Gromov-Witten Invariants de to Ruan-Tian.
Let $X$ be a smooth projective variety over $\mathbb C$. Fix a point $x\in X$, a homology class $A\in H_2(X(\mathbb C),\mathbb Z)$ and very ample divisors in general position $H_i\subset X$, $i=1,...,k$.
Let $y_0,...,y_k\in \mathbb CP^1$ be general points. Take maps $f:\mathbb CP^1\to X$ such that $f_*[\mathbb CP^1]=A$, $f(y_0)=x$ and $f(y_i)\in H_i$
Ruan-Tian, introduced an invariant
$$\tilde F_{A,X}(x,H_1,...,H_k;y_0,...,y_k):={\text{number of such maps}}$$
Gromov-Witten theory of pseudo-holomorphic curves shows that one can make a similar definition where $X$ is replaced by a symplectic manifold $(M,\omega)$. Then the corresponding invariant is denoted by $$\tilde \Phi_{A,X}(x,H_1,...,H_k;y_0,...,y_k):={\text{number of such maps}}$$
Ruan-Tian, showed that if $\tilde \Phi_{A,X}(x,H_1,...,H_k;y_0,...,y_k):={\text{number of such maps}}$ then there is a rational map $f:\mathbb CP^1\to X$ such that $f_*[\mathbb CP^1]=A$, $f(y_0)=x$ and $f(y_i)\in H_i$
Moreover, $\tilde \Phi_{A,X}(x,H_1,...,H_k;y_0,...,y_k)=\tilde F_{A,X}(x,H_1,...,H_k;y_0,...,y_k)$ if the following conditions are satisfied.

If $C_1,...,C_m\subset X$ are rational curves such that $\sum [C_i]=A$ and $x\in C_1$, then $m=1$
If $g:\mathbb CP^1\to X$ is any map such that $g_*[\mathbb CP^1]=A$, $g(y_0)=x$ then $H^1(\mathbb CP^1,g^*TX)=0$

Existence of rational curves are very important in the classification of the solution of K\"ahler Ricci flows .
i.e an effective way to consider  Green-Griffiths-Lang conjecture is using classification of the solutions of relative Kahler Ricci flow and study of existence of rational curve appears,
Comment: Let $X$ be a Moishezon 3-manifold, then $X$ is actually projective if it does not contain any rational curve, this result is due to Peternell, Thomas 98, and Kollar 91


Function satisfying $f^{-1} =f'$

Question: How many functions are there which are differentiable on $(0,\infty)$ and that satisfy the relation $f^{-1}=f'$?
Comment: If $f^{-1}$ means $1/f$, then yes, it is an easy differential
equations question. On the other hand if $f^{-1}$ is
the functional inverse of $f$, then it looks pretty hard.
Comment: What is the motivation for this question?
Comment: It seems that this was a "piece of cake" question for John Conway, RIP.
https://www.scottaaronson.com/blog/?p=4732#comment-1836703
Comment: @pisoir Thanks for sharing :)
Answer: Seems like we have here yet another vindication of Léo Sauvé's famed dictum...
I am going to try to sketch below the awe-inspiring solution to this problem with which A. C. Hindmarsh came up and which was showcased on page 696 of the sixth issue of volume 76 (1969) of the American Mathematical Monthly. As far as I know, the problem was originally proposed by H. L. Nelson and appeared on page 779 of volume 75 (1968) of the Monthly: oddly enough, it would make its way to the problem & solutions column of the Monthly once again in 1976 (vol. 83, no. 4, p. 293); however, on that occasion it would be attributed to a Nathaniel Grossman from UCLA.
Solution. We wish to determine all functions $f \colon [0,\infty) \to [0,\infty)$ such that $f(0)=0$ and $f^{\prime}(x) = f^{-1}(x)$ for every $x \in I:=(0,\infty)$. We shall prove that, apart from the function mentioned by Tsuyoshi Ito in his reply, there is no other function $f$ which satisfies all the constraints under consideration.
First off, we notice that if $f$ is a function that does the job, then $f$ must be $\mathcal{C}^{1}$ and strictly increasing in $(0,\infty)$. Then, differentiating the identity $$f(f^{\prime}(x))=x$$
repeatedly, we obtain that $f$ is a function of class $\mathcal{C}^{\infty}$. What is more, we obtain that $f^{\prime \prime}>0$, $f^{\prime \prime \prime} < 0, \ldots, (-1)^{k}f^{(k)}>0$; it follows from Bernstein's theorem on regularly monotonic functions that $f$ is a real-analytic function on $(0,\infty)$.
Now, from the identity
$$\frac{d}{dx} f(f(x)) = f^{\prime}(f(x))f^{\prime}(x) = xf^{\prime}(x)$$
we get that
$$f(f(x)) = \int_{0}^{x} y \, f^{\prime}(y) \, dy$$ for every $x \in I$. This allows us to ascertain that $f$ has a fixed point $a \in I$: if this were not the case, the function $F \colon I \to \mathbb{R}$, defined for every $x \in I$ as $F(x)= f(x)-x$, would be of fixed sign. We claim that such a thing is not possible: indeed, if $f(x)>x$ for every $x \in I$, then $y = f^{\prime}(f(y)) > f^{\prime}(y)$ for every $y \in (0,x)$ and whence
$$ x < f(f(x)) = \int_{0}^{x} y \, f^{\prime}(y) \, dy < \int_{0}^{x} y^{2} \, dy = \frac{x^{3}}{3},$$
which doesn't necessarily hold when $x$ is sufficiently small; since the assumption that the inequality $f(x)<x$ holds for every $x \in I$ allows us to derive a similar contradiction, we conclude that any solution $f$ to the functional-differential in question does have a fixed point $a\in I$. Further, the strict convexity of $F$ implies that $F$ has at most two zeros, counting the one it has at $x=0$. Thus, $f$ has exactly one fixed point $a\in I$, with $f(x)<x$ in $(0,a)$, $f(x)>x$ in $(a,\infty)$, $f^{\prime}(x)>x$ in $(0,a)$, and $f^{\prime}(x)<x$ in $(a,\infty)$.
The uniqueness of the solution to the problem is established by means of the fixed point whose existence has just been proven. Let us suppose that $f_{1}$ and $f_{2}$ are two functions satisfying all the constraints under consideration and let $g:=f_{1}-f_{2}$. Moreover, let us denote with $a_{i}$ the unique fixed point of $f_{i}$ in the interval $I$. Without loss of generality, we can suppose that $a_{1} \geq a_{2}$.
The possibility that $a_{1}>a_{2}$ leads us to a contradiction. (I am not adding all the details behind the corresponding analysis for the moment. I consider this is the least transparent part of Mr. Hindmarsh's argument. Can any of you, fellow MO-ers, provide a more limpid justification of this part of the solution?)
If $a_{1}=a_{2}=a$, then it is not difficult to convince oneself that $0=g(a)=g^{\prime}(a) = g^{\prime \prime}(a)  =\ldots$; being $g$ a real-analytic function in $I$, the latter equalities implies that $g$ vanishes identically and we are done.
QED.
Answer: Wow.  I remember that I thought exactly the same problem out of curiosity as a high school student but did not reach an answer.  In fact, I was thinking about posting this problem on MathOverflow!
At least it is easy to construct one solution: f(x)=xφ/φφ−1, where φ=(1+√5)/2 is the golden ratio.
Edit: Corrected the calculation.  Thanks to Aaron Meyerowitz for spotting the error!
Comment: Which does not answer the question, as far as I can tell.
Comment: @Didier Piau: It clearly does not.  In case anyone is wondering, the asker posted the answer shortly after Christian Blatter posted his related analysis, and deleted it after I asked him if he had posted the question knowing the answer.
Answer: Let $a=1+p>1$ be given. We shall construct a function $f$ of the required kind with $f(a)=a$ by means of an auxiliary function $h$, defined in the neighborhood of $t=0$ and coupled to $f$ via $x=h(t)$, $f(x)=h(a t)$, $f^{-1}(x)=h(t/a)$. The condition $f'=f^{-1}$ implies that $h$ satisfies the functional equation $$(*)\quad h(t/a) h'(t)=a h'(at).$$ Writing $h(t)=a+\sum_{k \ge 1} c_k t^k$ we obtain from $(*)$ a recursion formula for the $c_k$, and one can show that $0< c_r<1/p^{r-1}$ for all $r\ge 1$. This means that $h$ is in fact analytic for $|t|< p$, satisfies $(*)$ and possesses an inverse $h^{-1}$ in the neighborhood of $t=0$. It follows that the function $f(x):=h(ah^{-1}(x))$ has the required properties.
Comment: I know little about analysis, so my apologies if this is a silly question.  Are you solving a version of the problem where the function f is not necessarily defined on (0,∞) but is defined on some interval (0,b) (which is also an interesting problem)?
Comment: The function $f$ constructed here is a priori only defined in a neighborhood of the point $a$.
Comment: Just a naive question: I don't see the definition of the constant $p$ anywhere. Do you mean that the inequalities $00$?
Comment: @PedroLauridsenRibeiro: The function so constructed is defined in the neighborhood of the point $a$, where it is assumed that $a>1$. Given $a$ the quantity $p>0$ is defined by $a=1+p$ in the first sentence of the answer.
Comment: Oh, right, my bad. Sorry for that, thanks! (nice answer, by the way)
Comment: Is this a complete general solution? Or put differently, how do you know that every solution exhibits at least one fixpoint i.e. $f(x)=x$ on the positive real line? Indeed, the solution $f(x)=ax^b$ does have a fixpoint $x=\left(\frac{1}{a}\right)^{\frac{1}{b-1}}$, but generally?
Comment: @Diger: No. I just wanted to present a solution that is essentially different from $x\mapsto c x^\alpha$.
Comment: I just saw the answer by jose hdz stgo. Apparently under the assumptions $f:[0,\infty) \rightarrow [0,\infty)$ and $f(0)=0$, the solution $f$ does indeed exhibit a fixpoint $a\neq 0$. But then, since your $a$ does not necessarily have to equal the fixpoint $x=\left(\frac{1}{a}\right)^{\frac{1}{b-1}}$ of the solution $x \mapsto ax^b$, those solutions seem to be different. How does this fit into the picture of uniqueness of solutions of first order ode's?
Comment: We have a strange functional equation, but not an ODE. (I have not studied the later solutions to the problem.)
Answer: This question is more complicated than it seems
If $f^{-1}(x)=f'(x)$ then $f(f^{-1}(x))=f(f'(x))$ or $x=f(f'(x))$
First derivative is giving
$\displaystyle 1=f'(f'(x))f''(x)$
Now replace $y=f'(x)$
$\displaystyle y(y(x))y'(x)=1$
Instead of the above we will solve a more general:
$\displaystyle g(y(x))y'(x)=1$
This one has a solution expressed as
$\displaystyle \int_{1}^{y(x)}g(r) \mathrm{d} r = x+c$
Now since we want $y(x)=g(x)$ we have
$\displaystyle \int_{1}^{y(x)}y(r) \mathrm{d} r = x+c$
$\int_{1}^{y(x)}y(r) \mathrm{d} r$ is actually a curious operator which we will represent as $\mathfrak{R}(y(x))_{1}$
Now this operator has its inverse and this is what we are looking for. For a function $h(x)$ we want to know $s(x)$ so that
$\displaystyle \mathfrak{R}(s(x))=h(x)$
We will call $\mathfrak{R}^{-1}()$ the integral root.
As a new operator we need to examine it a little bit. We can create a table for some known functions first
$\begin{matrix} h(x) & \mathfrak{R}^{-1}(h(x))_{1} \\  & \\ \frac{1}{2}(x^2-1) & x\\ \frac{1}{3}(x^6-1) & x^2\\ 1 - \ln(x)(1 - \ln(\ln(x))) & \ln(x)\\ e^{e^x}-e & e^x\\ -\ln(x) & \frac{1}{x}\\ \cos(1)-\cos(\sin(x)) & \sin(x)\\ \frac{2}{3}(x^{\frac{3}{4}}-1) & \sqrt{x} \end{matrix}$
We do not ignore constant term since integral root is very sensitive operator and we define in general integral root with base $b$ as:
$\mathfrak{R}(h(x))_{b}=\int_{b}^{f(x)}f(r) \mathrm{d} r$
We will return to the importance of base later but for now we say that the function does not have to be defined everywhere and base can help about it. So, all we need to find the integral root of $h(x)=x$.
The operator resembles a normal derivative/integration except that it is extending it all, it is giving sort of a faster result.
It is a deep question if this operator has unique values. (We will hint something into that direction but overall this is a very good subject for some semester work.)
Notice that the operator is very sensitive to the constant value and this one cannot be ignored.
Since powers of $x$ appears from the powers of $x$, we could try the solution in the most general form as $g(x)=ax^b+f(x)$ however this will convince us very quickly that for any solution defined everywhere $f(x)=0$, since such solutions are very restrictive and it is not possible to drive constants the way we would like to, even adding $ax^b+c$ would create a solution that is useless. The way of dealing with constant term is by changing the base in general.
So, if we restrict ourselves to global world we have
$\displaystyle \mathfrak{R}(ax^b)_{1}=\frac{a^{b+2}x^{b(b+1)}}{b+1}-\frac{a}{b+1}$
Since we want
$\displaystyle \mathfrak{R}(ax^b)_{1}= x+c$
that requires $b(b+1)=1$ making the result
$ba^{b+2}x-ab$
This requires $ba^{b+2}=1$ as well which makes $a=(b+1)^{\frac{1}{b+2}}$
(Notice that these are not two different integral roots of the same function.)
Now our solution is $y(x)=f'(x)$ so we have it back as
$\displaystyle f(x)=\frac{a}{b+1}x^{b+1}=(b+1)^{-\frac{1}{b+1}}x^{b+1}$
where as we have mentioned $b(b+1)=1$
The reason we opt for this operator is that the function in question has derivative thus it is assumed that it is a nicely behaving function.
Let us prove that these two are the solutions
Derivative
$\displaystyle f'(x)=(b+1)^{-\frac{1}{b+1}}(b+1)x^{b}$
$\displaystyle f'(x)=(b+1)^{-\frac{1}{b+1}+1}x^{b}$
$\displaystyle f'(x)=(b+1)^{\frac{b+1-1}{b+1}}x^{b}$
$\displaystyle f'(x)=(b+1)^{\frac{b}{b+1}}x^{b}$
Inverse
$\displaystyle x=(b+1)^{-\frac{1}{b+1}}h(x)^{b+1}$
$\displaystyle (b+1)^{\frac{1}{b+1}}x=h(x)^{b+1}$
$\displaystyle (b+1)^{\frac{1}{(b+1)(b+1)}}x^{\frac{1}{b+1}}=h(x)$
$\displaystyle f^{-1}=h(x)=(b+1)^{\frac{b}{b+1}}x^{b}$
Finally let us use golden ratio to find what the solutions we are talking about
$\displaystyle b_{1}=-\phi$,$ b_{2}=\phi-1$
making the first solution actually complex and the second real:
$\displaystyle (-\phi+1)^{-\frac{1}{-\phi+1}}x^{-\phi+1}=(-\phi)^{-\phi}x^{-\frac{1}{\phi}}$
$\displaystyle \phi^{-\frac{1}{\phi}}x^{\phi}$
The two solutions we have are driven by differing a constant only, otherwise the integral root has the unique solution just like normal root has. It is possible that there are solutions that are not analytical or defined everywhere, otherwise the two given solutions are the only nice global solutions.
Apart from these global solutions that do not change if we change the integral root base, there is an option of having a local solution. For this we extend the function analytically at some point $x_{0}$ and ask that the function behaves as $x$ regarding the integral root at that point.
Then near $x_{0}$ that function will behave as required.
$\displaystyle f(x)=\sum\limits_{n=0}^{+\infty}c_{n}(x-x_{0})^n $
Basically we are asking
$\displaystyle \mathfrak{R}(\sum\limits_{n=0}^{+\infty}c_{n}(x-x_{0})^n)_{x_{0}} = x+c$
Notice that the change of base is very important, albeit purely technical for this particular task, as we have assumed that we know this function only around $x_{0}$
Then we need to have:
$\displaystyle \sum\limits_{n=0}^{+\infty}\frac{c_{n}}{n+1}(\sum\limits_{m=0}^{+\infty}c_{m}(x-x_{0})^m-x_{0})^{n+1}=x+f(x_{0})+c$
Obviously we can match all coefficients since the final coefficient by $x$ should be $1$ and all higher powers $0$. Solving all coefficient for $c_{k}$ will give local solutions for each $x_{0}$. We already have one such non trivial solution, but there could be more than that global one.
However, notice that the integral root base does not affect the answer, since the base deals with constant term only, and constant term is arbitrary. Instead of $1$ for our function we could take any constant.
This is to say that our local solution again has the same resolution which we have found when we started from $1$.
Unless there is some curious and undiscovered way the integral root can have more than two given solutions, one real and another complex, each local solution is equal to either of the two found global solutions.

Function satisfying $f^{-1} =f'$


Changing TCP/IP IPID sequence generation algorithm on Windows Server

Question: a recent security review on a customers webserver yielded the following results:

"[...]
  The system under test is using incremental ip ids.
  This means that every outgoing ip packet has an incrementing id number
  which can be used for stealth load analysis or for so called idle scans
  against third party systems.
  [...]"

A hping of the system is showing the incrementing id numbers:
<code>$ sudo hping3 -c 3 --fast -p 80 -S xxx.xxx.xxx.xxx
HPING xxx.xxx.xxx.xxx (tun0 xxx.xxx.xxx.xxx): S set, 40 headers + 0 data bytes
len=44 ip=xxx.xxx.xxx.xxx ttl=122 DF id=14360 sport=80 flags=SA seq=0 win=8192 rtt=802.2 ms
len=44 ip=xxx.xxx.xxx.xxx ttl=122 DF id=14361 sport=80 flags=SA seq=1 win=8192 rtt=807.1 ms
len=44 ip=xxx.xxx.xxx.xxx ttl=122 DF id=14362 sport=80 flags=SA seq=2 win=8192 rtt=801.6 ms
</code>
The system is a Windows Server 2003 SP2 (respectively multiple loadbalanced servers).
It may not be suitable as a zombie host in an idle scan as it is quite the opposite of idle. But if we can change the behaviour we want to change it.
I can't find any documentation about the IPID sequence generation algorithm in the Windows TCP/IP stack, e.g. if it's only incrementing by host or global or if the behaviour changed with later versions of Windows.
Just this one Patch Available to Improve TCP Initial Sequence Number Randomness
Can anyone point me to documentation about what version of windows is using which IPID sequence generation algorithm?
Are there any options to change the IPID generation?
Answer: http://msdn.microsoft.com/en-us/library/ms819768.aspx
indicates that it does already make random numbers.  You say that this is actually "multiple loadbalanced servers".  So what IP are you pinging?  That would be want you want to look at.
Comment: MSDN link is dead


Prove that the following language is not regular: $\{0^i1^j : i \neq j\}$

Question: I was trying to approach this proof, after multiple reads and attempts I am getting nowhere. If someone could help me out that would be great. Should I use the pumping lemma, if so how show I start, what word should I choose? Or should I use closure-properties and if so what irregularity should I show? I am genuinely so confused. Any help is appreciated.
Comment: Have you tried Myhill-Nerode theorem?
Answer: Let $L = \{0^i1^j : i \neq j\}$. You can prove that $L$ is not regular in many ways. Here are some examples.
Closure properties
If your language were regular then so would $0^*1^* \setminus L$ be, but that language is $\{0^n1^n : n \in \mathbb N\}$, which presumably you already know isn't regular.
Myhill–Nerode
The words $\{0^i : i \in \mathbb N\}$ are pairwise distinguishable modulo $L$: if $i \neq j$, then $0^i1^i \notin L$ but $0^j1^i \in L$. It follows that $L$ isn't regular.
Pumping lemma
If $L$ is regular then it satisfies the pumping lemma, say with constant $n$. Consider the word $w = 0^n 1^{n+n!} \in L$. According to the pumping lemma, there should be a decomposition $w = xyz$ such that $|xy| \leq n$, $|y| \geq 1$, and $xy^iz \in L$ for all $i \in \mathbb N$. Let $|y| = \ell$, so that $y = 0^\ell$. Pick $i = 1 + n!/\ell$. Then $xy^iz = 0^{n+n!} 1^{n+n!} \notin L$, contradicting the pumping lemma.
Comment: Thank you very much, I understand the basic procedure thanks to you. If I am right, you use closure properties to force your way to an irregular language that we know is irregular. I am still confused about the pumping lemma, but I guess you just get used to it through practice.
Answer: The language $L=\{0^i 1^j : i \neq j\}$ can be written equivalently as $L=\{0^i 1^j : i \lt j\} \cup \{0^i 1^j : i \gt j\} = L_1 \cup L_2$.
Now if we prove using the Pumping Lemma that either of the languages $L_1$ or $L_2$ are not regular, we are done.
Consider any string
$x = uvw: x \in L_1$.
$u=0^{i-a}$
$ v=0^a1^b$
$w=1^{j-b} : i\lt j, 0 \le a \le i, 0 \le b \le j, a+b\ge 1$.
Now pumping $x$ yields
$ x' = uv^nw = (0^{i-a})(0^a1^b)^n(1^{j-b})$
$ = 0^{i+a(n-1)}1^{j+b(n-1)}: \forall n\ge 0$
For $L_1$ to be regular, $x' \in L_1$,for all arbitrary choices of $i, j, a, b, n$,satisfying the above constraints.
If one chooses $a, b$ such that $a \gt b$, then it is evident that for some $n$, $i+a(n-1) > j + b(n-1)$ (For all $n \gt \frac{j-i}{a-b}-1$ precisely).
Hence, $\exists x' \notin L_1$, and therefore $L_1$ is not regular. This concludes that $L$ is NOT regular.
Comment: Try your argument on $L_2 = \{0^i1^j : i \ge j \}$.
Comment: You cannot prove that a language isn't regular by showing that it has a nonregular subset. It just doesn't follow. I gave you a counterexample to this technique.
Comment: The $L_2$ stated above is with $i \gt j$. Proving non-regularity for the language $\{  0^i1^j : i \ge j\} $ is trivial since it has the language $\{  0^i1^j: i = j \} $ as its subset.
Comment: The point is that the union of $L_1$ and the new $L_2$ is the language $0^*1^*$, which is regular.
Comment: Yes, that's another alway to think about it. It just works out for $0^*1^*$, since every regular language is also a CFL. But in general the union of two CFLs is another CFL, which need not be a regular language.


Why are sperm cells not attacked by the female immune system?

Question: Whenever a foreign particle enters into someone's body, it is attacked by the white blood cells. I just want how it is that, when sperms enter the female body, they are not attacked by the the woman's immune system?
Answer: Studies show semen does mount a considerable immune response in the female mucosa, however:

Seminal plasma redirects the differentiation of human dendritic cells (DCs) toward a regulatory profile. By promoting a tolerogenic profile in DCs, seminal plasma might favor fertility, but might also compromise the capacity of the receptive partner to mount an effective immune response against sexually transmitted pathogens.

Semen promotes the differentiation of tolerogenic dendritic cells.


The hypenated part of my name gets dropped off in Chat but the hyphen remains

Question: In chat conversations, my name appears as "Pierre-" when it should be "Pierre-Antoine" or at very least "Pierre".
Answer: Your name doesn't necessarily appear as "Pierre-"; that depends on the width of your browser window (and other issues like the font your browser uses, it's rendering engine, etc.)
These three screenshots of the same message were taken with no change other than changing the width of the window:

In Chrome 8 on my Windows 7 box, your user name appears as "Pierre-Antoine" in live chat when the window is about 1470 pixels wide.
Another thing to note is that there are actually two versions of your signature. If there's enough space (e.g. because you said several things in a row), you'll instead get this version:

– and in this case, it's clearly correct that the hyphen is on the first line.
Both versions of the signature use the browser's line breaking algorithm to determine what to show – in case of the small signature, everything but the first line is just hidden away from display.
So what to do? Unicode to the rescue!
We now consider a dash* in a username that is preceded and followed by neither another dash nor a whitespace character to be a hyphen, and we replace this dash with the corresponding unicode character.

In the large signature, we use the regular hyphen, ‐. This doesn't change any line-breaking behavior, but is just for typographical consistency – a hyphen looks a little bit different from a regular dash, and we want the small and large versions of the signature to look equal.
In the small signature, we instead use the sequence ‑. This is a zero-width space, followed by a non-breaking hyphen. This little trick does exactly what we want – it puts the line break before, not after the hyphen.

And behold**:

* The correct name is actually Hyphen-Minus, codepoint U+002D – typographically speaking, a dash is a totally different beast.
** Note that we currently only do this in the live chat, not in the transcript.
Comment: Fine work, and good presentation!.
Comment: Pedantically for true typographical consistency in your answer your punctuation dash should be a horizontal bar (U+2015) or an m-dash (U+2014), the latter being much easier of course (`—`).
Comment: @Richard: [This is actually debated](http://en.wikipedia.org/wiki/Dash#En_dash_versus_em_dash), which is why I tend to go with the spaced n-dash (being what I'm used to from German).
Comment: @balpha: German, hmmm :-). Just because some people have the wrong approach doesn't mean giving up the fight :-) Arguably, as the right here is an expansion/explanation of the left it should be a colon.
Comment: @balpha: More seriously, U+2110 Hyphen (i.e. `‐`) appears to be missing from several of the fonts in MSO's (and I assume SO's) style sheet: `Arial,Liberation Sans,DejaVu Sans,sans-serif`. Certainly it isn't in Arial. Depending on the browser and OS some other glyph is going to be selected, perhaps without the line breaking behaviour you want.
Comment: I didn't realize the browser width was the issue as I was seeing people with longer names than mine appearing. Makes sense now. Thanks guys :)


How do I know if I will drill into a hole in a wall that was already made?

Question: I drilled 2 large holes for mounting a flat screen in the bedroom.  One hole is in a wood stud and the other is a metal stud.  I will be renting out our apartment and will be taking the TV down and filling the holes and repainting walls.  If I ever plan to move back into this apartment and mount a TV again in the same spot, how do I avoid not drilling in the same exact spot?  Basically, I don't want to hit a portion of the same hole and create an even larger hole, making it very unsafe to mount a TV.  Is there a way to mark the spot so that I know to avoid it in the future?
Comment: Is this even a concern?  Shouldn't it be obvious when installing a wall anchor that it is secure?  (The screws don't strip when torquing them, and you should always load-test to at least 2x the use load.)  It's probably more likely that you catch the edge of a stud or find a void where a knot was than to find the same hole again.   Also, you could fill the hole with a mixture of sawdust and wood glue which would be quite strong and re-drillable.
Answer: Chip away the drywall over the hole and install a Stud Plate.  These are designed to stop anyone from drilling into a wire that runs through a stud.
Patch the drywall.  Next time, if you can't find the location, and accidentally drill in the same spot, you'll hit the stud plate.
Comment: This stud plate idea is the best. Later to find where they are in the finished wall just run a strong magnet over the wall area.
Answer: Why not just measure the height of your bracket and keep note of it, then next time mount it a few inches higher or lower so you don't risk hitting the same spots?
I suppose you could also plot the X,Y co-ordinates from a corner of the wall and mark those spots to avoid when you move back.
Answer: Why not just leave the bolts (lag, I assume) in the holes, screwed in below the level of the wall; then patch the wall. You can find them with a magnet if you ever want to reuse them.


Can Low Search keywords also search in categories?

Question: If I enter the keywords "Topic Name" into the search form, can Low Search also find entries that have been tagged with "Topic Name"? This would be something similar to Solspace's Super Search "keyword_search_category_name" parameter.
Answer: Yes. From the docs:

Low Search v2.4+ can also add category information to the index, making entries searchable by keywords present in their categories. Just like the regular channel fields, you can add weight to the category name, description and any of the category custom fields.
Note: if you're using ExpressionEngine 2.7+, making changes to a category will automatically update the index for the associated entries. However, if you're using an older version of EE, you will need to rebuild the index manually whenever you edit or delete a category.
Comment: Ah ha! Thanks Derek, this is was a new feature added in 2.4 I guess. This is amazingly perfect!