loops – Rigorously show that this program outputs $2n-$ #number of ones in binary representation of $n$ stars

Given following program:

while n > 0 do
    for i = 1 to n do
       print '*'
    n = n / 2

where $/$ is integer division as usual. We want to calculate exactly how many * are printed. By summing up $n+n/2+n/4+…+n/2^{lfloorlog_2nrfloor}$ we get $2n-1$ but only if $n$ is a perfect power of $2$. In this case we can do simple algebra by manipulating the sum and using sum of geometric sequence formula. The problem is the integer division if $n$ is not a power of two. If we denote $s$ to be number of $1$‘s in the binary representation of $n$, the result should be $2n-s$, but how to show this rigorously? My idea was to somehow show that for each $1$ in the binary representation, when we divide, we somehow lose the precision so $1$ less * is printed (because dividing by 2 is basically right bit shift).

dnd 5e – What counts as “wearing and carrying” for the Robe of Stars?

One of my Players has the Robe of Stars and my question is now can he, for example, put a rabbit in his bag and take it with him to the Astral Plane, because he carries it in his bag? I would think not but I am not sure. The wording is:

While you wear the robe, you can use an action to enter the Astral Plane along with everything you are wearing and carrying.

The “everything you are wearing and carrying” is confusing and doesn’t realy make it clear if it just means objects, or creatures as well.

And if he could take creatures with him, could he grapple someone and also take that creature with him because he is technically carrying/grappling this creature? For example a goliath grapples a goblin then activates the Robe. Would the goblin teleport with him?

psychology – Are stars a good rating system?

Stars rating systems have been working pretty well in practice from the user sideon giving a general idea of the quality of a product, but we can’t expect more than that from them.

The rating is familiar with most of the users because of:

  • Familiarity on the real world: It’s used worldwide in hotels as a quality scale.

  • Familiarity on the web: It has been used throughout massive-traffic websites with consistent results (shops sites, movies and series sites,etc).

There are some features to take in count to make them work as good as they can:

And when you display products, get sure of showing the number of votes done to make the rating more meaningful.

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Something to avoid: This way of showing reputation (Ebay as an example). Endless and impossible to remember colored stars.

enter image description here

As it is not possible to make some “coherence validation” between the amount of stars selected by the user and their comments, there always be some users that will fail with or without porpoise, but at the end it would tend to be the minority.

I think that the thing about the users’ tendency of voting 1 or 5 stars is something to take in count while analyzing this model, but the Like-Dislike approach is too extremist for rating products IMHO.
For me a good approach would be a system with 3 states, positive + negative + neutral, because talking about products you could think something is good but “not good enough”, or “not as expected” but still useful, and that information will be really useful for the product seller. Maybe 5 stars are too much for the average user to “decide” between them, so they end up falling on the extremes.

astrophotography – Proper exposure for taking a sunset, stars, and moonrise timelapse

I’m planning to take a sunset to nighttime to moonrise timelapse. On the day in question, the conditions are:

  • Sunset at 7pm
  • Nighttime at 8pm
  • Milky Way visibility at 8:30pm
  • Moonrise at 2:30am at 15% phase (visibility).

I have taken sunset timelapses before and I have done a little bit of astrophotography, but I haven’t combined them or taken good stars + moon photos.

For sunset timelapses, I generally use the following exposure settings:

  1. Set ISO 100.
  2. Set F/4 @ 10mm
  3. Set exposure compensation -1EV.
  4. Take a picture every 15 seconds.

For astrophotography, I use the following exposure settings:

  1. Set ISO 1600 (I think that’s the highest noise I’m willing to endure).
  2. Set F/4 @ 10mm
  3. Set shutter speed to between 60s – 90s (confirm exposure and adjust).

My first question is what are common settings for photographing stars with a 15% moon.

My second question is how to properly shift from sunset to stars to moon settings properly without creating a jittery timelapse (I use LRTimelapse for editing, btw).

Thank you

Though a few of these college stars

Though a few of these college stars may make a return for their college next year, others are playing in their last games of the school career. To get a number of those college athletes who are playing in their final NCAA games, it’ll be the end of line. However, there’ll be some players who will be fortunate enough to continue their basketball career and possibly be drafted into the NBA. That not only means that the NBA might have some recognizable NCAA celebrities from this present year, but also means that those gamers who get drafted will be making their way into NBA 2K22 when it releases later on this season. All these are NCAA players that you should keep an eye during March Madness as you’re likely to see in NBA 2K22.

Scottie Barnes (Florida State) (SF)

Scottie Barnes may not be playing basketball at the highest of levels at the instant when it comes to his shooting abilities, but that isn’t his strongest feature nonetheless. Scottie Barnes is an excellent playmaker who is able to help his teammates in getting the ball into the hoop. Barnes has only begun 7 out of his 19 games played this year that might appear like a let down. However, even though he hasn’t started a slew of games, Barnes remains averaging 10.4 PPG. Florida State values Barnes’ playmaking ability and even coming off the bench he is still a enormous threat on the ground. Barnes is shooting 49.7percent in the field and a unsatisfactory 56.9% from the free throw line.

For someone who is not even 20 years old yet, his game will continue to improve down the line. While his shooting in the field isn’t terrible, it will have to get better to become an elite competitor in the NBA. As it stands now, defense is a major portion of Scottie Barnes game. The amount of energy this man has at such a young age is also something which shouldn’t be brushed off. There are a few NBA teams which will see value in the kid by having them aside from the team. Even when Barnes ends up getting drafted, he might not get a ton of playing time. Regardless, he could be an important advantage in the NBA. In case Scottie Barnes ends up playing in the NBA next season, you may be able to play as him in NBA 2K22.

Should you require someone to come up clutch and hit a must-make 3 point taken, Moses Moody is a lethal go-to option. Moody can also defend his opposition at a really high quality which makes him not only lethal on offense, but defense too. While I don’t think they can make it any further than the sweet sixteen, maybe Moses Moody will help lead Arkansas to a magical run during the next month.

The NBA has evolved into a big 3-point league that’s the reason why I believe Moody would actually gel well in the league. At 18 decades of age, even when Moody gets drafted, it’ll be intriguing to see how long he gets to perform with. Every NBA team can use help from beyond the arc and thus why Moses Moody is a fantastic option for the future of many NBA teams. Each of the players on this list might be drafted and a number of them might not be. Only time will be able to solve that riddle. However, I do honestly believe that every one of those athletes are talented enough to make it to the NBA and you’ll see all five of those athletes in an NBA video game sooner or later. Hopefully, it is NBA 2K22.NBA 2K22: The Best Way to Acquire a Triple-Double
If you want to know more information about NBA2king , please lock on NBA2king

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R code for reading tabular data files and plotting light curves of modeled stars

Here is a minimal example of my task…

I have four 2-column files. profile1.data

  zone luminosity
1     1   1359.019
2     2   1359.030
3     3   1359.009
4     4   1358.988
5     5   1358.969
6     6   1358.951
7     7   1358.934
8     8   1358.917
9     9   1358.899
10   10   1358.881


   zone luminosity
1     1   1357.336
2     2   1357.352
3     3   1357.332
4     4   1357.310
5     5   1357.289
6     6   1357.270
7     7   1357.252
8     8   1357.233
9     9   1357.214
10   10   1357.194


   zone luminosity
1     1   1355.667
2     2   1355.687
3     3   1355.667
4     4   1355.644
5     5   1355.622
6     6   1355.602
7     7   1355.582
8     8   1355.562
9     9   1355.541
10   10   1355.520


   zone luminosity
1     1   1354.008
2     2   1354.032
3     3   1354.013
4     4   1353.990
5     5   1353.967
6     6   1353.945
7     7   1353.923
8     8   1353.902
9     9   1353.879
10   10   1353.857

I also have a vector named phases. There is one phase value for each profile.data

 rsp_phase1  rsp_phase2  rsp_phase3  rsp_phase4 
0.002935897 0.004602563 0.006269230 0.007935897 

What I am doing with this data is plotting luminosity vs phase for each zone. For example, to create a luminosity vs phase plot of the first zone, I grab the luminosity value from every profile in the directory at zone 1. This is my first plot. Then I do the same for the other zones. At the moment, I am accomplishing this through for loops in R.

for (zone_num in 1:10){
      width = 1200, height = 960)
  par(mar=c(5,4,4,2) + 2) 
  luminosities <- c()
  for (prof_num in 1:4) {
    prof.path <- file.path('LOGS_A1a', paste0('profile', prof_num, '.data'))
    if (!file.exists(prof.path)) next
    DF.profile <- read.table(prof.path, header=1, skip=5)
    luminosity <- DF.profile$luminosity(zone_num)
    luminosities <- c(luminosities, luminosity)
  plot.table <- data.frame(phases, luminosities)
  o <- order(phases)
  with(plot.table, plot(x=phases(o), y=luminosities(o),
                        main=paste("Zone",zone_num,"Light Curve",sep=" "),
                        type="l", pch=3, lwd = 6, col="purple", xlab=expression("Phase"),
                        ylab=expression("Luminosity " (L/L('u0298'))), cex.main=1.60,
                        cex.lab=1.80, cex.axis=1.60))

As you will realize, it seems that the biggest problem is that I am repeatedly reading the same files into R. This should be done once separately. Is there a way to avoid this and speed it up?

R code for reading tabular data files and plotting light curves of modeled stars

I am given a file named profile1.data that looks like this:

  zone luminosity
1    1   1359.019
2    2   1359.030
3    3   1359.009
4    4   1358.988
5    5   1358.969
6    6   1358.951

There are thousands of profiles in my working directory (named profileNUMBER.data). Every one of them has a unique value called a phase that I have beforehand (meaning there is the same number of phase values as there are profiles) and every one of them has 300 rows (thus 300 zones).

What I am doing with this data is plotting luminosity vs phase for each zone. For example, to create a luminosity vs phase plot of the first zone, I grab the luminosity value from every profile in the directory at zone 1. This is my first plot. Then I do the same for the other 299 zones. At the moment, I am accomplishing this through for loops in R.

for (zone_num in 1:300) { 

    luminosities <- c()

   for (prof_num in prof.idx$prof_num) { 
    prof.path <- file.path(cwd,log.directory.after.FA, paste0('profile', prof_num, '.data'))
    if (!file.exists(prof.path)) next 
    DF.profile <- read.table(prof.path, header=1, skip=5) 
      luminosity <- DF.profile$luminosity(zone_num)
      luminosities <- c(luminosities, luminosity)
    png(file.path(plot.set.dir, paste("Zone",zone_num,"Light_Curve.png",sep="_")), width = 750, height = 600)
    plot(x=phases, y=luminosities, main=paste(sets(set),"Zone",zone_num ,"Light Curve",sep=" "), pch=3, col="purple",
         xlab=expression("Phase"), ylab=expression("Luminosity " (L/L('u0298'))), cex.main=2.0, cex.lab=1.50, ceb.axis=1.80)


This is not the entire code and there are some variables that you do not see the definition of, but the point is for you to see how I structured the solution using for loops. I’m particularly interested in how to use R’s unique vectorized functions to speed this up.

dnd 5e – Which healing spells benefit from the Circle of Stars druid’s “Chalice” Starry Form?

The Circle of Stars druid’s Starry Form feature (TCoE, p. 38-39) lets the druid expend a use of Wild Shape to enter a starry form, choosing a constellation to glimmer on their body that grants certain benefits. The Chalice option grants the following benefit:

A constellation of a life-giving goblet appears on you. Whenever you
cast a spell using a spell slot that restores hit points to a
creature, you or another creature within 30 feet of you can regain hit
points equal to 1d8 + your Wisdom modifier.

Which healing spells benefit from/interact with the “Chalice” Starry Form?

It’s obvious how some healing spells (e.g. cure wounds or healing word) interact with it, and so I don’t think I need clarification on them – but some others are less obvious to me.

For instance, the goodberry spell creates berries that can be eaten within the next 24 hours to restore 1 HP to the creature:

Up to ten berries appear in your hand and are infused with magic for the duration. A creature can use its action to eat one berry. Eating a berry restores 1 hit point, and the berry provides enough nourishment to sustain a creature for one day.

Meanwhile, the healing spirit spell creates an intangible spirit that you can cause to heal a creature in the same space (XGtE, p. 157):

You call forth a nature spirit to soothe the wounded. The intangible
spirit appears in a space that is a 5-foot cube you can see within
range. The spirit looks like a transparent beast or fey (your choice).

Until the spell ends, whenever you or a creature you can see moves
into the spirit’s space for the first time on a turn or starts its
turn there, you can cause the spirit to restore 1d6 hit points to that
creature (no action required). The spirit can’t heal constructs or
undead. The spirit can heal a number of times equal to 1 + your
spellcasting ability modifier (minimum of twice). After healing that
number of times, the spirit disappears.

Finally, the aura of vitality spell creates an aura that moves with you and lets you use a bonus action to heal an ally in the aura (PHB, p. 216):

Healing energy radiates from you in an aura with a 30-foot radius.
Until the spell ends, the aura moves with you, centered on you. You
can use a bonus action to cause one creature in the aura (including
you) to regain 2d6 hit points.

(Aura of vitality isn’t normally on the druid spell list, but it’s added to the druid spell list by the “Additional Druid Spells” optional class feature (TCoE, p. 35).)

None of these 3 spells immediately heals a character at the moment it’s cast, but each one creates an effect that can then heal a creature. Do these qualify for the benefit of the Chalice form?

terminology – What are the key features of Stars and Wishes?


The oldest reference I could find is from August 2018, when Gauntlet RPG proposed Stars and Wishes as a softer alternative to the approach of “Roses & Thorns”, which also is at times worded as “Rose, Thorn & Bud”.

Roses & Thorns is meant to identify “I liked this, I disliked that” and possibly “This has potential”.

a variant of Rose Thorn & Bud in action

Oddly enough, even before Stars and Wishes became a thing, I was introduced to a similar system around 2010 in a table-round of WoD. The GM called it maneuver critique or at other times “Wishes, Notes, Critique”. It’s a variant of Rose, Thorn & Bud method.

Starting with the player right of the GM, each player would nominate one or more actions of other players that they found memorable, remarkable, or cool, and thought would be worth experience points for playing the character or showing character growth. You could not nominate your own character this way. After a nomination, one other person at the table (GM included) had to agree, turning the nomination into an XP. Only after the other players, the GM would dole out first other nominations for the players to vote on, and then points he definitely gave to players. Generally, most characters or players would get one or two nominations, and it was quite rare to leave the table with just the experience points for survived the session.

While this maneuver critique had a positive reinforcement for good actions (stars), it was at times used for some wishes but did neither require it nor give those any specific spotlight. In contrast to Stars and wishes, the Maneuver critique could and would at times be formulated rather harshly and in some cases accusatory in the critique part. Which indeed can hurt – to the point that a long-standing player stopped attending after people critiqued repeatedly that they are not comfortable with something.

Meaning of Stars & Wishes


Stars are simple: Every involved person shall point to one item, person, or incident that they really enjoyed during the session. It could be “I really loved how you portrayed that Rat-Chaos-Mutant’s speech, GM-Bob.” or “Christy, your Barbarian was so cool when she burst through the door yelling bloody murder.” Just name something that you really enjoyed.


Wishes are not so simple: It’s formulating about what you like to see in the future. But it should be constructive.

For example “Please, no more zombies” is not a valid wish. You need to formulate your wish in a positive light on how to make things better. The wish for different enemies should be formulated in a way to what you want to face, not just what you don’t want to face. “With all those zombies around, can we finally face the necromancer making them?” or “I think fighting a larger boss monster instead of just T-virus Zombies might be a nice change.”

Wishes also allow asking changes that players can do or that were harming your fun in the game in a positive manner. “Christy, could you try to not yell your battle cry into my ear next time you do your battle cry?” At times it can be used to suggest things about things that affect the game but are not in the game entirely. “I’d like if you’d drop a note if you are late in the future” is a valid wish in this regard.

While please get better and stay safe is a very nice wish to have, it isn’t entirely constructive. Still, one game recently had made almost all of us wish for health as more than half of us had to cut short (compared to other rounds) due to health reasons. Unless you really have nothing else to wish for, you shouldn’t use that one wish you have just for health.


In my experience, it helped to break the ice with the system if the player that introduced the system goes ahead and starts with it. When the system was introduced to me, the one bringing it up went ahead and started with making their stars and wishes that round. That was some year and a half ago. It also did help that I knew a similar system before.

One of my mainstay rounds is play-by-chat. In those sessions, we present our stars and wishes simultaneously, not in rounds as Gauntlet proposes. We put up a dedicated channel for those, and besides other almost ritualistic things at the end of the game, the words “don’t forget the stars and wishes” in the general channel have become a part of the closure rites in this round.

In a recent, short running group via voice chat, I just introduced the system at the end of the session with a very quick rundown of what is the system meant to do, and surprisingly, the GM jumped the wagon and said “Know what? good idea! Why don’t you start?” After setting the example, the others followed to name their most liked moments and what they’d like to have a little focus on next time. In a similar fashion to the play-by-chat example, we only had one call to everybody to name the Stars and Wishes together to keep us a little shorter – we had deadlines to keep.

in a more direct session, asking some questions at the outset like “Did everybody have fun?” and “Are you ok with the pace?” by the GM can help to open up, allowing players to get into the mindset to answer constructively before pointing out their stars.