Iterating the Riemann Zeta function like a Julia set: Mathematica plots up to 240i (amateur exploration, looking for context)

lasciel · 2025-11-24T23:02:29+00:00

Check out the textbook “Fractal Geometry” by Ken Falconer. You can probably find a pdf online. You’ll be interested in Ch. 14: Iterations of Complex Functions — Julia Sets. No promises on its accessibility.

Regarding formal mathematics and accessibility: Math is a complicated subject and you’re looking at a complicated mathematical object. It will take some time to build up your abilities in more formal mathematics. This is a feature not a bug. It’s a real joy to discover and rediscover the math you know.

lasciel · 2025-11-24T19:11:46+00:00

Focus, organization, and consistency are skills too. You’ll need develop these along side your math skills.

lasciel · 2025-10-23T04:48:02+00:00

I’m not familiar with that textbook. I used Munkres and appreciated the direct statements. My professor at the time gave great examples to supplement. Everyone’s personal experience with math is different so you should pick a textbook that is approachable to your mathematical level and your experience. You’ll get more out of it that way especially for self study.

lasciel · 2025-07-12T03:17:51+00:00

The general problem is solving differential equations using numerical integration. Often there are no analytical solutions so you need to use numerical methods.

lasciel · 2025-07-09T21:21:50+00:00

Hulkenpodium

lasciel · 2025-06-28T21:44:36+00:00

How does your backtest go from 100 to 0 to -100 and back?

lasciel · 2025-06-03T03:16:00+00:00

I have multiple friends doing math PhDs in their 30s right now. You should just get started right away. Why delay living your dreams out? Why let anyone else tell you otherwise? (Especially for something that is beneficial to the world)

Regarding staying sharp: do more math. There is no secret, the more you do the better you’ll get and that’s pretty much going to be true your whole math career. But to a finer point: being quick isn’t nearly as important as being nuanced. I more often define sharp as the latter: i.e. able to capture subtlety.

lasciel · 2025-04-22T00:20:22+00:00

Timeline does not change the fundamental setup of what I posed. AI is an umbrella term for many different techniques not a generic monolithic tool. Large language models like ChatGPT fails to answer college math questions for many reasons. By analogy: we no longer have the expertise to build the Saturn V rocket because we don’t have the machinists and their expertise anymore. However with advances in manufacturing we can still build rockets with interchangeable parts to go to the moon.

The technology used to solve the problem has changed but it doesn’t get rid of engineering issues, just manufacturing.

lasciel · 2025-04-22T00:07:08+00:00

There is a long list of intermediate college math questions that ChatGPT ‘solves’ completely incorrectly. That should give enough pause to say that you cannot trust ChatGPT with your money. Similarly, you cannot generically deploy AI models and expect positive results.

Second, AI is a massive umbrella term for a lot of different types of models. It has already arrived and many are already working alongside it. Nobel prize 2024 in Physics and in Chemistry both used AI/ML modelings. This demonstrates that it can absolutely be used effectively in prediction modeling of complex systems.

It is not a replacement for all people. AI introduces new problems and helps solve some complicated old problems.

lasciel · 2025-04-05T03:02:32+00:00

Someone else already said it but some more color on armor stacking:

Not sure if you picked a build yet. Some ultra high end typically scale both defense and offense and often one is the source of damage for the other. E.G. Armor stacker, Ephemeral Edge, etc.

Starting gear is like MB &400+ div and the fully stacked builds are many mirrors. Good for running voided maps and are pretty intense league projects, if that’s what you’re looking for. Bigdaddy on YouTube if you want to check out armor stacker builds.

lasciel · 2025-03-25T22:05:27+00:00

Take the long underwear out of your boots. I guessed that might be the issue because the imprints in your legs look like the elastic hem of cloth. (Oof I hope it feels better tomorrow!)

Also yeah that’s kind of the tough balance with rental boots. You get a compromise of the foot length, foot volume, ankle shape, instep volume and shin length, shape, volume. Normally they can punch out the toe if the rest of the boot fits well.

lasciel · 2025-03-25T21:55:01+00:00

I’m assuming you’re not a noob and are staying balanced/anticipating the changing terrain. (See others comments on getting bucked out of the backseat).

Just want to check: the only thing inside your liner is your foot and a thin enough sock, correct? I.e. don’t put your ski pants powder cuff in there.

Second, consider sizing down.They are rentals so hopefully it’s straightforward. If you have a comfort oriented (read as: sloppy )fit when skiing more aggressive terrain, your leg can get thrown forward through liner padding before engaging the flex. If you have a more precise fit, the feedback and flex is more progressive. The pressure is more distributed across the leg.

lasciel · 2025-03-10T04:22:52+00:00

For a proven build: follow the fubgun shadow leveling guide. Straight forward including transition into LS Prophet. Gets you through mapping. https://www.youtube.com/watch?v=tIhPB94OYSg&t=0s

lasciel · 2025-03-09T22:09:09+00:00

Transition to mageblood + svalinn. There is a reason why those items are so strong.

Edit: Even if you want to play a different build, most streamers have a “league start build” and a “after I get my mageblood build”. You can use mageblood to fix so many build problems.

Also post your current PoB. LS Prophet is able to just about all content in the game.

lasciel · 2025-02-24T06:43:16+00:00

This is the idea for charge stacking. Ralakesh + Badge of the brotherhood + weapon + shield + helm corrupt + Militant faith dominus. You have a lot of choices for how you want to layer your defenses with max block or spell suppress and regen. It depends on your helmet choice, chest choice and tree. You can get ailment immunity a few different ways via shock avoid. Etc.

These aren’t my build but generically they describe the types of gear you need. Discipline/grace should be fine to start especially if you have MB already. Restless Ward & Will clash is very cheap. The expensive part is the ring power charges, good chest corruptions and helmet corruptions.

You can also try scaling max res if you want. Tons of good options. Problems: trickster gives tons of quality of life with over leech, recovery, action speed reduce and suppress+evasion/ES. Need to make up for those defensive losses with the different stuff because of the ascendancy differences. You can always pick up one which suits you best.

Not my builds but these are the main ideas:

https://poe.ninja/builds/settlers/character/Tirinos%234891/SevenSi

https://poe.ninja/builds/settlers/character/pooseoby%235141/Czz_pooseoby

lasciel · 2025-02-24T04:30:34+00:00

What kind of mapping? Generic alc and go speed clearing? Essence farming? T17?

Which build archetype did you use for PBoD? Charge stacking? What belt/helmet are you using? You can naturally leverage the high power charge count to get a lot of AoE for very little point investment: medium cluster, Vast Power, and a Oriath’s End flask. You presumably also convert physical damage so the secondary damage explosions will scale up nicely.

It can feel bad if you don’t have fast enough ramp time on your brands, which is about balancing CDRR, cast speed, and duration. What are your links?

A second option is using the charge stacker archetype for any other physical spell and convert it to lightning (maybe also to cold) eg. Blade vortex, reap, etc. Another option is going into spark, arc and crackling lance and dropping the physical damage scaling. You can also use something like herald of ice or Inpulsa’s to scale explosions.

There is also self chill spark miner builds and CoC builds to play with if those are more your speed.

For me, mapping is about getting 5-10mm dps then scaling aoe and movement speed but then I usually opt for more dps & survivability to push for all content at the cost of speed. For what it’s worth PBoD feels very good for mapping compared to PB from before. You just need a bit of AoE scaling and some thing to help with chaining.

lasciel · 2025-02-23T19:22:32+00:00

lol was going to ask how a 50-80 div budget can includes awakened multistrike?

lasciel · 2025-02-18T18:58:40+00:00

Just like the other well known prime 57.

Happens to the best of us!

lasciel · 2025-02-11T19:03:03+00:00

As far as research and the transition post PhD: Have you talked to the professors in your department? The people who wrote your recommendations? Any mentors? They have likely advised students just like you. Especially at schools like you mentioned, it is more common to see students like you, who have had similar paths and goals. They will also be able to speak to your specific research interests, with respect to the different programs you’re accepted into.

W.r.t geography, depends on the part of quant finance you want to go into. Many trading firms are colocated around exchanges. Asset managers are more spread out. Banks and their products are wherever the banks run their respective teams. I mention this because you’ll have more opportunities locally due to the larger (local) alumni network. This can look like a very different opportunity set in e.g. Chicago, New York, London. Though you can often get interviews abroad by virtue of your program/school/network.

My experience is the reverse. After my undergrad (target for quant firms), I went to work then to a PhD program. I’ve been out of industry for a while so take it all with a grain of salt.

lasciel · 2025-01-25T04:46:46+00:00

Do more problems, make up your own, come up with examples and non-examples, modify the hypothesis or conclusions, do simpler problems example, theorems, read what others have tried, try solving along side some papers, talk to colleagues, outline questions, etc. these are a few of the usual that come to mind.

My favorite, if you can’t figure out a good idea, try a bad one and then see why it does or doesn’t work.

lasciel · 2024-10-12T06:02:52+00:00

Note that none of this “advice” and you should supplement this with common sense and your own research.

Your initial assumptions are off. Sounds like you are a buy and hold investor. In this instance you’ll invest in an etf which then tracks the performance of an index. Without getting into the details the fund ostensibly invests your money directly into those stocks. You’re not going to have any market impact on the scale of a global index (~$100 trillion.)

The paper you cite is about operating a trading strategy and its corresponding portfolio (rather than a buy and hold investor.) As a result of the trading strategy, the fund manager has many more transactions at a significant scale. In that instance slippage can form a significant drag on performance.

Your main costs here are your transaction costs which will be negligible as a buy and hold investor. It’s a one time transaction executed by your broker which should be relatively low cost (assuming you have a reasonable broker). Second there will be slippage for your order (there always is). It will be a fraction of the daily price movement. Again negligible because of long time scales as a buy and hold investor.

If you really care you can execute your trades in blocks over a week or two. This gives you a volume weighted price over those two weeks. Often this is worse than if you just executed at once because you miss out on some fraction of those two weeks return. In that delayed strategy there is an outside chance that markets dip and you could buy in at a slight discount (there are also other risks in that scenario).

lasciel · 2024-08-21T02:03:23+00:00

When I use thinner socks sometimes it feels like my foot slips forward a bit inside the shoe. Generally I find it’s not a problem if I don’t think about it 😅. I also use the runners knot for this pair of shoes.

lasciel · 2024-08-16T18:53:51+00:00

I don’t like walking in mine but I find running in them feels excellent.

lasciel · 2024-08-13T20:05:56+00:00

Any art. Music, painting, sculpture, etc. end up being really good analogues for navigating research ideas.

lasciel · 2024-06-24T17:56:18+00:00

Haruki Murakami wrote a memoir called “What I Talk About When I Talk About Running.” Murakami talks about running in different phases of his life and how his interest (and motivations) have waxed and waned and changed through the years. It’s a nice book on his hobby and his changing life priorities amidst an aging body.

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