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A Gentle Introduction to Algebraic Operads
Felicia Ferraioli
https://arxiv.org/abs/2508.01886 https://arxiv.org/pdf/2508.01886

A Gentle Introduction to Algebraic Operads
This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative, commutative, and Lie algebras can be fully recovered as categories of representations of three archetypal operads: $\mathsf{As}$, $\mathsf{Com}$ and $\mathsf{Lie}$ -- the so-called 'three graces' of algebra. Following a deductive and self-contained approach, th…

This https://arxiv.org/abs/2407.02313 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Casimir-like probe for 4D Einstein-Gauss-Bonnet gravity
Virtual transitions in a Casimir-like configuration are utilized to probe quantum aspects of four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity. This study employs a quantum optics-based approach, wherein an Unruh-DeWitt detector (modeled as a two-level atom) follows a radial timelike geodesic, falling freely into an uncharged, nonrotating black hole described by 4D EGB gravity, becoming thermalized in the usual Unruh manner. The black hole, asymptotically Minkowskian, is enclosed by a Cas…

Optimization of the multiple sampling and signal extraction in non-destructive exposures
B. Kubik, R. Barbier, A. Castera, E. Chabanat, S. Ferriol, G. Smadja
https://arxiv.org/abs/2506.04904

Optimization of the multiple sampling and signal extraction in non-destructive exposures
We derive the full covariance matrix formulae are derived for proper treatment of correlations in signal fitting procedures, extending the results from previous publications. The straight line fits performed with these matrices demonstrate that a significantly higher signal to noise is obtained when the fluence exceeds 1 e/sec/pix in particular in long (several hundreds of seconds) spectroscopic exposures. The improvement arising from the covariance matrix is particularly strong for the initial…

On the Farrell--Tate $K$-theory of $\text{Out}(F_n)$
Naomi Andrew, Irakli Patchkoria
https://arxiv.org/abs/2505.21803 https://arxiv.o…

On the Farrell--Tate $K$-theory of $\text{Out}(F_n)$
Using Lück's Chern character isomorphism we obtain a general formula in terms of centralisers for the $p$-adic Farrell--Tate $K$-theory of any discrete group $G$ with a finite classifying space for proper actions. We apply this formula to $\text{Out}(F_n)$. The case $n=p+1$ turns out to be especially interesting for the following reason: Up to conjugacy there is exactly one order $p$ element in $\text{Out}(F_{p+1})$ which does not lift to an order $p$ element in $\text{Aut}(F_{p+1})$. We compu…

@… Nudge-nudge!
https://tapbots.social/@ivory/114581036568303599

Leeds former head teacher faces no charges following terrorism arrest for holding up a graphic from a satirical magazine.
https://www.bbc.co.uk/news/articles/cz9kdq84j3lo

Leeds former head teacher's terror arrest shock over protest cartoon
Jon Farley is held by police under the Terrorism Act for six hours over a placard he was carrying.

X-ray diffraction from smectic multilayers: crossover from kinematical to dynamical regime
V. V. Samsonov, K. V. Nikolaev, B. I. Ostrovskii, S. N. Yakunin
https://arxiv.org/abs/2505.23547

X-ray diffraction from smectic multilayers: crossover from kinematical to dynamical regime
We study X-ray diffraction in smectic liquid crystal multilayers. Such systems are fabricated as freely suspended films and have a unique layered structure. As such, they can be described as organic Bragg mirrors with sub-nanometer roughness. However, an interesting peculiarity arises in the diffraction on these structures: the characteristic shape of diffraction peaks associated with dynamical scattering effects is not observed. Instead, the diffraction can be well described kinematically, whi…

Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials
Huxiao Luo, Shiying Wang
https://arxiv.org/abs/2507.20069 https://arxi…

Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials
We establish the following fractional Trudinger-Moser type inequality with logarithmic convolution potential $$ \sup_{u\in W^{\frac{1}{2},2}_0(I),\|u\|_{W_0^{\frac{1}{2},2}}\leq1}\int_{I} \int_{I} \log \frac{1}{|x-y|} G(u(x))G(u(y)) \, dx \, dy<+\infty,$$ where $G(s)\leq C\frac{e^{πs^{2}}}{(1 + |s|)^γ}~ \forall s\in\mathbb{R}$ with some constant $C>0,γ\geq1$, the domain $I\subset\mathbb{R}$ is a bounded interval. This type of inequality in the entire space $\mat…

Fourier minimization and imputation of time series
Will Burstein, Alex Iosevich, Azita Mayeli, Hari Sarang Nathan
https://arxiv.org/abs/2506.19226 https://…

Fourier minimization and imputation of time series
One of the most common procedures in modern data analytics is filling in missing values in times series. For a variety of reasons, the data provided by clients to obtain a forecast, or other forms of data analysis, may have missing values, and those values need to be filled in before the data set can be properly analyzed. Many freely available forecasting software packages, such as the sktime library, have built-in mechanisms for filling in missing values. The purpose of this paper is to adapt …

The Persistence of Nonlinear Gravitational Wave Memory
Robert R. Caldwell
https://arxiv.org/abs/2506.20751 https://arxiv.org/pdf/2506…

The Persistence of Nonlinear Gravitational Wave Memory
Nonlinear gravitational wave memory is a surprise of theoretical physics. Whereas it is understood that a gravitational wave induces oscillatory squeezing and stretching motion in a collection of freely-falling test masses, it is unexpected that the wave leaves a residual displacement of the test masses. This displacement is the tribute in memoriam to the passing wave. The memory originates in a nonlinear feature of gravitation. Whilst merging black holes are a significant source of gravitation…