Tootfinder

Planned to take today off, so of course I scratched an itch I've been having at work instead:
This is a button you could drop into any app (probably only in debug mode) to get an embedded a11y inspector. It also dumps the selected nodes to logcat.
I'm not sure if something like this already exists, but I wanted something we could drop in the #JetpackCompose demo app …

Jimmy Kimmel made a fairly compelling demonstration for why banning TikTok isn't a bad idea.
People fighting to not ban tobacco because alcohol exists is what I've seen from some in the Democrat caucus.
https://youtube.com/watch?v=LWTNEARMoLk
Alternative 🔗:<…

Hot take because I like the #GoodTechThings newsletter Forrest makes:
Stack overflow exists because primary documentation generally sucks and will continue to.
Otherwise why would (usually outdated) tutorials exist?
As @… points out... ChatGPT is good at being welcoming, stackoverflow is bad at it, and both are good at outdated wrong answers.
All docs on the internet have sucked longer than you think (yes, before SEO ruined things). It's just the paradox of knowledge: when you've known something so long you forget how far you've come and how hard it was to learn.
Was helping someone new to tech, tried looking back at some tutorials and gosh they didn't include all the papercuts I went through. Even official docs of commercial providers are not free of that. Some primary docs are just plain wrong or outdated.
#StackOverflow #DevRel
https://newsletter.goodtechthings.com/p/closed-as-unhelpful-an-elegy-for

On closed definable subsets in Hensel minimal structures
Krzysztof Jan Nowak
https://arxiv.org/abs/2403.08039 https://arxiv.org/pdf/2…

On closed definable subsets in Hensel minimal structures
This paper deals with Hensel minimal structures on non-trivially valued fields $K$. The main aim is to establish the following two properties of closed 0-definable subsets $A$ in the affine spaces $K^{n}$. Every such subset $A$ is the zero locus of a continuous 0-definable function $f:K^{n} \to K$, and there exists a 0-definable retraction $r: K^{n} \to A$. While the former property is a non-Archimedean counterpart of the one from o-minimal geometry, the former does not hold in real geometry in…

Automated Classification of Body MRI Sequence Type Using Convolutional Neural Networks
Kimberly Helm, Tejas Sudharshan Mathai, Boah Kim, Pritam Mukherjee, Jianfei Liu, Ronald M. Summers
https://arxiv.org/abs/2402.08098

Automated Classification of Body MRI Sequence Type Using Convolutional Neural Networks
Multi-parametric MRI of the body is routinely acquired for the identification of abnormalities and diagnosis of diseases. However, a standard naming convention for the MRI protocols and associated sequences does not exist due to wide variations in imaging practice at institutions and myriad MRI scanners from various manufacturers being used for imaging. The intensity distributions of MRI sequences differ widely as a result, and there also exists information conflicts related to the sequence typ…

Flash forward a couple of years, and this is where we're at.
The editor-in-chief of a mainstream newspaper considers it "outright harassment" when those viciously targeted by her columnist ask for proof that columnist actually exists.
While the holding company of the newspaper admits that columnists at the paper "withhold their true identities for their own personal reasons". Which are not disclosed.
This on material that seeks to discredit other media organisations.

This https://arxiv.org/abs/2301.03835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A non-compact convex hull in generalized non-positive curvature
In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the analog of a question of Gromov about compactness properties of convex hulls has a negative answer in this setting. Specifically, we prove that there exists a complete metric space $X$ that admits a conical bicombing $σ$ such that $X$ has a finite subset whose closed $σ$-convex hull is not compact.

Tech -people dogma is tiring. 😫
The dogma shows up more on social media, but it exists IRL as well.
I wonder it's not really #dogma, but people too proud to admit they are wrong or someone else was right. Might also be people disappointed they could not find a fault they were so sure to find in another person/position.
I've seen all shades of it on my TL just recently. And t…

The AI Tool that I want is this: It takes in my handwriting and only slightly adjusts it to a more neatly written cursive.
(I'm not looking to text recognition; this is purely image processing.)
If this already exists, please let me know.
#ai #generativeai

This https://arxiv.org/abs/2310.11519 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some counterparts of Rickart $*$-algebras
In the present paper, we introduce and study counterparts of Rickart involutive algebras, i.e., almost inner Rickart algebras. We prove that a nilpotent associative algebra, which has no nilpotent elements with nonzero square roots, is an almost inner Rickart algebra. A nilpotent associative algebra, which has no nilpotent elements with a square root $b$ such that $b^3\neq 0$, is not an almost inner Rickart algebra if there exists a nonzero element $a$ such that $a^2\neq 0$. As a main result of…

LLMs Still Can't Avoid Instanceof: An Investigation Into GPT-3.5, GPT-4 and Bard's Capacity to Handle Object-Oriented Programming Assignments
Bruno Pereira Cipriano, Pedro Alves
https://arxiv.org/abs/2403.06254

LLMs Still Can't Avoid Instanceof: An Investigation Into GPT-3.5, GPT-4 and Bard's Capacity to Handle Object-Oriented Programming Assignments
Large Language Models (LLMs) have emerged as promising tools to assist students while solving programming assignments. However, object-oriented programming (OOP), with its inherent complexity involving the identification of entities, relationships, and responsibilities, is not yet mastered by these tools. Contrary to introductory programming exercises, there exists a research gap with regard to the behavior of LLMs in OOP contexts. In this study, we experimented with three prominent LLMs - GPT-…

I've been reading "On Green” (https://joecarlsmith.com/2024/03/21/on-green) and its following article, “On Attunement” with some interest today. I am uninterested in the ways he is focused on “AGI”, but that might actually be part of what he's saying and missing.
They talk about the philosophy of green in the "magic the gathering" sense, which has five core modes of things, and being a game, designed to balance. It's an attractive system and not without merit as a philosophical labeling system. In short: white, moral; blue, knowledge and rationality; red, passion and desire; black, power and achievement. And green. Green is the subject they can't identify clearly.
I don't think they really understand green. (They come from a very rationalist place, and that's not a good mode to understand Green)
Green is the domain of systems thinking and of ecology. It's one of flexible boundaries and hierarchies that vanish when you look at them for long. They talk about philosophical agents and try to fit a green philosophical stance into that framework, but it misses: the very idea of a self is nebulous in a green philosophy. Yes, it obviously exists, we are all separate from each other. But also we are inseparable from each other. Green is a philosophy of relationality and multiple perspectives and ever shifting viewpoints. It's not just yin, passive, permissive, but holistic. It's not that it lets the Other in, it's that it actively is in relation with the Other. The other is the self, the self is the other.
The essays also label green as conservative, and this is not quite true. It is not about being slow or regressive or traditional, but about being whole. They can't quite see that green's willingness to accept death and pain as things that happen and also its strong preservationist stance are not opposed to each other. It seems incoherent, but it's not: death and pain are things that happen to living parts of an ecosystem. They matter, but so too does the whole matter. Where so many blue rationalists see statistical and demographic counts of deaths and "sentient beings harmed”, green sees a whole ecosystem where some of that is deeply natural. It's unnatural, ecosystem-harming deaths that are disasters in the green philosophy. Wholesale extinctions. Protracted, painful deaths, as much for the wound they cause outside the individual as the individual suffering as well. But we all come to an end, and to change that wholesale would end so many kinds of relationship, so many things.
Green revels in the illegible, the incomplete, and the connected. It's easy to be green-blind, to ignore the subtle systemic effects. So many of us want simple cause and effect, rather than action and plurality of reactions.
Green's ability to embrace the illegible lets it deal with Red chaos; its resilience tempers red passion. It can ally with White philosophies into a pastoral, conservative, moralistic framework. It ends up at odds with the rationalist Blue and the power-hungry Black, because they drive disequilibrium, but more than just transition to new stable ecologies, they drive systems permanently out of stability, destroying relationships in their path. When confronted with this, they will deny it because the objects are still there. Preserved. Catalogued. Legible and accounted for. Perhaps used instrumentally. Perhaps wrecked for some "greater purpose” but only acknowledged as objects. The relationships between things remain illegible.

On CLT and non-CLT groups
Marius T\u{a}rn\u{a}uceanu
https://arxiv.org/abs/2403.05774 https://arxiv.org/pdf/2403.05774

On CLT and non-CLT groups
In this note, we prove that for every integer $d\geq 2$ which is not a prime power, there exists a finite solvable group $G$ such that $d\mid |G|$, $π(G)=π(d)$ and $G$ has no subgroup of order $d$. We also introduce the CLT-degree of a finite group and answer two questions about it.

On the large deviation principle for Metropolis-Hastings Markov Chains: the Lyapunov function condition and examples
Federica Milinanni, Pierre Nyquist
https://arxiv.org/abs/2403.08691

On the large deviation principle for Metropolis-Hastings Markov Chains: the Lyapunov function condition and examples
With an aim to analyse the performance of Markov chain Monte Carlo (MCMC) methods, in our recent work we derive a large deviation principle (LDP) for the empirical measures of Metropolis-Hastings (MH) chains on a continuous state space. One of the (sufficient) assumptions for the LDP involves the existence of a particular type of Lyapunov function, and it was left as an open question whether or not such a function exists for specific choices of MH samplers. In this paper we analyse the properti…

Tech -people dogma is tiring. 😫
The dogma shows up more on social media, but it exists IRL as well.
I wonder it's not really #dogma, but people too proud to admit they are wrong or someone else was right. Might also be people disappointed they could not find a fault they were so sure to find in another person/position.
I've seen all shades of it on my TL just recently. And t…

Capitalism as a natural followup to religion
Religion teaches you that you need to toil all your life for the elites, and you're going to reap the reward in the afterlife. That is, if such a thing exists. If it doesn't, it's not like you're going to be around to complain.
Capitalism teaches you that you need to toil most of your life for the elites, and you're going to reap the reward of a nice, cozy retirement. That is, if you live long enough to enjoy it. If you don't, it's not like you're going to be around to complain.
Well, technically you may not be healthy enough, or have a pension high enough, to actually enjoy the retirement. But it's not their fault — you haven't been taking good care of yourself, you haven't been working hard enough, or perhaps it's the fault of these lazy youngsters, or immigrants, or… In either case, if you were a good, god-fearing person, you're still up for the other reward, right?
Oh, and in both cases, it's important to reproduce. We must breed, so that future generations can continue toiling for the elites.
#AntiCapitalism

This https://arxiv.org/abs/2310.11519 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some counterparts of Rickart $*$-algebras
In the present paper, we introduce and study counterparts of Rickart involutive algebras, i.e., almost inner Rickart algebras. We prove that a nilpotent associative algebra, which has no nilpotent elements with nonzero square roots, is an almost inner Rickart algebra. A nilpotent associative algebra, which has no nilpotent elements with a square root $b$ such that $b^3\neq 0$, is not an almost inner Rickart algebra if there exists a nonzero element $a$ such that $a^2\neq 0$. As a main result of…

Variety of mutual-visibility problems in hypercubes
Danilo Kor\v{z}e, Aleksander Vesel
https://arxiv.org/abs/2405.05650 https://arxiv…

Variety of mutual-visibility problems in hypercubes
Let $G$ be a graph and $M \subseteq V(G)$. Vertices $x, y \in M$ are $M$-visible if there exists a shortest $x,y$-path of $G$ that does not pass through any vertex of $M \setminus \{x, y \}$. We say that $M$ is a mutual-visibility set if each pair of vertices of $M$ is $M$-visible, while the size of any largest mutual-visibility set of $G$ is the mutual-visibility number of $G$. If some additional combinations for pairs of vertices $x, y$ are required to be $M$-visible, we obtain the total (eve…

Folks, this is a deceptive design pattern. There is a very clear third option here (keep me updated on this campaign’s progress only) that is not implemented for marketing reasons.
I expect better from a platform that exists to effect ‘progressive change across Ireland’.
#ireland #uplift

QUOTE OF THE DAY
“Worries are pointless. If there’s a solution, there’s no need to worry. If no solution exists, there’s no point to worry.”
— Matthieu Ricard
Agree, disagree — be inspired or not.
QOTD is fuel for conversation, and food for thought.
#QOTD
#QuoteOfTheDay

EU teens start having sex at higher ages than US teens. It's not forbidden fruit for them.
If anyone had any evidence that setting the age of consent at 14 was harmful to German youth, they'd take it to parliament and get the law changed.
but no such evidence exists.

It is remarkable how many educated, intelligent adults do not know that email’s “reply all” option exists.

“When I was starting to make work about nuclear issues, I wondered: How do you capture something that is not in front of you? If the camera is a device that has a lens pointed forward and captures what exists in front of you, how do I capture something that's gone or invisible, like radiation or history or memory?” said artist Kei Ito. Read more in this interview with him:

This https://arxiv.org/abs/2312.15110 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hypertrace and entropy gap characterizations of property (T) for $\mathrm{II}_1$ factors
We establish a hypertrace characterization of property (T) for $\mathrm{II}_1$ factors: Given a $\mathrm{II}_1$ factors $M$, $M$ does not have property (T) if and only if there exists a von Neumann algebra $\mathcal{A}$ with $M\subset \mathcal{A}$ such that $\mathcal{A}$ admits a $M$-hypertrace but no normal hypertrace. For $M$ without property (T), such an inclusion $M\subset \mathcal{A}$ also admits vanishing Furstenberg entropy. With the same construction of $M\subset \mathcal{A}$, we also e…

If copyright is real then the AI machines owe the artists of humankind (which is to say all of us) more money than exists in the banking systems of the planet.
If copyright is not real then the companies that trained those models have no right to exclusive ownership of the weights.
I bet somehow the law conspires to make it the worst of either option.
#ai #copyright #copyleft

Do you have a “dream place?” There’s a house I visit only in my dreams, but I go there at least once a week, sometimes as often as 3 or 4 times a week. It’s not a place that exists in my “real” life—it’s not a house I’ve ever lived in or visited. In one dream, it’s a friend’s house—in another, it’s my ex-husband’s. Once, my 2nd steady boyfriend (from 45 yrs ago) lived there. Another time, my old roommate Wanda & I were moving into it. Once, I was hiding in it.

This https://arxiv.org/abs/2209.10275 has been replaced.
link: https://scholar.google.com/scholar?q=a

Tight Exponential Strong Converse for Source Coding Problem with Encoded Side Information
The source coding problem with encoded side information is considered. A lower bound on the strong converse exponent has been derived by Oohama, but its tightness has not been clarified. In this paper, we derive a tight strong converse exponent. For the special case such that the side-information does not exists, we demonstrate that our tight exponent of the WAK problem reduces to the known tight expression of that special case while Oohama's lower bound is strictly loose. The converse part is …

#TIL:
1. Tapirs are most closely related to equines and rhinos.
2. Mammalian phylogeny is a realm of turmoil that exceeds the worst nightmares of GRRM trying to flesh out Westeros genealogies and their backstories.
3. There's a classification group with broad support that is based on their having scrotums and not being Primates.
4. The slur “wastebasket clade" exists, bu…

QUOTE OF THE DAY
“Worries are pointless. If there’s a solution, there’s no need to worry. If no solution exists, there’s no point to worry.”
— Matthieu Ricard
Agree, disagree — be inspired or not.
QOTD is fuel for conversation, and food for thought.
#QOTD
#QuoteOfTheDay

This https://arxiv.org/abs/2308.15574 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

On the improved dynamics approach in loop quantum black holes
In this paper, we consider the Böhmer-Vandersloot (BV) model of loop quantum black holes obtained from the improved dynamics approach. We adopt the Saini-Singh gauge, in which it was found analytically that the BV spacetime is geodesically complete. We show that black/white hole horizons do not exist in this geodesically complete spacetime. Instead, there exists only an infinite number of transition surfaces, which always separate trapped regions from anti-trapped ones. Comments on the improve…

“Whether a president should have criminal immunity in some specific circumstances is an abstract question for another day, because efforts to stay in office and use the levers of the presidency are certainly not those specific circumstances. The appeals have delayed matters long enough at the expense of the right of the American people to a fair and speedy trial.”

The Public Has a Right to Trump's Speedy Trial
No good legal reason exists to delay Donald Trump’s January 6 trial any further.

This https://arxiv.org/abs/2310.01076 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

A Pareto tail plot without moment restrictions
We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which is not meaningful for distributions without existing mean, and which has a nonstandard behaviour if the mean is finite, but the second moment does not exist. The construction of the plot is based on the so called principle of a single huge jump, which differe…

This https://arxiv.org/abs/2211.06617 has been replaced.
link: https://scholar.google.com/scholar?q=a

Empirical Risk Minimization with Relative Entropy Regularization
The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $σ$-finite measure, and not necessarily a probability measure. Under this assumption, which leads to a generalization of the ERM-RER problem allowing a larger degree of flexibility for incorporating prior knowledge, numerous relevant properties are stated. Among these properties, the solution to this problem, if it exists, is shown to…

A Jpeg for a photograph makes sense unless a PNG exists. An MKV for a movie, sure, why not? A FLAC for a song? Perfect.
What about a vinyl record?? How do I store the cover as its own entity, all the songs as their own entity, all the lyrics and sheet music as separate entities, and then register a database entry that ties all these individual database entries together into an album?

This https://arxiv.org/abs/2402.04308 has been replaced.
link: https://scholar.google.com/scholar?q=a

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of t…

This https://arxiv.org/abs/2105.07947 has been replaced.
link: https://scholar.google.com/scholar?q=a

Abelian covers and second fundamental form
We give some conditions on a family of abelian covers of ${\mathbb P}^1$ of genus $g$ curves, that ensure that the family yields a subvariety of ${\mathsf A}_g$ which is not totally geodesic, hence it is not Shimura. As a consequence, we show that for any abelian group $G$, there exists an integer $M$ which only depends on $G$ such that if $g >M$, then the family yields a subvariety of ${\mathsf A}_g$ which is not totally geodesic. We prove then analogous results for families of abelian covers …

This https://arxiv.org/abs/2101.12593 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Symbol Length of Fields with finite Square Class Number
Let $F$ be a field of characteristic not $2$ with finitely many square classes. Using combinatorial arguments applied to objects related to vector spaces over finite fields, we deduce an upper bound for the number of Pfister forms over $F$. Moreover, we compute upper bounds for the $n$-symbol length $F$ ($n\in\mathbb N$), i.e., the smallest integer $\mathrm{sl}_n(F)\geq 0$ such that to each quadratic form $ϕ\in \mathsf I^n(F)$ there exists some $0\leq k\leq \mathrm{sl}_n(F)$ and Pfister forms …

This https://arxiv.org/abs/2210.06279 has been replaced.
link: https://scholar.google.com/scholar?q=a

The moment problem for random objects in a category
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average number of epimorphisms to a fixed object. When the moments do not grow too fast, we give a necessary and sufficient condition for existence of a distribution with those moments, show that a unique such measure exists, give formulas for the measure in terms of th…

TIL about this, too! I have a feeling @… or @… might find it interesting…
http…

Popularity and Perfectness in One-sided Matching Markets with Capacities
Gergely Cs\'aji
https://arxiv.org/abs/2403.00598 https://

Popularity and Perfectness in One-sided Matching Markets with Capacities
We consider many-to-one matching problems, where one side corresponds to applicants who have preferences and the other side to houses who do not have preferences. We consider two different types of this market: one, where the applicants have capacities, and one where the houses do. First, we answer an open question by Manlove and Sng (2006) (partly solved Paluch (2014) for preferences with ties), that is, we show that deciding if a popular matching exists in the house allocation problem, where …

Smoothly slice links in $S^2 \times S^2$ or $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$
Marco Marengon, Clayton McDonald
https://arxiv.org/abs/2403.00057 h…

Smoothly slice links in $S^2 \times S^2$ or $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$
For $X = S^2 \times S^2$ and $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$, we show that there exists a link with 2 components which is not smoothly slice in $X$. By contrast, it is well-known that every knot (i.e., link with 1 component) is smoothly slice in both $S^2 \times S^2$ and $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. Our proof uses classical topological and smooth obstructions, as well as constructive arguments to exploit the symmetries of the problem. As a side note, we also show tha…

I really hope we can get some good people from Threads to move over before Meta starts to do even more untrustworthy things.
Besides the absolutely absurdly move of following and pushing a fake"Fediverse" account that makes people think Fediverse is a single entity or organization, they've already started discussions about expansions to AP to allow platforms to support ads and other shitty ways of monetization.
Fedi needs to make money to survive, I know that. I am behind that, but ads are the shadiest of all the monetization methods because of tracking. Nobody wants to be tracked no matter how "innocent" their activities are.
They've been REALLY quiet since activating AP on their end in a seemingly bad faith move to make the Fediverse seem "useless and pointless to use" by forcing users to educate themselves on the Fediverse if they even know it exists while also making the option to turn it on obscenely hard to locate from normal use.
All in all, I'm VERY skeptical of Meta's intentions and don't really think they'll end up fully federating in the end becuase "why enable a feature that a wide number of our users think is a useless feature?". I feel right now is as far as they're gonna go with it, maybe worldwide, but still one way because that benefits them, not us, and they won't push a feature that people think is useless.
Obviously this is intentional bad faith tactics, but they still have time to prove me wrong and I really hope they do. I really really hope one day we get full federation, but I would be very delusional to have high hopes that such a thing will ever occur given this week's revelations.🤦‍♂️
#Fediverse #Fedi #Meta #Threads #Mastodon

This https://arxiv.org/abs/2212.12561 has been replaced.
link: https://scholar.google.com/scholar?q=a

An active learning method for solving competitive multi-agent decision-making and control problems
To identify a stationary action profile for a population of competitive agents, each executing private strategies, we introduce a novel active-learning scheme where a centralized external observer (or entity) can probe the agents' reactions and recursively update simple local parametric estimates of the action-reaction mappings. Under very general working assumptions (not even assuming that a stationary profile exists), sufficient conditions are established to assess the asymptotic properties o…

This https://arxiv.org/abs/2404.17771 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

Charaterization of dim light response in DVS pixel: Discontinuity of event triggering time
Dynamic Vision Sensors (DVS) have recently generated great interest because of the advantages of wide dynamic range and low latency compared with conventional frame-based cameras. However, the complicated behaviors in dim light conditions are still not clear, restricting the applications of DVS. In this paper, we analyze the typical DVS circuit, and find that there exists discontinuity of event triggering time. In dim light conditions, the discontinuity becomes prominent. We point out that the …

This https://arxiv.org/abs/2310.03366 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Elementary Properties of Free Lattices
We start a systematic analysis of the first-order model theory of free lattices. We prove several results. Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as there is a positive $\exists \forall$-sentence true in $\mathbf F_3$ and false in $\mathbf F_4$. Secondly, we show that every model of $\mathrm{Th}(\mathbf F_n)$ admits a canonical homomorphism into the profinite completion $\mathbf H_n$ of $\mathbf F_n$. Thirdly, we show that $\mathbf H_n$ is …

An elliptic problem in dimension N with a varying drift term bounded in $L^N$
Juan Casado-D\'iaz
https://arxiv.org/abs/2403.03115 https://

An elliptic problem in dimension N with a varying drift term bounded in $L^N$
The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in $L^N(Ω)$, with $N$ the dimension of the space. It is known that there exists a unique solution for each of these problems in the Sobolev space $H^1_0(Ω)$. However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in \cite{boc1}, and a regularization ob…

This https://arxiv.org/abs/2304.03444 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A conformal heat flow for harmonic maps does not develop finite time bubbling
A conformal heat flow for harmonic maps is a system of evolution equations combined with harmonic map flow with metric evolution in conformal direction. It is known that global weak solution of the flow exists and smooth except at mostly finitely many singular points. In this paper, we show that finite time singularity does not occur, unlike usual harmonic map flow.

This https://arxiv.org/abs/2207.04235 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Class of Rearrangement Groups that are not Invariably Generated
A group $G$ is invariably generated if there exists a subset $S \subseteq G$ such that, for every choice $g_s \in G$ for $s \in S$, the group $G$ is generated by $\{ s^{g_s} \mid s \in S \}$. In [GGJ16] Gelander, Golan and Juschenko showed that Thompson groups $T$ and $V$ are not invariably generated. Here we generalize this result to the larger setting of rearrangement groups, proving that any subgroup of a rearrangement group that has a certain transitive property is not invariably generated.

Learning and Sustaining Shared Normative Systems via Bayesian Rule Induction in Markov Games
Ninell Oldenburg, Tan Zhi-Xuan
https://arxiv.org/abs/2402.13399

Learning and Sustaining Shared Normative Systems via Bayesian Rule Induction in Markov Games
A universal feature of human societies is the adoption of systems of rules and norms in the service of cooperative ends. How can we build learning agents that do the same, so that they may flexibly cooperate with the human institutions they are embedded in? We hypothesize that agents can achieve this by assuming there exists a shared set of norms that most others comply with while pursuing their individual desires, even if they do not know the exact content of those norms. By assuming shared no…

This https://arxiv.org/abs/2306.04326 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csFL_…

Deciding whether an Attributed Translation can be realized by a Top-Down Transducer
We prove that for a given partial functional attributed tree transducer with monadic output, it is decidable whether or not an equivalent top-down transducer (with or without look-ahead) exists. We present a procedure that constructs an equivalent top-down transducer (with or without look-ahead) if it exists.

This https://arxiv.org/abs/2402.04308 has been replaced.
link: https://scholar.google.com/scholar?q=a

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of t…

This https://arxiv.org/abs/2305.06719 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Geodesically complete cyclic cosmologies and entropy
We demonstrate that there exists a class of cyclic cosmological models, such that these models can in principle solve the problem of the entropy growth, and are at the same time geodesically complete. We thus show that some recently stated conclusions, according to which cyclic cosmologies solving the problem of entropy growth can not be geodesically complete due to the Borde-Guth-Vilenkin (BGV) theorem, are not justified. We also add a short conceptual discussion on entropy and cyclic cosmolog…

Representation functions with prescribed rates of growth
Christian T\'afula
https://arxiv.org/abs/2405.01530 https://arxiv.org/pd…

Representation functions with prescribed rates of growth
Fix $h\geq 2$, and let $b_1$ , $\ldots$, $b_h$ be not necessarily distinct positive integers with $\gcd = 1$. For any subset $A\subseteq \mathbb{N}$, write $r_{A}(n)$ ($n\geq 0$) for the number of solutions $(k_1,\ldots,k_h)\in A^h$ to \[ b_1 k_1 + \cdots + b_h k_h = n. \] For which functions $F$ with $F(n) \leq r_{\mathbb{N}}(n)$ can we find $A\subseteq \mathbb{N}$ such that $r_{A}(n)\sim F(n)$? We show that if $F$ is regularly varying, then there exists such an $A$ provided $\lim\limits_{n\to…

On Classification of compact complex surfaces of class VII
Georges Dloussky
https://arxiv.org/abs/2403.20178 https://arxiv.org/pdf/24…

On Classification of compact complex surfaces of class VII
Let $S$ be a minimal compact complex surface with Betti numbers $b_1(S)=1$ and $b_2(S)\ge 1$ i.e. a compact surface in class VII$_0^+$. We show that if there exists a twisted logarithmic 1-form $τ\in H^0(S,Ω^1(\log D)\otimes \mathcal L_λ)$, where $D$ is a non zero divisor and $\mathcal L\in H^1(S,\mathbb C^\star)$, then $S$ is a Kato surface. It is known that $λ$ is in fact real and we show that $λ\ge 1$ and unique if $S$ is not a Inoue-Hirzebruch surface. Moreover $λ=1$ if and only if $S…

This https://arxiv.org/abs/2401.14344 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

From the Choi Formalism in Infinite Dimensions to Unique Decompositions of Generators of Completely Positive Dynamical Semigroups
Given any separable complex Hilbert space, any trace-class operator $B$ which does not have purely imaginary trace, and any generator $L$ of a norm-continuous one-parameter semigroup of completely positive maps we prove that there exists a unique bounded operator $K$ and a unique completely positive map $Φ$ such that (i) $L=K(\cdot)+(\cdot)K^*+Φ$, (ii) the superoperator $Φ(B^*(\cdot)B)$ is trace class and has vanishing trace, and (iii) ${\rm tr}(B^*K)$ is a real number. Central to our proof …

Graph Partitioning With Limited Moves
Majid Behbahani, Mina Dalirrooyfard, Elaheh Fata, Yuriy Nevmyvaka
https://arxiv.org/abs/2402.15485 https://

Graph Partitioning With Limited Moves
In many real world networks, there already exists a (not necessarily optimal) $k$-partitioning of the network. Oftentimes, one aims to find a $k$-partitioning with a smaller cut value for such networks by moving only a few nodes across partitions. The number of nodes that can be moved across partitions is often a constraint forced by budgetary limitations. Motivated by such real-world applications, we introduce and study the $r$-move $k$-partitioning~problem, a natural variant of the Multiway c…

This https://arxiv.org/abs/2111.10409 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Acrobatics of BQP
One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the behavior of quantum polynomial-time ($\mathsf{BQP}$) can be remarkably decoupled from that of classical complexity classes like $\mathsf{NP}$. Specifically: -There exists an oracle relative to which $\mathsf{NP^{BQP}}\not\subset\mathsf{BQP^{PH}}$, resolving a 2005…

This https://arxiv.org/abs/2308.06176 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Phase transitions and thermodynamic cycles in the broken PT-regime
We propose a new type of quantum thermodynamic cycle whose efficiency is greater than the one of the classical Carnot cycle for the same conditions for a system when viewed as homogeneous. In our model this type of cycle only exists in the low temperature regime in the spontaneously broken parity-time-reversal (PT) symmetry regime of a non-Hermitian quantum theory and does not manifest in the PT-symmetric regime. We discuss this effect for an ensemble based on a model of a single boson coupled …

Tinker or Transfer? A Tale of Two Techniques in Teaching Visualization
Adam Hyland, Murtaza Ali
https://arxiv.org/abs/2404.10967 https://

Tinker or Transfer? A Tale of Two Techniques in Teaching Visualization
In education there exists a tension between two modes of learning: traditional lecture-based instruction and more tinkering-based creative learning. In this paper, we outline our efforts as two Ph.D. students (who are skilled in visualization but are not, importantly, professionally trained visualization experts) to implement creative learning activities in an information visualization course in our home department. We describe our motivation for doing so, and how what began out of necessity tu…

This https://arxiv.org/abs/2401.05911 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Criterion for ultra-fast bubble walls: the impact of hydrodynamic obstruction
The Bödeker-Moore thermal friction is usually used to determine whether or not a bubble wall can run away. However, the friction on the wall is not necessarily a monotonous function of the wall velocity and could have a maximum before it reaches the Bödeker-Moore limit. In this paper, we compare the maximal hydrodynamic obstruction, a frictional force that exists in local thermal equilibrium, and the Bödeker-Moore thermal friction. We study the former in a fully analytical way, clarifying it…

This https://arxiv.org/abs/2301.03835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A non-compact convex hull in generalized non-positive curvature
In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the analog of a question of Gromov about compactness properties of convex hulls has a negative answer in this setting. Specifically, we prove that there exists a complete metric space $X$ that admits a conical bicombing $σ$ such that $X$ has a finite subset whose closed $σ$-convex hull is not compact.

This https://arxiv.org/abs/2312.13973 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Products of $Δ$-sets
We prove the consistency of the existence of a $Q$-set whose square is not a $Δ$-set and that if there is a $Δ$-set, then there exists a $Δ$-set whose all finite powers are $Δ$-sets.

This https://arxiv.org/abs/2403.10560 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Holographic Phase Retrieval via Wirtinger Flow: Cartesian Form with Auxiliary Amplitude
We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex…

Magnetization and exchange-stiffness constants of Fe-Al-Si alloys at finite-temperatures: A first-principles study
Shogo Yamashita, Akimasa Sakuma
https://arxiv.org/abs/2403.14096

Magnetization and exchange-stiffness constants of Fe-Al-Si alloys at finite-temperatures: A first-principles study
We investigated the magnetic properties of Sendust (Fe-Al-Si) alloys not only at 0 K but also at finite-temperatures by means of the first-principles calculations assuming A2, B2, and DO3 structures. We confirmed that the itinerant characteristics of 3d electrons of Fe are not negligible for A2 and B2 structures and a significantly small exchange stiffness constant exists at zero-temperature in a B2 structure. However, the calculated Curie temperatures are in the same order for all structures; …

Top cell attachment for a Poincare Duality complex
Stephen Theriault
https://arxiv.org/abs/2402.13775 https://arxiv.org/pdf/2402.1377…

Top cell attachment for a Poincare Duality complex
Let M be a simply-connected closed Poincare Duality complex of dimension n. Then M is obtained by attaching a cell of highest dimension to its (n-1)-skeleton M'. Conditions are given for when the skeletal inclusion i:M' --> M has the property that the based loops on i has a right homotopy inverse. This is an integral version of the rational statement that such a right homotopy inverse always exists provided the rational cohomology of M is not generated by a single element. New methods are devel…

Shadow Hamiltonians of structure-preserving integrators for Nambu mechanics
Atsushi Horikoshi
https://arxiv.org/abs/2403.11612 https://

Shadow Hamiltonians of structure-preserving integrators for Nambu mechanics
Symplectic integrators are widely implemented numerical integrators for Hamiltonian mechanics, which preserve the Hamiltonian structure (symplecticity) of the system. Although the symplectic integrator does not conserve the energy of the system, it is well known that there exists a conserving modified Hamiltonian, called the shadow Hamiltonian. For the Nambu mechanics, which is one of the generalized Hamiltonian mechanics, we can also construct structure-preserving integrators by the same proce…

This https://arxiv.org/abs/2101.12593 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Symbol Length of Fields with finite Square Class Number
Let $F$ be a field of characteristic not $2$ with finitely many square classes. Using combinatorial arguments applied to objects related to vector spaces over finite fields, we deduce an upper bound for the number of Pfister forms over $F$. Moreover, we compute upper bounds for the $n$-symbol length $F$ ($n\in\mathbb N$), i.e., the smallest integer $\mathrm{sl}_n(F)\geq 0$ such that to each quadratic form $ϕ\in \mathsf I^n(F)$ there exists some $0\leq k\leq \mathrm{sl}_n(F)$ and Pfister forms …

Killing Fields on Compact m-Quasi-Einstein Manifolds
Eric Cochran
https://arxiv.org/abs/2404.17090 https://arxiv.org/pdf/2404.17090
arXiv:2404.17090v1 Announce Type: new
Abstract: We show that given a compact, connected $m$-quasi Einstein manifold $(M,g,X)$ without boundary, the potential vector field $X$ is Killing if and only if $(M, g)$ has constant scalar curvature. This extends a result of Bahuaud-Gunasekaran-Kunduri-Woolgar, where it is shown that $X$ is Killing if $X$ is incompressible. We also provide a sufficient condition for a compact, non-gradient $m$-quasi Einstein metric to admit a Killing field. We do this by following a technique of Dunajski and Lucietti, who prove that a Killing field always exists in this case when $m=2$. This condition provides an alternate proof of the aforementioned result of Bahuaud-Gunasekaran-Kunduri-Woolgar. This alternate proof works in the $m = -2$ case as well, which was not covered in the original proof.

Global rigidity of smooth ${\mathbb Z}\ltimes_\lambda{\mathbb R}$-actions on ${\mathbb T}^2$
Changguang Dong, Yi Shi
https://arxiv.org/abs/2403.10060 https…

Global rigidity of smooth ${\mathbb Z}\ltimes_λ{\mathbb R}$-actions on ${\mathbb T}^2$
For $λ>1$, we consider the locally free ${\mathbb Z}\ltimes_λ{\mathbb R}$ actions on ${\mathbb T}^2$. We show that, if the action is $C^r$ with $r\geq2$, then it is $C^{r-ε}$-conjugate to an affine action generated by a hyperbolic automorphism and a linear translation flow along expanding eigen-direction of the automorphism. In contrast, there exists a $C^{1+α}$-action which is semi-conjugate, but not topologically conjugate to an affine action.

Graph Partitioning With Limited Moves
Majid Behbahani, Mina Dalirrooyfard, Elaheh Fata, Yuriy Nevmyvaka
https://arxiv.org/abs/2402.15485 https://

Graph Partitioning With Limited Moves
In many real world networks, there already exists a (not necessarily optimal) $k$-partitioning of the network. Oftentimes, one aims to find a $k$-partitioning with a smaller cut value for such networks by moving only a few nodes across partitions. The number of nodes that can be moved across partitions is often a constraint forced by budgetary limitations. Motivated by such real-world applications, we introduce and study the $r$-move $k$-partitioning~problem, a natural variant of the Multiway c…

This https://arxiv.org/abs/2310.03366 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Elementary Properties of Free Lattices
We start a systematic analysis of the first-order model theory of free lattices. Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as there is a positive $\exists \forall$-sentence true in $\mathbf F_3$ and false in $\mathbf F_4$. Secondly, we show that every model of $\mathrm{Th}(\mathbf F_n)$ admits a canonical homomorphism into the profinite-bounded completion $\mathbf H_n$ of $\mathbf F_n$. Thirdly, we show that $\mathbf H_n$ is isomorphic to the …

This https://arxiv.org/abs/2401.10152 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sums of square roots that are close to an integer
Let $k \in \mathbb{N}$ and suppose we are given $k$ integers $1 \leq a_1, \dots, a_k \leq n$. If $\sqrt{a_1} + \dots + \sqrt{a_k}$ is not an integer, how close can it be to one? When $k=1$, the distance to the nearest integer is $\gtrsim n^{-1/2}$. Angluin-Eisenstat observed the bound $\gtrsim n^{-3/2}$ when $k=2$. We prove there is a universal $c>0$ such that, for all $k \geq 2$, there exists a $c_k > 0$ and $k$ integers in $\left\{1,2,\dots, n\right\}$ with $$ 0 <\|\sqrt{a_1} + \dots + \…

Linear bounds on treewidth in terms of excluded planar minors
J. Pascal Gollin, Kevin Hendrey, Sang-il Oum, Bruce Reed
https://arxiv.org/abs/2402.17255 htt…

Linear bounds on treewidth in terms of excluded planar minors
One of the fundamental results in graph minor theory is that for every planar graph $H$, there is a minimum integer $f(H)$ such that graphs with no minor isomorphic to $H$ have treewidth at most $f(H)$. A lower bound for ${f(H)}$ can be obtained by considering the maximum integer $k$ such that $H$ contains $k$ vertex-disjoint cycles. There exists a graph of treewidth ${Ω(k\log k)}$ which does not contain $k$ vertex-disjoint cycles, from which it follows that ${f(H) = Ω(k\log k)}$. In particul…

Characterization of Isometric Words based on Swap and Mismatch Distance
M. Anselmo, G. Castiglione, M. Flores, D. Giammarresi, M. Madonia, S. Mantaci
https://arxiv.org/abs/2404.13577 https://arxiv.org/pdf/2404.13577
arXiv:2404.13577v1 Announce Type: new
Abstract: In this paper we consider an edit distance with swap and mismatch operations, called tilde-distance, and introduce the corresponding definition of tilde-isometric word. Isometric words are classically defined with respect to Hamming distance and combine the notion of edit distance with the property that a word does not appear as factor in other words. A word f is said tilde-isometric if, for any pair of f-free words u and v, there exists a transformation from u to v via the related edit operations such that all the intermediate words are also f -free. This new setting is here studied giving a full characterization of the tilde-isometric words in terms of overlaps with errors.

This https://arxiv.org/abs/2403.16255 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Phase retrieval on circles and lines
Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on various sets $A$. We first prove that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $π$. The same conclusion is valid when $f$ and $g$ are in the Nevanlinna class and $A$ is the union of the unit circle and an interior circle, tangential or not. We also p…

This https://arxiv.org/abs/2402.12838 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Extending the Scope of Inference About Predictive Ability to Machine Learning Methods
Though out-of-sample forecast evaluation is systematically employed with modern machine learning methods and there exists a well-established classic inference theory for predictive ability, see, e.g., West (1996, Asymptotic Inference About Predictive Ability, Econometrica, 64, 1067-1084), such theory is not directly applicable to modern machine learners such as the Lasso in the high dimensional setting. We investigate under which conditions such extensions are possible. Two key properties for s…

Modifying an Instance of the Super-Stable Matching Problem
Naoyuki Kamiyama
https://arxiv.org/abs/2402.11918 https://arxiv.org/pdf/24…

Modifying an Instance of the Super-Stable Matching Problem
Super-stability is one of the stability concepts in the stable matching problem with ties. It is known that there may not exist a super-stable matching, and the existence of a super-stable matching can be checked in polynomial time. In this paper, we consider the problem of modifying an instance of the super-stable matching problem by deleting some bounded number of agents in such a way that there exists a super-stable matching in the modified instance. First, we prove that if we are allowed to…

This https://arxiv.org/abs/2211.06617 has been replaced.
link: https://scholar.google.com/scholar?q=a

Empirical Risk Minimization with Relative Entropy Regularization
The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $σ$-finite measure, and not necessarily a probability measure. Under this assumption, which leads to a generalization of the ERM-RER problem allowing a larger degree of flexibility for incorporating prior knowledge, numerous relevant properties are stated. Among these properties, the solution to this problem, if it exists, is shown to…

This https://arxiv.org/abs/2302.09454 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Realizability of Some Combinatorial Sequences
A sequence $a=(a_n)_{n=1}^\infty$ of non-negative integers is called realizable if there is a self-map $T:X\to X$ on a set $X$ such that $a_n$ is equal to the number of periodic points of $T$ in $X$ of (not necessarily exact) period $n$, for all $n\geq1$. The sequence $a$ is called almost realizable if there exists a positive integer $m$ such that $(ma_n)_{n=1}^\infty$ is realizable. In this article, we show that certain wide classes of integer sequences are realizable, which contain many famou…

This https://arxiv.org/abs/2311.05118 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Higher incoherence of the automorphism groups of a free group
Let $F_n$ be the free group on $n \geq 2$ generators. We show that for all $1 \leq m \leq 2n-3$ (respectively for all $1 \leq m \leq 2n-4$) there exists a subgroup of $\operatorname{Aut}(F_n)$ (respectively $\operatorname{Out}(F_n)$) which has finiteness of type $F_{m}$ but not of type $FP_{m+1}(\mathbb{Q})$, hence it is not $m$-coherent. In both cases, the new result is the upper bound $m= 2n-3$ (respectively $m = 2n-4$), as it cannot be obtained by embedding direct products of free noncyclic …

Linear bounds on treewidth in terms of excluded planar minors
J. Pascal Gollin, Kevin Hendrey, Sang-il Oum, Bruce Reed
https://arxiv.org/abs/2402.17255 htt…

Linear bounds on treewidth in terms of excluded planar minors
One of the fundamental results in graph minor theory is that for every planar graph $H$, there is a minimum integer $f(H)$ such that graphs with no minor isomorphic to $H$ have treewidth at most $f(H)$. A lower bound for ${f(H)}$ can be obtained by considering the maximum integer $k$ such that $H$ contains $k$ vertex-disjoint cycles. There exists a graph of treewidth ${Ω(k\log k)}$ which does not contain $k$ vertex-disjoint cycles, from which it follows that ${f(H) = Ω(k\log k)}$. In particul…

This https://arxiv.org/abs/2403.10560 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Holographic Phase Retrieval via Wirtinger Flow: Cartesian Form with Auxiliary Amplitude
We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex…

The Andoni-Naor-Neiman inequalities and isometric embeddability into a $\mathrm{CAT}(0)$ space
Tetsu Toyoda
https://arxiv.org/abs/2404.13871 https://arxiv.org/pdf/2404.13871
arXiv:2404.13871v1 Announce Type: new
Abstract: Andoni, Naor and Neiman (2018) established a family of quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. As stated in their paper, this family seems to include all previously used quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. We prove that there exists a metric space that satisfies all inequalities in this family but does not admit an isometric embedding into any $\mathrm{CAT}(0)$ space. More precisely, we prove that the $6$-point metric spaces constructed by Nina Lebedeva, which are known to admit no isometric embedding into any $\mathrm{CAT}(0)$ space, satisfy all inequalities in this family.

Characterization of Isometric Words based on Swap and Mismatch Distance
M. Anselmo, G. Castiglione, M. Flores, D. Giammarresi, M. Madonia, S. Mantaci
https://arxiv.org/abs/2404.13577 https://arxiv.org/pdf/2404.13577
arXiv:2404.13577v1 Announce Type: new
Abstract: In this paper we consider an edit distance with swap and mismatch operations, called tilde-distance, and introduce the corresponding definition of tilde-isometric word. Isometric words are classically defined with respect to Hamming distance and combine the notion of edit distance with the property that a word does not appear as factor in other words. A word f is said tilde-isometric if, for any pair of f-free words u and v, there exists a transformation from u to v via the related edit operations such that all the intermediate words are also f -free. This new setting is here studied giving a full characterization of the tilde-isometric words in terms of overlaps with errors.

This https://arxiv.org/abs/2310.11519 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some counterparts of Rickart $*$-algebras
In the present paper, we introduce and study counterparts of Rickart involutive algebras, i.e., almost inner Rickart algebras. We prove that a nilpotent associative algebra, which has no nilpotent elements with nonzero square roots, is an almost inner Rickart algebra. A nilpotent associative algebra, which has no nilpotent elements with a square root $b$ such that $b^3\neq 0$, is not an almost inner Rickart algebra if there exists a nonzero element $a$ such that $a^2\neq 0$. As a main result of…

This https://arxiv.org/abs/2403.16255 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Phase retrieval on circles and lines
Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on various sets $A$. We first prove that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $π$. The same conclusion is valid when $f$ and $g$ are in the Nevanlinna class and $A$ is the union of the unit circle and an interior circle, tangential or not. We also p…

This https://arxiv.org/abs/2311.07846 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spreading primitive groups of diagonal type do not exist
The synchronisation hierarchy of finite permutation groups consists of classes of groups lying between 2-transitive groups and primitive groups. This includes the class of spreading groups, which are defined in terms of sets and multisets of permuted points, and which are known to be primitive of almost simple, affine or diagonal type. In this paper, we prove that in fact no spreading group of diagonal type exists. As part of our proof, we show that all non-abelian finite simple groups, other t…

Wild solutions of the 3D axisymmetric Euler equations
Patrick Brkic, Emil Wiedemann
https://arxiv.org/abs/2404.08407 https://arxiv.or…

Wild solutions of the 3D axisymmetric Euler equations
We consider the Cauchy problem for the 3D incompressible axisymmetric swirl-free Euler equations. The convex integration method developed by De Lellis and Székelyhidi rules out the possibility that the Euler equations admit unique admissible weak solutions. It had remained conceivable, though, that axisymmetry of the solution might serve as a selection criterion. Using a surprising link to the 2D isentropic compressible Euler equations, we will show that this is not the case: There exists init…

The Andoni-Naor-Neiman inequalities and isometric embeddability into a $\mathrm{CAT}(0)$ space
Tetsu Toyoda
https://arxiv.org/abs/2404.13871 https://arxiv.org/pdf/2404.13871
arXiv:2404.13871v1 Announce Type: new
Abstract: Andoni, Naor and Neiman (2018) established a family of quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. As stated in their paper, this family seems to include all previously used quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. We prove that there exists a metric space that satisfies all inequalities in this family but does not admit an isometric embedding into any $\mathrm{CAT}(0)$ space. More precisely, we prove that the $6$-point metric spaces constructed by Nina Lebedeva, which are known to admit no isometric embedding into any $\mathrm{CAT}(0)$ space, satisfy all inequalities in this family.

This https://arxiv.org/abs/2206.13635 has been replaced.
link: https://scholar.google.com/scholar?q=a

Coloring hypergraphs with excluded minors
Hadwiger's conjecture, among the most famous open problems in graph theory, states that every graph that does not contain $K_t$ as a minor is properly $(t-1)$-colorable. The purpose of this work is to demonstrate that a natural extension of Hadwiger's problem to hypergraph coloring exists, and to derive some first partial results and applications. Generalizing ordinary graph minors to hypergraphs, we say that a hypergraph $H_1$ is a minor of a hypergraph $H_2$, if a hypergraph isomorphic to $H_…

This https://arxiv.org/abs/2203.17160 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Busemann--Hausdorff densities of dimension two and of codimension two, with an application to Plateau Problem
The purpose of this paper is twofold. First, we describe one (presumably) new case, in which Busemann--Hausdorff densities are convex. We apply the corresponding result to prove the existence of minimizing rectifiable chains of codimension two in complex finite dimensional normed vector spaces. Second, we prove that for each $n\geq 4$, there exists an $n$ dimensional normed space in which the corresponding two dimensional Busemann--Hausdroff density is not totally convex. This gives a negative …

This https://arxiv.org/abs/2403.08039 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On closed definable subsets in Hensel minimal structures
This paper deals with Hensel minimal structures on non-trivially valued fields $K$. The main aim is to establish the following two properties of closed 0-definable subsets $A$ in the affine spaces $K^{n}$. Every such subset $A$ is the zero locus of a continuous 0-definable function $f:K^{n} \to K$, and there exists a 0-definable retraction $r: K^{n} \to A$. While the former property is a non-Archimedean counterpart of the one from o-minimal geometry, the former does not hold in real geometry in…

Phase retrieval on circles and lines
I. Chalendar, J. R. Partington
https://arxiv.org/abs/2403.16255 https://arxiv.org/pdf/2403.16255…

Phase retrieval on circles and lines
Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on various sets $A$. We first prove that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $π$. The same conclusion is valid when $f$ and $g$ are in the Nevanlinna class and $A$ is the union of the unit circle and an interior circle, tangential or not. We also p…

This https://arxiv.org/abs/2308.03503 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On 1-Konig-Egervary Graphs
Let $α(G)$ denote the cardinality of a maximum independent set, while $μ(G)$ be the size of a maximum matching in $G=\left( V,E\right) $. Let $ξ(G)$ denote the size of the intersection of all maximum independent sets. It is known that if $α(G)+μ(G)=n(G)=\left\vert V\right\vert $, then $G$ is a König-Egerváry graph. If $α(G)+μ(G)=n(G) -1$, then $G$ is a $1$-König-Egerváry graph. If $G$ is not a König-Egerváry graph, and there exists a vertex $v\in V$ (an edge $e\in E$) such that $G-…

This https://arxiv.org/abs/2403.08039 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On closed definable subsets in Hensel minimal structures
This paper deals with Hensel minimal structures on non-trivially valued fields $K$. The main aim is to establish the following two properties of closed 0-definable subsets $A$ in the affine spaces $K^{n}$. Every such subset $A$ is the zero locus of a continuous 0-definable function $f:K^{n} \to K$, and there exists a 0-definable retraction $r: K^{n} \to A$. While the former property is a non-Archimedean counterpart of the one from o-minimal geometry, the former does not hold in real geometry in…

This https://arxiv.org/abs/2404.13871 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Andoni-Naor-Neiman inequalities and isometric embeddability into a $\mathrm{CAT}(0)$ space
Andoni, Naor and Neiman (2018) established a family of quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. As stated in their paper, this family seems to include all previously used quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. We prove that there exists a metric space that satisfies all inequalities in this family but does not admit an isometric embedding into any $\mathrm{CAT}(0)$ space. More precisely, we prove that the $6$-point me…

Minimax Optimal rates of convergence in the shuffled regression, unlinked regression, and deconvolution under vanishing noise
Cecile Durot, Debarghya Mukherjee
https://arxiv.org/abs/2404.09306

Minimax Optimal rates of convergence in the shuffled regression, unlinked regression, and deconvolution under vanishing noise
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc. However, a notable gap exists in the existing literature, particularly in vanishing noise, i.e., how the rate of estimation of the underlying signal scales with the error variance. This paper aims to bridge this gap by delving into the monotone function estim…

On a conjecture on shifted primes with large prime factors, II
Yuchen Ding
https://arxiv.org/abs/2402.09829 https://arxiv.org/pdf/240…

On a conjecture on shifted primes with large prime factors, II
Let $\mathcal{P}$ be the set of primes and $π(x)$ the number of primes not exceeding $x$. Let also $P^+(n)$ be the largest prime factor of $n$ with convention $P^+(1)=1$ and $$ T_c(x)=\#\left\{p\le x:p\in \mathcal{P},P^+(p-1)\ge p^c\right\}. $$ Motivated by a 2017 conjecture of Chen and Chen, the author [6] proved that there exists some absolute constant $c<1$ such that \begin{align}\label{eq1} \limsup_{x\rightarrow\infty}T_{c}(x)/π(x)<1/2. \end{align} In this note, the prior result is consid…