TL;DR - I read this book, and found it very useful in solving some organizational / management problems I was encountering.

The Book

https://preview.redd.it/xpwxe0f3wi881.png?width=1122&format=png&auto=webp&s=df1dcfa2cc2f7c2c64e44bd210f1afc17a7c365b

Problem I was solving: Bridging some gaps in my knowledge regarding how to design and structure teams in larger, complicated programs with lots of stakeholders, especially with government clientele. Also, I was looking for some clear frameworks to describe some issues some of my product teams were having: Product people on one particular team reporting that they didn't feel like they were equipped to meet the demands placed on them for a number of reasons, and that they and some others were starting to feel burnt out

Context: I'm a Product Management Leader at a design and engineering services firm that builds software for CMS (Centers for Medicaid and Medicare Services). I have ~10 YOE in healthcare product management, all in startups or growth-phase companies, with ~5 YOE in engineering before that. I've read and applied most of the more popular design thinking / product management books, e.g. Marty Cagan's books, Service Design, etc.

How it helped me, and why you might want to read it: The book provided a clear framework grounded in Conway's Law for structuring teams in an organization to meet the needs of users and align with the architecture of the systems you're building (whether they're services or software or hardware). It put product teams into the context of a larger, more flexible framework that covers more real-world circumstances that product leadership may encounter in large systems and programs. There's probably a better summary, but I now have a very useful framework to typify teams and the modes of interaction they use to communicate, and I can leverage that framework and a number of best practices in my recommendations for improving the way we fulfill our contracts and meet the needs of users, or even informing how we should bid on contracts.

Who I would recommend read the book (how much value I think you'll get out of it):

• 10/10 - Directors of Product or Product Management practice
• 10/10 - Leadership of product-led organizations (e.g. CTO, Dir. of Engineering, Dir. of HCD, etc)
• 7/10 - Senior-level Product People with some influence on team

In several physics research papers I’ve seen the cross product be used for two blackboard bold letters like:

(x,ω)εR^d x S^d-1

Where R and S are the blackboard bold letters, x is the cross product, and ε is the contained in symbol.

So blackboard bold S represents a sphere of dimension d-1 and R is the real number space of dimension d.

Does this have to do with topology? What is the meaning behind this cross product? Thanks!

In the wiki page of the Product Topology,they say:

>This shows that the product space is a product in the category of topological spaces. It follows from the above universal property that a map f : Y → X is continuous if and only if fi = pi o f is continuous for all i in I.

Does it actually follow though? If f is a function f : Y → X, and  fi = pi o f are continuous, ie morphisms. Then then there's exactly one continuous f' : Y → X, ie exactly one morphism. Therefore f'=f right? Well no, f is not a morphism a priori! The universal property says there exists exactly one morphism, not exactly one function. It would only say what's claimed if we already knew f was a morphism, ie continuous, but that is what we want to prove.

So proving the two conditions are equivalent is not as simple as they make it seem right?

Thanks for taking the time to read my question.

Is the inductive dimension sufficient? Dimension wouldn't be defined, right? I can't think of anything else though, given that [; \mathbb{R}^\omega ;] has almost all the other standard properties such as Hausdorffness, normality, second countability, etc.

An exercise in Kirk and Davis's "Lecture Notes in Algebraic Topology" is the following:

If (X,A) and (Y,B) are cofibrations, show (XxY,XxB u AxY) is a cofibration.

I've tried it both from the angle of retracts of XxYxI and directly extending the homotopy, but no matter how I try to combine the retractions or extensions I can't seem to come up with a formula for the new one.

It seems easy to show (XxY,AxB) is a cofibration.

https://imgur.com/a/EMVJP

I am having trouble understanding everything after Alternatively. YxY gets a topology as a subspace of X x X. What does that mean?

I know a subspace for a subset Y of X is the collection of sets {Y∩O: with O in (X,T)}. And I know that a basis for the product topology for X x X, is { AxB : A, B are in (X,T)}, But what is a subspace for YxY? Is it just the set { YxY ∩ OxU : O, U are open sets in X x X}?

Not really looking for the answer since its a homework, but looking for help to see if I understand the definition of what a subspace of the form YxY is.

What do compact sets look like in the product topology of countably infinite "copies" of the real line?

My intuition says that the set must be compact in each copy of the real line, that is, that if C has any hope of being compact in the product space then p(C) must be compact in the real line where p is the projection map.

Functionality feedback: https://news.ycombinator.com/item?id=15618391

Prove that any product of spheres can be embedded in Cartesian space of one dimension higher.

I need to show that if X is the product of Xi where i comes from an index set I, and if the product space X is T2, then all the factor spaces Xi are also T2. My study of product spaces is pretty limited to the coordinate projection functions and the standard base of the product topology, so using that is ideal.

This is more a case of a random thought that's been bothering me for a couple of days than anything else, but I'm having trouble tracking down anything even slightly relevant to it.

What I'm trying to do is figure out properties of the space (and I'm aware that it's possible that this doesn't even form a well-founded space) produced as follows:

Take S = the closed interval [0, 1], T = an empty space initially, and n = 1 initially. Repeat, countably many times, removing the middle third of each of the 2^(n-1) intervals remaining in S and putting the product of open intervals (0,1)^n into T for each interval removed from S this way.

The main problem I'm seeing is that, apparently, T is equivalent to the union of two copies of the product of T with the open interval (0,1) and a copy of the open interval (0,1)... and I'm wondering if I'm just looking at something that isn't well-founded, or if it's some ridiculous counterpart to the long line, or... well, is this something someone can point me to a reasonable reference for what I'm doing wrong (if anything)?

http://i.imgur.com/OMwG88O.png

I think I have the right idea for doing this problem but I have no idea how to write it mathematically without it turning into a mess. I thought maybe there's a way to do with projection functions but I'm not sure how.

Since F is continuous its inverse image of an open set is open in Y*1* x Y*1* which means by definition Y*1* and Y*2* are open. Then, since f and g are continuous, the inverse image of open sets is open so you end up with an open set in X*1* and X*2*, so F must be continuous. Since G shares all of F's values, then G must be continuous.

I have no idea how to write this mathematically^

And, I have a more general question that I believe is getting me stuck in a couple other problems. So I'll ask the general question here before making threads for the problems themselves.

What are closed sets in the general product topology? So, open sets are the Cartesian product of sets for every index in your indexing set, where a finite amount of the sets are open and the rest are the entire space. So, the complement of that seems to me to be the empty set? If some of the coordinates are the space then the complement for those coordinates is the empty set so the whole Cartesian product is the empty set? This doesn't seem right based on the questions I'm reading in my book.

Thanks for any help. I'll probably be posting more topology problems tonight and I'd really appreciate any help on any of them.

Pick an open cover of [; X \times Y ;]. The sets will be on the form [; U \times V ;] for open sets U,V in X and Y respectively. If we project these down we get open covers for X and Y and they must contain finite subcovers U' and V'. Now the set of all products of these sets must be finite, cover [; X \times Y ;] and be a subcover of the original cover.

Is this correct or am I missing something? It seems to simple.

http://i.imgur.com/YojmkAP.png

Crossposting this from r/cheatatmathhomework.

So for a) I looked at the complement of what I assume x to be (their notation confuses me)

x=(1, 1, 1, ...) Let A = (-∞, 1) U (1, ∞) Then, X\x = A x A x A ....

So it would seem I have to show that this is open to show x is closed. But in the lower limit topology A is open since for every point in A I can fit a base member within A. So, X\x is the Cartesian product of an infinite amount of open sets. But, that breaks the definition of an open set in a product topology as only having finitely many sets in the Cartesian product that aren't equal to the whole space.

Any help? I really have no idea what's going wrong here

I'm trying to get some intuition for smash products.

I looked at the smash product of S^1 and S^1, and, just like Wikipedia says, I can see how this is homeomorphic to S^2.

I tried thinking about the smash product of R with R, and I can't think of anything that it's homeomorphic to. Is there anything 'obvious' (i.e. fairly familiar) that it is homeomorphic to?

Cheers.

P.S. the smash product of X and Y is the space obtained by identifying all points (x_0, y) and (x, y_0) in the product space (X x Y).

So if I'm thinking about it right, the smash product of R with R is R^2 with a pair of perpendicular lines parallel to the x- and y-axes identified.

Let X_i be a topological T1 space with more than one element. Prove that the topological product X_i does not have a countable neighborhood basis at any of its points.

• Note: i \in I where I is an uncountable index set.

TL;DR: Propmaster wants to scan assets for sale to some vfx shops. Due to volume of objects, whats the level of quality this would necessitate? Is 16K /8K enough, or UDIMS as well? Manual, great topology, or zRemeshed / auto remeshed topology acceptable?

———

Hi guys! Really need your help / experience with this.

Problem: I’m not a modeler. (I work in film production currently and am transitioning to... animation). A prop master I’m friends with is hoping to generate his prop collection in CG for use in VFX (we have relationships with some of the small shops here in NYC).

I’ve done photogrammetry before on a basic level for myself. I feel comfortable retopologizing in 3Dcoat, I use Zbrush quite a bit and am learning Maya.

But I’m not sure where to aim with this. Is it realistic to expect a VFX shop to ever use an asset without UDIMS, even if it had an 8 or 16k texture set?

Additionally... Worried about the modeling element. It would be much faster if I could get by with ZRemesher or a decimated scan from the photogrammetry soft- but is that remotely realistic? Would anyone ever use an auto retopo’d mesh in production?

Granted- we work in TV mostly and aren’t necessarily talking about aiming for a big shop to use this as that sounds unlikely at any level of quality...

Could you guys help me out with your opinion on this? Additionally- if you have an opinion on the viability of selling scans. It’s sort of a unique position he’s in: very close with all the NYC prop houses so a large library of unique props. But the upfront difficulty of scanning everything, plus retopo etc.... eh. I don’t really know as I don’t work on the post side. Also not sure what the quality of Megascans objects topology is.

Feel a bit out of my element but would love y’all’s opinions.

Thanks!!

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Now that I should hopefully be done with internship interviews for the rest of my life, here's a mega list of almost every interview question I was asked from 150+ interviews at Facebook, Apple, Amazon, Nvidia, Google, Microsoft, Qualcomm, Analog Devices, Texas Instruments, Northrop Grumman, SpaceX, Tesla, etc. This is going to be a massive step up from "part 1" that I posted a while back now that I have more coursework, internships, and interviews under my belt.

This was originally going to be part of the Interviews chapter of my internship search guide, but that post just got WAY too long so I decided to create a separate post just for this repository of questions. That post is still chock-full of interview advice and experiences, so check it out when it's ready! And before you get started, take a guess at how many questions this list has! (bonus points if you comment your guess because I'm also curious about your guesses!)

If you're reading this on Reddit (or not my website), check this post out on my website! You'll get this super cool table of contents bar that will make navigation much easier through this massive post. Any updates to this list will be reflected on my website, not this Reddit post or anything else. Also Reddit only allows posts up to 40,000 characters and my full list way exceeds that so you'll need to hop over to my website to get everything else. For some reason, Reddit has trouble recognizing my list so this Reddit post will have bullet points to identify questions, while my website has a BIG numbered list. And more importantly, you'll be giving me ad revenue!

Disclaimers and Notes

• These questions were for internships, but there's a lot of overlap with full-time (FT) interviews. In fact, I'm doing FT interviews at the time of writing this and they basically ask the same stuff, there are usually just more FT interviews so they have an opportunity to dive deeper and ask more questions I'd even say some of my internship interviews were harder/more in depth than my FT interviews. If the questions end up being super similar, I may just rename this post instead of making a new one lol.
• These questions are reflective of my s

Compression can be daunting to beginners: compression is everywhere when producing popular music (all genres, really), and is even present on classical music to a minor extent, but dialing in that compression is really done on a case-by-case basis. It depends on the genre, it depends on the sound you want to achieve, and also the kind of track you're processing (is it a drum? A guitar? A bass guitar? Vocals? Is it a bus or a single track? etc.). This post has the aim to provide some very general pointers to compression in a way that many articles on the matter seem to overlook.

Compression levels

For starters, how much should you compress? Of course it depends, but generally speaking, in the context of compression (so let's say, at 4:1 ratios and below, over which I'd tend to talk about limiting, since 8:1 ratios are quite aggressive already):

0-3dB compression (peak meters): light compression*.* When should you use light compression? When compression isn't all that needed, simply put :D for example on electric guitars, especially on crunch sounds and over, you rarely need lots of compression, if any at all, since the amp or the stompbox is already doing a lot of compression. Buses, generally speaking, benefit from light compression to glue stuff together (true both of the master bus and sub-buses). Or maybe you might use a compressor set lightly at the end of an FX chain that also includes other compressors just to level the track a touch (and letting you use less compression before, for a more natural sound). You'll also often find yourself using longer attack and release times with light compression, as the purpose is just to make things that little bit smoother and make tracks or buses sit better in the mix.

3-7dB compression (peak meters): medium compression. When should you use medium compression? On uneven tracks that need to be made a bit more homogenous and fatter. An uncompressed snare or kick drum might sound a bit clicky and weak in the mix, and they might benefit from squashing those transients and lifting the body a bit. A bass guitar, especially when played with a pick or slapped, might drop in and out of the mix when uncompressed, being too loud and too quiet at the same time (or rather, at different times in their envelope). Vocals in louder mixes might need to be a bit more "in your face" (vocals are sort of a different matter, they usually need a lot of work for modern-sounding productions, whether you like it or

Do your worst!

UniFi’s Advanced Wi-Fi settings are often misunderstood. The defaults are usually safe, but it’s helpful to understand what these settings do while setting up a network or troubleshooting an issue. Ubiquiti doesn’t do the best job at explaining, so lets go through them one by one.

These settings and descriptions are using the default “new” interface, and they are current as of UniFi Network Application version 6.5.53. I also list the settings that are only available in the classic/old interface at the end.

UniFi's Wi-Fi Settings

Table of Contents

• Creating a New UniFi Wi-Fi Network
• Advanced Wi-Fi Settings
  • Wi-Fi Band
  • Optimize IoT Wi-Fi Connectivity
  • AP Groups
  • UAPSD
  • High Performance Devices
  • Proxy ARP
  • Legacy Support
  • Multicast Enhancement (IGMPv3)
  • BSS Transition
  • L2 Isolation
  • Enable Fast Roaming
• Bandwidth Profile
• Security Settings
  • Security Protocol
  • If WPA3 is selected...
  • Hide Wi-Fi Name
  • PMF (Protected Management Frame)
  • Group Rekey Interval
• MAC Authorization Settings
• 802.11 Rate and Beacon Controls
  • Override DTIM Period
  • 2.4. GHz Data Rate Control
  • 5 GHz Data Rate Control
• Wi-Fi Scheduler
• Settings only available in the old UI

Creating a New UniFi Wi-Fi Network

In the UniFi interface, network settings are divided into Wi-Fi, Networks, and Internet.

• Wi-Fi controls your wireless connections, including SSID, password, and other advanced settings.
• Networks controls your LAN networks and VLANs, including DHCP, DNS, and IP addresses.
• Internet controls your WAN connections, including VLANs, IP addresses, and Smart Queues for QoS.

By default, UniFi has one LAN network, which is used for all wired and wireless connections. Creating additional networks allows you to segment and restrict traffic. This is commonly used for guest or IoT devices, or separating devices or areas into different network groups. Before diving into wireless settings, setup your networks and VLANs first. This can be done by modifying the default LAN, or by creating a new network under the Networks tab.

If the network you want to use for Wi-Fi has been created, go to Settings → Wi-Fi → Add New Network.

[Creating a new Wi-Fi network](https://preview.redd.it/sfusa5oclc181.png?width=2558&format

Hello!

I have long been an admirer for pfsemse and the whole 'homelab'-thing.
We will be moving to our new build house later this year and i saw the perfect opportunity to learn more in networking and play around with a pfsense.

We will be having 500/500 connection.
Here you can see a Topology of my network (this is how i want it to be)

https://preview.redd.it/t202fu7ulib81.png?width=1237&format=png&auto=webp&s=ea6b06cc20b9375fcec143627df6cfd1cb74fad8

What i want:

Be able to run WireGuard on my network, read that McDonald's videos and lawerence systems about the package.

I do want to be able to top my connection via Wireguard. 500/500.

Hardware

I've been looking into 2 possible hardwares.
Either

TLSense J4125

or

TLSense 4200U

Hopefully you can help me, thanks!

I'm surprised it hasn't decade.

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

Because she wanted to see the task manager.

Heard they've been doing some shady business.

My POV is of a physicist interested in the mathematical foundations of GR (and other metric theories of gravity) and whose knowledge of topology and real analysis is all self-taught and patchy. So I suppose "point set topology" is my only interest here, and that's what I'm asking about. I understand that pure mathematicians don't need a reason, they just like having algebraic structures to poke and prod, so if you're a pure mathematician just pretend you care about applications for a second.

I first was introduced to it as the study of "continuity of maps", and I learned how the topology 101 definition of a continuous map maps (heh) exactly to the epsilon-delta definition of continuity in real analysis. Then I went digging through real analysis and topology books and I think I've pieced together the following applied mathematician's/physicist's motivation of topology:

>With metric spaces we study the continuity of maps (and hence differentiability, which we need for physics) using a generic definition of "distance" (not necessarily Euclidean distance, or a vector inner product, or something like that). Topology is the study of continuity of maps at its most fundamental, i.e. without needing to invoke a concept of "distance", so that continuity can be studied in contexts more general that functions from R to R. In this way we can study differentiability with the absolute minimum of assumptions and extra structure.

Okay that all sounds fine, but it seems to me that any topological space we'd want to study would have a metric defined on it, and the open sets that make up a topology on a given set are usually chosen to be workable with a (generic) metric. And so it seems to me that the "minimal assumptions and minimal structure" thing is a bit misleading since we're really choosing open sets (or bases for them) with (generic) metrics in mind. So we've kind of built the metric space structure into our topologies with our choices of open sets. Or if not the full structure, the socket that it plugs into.

I'm worried that if (given a set) we constructed the open sets of a topology for it in some way not amenable to a metric space, then for that topology we'd have maps that would fit the definition of "continuous" but wouldn't be what anyone would actually call continuous, if presented with the map in isolation, but right now this is just a vague idea in my head that I haven't pinned down.

In which case, why not just talk about metric spaces all the

BamBOO!

They’re on standbi

Pilot on me!!

Christopher Walken

Nothing, he was gladiator.

https://preview.redd.it/1akzuf4srzr71.png?width=935&format=png&auto=webp&s=62582fde76e90e02b9169ceec8c21502b3abc6c8