Tootfinder

Are Depth-2 Regular Expressions Hard to Intersect?
Rocco Ascone, Giulia Bernardini, Alessio Conte, Veronica Guerrini, Giulia Punzi
https://arxiv.org/abs/2507.03593

Are Depth-2 Regular Expressions Hard to Intersect?
We study the basic regular expression intersection testing problem, which asks to determine whether the intersection of the languages of two regular expressions is nonempty. A textbook solution to this problem is to construct the nondeterministic finite automaton that accepts the language of both expressions. This procedure results in a $Θ(mn)$ running time, where $m$ and $n$ are the sizes of the two expressions, respectively. Following the approach of Backurs and Indyk [FOCS'16] and Bringmann…

Quantum repeaters based on stationary and flying Gottesman-Kitaev-Preskill qudits
Stefan H\"aussler, Peter van Loock
https://arxiv.org/abs/2508.00530 https://

Quantum repeaters based on stationary and flying Gottesman-Kitaev-Preskill qudits
There are various approaches to long-range quantum communication based on conceptually different forms of quantum repeaters. Here we explore a quantum repeater scheme that employs quantum error correction (QEC) both on the flying (light) qubits and on the stationary (matter) qubits. The idea is to combine the benefits of encoded one-way and two-way schemes where effective channel transmission and loss scaling are enhanced by means of photon loss codes and encoded quantum memories, respectively,…

Sonnet 121 - CXXI
'Tis better to be vile than vile esteemed,
When not to be receives reproach of being;
And the just pleasure lost, which is so deemed
Not by our feeling, but by others' seeing:
For why should others' false adulterate eyes
Give salutation to my sportive blood?
Or on my frailties why are frailer spies,
Which in their wills count bad what I think good?
No, I am that I am, and they that level
At my abuses re…

How popular media gets love wrong
Okay, my attempt at (hopefully widely-applicable) advice about relationships based on my mental "engineering" model and how it differs from the popular "fire" and "appeal" models:
1. If you're looking for a partner, don't focus too much on external qualities, but instead ask: "Do they respect me?" "Are they interested in active consent in all aspects of our relationship?" "Are they willing to commit a little now, and open to respectfully negotiating deeper commitment?" "Are they trustworthy, and willing to trust me?" Finding your partner attractive can come *from* trusting/appreciating/respecting them, rather than vice versa.
2. If you're looking for a partner, don't wait for infatuation to start before you try building a relationship. Don't wait to "fall in love;" if you "fall" into love you could just as easily "fall" out, but if you build up love, it won't be so easy to destroy. If you're feeling lonely and want a relationship, pick someone who seems interesting and receptive in your social circles and ask if they'd like to do something with you (doesn't have to be a date at first). *Pursue active consent* at each stage (if they're not interested; ask someone else, this will be easier if you're not already infatuated). If they're judging you by the standards in point 1, this is doubly important.
3. When building a relationship, try to synchronize your levels of commitment & trust even as you're trying to deepen them, or at least try to be honest and accepting when they need to be out-of-step. Say things and do things that show your partner the things (like trust, commitment, affection, etc.) that are important in your relationship, and ask them to do the same (or ideally you don't have to ask if they're conscious of this too). Do these things not as a chore or a transaction when your partner does them, but because they're the work of building the relationship that you value for its own sake (and because you value your partner for themselves too).
4. When facing big external challenges to your commitment to a relationship, like a move, ensure that your partner has an appropriate level of commitment too, but then don't undervalue the relationship relative to other things in life. Everyone is different, but *to me*, my committed relationship has been far more rewarding than e.g., a more "successful" career would have been. Of course worth noting here that non-men are taught by our society to undervalue their careers & other aspects of their life and sacrifice everything for their partners, which is toxic. I'm not saying "don't value other things" but especially for men, *do* value romantic relationships and be prepared to make decisions that prioritize them over other things, assuming a partner who is comfortable with that commitment and willing to reciprocate.
Okay, this thread is complete for now, until I think of something else that I've missed. I hope this advice is helpful in some way (or at least not harmful). Feel free to chime in if you've got different ideas...
#relationships #love

Bengals, DE Trey Hendrickson finalizing new contract for 2025 season https://www.nfl.com/news/bengals-trey-hendrickson-receives-pay-raise-for-2025-following-contract-negotiations

Hamiltonian Systems as an Example of Invariant Measure
Daniel Ferreira Lopes
https://arxiv.org/abs/2509.04248 https://arxiv.org/pdf/2509.04248

Hamiltonian Systems as an Example of Invariant Measure
Hamiltonian systems are a classical example in the ergodic theory of flows with an invariant measure. In this matter, we present a brief introduction to measure theory and prove the Poincare recurrence theorem to present the conditions for a system to be conservative. In the following, we discuss the Hamiltonian differential equations, vector fields, and its respective flows as an example of this invariance.

:crt_w_prompt:

Automated calibration of simulated galaxy catalogues for cosmological analyses
I. Tutusaus, P. Fosalba, L. Blot, P. Tallada-Cresp\'i, J. Carretero, F. J. Castander, E. J. Gonzalez, A. Alarcon
https://arxiv.org/abs/2507.23451

Automated calibration of simulated galaxy catalogues for cosmological analyses
Simulated galaxy catalogues have become an essential tool for preparing and exploiting observations from galaxy surveys. They constitute a key ingredient in modelling the systematic uncertainties present in the analysis. However, in order to reach the large volume and high precision required for galaxy surveys, we generally populate dark matter haloes with galaxies following certain theoretical recipes. Such recipes contain free parameters that are calibrated comparing the simulations against o…

On a Ramsey--Tur\'{a}n variant of Roth's theorem
Matija Buci\'c, Micha Christoph, Jaehoon Kim, Hyunwoo Lee, Varun Sivashankar
https://arxiv.org/abs/2507.22831 https:…

On a Ramsey--Turán variant of Roth's theorem
A classical theorem of Roth states that the maximum size of a solution-free set of a homogeneous linear equation $\mathcal{L}$ in $\mathbb{F}_p$ is $o(p)$ if and only if the sum of the coefficients of $\mathcal{L}$ is $0$. In this paper, we prove a Ramsey--Turán variant of Roth's theorem, with respect to a natural notion of ``structured'' sets introduced by Erdős and Sárközy in the 1970's. Namely, we show that the following statements are equivalent: $(a)$ Every solution-free set $A$ of $…

In Ursula K. Le Guin's "A Man of the People" (part of "Four Ways to Forgiveness") there's a scene where the Hainish protagonist begins studying history. It's excellent in many respects, but what stood out the most to me was the softly incomprehensible idea of a people with multiple millions of years of recorded history. As one's mind starts to try to trace out the implications of that, it dawns on you that you can't actually comprehend the concept. Like, you read the sentence & understood all the words, and at first you were able to assemble them into what seemed like a conceptual understanding, but as you started to try to fill out that understating, it began to slip away, until you realized you didn't in fact have the mental capacity to build a full understanding and would have you paper things over with a shallow placeholder instead.
I absolutely love that feeling, as one of the ways in which reading science fiction can stretch the brain, and I connected it to a similar moment in Tsutomu Nihei's BLAME, where the android protagonists need to ride an elevator through the civilization/galaxy-spanning megastructure, and turn themselves off for *millions of years* to wait out the ride.
I'm not sure why exactly these scenes feel more beautifully incomprehensible than your run-of-the-mill "then they traveled at lightspeed for a millennia, leaving all their family behind" scene, other than perhaps the authors approach them without trying to use much metaphor to make them more comprehensible (or they use metaphor to emphasize their incomprehensibility).
Do you have a favorite mind=expanded scene of this nature?
#AmReading