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A density counterpart of the Scheepers covering property
Leandro Aurichi, Fortunato Maesano, Lyubomyr Zdomskyy
https://arxiv.org/abs/2510.11033 https://arx…

A density counterpart of the Scheepers covering property
We introduce a density counterpart of the Scheepers covering property $\bigcup_{\mathrm{fin}}(\mathcal O,Ω)$ and study its relations to known combinatorial density property. In particular, we show that it is equivalent to the $M$-separability under the Near Coherence of Filters principle of Blass and Weiss.

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Replaced article(s) found for math.AP. https://arxiv.org/list/math.AP/new
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- Global solvability of the Laplace equation in weighted Sobolev spaces
Bilal T. Bilalov, Natavan P. Nasibova, Lubomira G. Softova, Salvatore Tramontano

LibEMER: A novel benchmark and algorithms library for EEG-based Multimodal Emotion Recognition
Zejun Liu, Yunshan Chen, Chengxi Xie, Huan Liu
https://arxiv.org/abs/2509.19330 ht…

LibEMER: A novel benchmark and algorithms library for EEG-based Multimodal Emotion Recognition
EEG-based multimodal emotion recognition(EMER) has gained significant attention and witnessed notable advancements, the inherent complexity of human neural systems has motivated substantial efforts toward multimodal approaches. However, this field currently suffers from three critical limitations: (i) the absence of open-source implementations. (ii) the lack of standardized and transparent benchmarks for fair performance analysis. (iii) in-depth discussion regarding main challenges and promisin…

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Concentrated sets and the Hurewicz property
Valentin Haberl, Piotr Szewczak, Lyubomyr Zdomskyy
https://arxiv.org/abs/2511.09320 https://arxiv.org/pdf/2511.09320 https://arxiv.org/html/2511.09320
arXiv:2511.09320v1 Announce Type: new
Abstract: A set of reals $X$ is $\mathfrak{b}$-concentrated if it has cardinality at least $\mathfrak{b}$ and it contains a countable set $D\subseteq X$ such that each closed subset of $X$ disjoint with $D$ has size smaller than $\mathfrak{b}$. We present ZFC results about structures of $\mathfrak{b}$-concentrated sets with the Hurewicz covering property using semifilters. Then we show that assuming that the semifilter trichotomy holds, then each $\mathfrak{b}$-concentrated set is Hurewicz and even productively Hurewicz. We also show that the appearance of Hurewicz $\mathfrak{b}$-concentrated sets under the semifilter trichotomy is somewhat specific and the situation in the Laver model for the consitency of the Borel Conjecture is different.
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Objective clustering protocol for single-molecule data: A lifetime vs. intensity study
Michael Lovemore, Joshua Botha, Gonfa Assefa, Tjaart Kruger
https://arxiv.org/abs/2510.05665

Objective clustering protocol for single-molecule data: A lifetime vs. intensity study
Single-molecule spectroscopy (SMS) is an exceptionally sensitive technique, but its inherently limited photon budget produces noisy data that can readily lead to subjective analyses, fitting errors, and reduced statistical power, obscuring true subpopulations and their dynamics. Here, we present an unbiased, objective method to cluster two-dimensional single-molecule data and demonstrate it on fluorescence lifetime-intensity correlations. The clustering method is based on Gaussian mixture model…

Polymer-based probabilistic bits for thermodynamic computing
Stephen H. Foulger, Yuriy Bandera, Igor Luzinov, Travis Wanless, Lubomir Kostal, Vojtech N\'adazdy, Petr Janovsk\'y, Jarmila Vil\v{c}\'akov\'a
https://arxiv.org/abs/2509.21372

Polymer-based probabilistic bits for thermodynamic computing
Probabilistic bits (p-bits) are stochastic hardware elements whose output probability can be tuned by an input bias, offering a route to energy-efficient architectures that exploit, rather than suppress, fluctuations. Here we report p-bit generation in an organic memristive device, establishing polymers as the first class of soft-matter systems to realize probabilistic hardware. The active element is a dithieno[3,2-b:2',3'-d]pyrrole (DTP)-backbone polymer with pendant triphenylamine (TPA) group…

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