Tootfinder

On rationality of certain Eisenstein cohomology
Yubo Jin, Dongwen Liu, Binyong Sun
https://arxiv.org/abs/2506.06738 https://arxiv.org…

On rationality of certain Eisenstein cohomology
In this paper, we study the Eisenstein cohomology coming from Eisenstein series associated to degenerate principal series representations and prove certain rationality result.

"But Wall Street professionals, like so many other ostensibly smart people, refused to see Trump clearly, mistaking his skill as a demagogue for wisdom as a policymaker. “I don’t think this was foreseeable,” a mournful Ackman posted on X on Monday. “I assumed economic rationality would be paramount.” What an odd assumption to make about a man who bankrupted casinos.
Berezin thinks Wall Street still hasn’t come to terms with the cost of the nascent Trump presidency. “I do think that at this point we might have passed the event horizon, meaning that even if Trump backs off from the tariffs, there’s been enough damage done to the U.S. economy, to the global economy, to investor confidence, consumer confidence, that we’re probably going to see a recession regardless of what happens,” he said.""
#GiftArticle #USPolitics
https://www.nytimes.com/2025/04/07/opinion/trump-stock-market-wall-street.html?unlocked_article_code=1.-E4.q7Gk.5YS3EpoLnh8C&smid=url-share

Designing DSIC Mechanisms for Data Sharing in the Era of Large Language Models
Seyed Moein Ayyoubzadeh, Kourosh Shahnazari, Mohammmadali Keshtparvar, MohammadAmin Fazli
https://arxiv.org/abs/2506.05379

Designing DSIC Mechanisms for Data Sharing in the Era of Large Language Models
Training large language models (LLMs) requires vast amounts of high-quality data from institutions that face legal, privacy, and strategic constraints. Existing data procurement methods often rely on unverifiable trust or ignore heterogeneous provider costs. We introduce a mechanism-design framework for truthful, trust-minimized data sharing that ensures dominant-strategy incentive compatibility (DSIC), individual rationality, and weak budget balance, while rewarding data based on both quality …

Twisted associative algebras associated to vertex algebras
Shun Xu
https://arxiv.org/abs/2506.01321 https://arxiv.org/pdf/2506.01321

Twisted associative algebras associated to vertex algebras
Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show that for a vertex operator algebra, $g$-rationality, $g$-regularity, and twisted fusion rules are independent of the choice of the conformal vector.

On the Virtual Euler Characteristic of the Moduli Space of Stable Pairs on Surfaces
Ana Pavlakovi\'c
https://arxiv.org/abs/2505.23531 https://

On the Virtual Euler Characteristic of the Moduli Space of Stable Pairs on Surfaces
We study the stable pair theory on toric surfaces and determine the virtual tangent space over the fixed point loci. Further, we present a program to compute the virtual Euler characteristic, illustrated by the case of the projective plane. As an application, conjectures regarding rationality and symmetry are supported by verification of a special case.

This https://arxiv.org/abs/2502.07585 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

On the existence of pure epsilon-equilibrium
We show that for any $ε>0$, as the number of agents gets large, the share of games that admit a pure $ε$-equilibrium converges to 1. Our result holds even for pure $ε$-equilibrium in which all agents, except for at most one, play a best response. In contrast, it is known that the share of games that admit a pure Nash equilibrium, that is, for $ε=0$, is asymptotically $1-1/e\approx 0.63$. This suggests that very small deviations from perfect rationality, captured by positive values of $ε$, …

This https://arxiv.org/abs/2505.07501 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

The Complexity of Pure Strategy Relevant Equilibria in Concurrent Games
We study rational synthesis problems for concurrent games with $ω$-regular objectives. Our model of rationality considers only pure strategy Nash equilibria that satisfy either a social welfare or Pareto optimality condition with respect to an $ω$-regular objective for each agent. This extends earlier work on equilibria in concurrent games, without consideration about their quality. Our results show that the existence of Nash equilibria satisfying social welfare conditions can be computed as …