How does procedure failure rate affect sample size in a randomized clinical trial?

Question: I am currently conducting medical research. It is a randomized blinded clinical trial to compare patient indicators of rehabilitation after a surgical procedure . One group of patients receives an injection of local anesthetic near a sensory nerve; the second group of patients receives the same injection of local anesthetic near the same nerve but also receives a catheter near the nerve to provide a continuous infusion of local anesthetic. The two groups are measured on certain parameters of rehabilitation over a 24-hour period and data from both groups will be compared. The injections and catheter placement are done using ultrasound and there is a failure rate--either because the medication was not placed in the right place (primary failure) or the catheter becomes dislodged (under the skin) at some point during the study period(secondary failure) We will not know if the injection was improperly placed or if the catheter became dislodged during the 24 hour period.(The catheter could also work initially and become dislodged at some unknown point during the study) If the study is randomized is it necessary to know (or have an estimate of ) the failure rate of injections of local anesthetic and catheter placements in order to determine the appropriate number of study patients to ensure that the results will be sufficiently powered?
Comment: What sorts of outcomes are you looking at? I ask because the effect size you want to detect is an important part of power analysis. For the study more broadly, are you looking at the effects of using the catheter specifically, or are you looking at patient outcomes with and without the catheter?
Comment: @mcmillc With that information in mind I will strongly endorse mdewey's answer. Intent to treat seems like the right approach, in which case the failure rate (unknown or otherwise) will be represented in your data by a change in the average effect of the catheter on your outcomes. Since the catheterization fails some of the time, applicable results will reflect that real-world condition rather than the "pure" effect of failure-less catheter placement. So your study population size shouldn't change (from this, at least).
Comment: @EdM That's my argument, so I think we agree (provided I am interpreting your comment correctly). The examination isn't of the performance of a catheterization that is known to be successful but rather of how use of a catheter affects outcomes. The failure rate of catheterization in the study should be similar to that in the field. So even if power to detect the effect of *successful* catheterization decreases as a result of increased variance due to catheterization failures, the power to detect the effect of catheterization (given that failures sometimes occur) should be the same. Right?
Comment: What is not clear to me is what you do with the data from patients that have the secondary failure.  Throwing out the data could create unknown bias. Such problems are sometimes remedied by imputation if there are characteristics of the patients that have secondary failures that can relate to the patients with primary failures.
Comment: As I read Upper_Case's comment and review the question again.  I am wondering whether or not the objective is to see if the adding of the catheter reduces or increases the chance of failure compared to the injection alone.  Does the type of failure really matter?  If not maybe you can lump primary and secondary failures as simply failures. Are you trying to compare treatments with respect to efficacy and safety? If so failures might be a safety issue.  But you also say you have several measures of rehabilitation (a measure of efficacy).  Maybe you need to concentrate on one measure.
Comment: The end of my last comment was that I was referring to a measure of rehabilitation and I think that might be necessary to make progress on the sample size issue.
Comment: Upper Case. Thank you for your comments.In response to your questions:
The primary variable is knee flexion in degrees following total knee replacement. Secondary variables include NRS pain pain score (0 - 10) and results of the TUG test —time  to get up from a chair, walk 3 meters and return to the chair.  Study powered to find a 20% difference in knee flexion between groups. Patients who receive a single injection receive a sham catheter hidden below bandages so both patient groups are unaware of if they are receiving a continuous infusion.
Comment: Thank you Michael. Comments much appreciated.
The objective is to see if adding a catheter results in parameters mentioned above. We are looking at efficacy, not safety. No danger to the patient if the catheter does not work.  Based on sensory testing results, we estimate that the primary failure rate could be around  30% but this was not known until the end of the study and could not have been incorporated into sample size estimates. The problem is that we will not necessarily know which patients with catheters  have secondary failure.
Comment: If the catheter comes out above the skin we would know However, if the catheter moves away from the nerve (but still under the skin) it may be too far to have full effect. Short of checking every patient with ultrasound daily —a very time-intensive, impractical process—we would not know which catheters had moved internally. Literature reports primary failure rates of 0.5 - 26%; secondary failure rates of 25%-50%. Is there a formula that would allow one to to incorporate procedure failure rate such as the one described into sample size determinations.
Comment: @Upper_Case intention-to-treat is clearly the way to proceed with analysis here. In terms of power, however, the failures might be expected to increase the variance of outcomes and thus diminish the power to detect any given average real-world effect of the catheter on outcome.
Comment: @Upper_Case it depends on the assumptions made about outcome variance in study design. Power depends on both the desired detectable effect and the _variance_ of the effect. In my experience, people often don't pay adequate attention to that variance. If the design made an assumption about variance of results from _successful_ catheterizations, then additional variance from failures will diminish power. If the assumption about variance included variance from failures, then the power calculation is OK. As I read the question, variance from failures might not have been considered during design.
Answer: From the point of intention to treat it is not necessary to take this into account because everybody should be included in the analysis in the arm to which they are randomised. The failure rate is an inherent part of the treatment. If you want to compare the effect of actually receiving the treatment in the two arms that is a different mater but from your description I assume that is unknowable.
As a side issue I do not see how you can maintain masking if you are catheterising in one group but not the other. You can, and should, mask the outcome assessors but surely everybody else: patients, investigators, clinical team, ... will know.
Edited in response to comments
My last paragraph is not relevant now as the OP has kindly elaborated on their ingenious scheme for employing a sham catheter.
Just for reference for people coming upon this who may not know about it intention to treat is described in this Wikipedia article and the alternative complier average causal effect is outlined in many articles including this open access one. There does not seem to be a Wikipedia entry for it.
Comment: I was going to ask: what is "blinded" supposed to mean in this context? (But perhaps there is a standard answer? This is far from my field!)
Comment: I think we are jumping the gun by providing answers before we really understand the study more clearly.  Specifically what is the ultimate objective (as Upper Case mentioned).  Is safety part of the objective?  Does type of failure matter?  What statistical methods are being used (hypothesis testing, survival analysis, etc.)?
Comment: @GeoMatt22 I prefer the term masking as I find it offensive to speak of blinding patients but it is the standard term unfortunately except in ophthalmology for obvious reasons.
Comment: Sorry, I did understand the use of blinding = masking. But in controlled studies, I thought "blind" meant the patients did not know which group the were in (treatment vs. control), and if "double blind" then the doctors also did not know. So I was agreeing with your 2nd paragraph ... but not sure if there was another meaning to "blinded" that I was missing.
Answer: The power of your study depends on the magnitude of the difference you hope to detect between the two treatments, the variability among participants in terms of their responses to the treatments, and the number of participants. Insofar as the possibility of placement failure increases the variability of responses among participants, it will necessarily decrease the power for detecting a particular difference between the treatments, given the same number of participants. As an extreme example, if there always was placement failure you would be unable to detect any differences at all.
That said, placement failure seems inherent in these treatments so this would seem to be a fair test of their differences in clinical practice (except for the caution raised by @mdewey about whether this is really masked, unless all get catheterized but some receive placebo instead of anesthetic, or unless you are willing to accept a possible placebo effect simply due to catheterization that doesn't correspond to the continued anesthetic infusion). With treatment failure you may not be able to detect as small a difference as you might like, so an estimate of treatment failure should be considered in your design.
Answer:
Random uncertainty decreases the precision of an experiment.
Systematic uncertainty decreases the accuracy of an experiment.

The Standard deviation , $s$ equals the square root of the sum of squares of differences $/ N$ (population).
The standard deviation of the mean value of a set of measurements $σ_m$
, ("sigma-em")
$σ_m=s/√N$
When we speak of the uncertainty σ of a set of measurements made under identical conditions, we mean that number $σ_m$ and not $s$. There are two common ways to state the uncertainty of a result: in terms of a $σ$, like the standard deviation of the mean $σ_m$, or in terms of a percent or fractional uncertainty, "epsilon", $\epsilon$.
If the uncertainty of results does not change with quality or experience then the rate of change of standard deviation of the mean value with growing data set size will be small. It is both an indicator of process quality and significant population size.
Referring to Shannon's Law and digital communication we know that the Noise to Signal ratio or standard deviation is arithmetically related to the error rate is directly proportional on a log-log scale ( although we usually use the inverse or S to N ratio (SNR)) where 10:1 or 10dB to 15 dB or 30:1 is usually the threshold of noise where you have a 50/50 chance of error depending how how you discriminate the results "good or bad" and 20dB is 1% noise, the error rate is quite small. (more astute statisticians are welcome improve or correct this description)
You must decide your own population size and and error threshold and thus population size for significant results depending on the weight of the error. ( longer recovery period vs loss of added cost, infection or whatever)
A typical calculation is a measure of the improved recovery time with a standard deviation with and without additional treatment.  Then plotting the standard deviation over time for each medical team is an indicator of their treatment efficacy improvement rate.
IMHO, blinding the test is less important than defining the measurement methods of observation of recovery accurately, confidence in skill , if this can be measured somehow with measurable thresholds, tolerances and bias inputs.  (neglect or more attention may bias the results in either direction)  (blind test results are somewhat meaningless without these details because they only apply to the team that repeated the process and not all teams unless a larger measurement takes place.)

Even with a large sample base,  every precedure must be a measurable parameter with a tolerance to obtain a reliable prediction of the outcome.  ( e.g. placement, adhesion secured, patient motion etc.)  Reducing the deviation improves the success rate.  Design of Experiments (DoE) can be done to optimize the process. (beyond scope of this answer)


In thermodynamic systems why must the free energy of the system be minimized?

Question: Is this somehow a consequence of the second law of thermodynamics?
Comment: I'll take a go, this is incomplete but might serve to start some discussion. The free energy is special because it define an energy at which you can add/remove particles without a change in entropy. The actual value of free energy is dependent on the physical properties of the system, but once the free energy is minimised you have maximised entropy, so the system is in quasi equilibrium (just not yet in chemical equilibrium).
Answer: Let's say we have a system where the number of states at an energy $U$ is given by the function $N(U)$, so that the entropy $S(U)$ is given by $S(U)=\log N(U)$.
Now suppose this system is put in contact with a large thermal resevoir at temperature $T$. What energy will our system likely have after this contact has been made?
To answer this question we must ask how many states there are where our system has an energy $U$. We know the total number of states for our system is $e^S$, but what is the total number of states for the resevoir? The total number of states for the resevoir is similarly $e^{S_R(U_{\textrm{Total}} - U)}$, where $S_R(U_{\textrm{Total}}-U)$ is the entropy of the resevoir when it has energy $U_{\textrm{Total}}-U$ and $U_{\textrm{Total}}$ is the total energy of the bath plus resevoir system.
Since the state of the resevoir and the state of our system can be chosen independently, the total number of states for the combined system is the product of the number of states for the individual system. Thus the total number of states for the combined system is $e^S e^{S_R(U_{\textrm{Total}} - U)} =e^{S(U)+ S_R(U_{\textrm{Total}} - U)}$. If we expand the entropy of the resevoir we find
\begin{equation}
\begin{aligned}
S_R(U_{\textrm{Total}} - U) &\approx S_R(U_{\textrm{Total}}) - U * \partial_U S \\
&= S_R(U_{\textrm{Total}}) -  U /T \\
\end{aligned}
\end{equation}
 so that the total number of states is proportional to $e^S e^{- U/T} =e^ {S- U/T} = e^{(TS-U)/T} = e^{-F/T} $.
The system will almost certainly have the most probably energy. The most probably energy is the one that corresponds to the most states. Therefore it is the one that maximizes $e^{-F/T}$. Therefore it must be the one that minimizes $F$.
Answer: Strictly speaking a thermodynamic system is at equilibrium if and only if the free energy is at a local minimum in phase space. If the free energy was not at a minimum, the system would have a driving force that would pull it toward a local minimum. Think of a ball rolling down a hill. As the system falls toward the minimum, entropy is generated. So you can think of it as a consequence of the 2nd law, or vice-a-versa.
It's worth noting that an equilibrium system is not necessarily at a global minimum. For example, a super heated liquid is in a shallow minimum of phase space. Add a little energy to it to bump it out of this minimum, and bang! Tons of energy is released (and entropy generated) as it falls to a much deeper minimum.
Also, technically, there is no way to know if a thermodynamic system is at a global minimum. You'd have to map out the entire phase space of the system, which is unknown.


Why are sound waves longitudinal even though they are mechanical energy?

Question: Waves on a string, ripples on a pond are transverse waves generated by mechanical energy and in the simplest form oscillations. Sound also is a form of energy and basically oscillations. What makes sound unique in the fact that it is longitudinal ?
Comment: Sound, in a solid, can be transverse as well.
Comment: In line with Jon Custer's comment, I think the question should be "why can waves not be transverse in a gas"?
Comment: I think I would add that waves in a gas are pressure waves. Their transport is longitudinal as they are propagated through collisions. Look at how a speaker is moving, it is moving back and forth pushing and pulling the air. The pressure wave will be in the propagation direction.
Answer: In order for mechanical waves to propagate there needs to be some form of "restoring force" that tries to bring the system back to equilibrium. For longitudinal waves in gases this restoring force is supplied by pressure in the medium. However, there is no restoring force in a gas for bulk shear movement of the gas particles. Therefore, there is no transverse wave propagation in gases.
However, as mentioned in the comments, sound can also propagate transversely through solids, where there is a restoring force due to shear movement. The fact that both bulk transverse and longitudinal waves can propagate through solids, but only bulk longitudinal waves can propagate through fluids, is important in studying seismic waves, since the Earth is made up of both solid and fluid components.
Comment: To add to this: surface waves on water appear to be transverse not longitudinal, even though water and air are both fluids. In this case the "restoring force" is gravity, which causes the pressure in the water to change with depth. Surface waves are significantly more complicated to model than waves in a single solid or fluid medium.
Comment: @alephzero: …and, indeed, transverse [gravity waves](https://en.wikipedia.org/wiki/Gravity_wave) (not to be confused with [*gravitational* waves](https://en.wikipedia.org/wiki/Gravitational_wave)!) can occur even without a liquid surface, e.g. in the Earth's atmosphere. So you _can_ have a kind of bulk transverse wave in a fluid medium, as long as the medium isn't homogeneous and there's some restoring force like gravity maintaining the inhomogeneity. And of course we haven't even got to weird things like [magnetohydrodynamic](https://en.wikipedia.org/wiki/Magnetohydrodynamics) waves yet.
Comment: @alephzero Right. I didn't really want to touch surface waves, which is why I used the word "bulk" when appropriate.


Can you still track an iPhone after it has been logged out of iCloud?

Question: If my iPod touch 5 gets stolen and logged out of the iCloud account, can I still track it without having Find My iPhone? If they restore it which would log me out I can still track it by Wi-Fi right?
Answer: No, once Find My iPhone has been removed, the device cannot be tracked.
However, I believe you are underestimating how difficult it is to remove Find My iPhone from a device. To log out an iCloud account with an active Find My iPhone service, you need to enter the iCloud password, which would require them to have this information.
Furthermore, restoring the device requires disabling Find My iPhone as mentioned above, or entering DFU mode which activates Activation Lock requiring your Apple ID to unlock the device. All the while, your device can still be tracked using Find My iPhone.


Algorithm confirmation

Question: I have an algorithm in textual form(in English) from a research paper that deals with meteorology/climatology . If I convert the textual algorithm into pseudo code can I ask it as a question here for confirmation or does it belong to Computational Science Stack Exchange ? The data structures that will support the algorithm are irrelevant as far the question is concerned.
Comment: In addition to pseudo code, another way to represent an algorithm is via a flowchart.
Answer: We never ended up discussing it really but the last time we mentioned it people seemed ok with it. I would certainly think that it would be on-topic as long as the question stops at the algorithm, i. e. off-topic if the question is about dealing with errors in the code but on-topic if trying to figure out the validity of an algorithm.
Comment: there will not be any "code" specific to a programming language in my question. It will be "psuedocode" i.e. language agnostic. The algorithm in the research paper is mostly English with some explanation. I want to convert it to suitable code but  I have to verify if my algorithm is  correct or not.
Comment: Then I see no problem with you asking the question

Algorithm confirmation


jasper variable expression

Question: I want to declare a variable in a Jasper, of type Integer, that is incremented at the footer of one of my report groups, and reset to 0 at the footer of another report group. How can I specify this in the expression for the variable?
Answer: In the Report Inspector, right-click "Variables" to create a new variable. Name it, set the variable class to java.lang.Integer. Set the calculation type (maybe you're summing over a group?), set the rest type to group, set the rest group to the name of your group, and set the initial value expression to 0 to reset it when a new group begins.

jasper variable expression


What was the price of a theatre ticket in London during WW2?

Question: I would like to know the price of a theatre ticket in the city of London during the second world war.
I can't find this information anywhere.
Comment: Thank you for your question; please consider revising it to be more in line with our community expectations. Like other stacks, we expect questions to [provide evidence of prior research](https://interpersonal.meta.stackexchange.com/a/3227/1599). That helps us to understand the question, and avoids our repeating work you've already done. Our [help], and [other stacks](https://interpersonal.meta.stackexchange.com/questions/3224/how-do-i-write-a-good-question) provide additional resources to assist with revisions. Please revise your question to document your preliminary research.
Comment: Presumably this is London, England (and not just the City of London)?
Comment: Check the London newspaper archives for WW2 for theatre advertisments. They will probably show a range of prices depending on the seating (stalls, balcony, boxes, etc.)
Answer: UK Pre-decimal Currency: there were twenty shillings (s) to a pound and twelve pence (d) to a shilling. If written '7/6, this means 7 shillings and 6 pence.
Exchange rate: for most of the war, £1 = $4.03 so 1 shilling was about 20 US cents.
Prices varied enormously, depending on the theatre, the cast, and (especially) where you were seated. A box for four or five cost several pounds while some stall seats and the balcony could be as little as 2s6d (2 shillings and six pence, about £5 in today's money). At least one theatre offered anumber free tickets to servicemen. Worth noting, though, is that few theatres in central London were open (especially at night) until the London Blitz was over (May 1941).

The example below is for the Q theatre, near Kew Bridge (Hounslow, London), in 1944.

Source
The programme also carried this message in case of an air raid warning during a performance:

Such notices were found in all programmes:

The programmes always include instructions on what to do in the case
of an air raid. Audiences were warned that an air raid was in progress
through illuminated signs, and were free to leave for a shelter if
they wished: 'All we ask is that ' if you feel you must go you will
depart quietly and without excitement', as the programme for Olivier's
Richard III at the New Theatre put it in September 1944. Many
theatregoers preferred to stay put and enjoy the play.

The Windmill Theatre remained open throughout the war (except for 12 days in Sept. 1939) with the Windmill Girls as the main attraction. A special midnight matinee in 1940 cost 1 guinea (1 pound and 1 shilling, or about $4.20 at the time); as this was for war relief, the ticket price was likely inflated. However, for a while (at least) the theatre was giving 500 free tickets a week to soldiers.

"Windmill Theatre Special Revudeville Show.2nd February,1940." Text and Image source.
The Stoll Theatre in Kingsway (central London) had prices ranging from 2s6d (balcony) to 10s6d for a performance of Show Boat in 1943. The London Palladium had an even greater range of prices as it also had boxes, though the example below is for a revue from just after the war (1946).

Source
A little before the war (1937), the Theatre Royal, Haymarket advertised the following prices for a performance of Juno and the Paycock by Sean O'Casey. Again, you can see that prices depend on location within in the theatre.

During the London Blitz especially, the choice of performances was very limited due to the closure of theatres.

Air raids disrupted performances. These problems were ventilated
regularly and fully in trade journals like Theatre World which
lamented in October 1940 that due to the Blitz 'The choice of the
Londoner is now restricted to the delights of the Revudeville at the
Windmill and the lunch-time ballet hour at the Arts Theatre Club, to
which must be added the brave venture of Shakespeare at the
Vaudeville, matinées only'. Things got easier once the Blitz was over,
but the flying bombs of 1944 brought another crisis, closing many
shows...

Nonetheless,

It rapidly became clear that the continuation of normal leisure
facilities would be essential to maintain general morale and some
sense of normality. Londoners and visitors alike needed some
distraction from long working hours, CD commitments, travel problems
and air raids, and theatre-going was a popular pastime.

Productions in 1940 and 1941 included such major stars as John Gielgud, Robert Donat, Alec Guinness, and Michael Redgrave. Also, theatre productions could serve a useful propaganda purpose. Consequently, many productions were subsidized by the government through the Council for Encouragement of Music and the Arts (CEMA) - see, for example, this production of George Bernard Shaw's Arms and the Man.
Answer: According to terramedia.co.uk the average price of a theater ticket in London in 1940 was 4.37 pence. The site has prices for other years if you need that information.,
Comment: Those are the prices for movie theatres rather than for stage productions.


How to work around IE6/IE7 margins disappearing when relatively-positioned floated div is moved with jquery .hover()?

Question: Here is my code:
http://jsbin.com/uhera3/edit
When I use jQuery to .hover(), the relatively positioned floated divs jump to the left (seemingly losing their margins) in IE7.
Any ideas how to fix this?
Answer: I'd suggest implementing IE conditional tags and making an ie-fix.css file.


ios twitter OATH integration not working

Question: I am using Oath authentication in my ios app for twitter integration.
It was working fine earliar but now when I authenticate user then it sends me on this page. Whats going wrong. is there any change in API?
Answer: I think you are using older API that stopped working So now you have to go for new Solution.
Apple Introduced Social Framework that Allows Facebook, Twitter sharing without doing much more & with less efforts.
use This.
Hope this will help.


Is there a free (libre) open source alternative to memtest86+ that works with UEFI?

Question: In light of memtest86+ not working with UEFI, is there an open source alternative or something I can use from grub to test memory?
Comment: Is this a statement of principle ("_must be open source_") or a statement of financial necessity ("_must be free_")?
Comment: @roaima the closed-source memtest86 is available for gratis (mentioned in the linked AU post), so I'd say it's a statement of principle (or other necessity such as validating source code)
Comment: You might use memory stressers that work inside an OS (e.g. inside Linux, as a userland program & process)
Comment: BTW, ten years ago I had a (MSI S270 Turion) laptop with faulty memory: memtest did not detect anything, but kernel compilation failed very often. Replacing the memory modules fixed the issue
Comment: It's a fair request for clarification, but yes libre.
Answer: Yes, there is, and it is now Memtest86+ v6 itself. This is a new version of Memtest86+, based on PCMemTest, which is a rewrite of Memtest86+ which can be booted from UEFI. Its authors still label it as not ready for production, but it does work in many configurations.
Binaries of Memtest86+ v6 are available on memtest.org.
Alternatively, the Linux kernel itself contains a memory test tool: the memtest option will run a memory check with up to 17 patterns (currently). If you add memtest to your kernel boot parameters, it will run all tests at boot, and reserve any failing addresses so that they're not used. If you want fewer tests, you can specify the number of patterns (memtest=8 for example).
This isn't as extensive as Memtest86+'s tests, but it still gives pretty good results.
Some distribution kernels don't include this feature; you can check whether it's available by looking for CONFIG_MEMTEST in your kernel configuration (try /boot/config-$(uname -r)). The kernel won't complain if you specify memtest but it doesn't support it; when it does run, you should see output like
[    0.000000] early_memtest: # of tests: 17
[    0.000000]   0x0000000000010000 - 0x0000000000099000 pattern 4c494e5558726c7a
[    0.000000]   0x0000000000100000 - 0x0000000003800000 pattern 4c494e5558726c7a
[    0.000000]   0x000000000500d000 - 0x0000000007fe0000 pattern 4c494e5558726c7a
[    0.000000]   0x0000000000010000 - 0x0000000000099000 pattern eeeeeeeeeeeeeeee
[    0.000000]   0x0000000000100000 - 0x0000000003800000 pattern eeeeeeeeeeeeeeee
[    0.000000]   0x000000000500d000 - 0x0000000007fe0000 pattern eeeeeeeeeeeeeeee
[    0.000000]   0x0000000000010000 - 0x0000000000099000 pattern dddddddddddddddd
[    0.000000]   0x0000000000100000 - 0x0000000003800000 pattern dddddddddddddddd
[    0.000000]   0x000000000500d000 - 0x0000000007fe0000 pattern dddddddddddddddd
[    0.000000]   0x0000000000010000 - 0x0000000000099000 pattern bbbbbbbbbbbbbbbb
[    0.000000]   0x0000000000100000 - 0x0000000003800000 pattern bbbbbbbbbbbbbbbb
...

while the kernel boots (or in its boot logs, later).
You can use QEMU to get a feel for this:
qemu-system-x86_64 -kernel /boot/vmlinuz-$(uname -r) -append "memtest console=ttyS0" -nographic

(or whichever qemu-system-... is appropriate for your architecture), and look for "early_memtest". To exit QEMU after the kernel panics, press Ctrla, c, q, Enter.
Answer: You can add the freeware (free beer) version of the latest memtest86 into UEFI Grub2 on Ubuntu.
Based on a tutorial, I took the following steps on a remote Ubuntu 16.04 server to add memtest86 to UEFI Grub2:

Firstly, note that grub2 does not show memtest86 nor memtest86+:

This is despite the fact my boot folder clearly has memtest86+. See image below.

Download memtest86-usb.zip to laptop

Send the zip file to the remote machine, then unzip it somewhere (e.g. /home/<username>/memtest86-usb/)

We need to analyze memtest86-usb.img using fdisk -lu memtest86-usb.img to see it's mount offset.

We want to mount the second device listed in the above output, memtest86-usb.img2. The above image shows each sector is 512 Bytes, and memtest86-usb.img2 starts at sector 514048. Therefore it starts at 514048*512 Bytes=263192576 Bytes.

Create a folder (e.g. /home/<username/memtest-tmp) and mount it:
mkdir /home/<username>/memtest-tmp
sudo mount -o loop,offset=263192576 /home/<username>/memtest86-usb/memtest86-usb.img

Use lsblk to check details about the EFI partition as well as your mounted .img file

In the above picture, we note the following:

Where the EFI partition is mounted, here it's at /boot/efi.

Note, in my server, I have the option of choosing the boot mode to be legacy or UEFI in the BIOS setup. I had previously set it to legacy and thus the /boot/efi folder did not exist. Changing the boot mode to UEFI allowed me to see the /boot/efi folder and verify that the EFI partition is mounted there.

The device number. Device name is sda1; thus it's the letter a. This is important later.
The partition number. Device name is sda1; thus it's partition 1. This is important for later
As a sanity check, we also note that memtest86-usb.img2 was mounted to /home/<username>/memtest-tmp.

Next, we verify that the mount point contains an EFI/BOOT folder` and view its contents:

Next, we simultaneously copy and rename /home/<username>/memtest-tmp/EFI/BOOT to /boot/efi/EFI/memtest86 (assuming the target folder /boot/efit/EFI/memtest86):

Next we create a GRUB chainloader entry. Create a file /etc/grub.d/42_memtest, with contents similar to the following:
#!/bin/sh
exec tail -n +3 $0
# This file provides an easy way to add custom menu entries.  Simply type the
# menu entries you want to add after this comment.  Be careful not to change
# the 'exec tail' line above.

menuentry 'memtest86' {
insmod part_gpt
insmod fat
set root='hd0,gpt1'
if [ x$feature_platform_search_hint = xy ]; then
    search --no-floppy --fs-uuid --set=root --hint-bios=hd0,gpt1 --hint-efi=hd0,gpt1 --hint-baremetal=ahci0,gpt1 4418-37D3
else
    search --no-floppy --fs-uuid --set=root 4418-37D3
fi
chainloader /EFI/memtest86/BOOTX64.efi}

In the above picture, we did set root='hd0,gtp1, because our EFI partion was noted as device name = sda1. According to the grub2 convention...

The a in sda corresponds to the 0 in hd0
The 1 in sda1 corresponds to the 1 in gtp1.
We can use the gpt* format to specify partition 1 of device sda because we did insmod part_gpt. We can recognize the disk label type as gpt using the fdisk -l command, and also from looking at the /boot/grub/grub.cfg file.

Also note that we used the EFI partition's UUID, which can be obtained from the blkid command which shows the UUID of all partitions on your machine.

We update grub2 with update-grub2.

Restart and you should see memtest86 in grub2
Comment: A now-deleted answer suggests that "the file `/etc/grub.d/42_memtest` needs to be made executable". I cannot test this at the moment, so I'll leave it here for consideration.
Comment: Please outline the complete steps described in the tutorial. Keep the tutorial link as reference. You do not need to include the screenshots.
Comment: Note that the OP was already aware of memtest86, but was asking for a FLOSS solution.
Comment: The commands after `set root='hd0,gpt1'` find the filesystem with UUID 4418-37D3 and set `$root` to point to it.  So the set command effectively does nothing and can be removed.  Changing it to another disk will just be ignored.  The grub.cfg probably already finds the EFI partition and sets $boot to it.  So `chainloader ($boot)/EFI/memtest86/BOOTX64.efi` would work with needing to find the partition a second time.
Answer: Memtest 6 should work with uefi.
A beta is available at memtest.org
code is available at https://github.com/memtest86plus/memtest86plus
Memtest86+ v6.00 Beta 2
Released: 2022-06-03
v6 is NOT READY for production yet!
Please consider the actual code as experimental and expect crashes and freezes. First non-beta release is expected this summer.
Even though it is beta, I tried it out, downloaded the iso, dd'ed it to a usb stick and could boot it from uefi and it ran memtest just like I'm used to.


how to undo unsuccessful package upgrade

Question: I regularly update my system with "sudo apt update && sudo apt upgrade". It usually works fine. But once upon a time I got a buggy update to Network Manager. I could not connect to network, and had to re-install the system. Is there any easier way to fix broken system in such a situation? Any way to roll-back an upgrade, preferably without network connection?
Comment: You may want to consider using btrfs along with apt-btrfs-snapshot in the future instead of ext4. Although, I do believe it's not recommended for production.
Answer: It isn't possible using apt or apt-get, because you don't have this version offline anymore, but you can do this by downloading older version in .deb package and installing it by dpkg -i filename.deb.


127 million bytes but 204MB on disk?

Question:
Am I missing something basic or is this a bug ?
Comment: Does this answer your question? [Size in bytes is significantly less ( half the size) then size in MB in get info window](https://apple.stackexchange.com/questions/112015/size-in-bytes-is-significantly-less-half-the-size-then-size-in-mb-in-get-info)
Comment: This question unnecessarily relies on an image.
Answer: It's not beyond the realms of possibility. Allocation block size is 4k. If every file was 5k, then they'd each take up 8k on disk, which gives 218MB.
Comment: To expound on that point: I had a situation with about a million or so small files, each about 1KB, which due to the block size, ended up taking up over 4 GB instead of <1 GB, on disk.
Comment: The average file size is 4660.5 bytes, which would agree with your analysis. The average allocated space for each file is 7848.7 bytes
Answer: If all the files are below the allocation block size of the disk by a lot, then that could make perfect sense.
27,254 items all below an allocation block size of 8,192 bytes would lead to an "on disk" size of about 213 MB.
Comment: APFS block size is 4k, so you'd need file sizes to spill over the first block to reach 8k.

127 million bytes but 204MB on disk?


What is the purpose of making authorship of scientific papers public?

Question: Anonymity has the advantage of removing unnecessary bias. It draws the reader's attention on the subject without allowing it to check the authors' affiliations out.
Public display of authors' names and affiliations seems to only be a source for prejudice.
Anonymity would be advantageous to the peer review process, too.
Authors could still be registered with the editor and would remain in any case responsible for what they write.
Comment: What would be the point of anonymity? Why make scientific publishing more like Facebook? Conspiracy anyone?
Comment: One more reason that Buffy did not cover: why would anyone spend time on doing intense and difficult research, only to disappear behind a screen and with nothing to show for their efforts, not even a boost for their ego if not their career? With anonymous publication, you will mostly get shallow and fast responses, with perhaps some interspersed gems of quick clever insights, or standard textbook wisdom a la Papyrus Rhind. I would even venture so far as to claim (without proof) that maybe the rise of systematic research may be linked to the emergence of rules on authorship and plagiarism.
Comment: Nothing stops one from using a pseudonym. But use it consistently.
Answer: This won't, and probably can't, be a complete listing of the reasons that almost all scientific papers are and should be associated publicly with their authors. I'll try to list reasons in the rough order of importance, but even that is hard.
If I know that an author has been writing valid papers in the past, it eases my burden of personally vetting the current one.
If I don't know the authors, then I have to depend on the complete validity and accuracy of the publisher's process, which was done by people who I also don't know.
The likelihood of collusion would be expected to increase if the public doesn't know authors but editors and reviewers do. This might be ameliorated somewhat if reviewer names were attached to papers instead of author names, but that has its own problems.
Plagiarism might be expected to increase with anonymity and might be difficult to check. "I wrote that" can be disputed by an editor, but that requires a separate process that might interfere with some other policies, such as confidentiality. The editor can't, for example, say "No, John and Mary wrote that" as it breaks confidentiality. Claims of authorship, both valid and invalid, will likely be made, breaking anonymity along with reducing trust.
Scientific reputations would be much more difficult to build and maintain with anonymity. There would be less incentive to write if there is no public recognition and there might be more incentive to write junk if it won't come back to haunt my career.
The same would be true for university and scientific lab reputations. Who do you trust? Who do you hire?
The incentive for intentionally misleading research would be increased if no one needs to stand behind results. It is already bad enough given the history of tobacco "research".
Probably lots more reasons are evident to others, but the above is a start.


Do United same day changes apply for travel starting on different airlines?

Question: I am slated to fly on UNited from CCU-DXB-EWR-ORD-DSM. The CCU-DXB is on Emirates (EK). The connection at EWR is too tight for my taste (1:23, I am surprised UA gave me a ticket on this connection). So, I would like to consider CCU-DEL-EWR-ORD-DSM. The CCU-DEL leg would be on Air India (AI) or Vistara. All other flights are on United metal. Would a SDC (same day change) be possible here? Thanks!
Comment: what did the airline say when you called them and asked?
Comment: My date of travel is not till in a few days, so I don't think I can do it. I have also read that SDC changes depend on who you get on the phone, so I thought knowing how things work before i make my call would be more useful for me.
Comment: SDC doesn't seem to be doing anything even for me as 1k premier member. The few times I tried there was never any availability and the terms seems no different from any other change. Your best bet is to go on the website right now and price out the change. If you are lucky it's the same cost or even cheaper. If it's more expensive SDC won't help.
Answer: No.  Same-day change is only available on United-Metal flights.
Once you are in the air on the first leg you might be able to use Same-day change change the later flights (using the United App), although given your itinerary it's unlikely that any alternatives will be available.
1 hour 23 minutes is a tight connection, but it's also very doable depending on the queues at immigration - especially if you are a US citizen, and even more so if you have no check baggage.  If you do miss-connect in Newark, United will move you to a later flight to get you to your final destination.
Comment: I don't get the purpose of the SDC. How is this different from any other change? You are still on the hook for the fare difference and United has waived almost all change fess.  They seem to imply that they wave price differences in the same fare class, but I though prices within a fare class don't move.. If they want to raise the price they close K fares and the price moves up to L fares.
Comment: @Hilmar Sounds like a new question to me. However the simple answer is that there are no fare differences with SDC, as well as no advance purchase requirements/etc.
Answer: In your shoes, unless you really have to get to Des Moines on that specific day, I would do nothing and try my luck with the connection they've given you.
If you're lucky, you'll make the connection, although I agree 1:23 is awfully tight for an international to domestic transfer anywhere in the US.  If you're not, United is responsible for getting you to DSM by some other route, and there should be plenty of possible connections from a major airport like EWR — although depending on time of arrival etc etc you might get delayed by up to a day.
Also bear in mind that regardless of what flights you originally book, you do have four (!) connections you need to make along the way, so it would be wise to allow some buffer in your plans in case something does go wrong along the way.
Comment: I've made international to domestic connections in less than 30 minutes. Of course that only works with Global Entry, no checked luggage and TSAPre Check :-)


How can I make Safari cmd+number shortcut switch tabs instead of opening the bookmark associated with that number?

Question: I'm used to switching tabs with cmd+x where x is a number and takes me to tab x in firefox and pretty much every other browser I've ever used.
I like safari's speed and would like to try it a bit, but the cmd+x shortcut is burned in my brain and every time I use safari I end up screwing up.
I'd like to know if its possible to change this behavior, because this simple thing is a stopper for me.
Comment: One more thing: the fact that "Show Previous Tab" and "Show Next Tab" are present in the Safari menu means that you can assign _any_ shortcuts for changing tabs in System Preferences (Keyboard->Shortcuts)
Comment: In addition, the current (6.0.3) behaviour of replacing whatever one had on the browser window is highly annoying. I often press cmd-1/2/3 in accident (i.e. while taking screen shots using shift-cmd-3/4). These keys REALLY should be reassigned by Apple. Bad feature. (I'm not the only one: https://discussions.apple.com/thread/3464021?start=0&tstart=0)
Comment: I'm putting a bounty on [this answer](http://apple.stackexchange.com/a/201259/5472) how to do this with Safari v9
Comment: As of OS X El Capitan, this feature is now enabled by default in Safari.
Answer: In case you are coming from Chrome and want to use
cmd+[0-9] for switching tabs (instead of cycling through your preset top sites) take a look at:
github.com/rs/SafariTabSwitching

Safari Tab Switching is a Safari SIMBL plugin which allow switching between tabs using Cmd+1-9.

Update:
Safari Version 9.0.2 (El Capitan) has native support for this:
Comment: This is exactly what I was looking for. I just updated to Yosemite and I was hoping to replace Chrome with Safari and cmd + 0-9 was one of the shortcuts I was missing. Thanks!
Comment: This is much nicer than Ctrl+Tab!
Comment: UPDATE: Looking at this issue - https://github.com/rs/SafariTabSwitching/issues/27 - helped me fix the problem. It now works for me on Safari 8.0.4
Comment: This did not work for me. I run safari 8.0.4 and Even though installation was successful, the `cmd` + `[0-9]` shortcut does not work
Comment: @gprasant I'm running Version 8.0.4 too. Perhaps have a look at the issue tracker on github?
Answer: Easy!
Ctrl+Tab and Ctrl+Shift+Tab
Comment: It seems you have answered your own question. That's a good way to share your knowledge, as said in Stack Exchange FAQs.
Answer: Check SafariTabSwitching.
Comment: This works perfectly for me. Safari 5.1.2/Lion.
Comment: Works for Safari 6.0.3/Mountain Lion :D
Comment: Works great in Safari 7/Mavericks too.
Comment: Updated for Safari 8 (10538.35.8) / Yosemite (10.10, 14A238x) too.
Answer: In El Capitan, OSX 10.11, this has been included as a new feature of Safari Version 9.0 (11601.1.50).
Go to Preferences > Tabs > Use ⌘-1 through ⌘-9 to switch tabs
Comment: OMG! FINALLY! HAVE ALL THE UPVOTES!
Comment: Why was this awarded 50 points?
Comment: Yeah, why not A MILLION?!!
Comment: Now I wish Finder tab can use the same shortcut!
Answer: In most native OS X applications, the key presses Cmd-Shift-[ and Cmd-Shift-] will cycle left and right through tabs, respectively. Safari understands these.
If you use something like BetterTouchTool, then you can assign gestures (such as a three-finger swipe left or right) to these key presses, and get tab cycling across most of OS X.
Comment: I go with these because they stack nicely with history.back and history.forward (Cmd-[ and Cmd-] respectively). Cursor keys often get stuck on input fields when attempting to navigate history.
Answer:
To go to the previous tab, press ⌘ Command ⇧ Shift ← Left
To go to the next tab, press ⌘ Command ⇧ Shift → Right

Traveller's note : These keyboards equivalents may be reversed in a right-to-left environment.
Answer: To go to the next tab ⎇ Control+Tab or
 ⇧ Shift+⌘ Command+] or ⇧ Shift+⌘ Command+→ Right
To go to the previous tab ⎇ Control+⇧ Shift+Tab or ⇧ Shift+⌘ Command+[ or ⇧ Shift+⌘ Command+← Left
Comment: this answer is the most complete
Comment: That's what I need.
Answer: Safari 9.0, released today for 10.9 Mavericks and 10.10 Yosemite, along side with the 10.11 El Capitan release, has introduced this natively.

There are two options. If checked, ⌘-1 through ⌘-9 will switch to tab 1 through 9, respectfully. This will change the original behavior of mapping to the favorites bar bookmark 1 through 9. Those will be changed to Command-Option-1 through Command-Option-9.
If unchecked, while it does not say it, the behavior is reversed. Command-Number will still be the favorites bar bookmark, while Command-Option-Number will be the tab. This flipping of behavior matches the Command-Click and Command-Option click behavior for opening a link.
It's undocumented.
Comment: Good catch. This should be upvoted more!
Answer: What about setting bookmarks 0-9 to be bookmarklets that change window tabs?
Comment: @yanis - if there's something specific you want to know, your best bet is to open a new question.
Comment: Looks like my only option, so far... I'll try that.
Comment: how can this be done?
Answer: I personally like the keyboard shortcut used in Chrome and Opera: Option+Cmd+(left/right arrow keys). This can be assigned in System Preferences-->Keyboard-->Shortcuts-->App Shortcuts. Press the plus button and add a pair for Safari with the command names "Show [Previous/Next] Tab" and then type the key sequences you want to use. Pretty handy. Good luck!
Comment: I also wanted to have chrome like shortcut but wasn't able to find the right command name for the shortcut. How did you find out the command? Is there a list provided by Apple?
Answer: control-tab
the simplest way
Answer: Yes ctrl + (0-9) by using this shortcut you can navigate across multiple tabs in windows
Comment: Could you explain how control + 0 is different than command + 0 ?
Comment: By "in windows" venu means "in Windows" -- It is, in this context, an entirely pointless and unhelpful suggestion. Ctrl for Windows, Cmd for OSX.
Comment: This suggestion is incorrect on OS X. Control-digits do nothing in Safari, and Command-digits open items in the Favorites bar.


Median of medians as robust mean of means?

Question: The location and scale of a normally distributed data can be estimated by sampling the data then taking the mean of the sample means and standard deviations, respectively. For non-normal (heavy-tailed) data, is it correct to take the median of the sample medians and IQR/MAD, instead? That is, is it correct to use the median of sample medians as a robust estimator of location similar to the mean of sample means for normal data?
Answer: If all the samples come from the same distribution, then yes the median of the sample medians is a fairly robust estimate of the median of the underlying distribution (though this need not be the same as the mean), since the median of a sample from a continuous distribution has probability 0.5 of being below (or above) the population median.
Added
Here is some illustrative R code.  It takes a sample from a normal distribution and a case with outliers where 1% of data is 10,000 times bigger than it should be.  It looks at the various statistics for the overall sample data (50,000 points) and then by the centre (mean or median) of the statistics of the 10,000 samples with 5 points in each sample.
<code>library(matrixStats)

wholestats <- function(x,n) {
     mea <- sum(x)/n
     var <- sum((x-mea)^2)/(n-1)
     sdv <- sqrt(var)
     qun <- quantile(x, probs=c(0.25,0.5,0.75))
     mad <- median(abs(x-qun[2]))
     c(mean=mea, variance=var, st.dev=sdv,
       median=qun[2], IQR=qun[3]-qun[1],
       MAD=mad)
    }

rowstats <- function(x,b) {
     rmea <- rowSums(x)/b
     rvar <- rowSums((x-rmea)^2)/(b-1)
     rsdv <- sqrt(rvar)
     rqun <- rowQuantiles(x, probs=c(0.25,0.5,0.75))
     rmad <- rowMedians(abs(x-rqun[,2]))
     c(mean=mean(rmea), variance=mean(rvar), st.dev=mean(rsdv),
       median=median(rqun[,2]), IQR=median(rqun[,3]-rqun[,1]),
       MAD=median(rmad))
    }

a <- 10000 # number of samples
b <- 5     # samplesize

set.seed(1)
d <- array(rnorm(a*b), dim=c(a,b))
doutlier <- array(d * ifelse(runif(a*b)>0.99, 10000, 1) , dim=c(a,b))
</code>
The median based statistics as expected are more robust, though they fail to show that the heavy tailed outlier variant is heavy tailed.
<code>> wholestats(d,a*b)
        mean     variance       st.dev   median.50%      IQR.75%          MAD
-0.002440456  1.011306552  1.005637386 -0.001610677  1.357029247  0.678706371
> wholestats(doutlier,a*b)
         mean      variance        st.dev    median.50%       IQR.75%           MAD
-3.425664e+00  9.591583e+05  9.793663e+02 -1.610677e-03  1.373658e+00  6.871415e-01
> rowstats(d,b)
        mean     variance       st.dev       median          IQR          MAD
-0.002440456  1.014611308  0.947630870  0.003460172  0.917642167  0.510115277
> rowstats(doutlier,b)
         mean      variance        st.dev        median           IQR           MAD
-3.425664e+00  9.607212e+05  1.685929e+02  3.460172e-03  9.301795e-01  5.175084e-01
</code>
Comment: Thanks! It seems that this method is not quite common or I'm just reading the wrong papers/books. Is it really not common? Is there a more standard way to solve the problem? Can you suggest keywords/references where I can learn more about this?
Comment: @ianalis: The median of sample medians works well, and is still close to the "true" median of 0; it is not the same as the overall median but there is no reason to expect that it would be.  The mean of sample means does give the overall mean (if the sample sizes are equal).  Combining measures of dispersion from different samples is more complicated, especially with median or quantile based measures: with variances the answer is to use the denominator $n-1$ to get unbiased estimates, as shown here.


Continuous reading mode in TexWorks built-in pdf viewer?

Question: I recently downloaded TeX Live 2013 to use LaTeX on my Windows 7 machine. I like the interface of the TeXworks editor that came with it because it is similar to TeXShop that I like a lot when I am using my office Mac, so I wanted something similar for my (Windows) home machine. It works great except that I cannot use its built-in PDF viewer in a continuous scroll mode. As I scroll down, at the end of each page it stops, and needs an extra scroll to jump to the next page, without the ability of showing the bottom of the previous page and the top of the new page at the same time. I could use another PDF viewer like acrobat but I think they do not support sync between the TeX document that created it so that I ctrl+click one to jump to the corresponding paragraph in the other, which is a big convenience that I don't want to give up either. Is there a way to configure TeX Live/TeXworks in a way to have continuous pdf view mode?
Comment: There is a [corresponding feature request](https://code.google.com/p/texworks/issues/detail?id=617&q=type%3DEnhancement&sort=-id). But since development somehow stagnates, this can take a while. That said, I think this question is off topic here.
Answer: Not possible in TeXworks at the moment, the viewer doesn't support it. There is an open feature request (https://github.com/TeXworks/texworks/issues/617), and there are plans to include it in the  next major release of TeX works (0.6): https://github.com/TeXworks/texworks/wiki/Roadmap
Answer: This problem is still present in 2016, TeXworks version 0.4.6-3.10.
I use a workaround which makes it a bit more tolerable:
Scale down the preview size so that one whole page fits into the window. Then one can cycle through the document without interruptions. The trade-off is a reduction in size/readability of the preview.
This can be done under Edit -> Settings -> Preview. In this menu, change the value for "fixed enlargement" to something below 100% until the page fits. One probably needs to restart the program to see the effect.
Note that I may have gotten the menu names wrong in these instructions, b.c. I'm using a German interface. It should be obvious, though, what is meant.


Interferometry experiment using laser beam reflection from object: does being closer to the object produce a better signal/measurement?

Question: Let's say we're conducting an interferometry experiment. The experiment is such that we're reflecting collimated laser light off some object and then using the information contained in the reflected light from the object to perform some measurement. Does being closer to the object (say, 1 metre instead of 10 metres) produce a better signal/measurement? The answer seems obvious, but I'd like to double-check and perhaps get some details about the physics. My thoughts here are that, unless the object has some kind of perfect reflectivity and the path is in a vacuum, not all of the reflected rays (even if the beam was collimated) will be reflected at a parallel angle, and, so, there will be some divergence that will cause the returning rays to miss the detector, resulting in lower signal / inferior measurement. Furthermore, it seems to me that, the rougher the surface of the object is, the better signal/measurement we'll get the closer we are, compared to, say, a mirror, right? (Although, I suspect this last point is confusing scattering with reflection, right?)
Answer: It really depends on what you want to do. Generally speaking, the farther you place the detector, the lower the amplitude you will measure of the scattered signal, and therefore you would want to detect the signal closer to the scatterer to get a better signal to noise ratio. On the other hand, perhaps you are going to analyse your measurement with some far-field theoretical solutions (approximations of the scattered signal far from the scatterer) and in this case you don't want to detect too close because your model no longer applies.
As for the angles, the detected signal changes depending on the angle in which you place your detector (the angle with respect to the incident signal and the scatterer). I would guess that the back-scattered signal is usually the one that contains for information about the scatterer, but this is only a guess and this probably depends on the characteristics of the region of the surface where the incident signal meets the scatterer.
Comment: "On the other hand, perhaps you are going to analyse your measurement with some far-field theoretical solutions (approximations of the scattered signal far from the scatterer) and in this case you don't want to detect too close because your model no longer applies." That's beyond what I was alluding to; I'm referring to relatively simple interferometry experiments.


Is there transformation of self through realization in Western Philosophy

Question: Transformation through realization a.k.a enlightenment is a recurring theme in eastern philosophy. Is there a counterpart for this in Western Philosophical writings?
Answer: "Transformation of self" and "transformation through realization" are both pretty opaque statements. There's definitely themes of "transformation" (e.g. Plato), "enlightenment" (e.g. Kant), "progress" (Hegel, Marx), "authenticity" (Kierkegaard, Heidegger), wonder (e.g., Plato, Aristotle, Aquinas), and other things through the philosophical corpus.
If your specific question is about the self, then there's a lot on the evolution of the idea of the self in Hegel's Phenomenology, Sartre's Being and Nothingness, Anti-Climacus's [Kierkegaard's] Sickness unto Death and Taylor's Sources of the Self.
If you mean specifically the religious-spiritual mode in which that occurs in some eastern thought, there are similar traditions about self-knowledge before God in the Christian mystics and some Western philosophers.
Comment: Thank you - I meant the transformation of the self through realization - not merely inquiry into the self/but the record that the subject of the inquiry undergoing an irrevocable change due to the inquiry/introspection and hence the assertion that it is a possibility for everyone.  After reading your and the other posts, Christian mystics, yes. And William James, Maslow etc. I guess.
Comment: @zrini Kierkegaard also suggests such a transformation in *Philosophical Fragments*
Answer: Yes there is. Read the "Cloud of Unknowing", "Dark Night of The Soul", "The Interior Castle", "The Philokalia", and "The Way of Perfection" all by Christian mystics.
Answer: Like many philosophical concepts, one need look no further than Plato. The Delphic maxim γνῶθι σεαυτόν or "know thyself" is oft used by his protagonist, Socrates.
Answer: The phrase you are looking for is the "beatific vision".  It is the idea that our perceptions of beauty, truth and goodness in this world are a glimpse into a deeper reality which is accessed through the soul and self knowledge.
The first occurrence I know of is in Plato's Republic, which explains how seeing the Forms frees a person from slavery and teaches them who they really are, and uses the city as an image of the soul in order to understand a correctly ordered soul.
This theme is picked up by Christian philosopher theologians such as Boethius, Augustine, Justin Martyr, Bonaventure and Aquinas.  It is also a standard hermeneutic principle during the Middle Ages, where the deepest meaning of religious scripture is how the soul achieves the beatific vision.  In fact, it is the defining pursuit of philosophy and theology during this time.
The best popular expression of this idea is the Divine Comedy by Dante, which is a story about the escape of the soul from a false understanding of self to achieving the beatific vision.
Answer: Yes, there is. Heraclitus, Socrates, Jesus, and Spinoza achieved it, even tho they didn't know the term, as had millions of humans who lived before the nuclear family apocalypse 3000 years ago. It is universal, Upanishads, for example, are all about it.
And it is the real enlightenment -- the opposite of its "ego death" fake. Your Ego is your Self, your human soul. "Ego death" is when your soul, your humanity dies. What is left is the animal mind, what we inherited as-is from our, well, animal ancestors. Pets are happy bc they are born, live, and die "enlightened". "Ego death" brings a person closer to the happy state of animals, but the latter are still ahead because they are incapable of suffering and they will never know death.
The real enlightenment achieved by fully developing your humanity, by letting your soul flourish. In scientific terms, it means acquiring a fully rational system of beliefs. For starters you must be your rational conscious Self -- you must think for yourself. Most people live as their egos, and it's impossible to convince any one of them to try and become Self.
The Self can actually think in terms of mental models -- 3-D models of some aspects of reality. Individual models can be pieced together like a jigsaw puzzle (also "connecting the dots") into a more comprehensive simulation. Fitting each piece, connecting models makes a eureka moment, the proverbial light bulb going off in your head. When you reach a critical mass, there will be a moment when everything falls in its places and your whole world lights up -- that's enlightenment. Before that moment you were wandering through your life like through a dense forest with your eyes closed. Enlightenment opens your eyes. It liberates you in general -- to see where you are going, to know what you are doing. And liberates you from fear. Only when you are not scared of death anymore you will not be afraid to live your life.


In my registry I have the 4.5 .NET framework indicated as installed, but I can still patch 4.5.2 manually

Question: I was trying to patch my Windows Server 2012s through a patching service, however the 4.5.2 patch was not showing up as applicable. After some digging with the service, we figured out that the registry key was indicating we only had 4.5 installed. However, I can manually patch the 4.5.2 framework just fine with a standalone installer. Shouldn't Windows Updates find this not applicable or why would this be?
Comment: `the registry key was indicating we only had 4.5 installed`. What is the version in the registry? What is the name of the standalone installer that you ran?
Comment: The release field says 378389, which based on this article, https://docs.microsoft.com/en-us/dotnet/framework/migration-guide/how-to-determine-which-versions-are-installed, says that's 4.5. It was one I got from the microsoft update catalog KB4532928.
Answer: The Windows Update detection logic is correct. .NET 4.5 is no longer supported, so it should be expected there would be no offering. You may want to consider updating to a version that is not end of life.
https://devblogs.microsoft.com/dotnet/support-ending-for-the-net-framework-4-4-5-and-4-5-1/
Answer: 4.5.2 is technically a different version of .Net than 4.5 and not just a patch. So it would be correct to not be offered a patch for 4.5.2 when 4.5 is installed but still be able to update to 4.5.2 with a 4.5.2 installer.
As @greg askew has said however, 4.5 is no longer supported. I would recommend updating to 4.8 which is the current version. See https://docs.microsoft.com/en-us/dotnet/framework/migration-guide/versions-and-dependencies for the available versions and the detection registry keys.


How can I make the plagiarism detector "Ithenticate" identify "θ-continuous" as a single word?

Question: I have a problem with the similarity index of one of my works since the plagiarism detector "Ithenticate" identifies θ-continuous as continuous. In my university, all that matters is the similarity index whatever the report shows. So if you please know a way to make Ithenticate identify θ-continuous as a single word, I will be very grateful. But please note that using parentheses around it like "θ-continuous" is not an option since no Journal will publish it this way. Thanks.
Comment: What happens if you write it as "theta-continuous"? Being familiar with software development, it would not surprise me if the tool just skipped everything that it can't make out to be a word (And all words are written in Latin alphabet aren't they?), leading to the exact problem you describe.
Comment: I can't quite believe that a single word is responsible for a problematic similarity index. There must be many more similarities between your text and published articles, if you reach a problematic level. Maybe if you take care of the other similarities, this one word won't matter any more. —— Also, if the similarity is obviously caused by a software problem (that is, the software is unable to differentiate θ-continuous from continuous) you should be able to bring up this problem with whoever is responsible for the evaluation of your text.
Comment: *Is* it even an actual word, or just something that you've coined with hyphenation or hyphenated to use as an adjectival phrase? There might be another way of phrasing your sentence if its use is so concerning.
Comment: Thank you all so much for your answers.  θ-continuous is known in topology but I am applying it in new concepts. I was also surprised that  θ is ignored and the words befor it and after it (even if only one word) are all considered as if   θ not there!.
Comment: Someone in the SuperUsers.StackExchange may know how to tweak Ithenticate to do what you want.
Answer: You can't
I looked through the web, searching for information about problems with Ithenticate and symbols or greek letter, and I couldn't find any information about how to change the bahviour of Ithenticate in such a way. You should probably just try to reduce the index through other means. To copy a comment from the now deleted user32754 so that it won't get lost in the future:

I can't quite believe that a single word is responsible for a problematic similarity index. There must be many more similarities between your text and published articles, if you reach a problematic level. Maybe if you take care of the other similarities, this one word won't matter any more. —— Also, if the similarity is obviously caused by a software problem (that is, the software is unable to differentiate θ-continuous from continuous) you should be able to bring up this problem with whoever is responsible for the evaluation of your text.

You could also try to write the word differently. Again, a comment, this time from the user fer-rum:

What happens if you write it as "theta-continuous"? Being familiar with software development, it would not surprise me if the tool just skipped everything that it can't make out to be a word (And all words are written in Latin alphabet aren't they?), leading to the exact problem you describe.

To support the above thesis I looked at what Ithenticate thinks about other letters and symbols. For example here you can find information about what Ithenticate thinks about symbols in their article Plagiarism Detection Software MISCONCEPTIONS under the heading "Plagiarism Detectors Are Easy to Deceive":

Especially as more academic institutions and publishers begin mandating the use of plagiarism detection software, there are increasing attempts to devise methods of tricking the system into passing off duplicated text as original. Students have gone to great lengths to cheat the system—substituting Cyrillic letters that look similar to Latin letters throughout the text, adding extra spaces between letters and words, or even adding "invisible" small letters in white font to differentiate the text, often posting their strategies online for others to use. What is less publicized is that behind the scenes, the creators of plagiarism detection software go to even greater lengths to anticipate cheating strategies and to incorporate fixes into their systems. Many plagiarism detection software systems automatically strip macros from submitted manuscripts and can easily detect oddly placed punctuation and invisible characters.

It's quite possible that your addition of the greek letter theta is simply recognized as an attempt to circumvent the normal rules for detecting plagiarism and there are methods in place to deal with such an attempt - namely ignoring this symbol.
It won't be easily possible to change this from your position. The exact rules won't be published anywhere. Otherwise everyone could simply get around the software and they wouldn't survive very long in the market.


Why do I need a Bonferroni correction if we are evaluating our primary outcome?

Question: We have completed a study comparing control with  vitamin D supplement and with bone building drug. The primary outcome is change in bone mineral density. My statistician states that because we are using ANOVA to compare control to vitamin D Control to Bone building drug and vitamin D to bone building we have to do a Bonferroni correction. But this is the primary end point of the study. Why would we need to do this correction?
Comment: Primary endpoint and primary outcome is the same, so the second last sentence does not make much sense. How many null hypotheses are tested in total to answer the primary research question? I'd say more than one, thus supporting your statistician.
Comment: maybe this can help you ? http://stats.stackexchange.com/questions/167289/is-there-a-multiple-testing-problem-when-performing-t-tests-for-multiple-coeffci/167338#167338
Answer: As quoted in an answer on this Cross Validated page, "this is a subject on which reasonable people can differ." See that page for links to further discussion.
Presumably there is an overall significant ANOVA or this wouldn't be an issue. Thus I take it that you have found some difference in bone density among your 3 groups (control, vitamin D, bone-building drug) and the question is which pairwise differences are "significant."
I'd suggest that you think about the significance tests as protecting you from fooling yourself about those pairwise differences. That said, the Bonferroni correction might be more conservative than necessary. With only 3 groups and an overall significant ANOVA, the Fisher LSD test could provide adequate protection, and the Holm-Bonferroni method, as noted on this page, provides a less conservative and more powerful alternative to the simple Bonferroni correction.
Finally, don't lose a focus on the magnitudes of the treatment effects, which are probably more important for guiding future work. It's too easy to get hung up on statistically "significant" differences that aren't of practical importance. For example, say you found that the bone-building drug led to a "significantly" higher bone density that was only 2% more than that with vitamin D. If the drug costs 200 times as much as vitamin D, what would you recommend as a policy decision: drug, or vitamin D?


Selecting only community partner Users in Apex code

Question: i have to select Only Users which are community partner Users.How to select them ??what will be the SOQL query for selecting partner Users ?? which field in User profile will tell whether the user is community partner User or not ??
Comment: Partner Users would have the AccountId and ContactId set on them, unless you also have Customer Community Users, you can filter using where AccountId != null and ContactId != null
Answer: You can select by Profile name. Check which profile your community users have, and use that in your query.
<code>[SELECT Id FROM User WHERE Profile.Name = 'Partner Community']
</code>
Answer: Partner portal users also have access to Community So, it is better to filter a query by Community license:
This will return all users who have a profile with license of community.
<code>List <User> communityUsers = [SELECT id, Name FROM User WHERE Profile.UserLicense.Name='Partner Community' OR Profile.UserLicense.Name='Customer Community'];
</code>


How to track orbit of an exoplanet?

Question: I was wondering if there is an established method to keep track of the orbit of an exoplanet assuming we know $a$ - the semi-major axis of the orbit, $e$ - the eccentricity of the orbit, and $i$ - the inclination of the orbit. Can we track its position once a month?
Comment: For additional clarification, what kind of tracking are you seeking: as viewed from the Earth (i.e. Earth-Sun-Exoplanet angle), celestial coordinates, simply the position of the exoplanet in its own orbital plane, etc.? Also note that there is the [Astronomy Stack Exchange](https://astronomy.stackexchange.com): you may receive a good response there too.
Comment: @NiharKarve I mean as tracked by the earth! Thank you!
Answer: Exoplanets are discovered and observed via a fairly wide range of indirect methods, and those are how we measure the parameters of their orbits. Some methods allow us to get complete determinations of the orbits and the exoplanet parameters, while others only allow us to provide constraints on those parameters. If you want to know where the exoplanet is in its orbit right now, then the answer will depend on what method was used to find it.
Wikipedia has a full page on the various methods used to detect exoplanets, but by a large margin the two main ones are transit photometry and radial-velocity imaging.

In transit photometry, we simply set a camera to stare at the star for years on end, hoping to catch the exoplanet passing between us and the star ("transiting"), at which point we detect a slight dip in the brightness of the star. A series of periodic dips allows us to infer the existence of the planet.
If an exoplanet is detected in this way but not with any other methods, we have no information about where it is except at the times when it transits. We get a good idea about how big the orbit must be, and we know how long we need to wait for another transit, but that's it.

In radial-velocity imaging, we measure the velocity of the star as it wobbles under the gravitational pull of the planet. This is limited in measuring the inclination of the orbit (it can't distinguish between a mid-inclination orbit from a higher-inclination one with a bigger, more massive planet), but it does provide a constant stream of data on the orbit.
As such, the orbit itself is fuzzier, but there is a degree to which you can, at any point, point your telescope at the star and get a direct, relevant signal about how the planet is doing.

For the small fraction of exoplanets where we're able to directly image the exoplanet itself, once the orbit has been established then yes, you can point your telescope at the star at any time and directly track the planet.

That's about as much as you can say at this level of detail -- for more, you should really take a deep dive into how the different detection methods work.
Answer: The short answer is yes. When a planet orbits a star then both the star and the planet are on opposite sides of their common center of mass at any point in time. Their distance to the common center of mass is proportional to their relative mass.
To simplify. When the star is in its left most position the planet is in its right most position as viewed from earth. The limit of how accurately you can determine the location of the planet is defined by how accurately you can measure the position of the star.
Comment: This isn't really applicable. If you want to track an exoplanet by direct imaging, then yes, you would be limited by the accuracy in measuring the position of the star -- but there is no technology that can track stars that accurately. Exoplanets are discovered and tracked via other, indirect methods.
Comment: The first exoplanets detected was precisely through the method I described.

https://en.wikipedia.org/wiki/Methods_of_detecting_exoplanets#Radial_velocity

How to track orbit of an exoplanet?


Infinite differentiability of a function with a removable discontinuity

Question: How would I prove that $\frac x{e^x-1}$ is infinitely differentiable?
(This question came up since the No 1 answer in Maclaurin series for $\frac{x}{e^x-1}$ states that the function is infinitely differentiable, which - at least to me - isn't obvious at the first glance. Both the function and all its derivatives have a power of $e^x-1$ in the denominator which causes a (removable) discontinuity in $x=0$, but I suppose the answer can't be to look the removability of this discontinuity for all derivatives, right?)
Comment: What the poster really meant was that $f(x)=\{ \frac{x}{e^x-1}$ if $x\neq 0$, $1$ if $x=0$ is infinitely differentiable.  In proving the differentiability you'd have to look at 1-sided limits in the definition of the derivative.
Comment: @mathematician I know, but still - how do I *prove* that this function is infinitely differentiable?
Comment: Inductively. The only point of concern is $x=0.$ Now take derivative at nonzero $x$'s and take derivative at zero using its definition as the usual quotient. If limit of $f'(x)$ as $x$ goes to zero is equal to $f'(o)$ the $f'$ is continuous, and that proves $f$ is $C^1.$ Then you must see a pattern emerging for second, third, ... derivatives.
Answer: Hint: Look at $g(x) = (e^x-1)/x$ instead. Then $g$ equals a power series that converges on all of $\mathbb R,$ hence is $C^\infty.$ Show that $g$ is never $0.$ Therefore …
Comment: I think this is a short, excellent idea for the asker. +1
Answer: Note that, if $f(x)$ is infinitely often differentiable and $f(0) \neq 0$ then $\frac{1}{f(x)}$ is infinitely often differentiable in $x=0$. This follows by induction, since you can show by induction that the $n$-th derivative of $\frac{1}{f(x)}$ is of the form $\frac{p(f, f^\prime, ..., f^{(n)})}{f^{2n}}$ with a polynomial  $p$ of $n+1$ variables.
Apply this to $f(x)= \frac{e^x-1}{x}$


How to make a no-break update for web application of WAR package under Tomcat?

Question: I have a host running Tomcat. Updating my web application is quite straight, upload the WAR package of the new web application to the Tomcat's webapps directory, then it is done. However, in the uploading process, the web application becomes invalid, I will get a 404 error if I try to access the web application when the WAR package is uploading. That means I get a short time break. Obviously, this is not good for production environment. How can I do if I want a no-break update?
Answer: Basically, your application is not running until Tomcat fully deploys it. There is no easy way to solve that. Well, not as easy as you put. But, there are ways to avoid that.
You need to have more than one Tomcat instance running. You need to make sure one will be up until the other can server the application. Two terms that can help you: Load Balance and Cluster. They might overlap each other but they are two different things, specially in Tomcat world.
You could try to bind your Tomcat with an Apache HTTP or any other web server, reverse proxy your application (let's say /app1) and when you need to deploy a new version, you would deploy the application under a new context (/app2) and redirect to the new context (Apache reverse proxy /app2 instead of /app1).
That is one way to do it with one host. You just need to be creative. :)
Searching for Load Balance and/or Cluster might give you other ideas as well.
Please feel free to ask more as you question was quite generic and you didn't provide much more information. :)


How do I change th location of Steam games in my Start Menu?

Question: I find the default "ProgramName" or "CompanyName/ProgramName" scheme of Windows' Start Menu hard to navigate, and always arrange it in a category structure ("Media/Winamp" and such). Unfortunately, Steam does not offer a choice of where to put it in Start Menu, and even if I move it manually to "Games/Steam", newly installed games still appear at "Steam". Moving them every time by hand is a hassle, and probably causes problems at uninstalling as well. Is there a way to override this location in Steam configuration/registry/etc?
Comment: Try this: move the contents of your Steam Start Menu folder into Games/Steam, then make a junction point from Steam to Games/Steam (`mkdir /J "%USERPROFILE%\Start Menu\Programs\Steam" "%USERPROFILE%\Start Menu\Programs\Games\Steam"`); it might clutter your Start Menu a bit, but at least it ought to work.
Comment: Thanks, this worked perfectly (though the command is called `mklink`). After giving the link the hidden attribute, it even disappears from start menu (that needed a restart to take effect, IIRC). Want to answerify it so I can accept?
Answer: You can make a Junction Point to trick Steam into creating its shortcuts into Games\Steam. Move your current shortcuts into your Games\Steam folder, delete the original Steam folder, and use the command

mklink /J "%USERPROFILE%\Start Menu\Programs\Steam" "%USERPROFILE%\Start Menu\Programs\Games\Steam"

This way, the shortcuts truly exist in your Games\Steam folder. You can then give the hidden attribute to your junction point to stop it from showing in the Start Menu.


Is it possible to get the name of a physical quantity related to a quantity, e.g. watts->power?

Question: Is there a way to get the name of the physical quantity given by a particular unit?  For example, QuantityUnit[Quantity[1, "Henries"]] returns "Henries",  but I want to know what "Henries" are a measure of.  That is, "electrical inductance".  Will Mathematica provide that kind of information?
Comment: You must be wrong. "Henries" has nothing to do with inductance. Try `WolframAlpha["Quantity Henries"]`. The correct answer is obviously "342037 people" :)
Comment: The problem could be also that several physical quantities can be measured in Henries (H). As noted, use W|A...
Answer: I'm not sure there isn't a way to do this without W|A but this gives what you are after:
WolframAlpha[#, {{"PhysicalQuantity", 1},
    "ComputableData"}] & /@ {"Henries", "Meters", "Volts"}
(* {"magnetic inductance", "length", "electric potential difference"} *)


Software for backing up SQL Server databases

Question: Since using the new version of Symantec, I've experienced lots of problems doing incremental backups of clients' SQL databases.
Is Windows Server backup a good alternative to Symantec Backup Exec 2012 for backing up SQL databases?
Answer: In my opinion, the best product for performing SQL backups is SQL Server itself.  When space permits, I backup to local disk (full + differential, tx log backups every 10 minutes).  These files can then be backed up by your third party software (to tape, NAS, etc.).
If I need to do an emergency restore (assuming a non-drive related issue), I already have the files local to the server, no need to mess around with restoring from tape or copying across a network.
One client of mine had used a third party software to backup files directly to tape (a proprietary format).  Two years later they needed to do a restore (audit).  They had a great deal of difficulty performing the restore because in the meantime they had upgraded the OS and the backup software, which no longer was compatible with the tapes they had from before.
Answer: Windows Server backup is probably the worst choice you can make. It is not specifically made for SQL backup and people report all kind of problems with it. More common is to use SQL Server Agent for SQL backups. But this is a poor choice too. First - it is not available in Express, the interface stayed practically the same for 12 years and is not user-friendly. Configuring email notifications is a nightmare, compression and encryption do not exist and there are no options to send backups to popular cloud storages. There are tons of 3rd party software that can do the job much easier.
SqlBak - an online service to schedule any types of backup (in standard format), send them to FTP, Dropbox, OneDrive, Azure, etc and restore just from a browser [Disclosure: I am affiliated with SqlBak]
SQLBackupAndFTP - a desktop application that does the same [Disclosure: I am affiliated with SQLBackupAndFTP]
Other popular choices are HandyBackup, iBackup, Litespeed,  - all of them will do the job better than the built-in MS tools.


What values to be taken for x-axis and y-axis?

Question: I did a lab on form and function in photosynthesis and I recorded the values of absorption spectrum in spinach chlorophyll extract. I have the following data and I need to draw a graph. I didn't understand what I should take for x-axis and for y-axis. Can anyone please explain this.
Comment: Are you trying to plot the slope, or are you also trying to do linear regression as well? The answer and sources that I give you depend on this.
Comment: @NabeehaChowdhury I need to draw a graph which describes, how many peaks does the absorption spectrum contain? and at what wavelength is the photosynthesis greatest? How does the color of an angiosperm leaf relate to the absorption spectrum you have generated?
Answer: It doesn't matter really, but for aesthetics sake, you'd plot the wavelength on x and the absorbance on y. We tend to visualize such data as spectral or absorbance as "peaks" on the range of interest. There's a fairly good example here. It has something to do with convention: traditionally
 the independent variable on x and the dependent variable on y. There's a good answer on cross-validated on the matter, too.


Why does the difference between terrestrial times and universal time, $\Delta T$, have such a strange behaviour?

Question: I was reading about ancient astronomy, and one of the main phenomena described is eclipses. Now, I read this 2016 paper by Stephenson, Morrison and Hohenkerk, in which they determine the values of the parameter $\Delta T=UT-TT$. For the pre-telescopic era, that is, from 700 BC to AD 1600, the parameter is simply a smooth quadratic function, while during the telescopic era, from 1600 to the present, it suddenly becomes erratic and oscillatory. I want to know why is this, what causes this parameter to have such a strange behaviour.
Comment: Related: https://en.wikipedia.org/wiki/%CE%94T_(timekeeping) $\Delta T$ has always been irregular, but the data from before the telescope era isn't sufficient to make precise estimates on short time scales, but we do know its long-term behaviour from solar eclipse data.
Comment: An example of a long term variation that has nothing to do with the Moon is the ongoing redistribution of mass that started with the end of the last glaciation, about 12000 years ago. There are parts of the far north that are still recovering from the weight of all of the ice that had built up during the last glaciation.
Comment: The Moon has nothing to do with short term (up to decades, perhaps even several millennia) variations in the Earth's rotation rate, but it has a whole lot to do with very long term (many millennia or longer) variations in the Earth's rotation rate.
Answer:
I want to know why is this, what causes this parameter to have such a strange behaviour.

TL;DR: Better observations.
Measurements were absolutely lousy before the telescope era, and remained fairly lousy throughout much of the telescope era. It has only been the recent several decades where very long baseline interferometry (VLBI) measurements have made measurements of the Earth's rotation rate precise. We are seeing apparently chaotic behavior because of those vastly improved measurements, rather than because the Earth's rotation rate suddenly became chaotic at the same time VLBI techniques were developed. The Earth's rotation rate has always been chaotic to some extent.
Answer: $ \Delta T $ is dependent upon the rotation of the Earth, which is affected by multiple factors.
Some of these factors are known and can be calculated/predicted, such as the gravitational pull of the Moon, the Sun, the planets, etc., but some take place inside the Earth itself: mantle currents, for example, are main contributors.
Since we can't predict or calculate mantle currents, this is why $ \Delta T $ seems erratic and "unpredictable."
Comment: Mantle currents are main contributors? Citation needed. Daily variations are mostly due  to weather. Seasonal variations are due to the uneven distribution of land and ocean between the northern and southern hemispheres. For example, the snow that accumulates over winter in the northern parts of the northern hemisphere does not have a counterpart in the southern hemisphere. Yearly to decadal changes are due partly to climate, partly to ocean currents. Longer term variations (decades to centuries) have largely been attributed to interactions between the Earth's core and the mantle/crust.
Comment: I suppose that even longer term variations might be attributable to mantle currents, but a citation would be nice.
Comment: I was writing out of memory, and you're right, I was a little off… However, mantle flows do affect Earth's tilt… See for example https://www.jpl.nasa.gov/news/scientists-id-three-causes-of-earths-spin-axis-drift