arXiv subjects

Alexey Orlov

Publications and source records attributed to Alexey Orlov.

4 recordsLinked to original sources

arXiv2026

The Classification of Supersingular Elliptic Curves in Characteristic 3

We provide an explicit classification of supersingular elliptic curves in characteristic~3 into isomorphism classes, and give explicit formulae for their point counts. This report was written specifically to support implementation of point counting in Hecke.jl; accordingly, the reasoning is concrete and elementary. After the first version appeared, we learned that the explicit classification was already obtained by Morain. We believe the present note remains useful in offering a more self-contained and implementation-oriented treatment. The explicit connection to previous Morain's classificaion is given in the appendix.

math.NT↗

arXiv2025

Thinking like a CHEMIST: Combined Heterogeneous Embedding Model Integrating Structure and Tokens

Representing molecular structures effectively in chemistry remains a challenging task. Language models and graph-based models are extensively utilized within this domain, consistently achieving state-of-the-art results across an array of tasks. However, the prevailing practice of representing chemical compounds in the SMILES format - used by most data sets and many language models - presents notable limitations as a training data format. In this study, we present a novel approach that decomposes molecules into substructures and computes descriptor-based representations for these fragments, providing more detailed and chemically relevant input for model training. We use this substructure and descriptor data as input for language model and also propose a bimodal architecture that integrates this language model with graph-based models. As LM we use RoBERTa, Graph Isomorphism Networks (GIN), Graph Convolutional Networks (GCN) and Graphormer as graph ones. Our framework shows notable improvements over traditional methods in various tasks such as Quantitative Structure-Activity Relationship (QSAR) prediction.

cs.LG↗

arXiv2021

The combinatorial method to compute the sum of the powers of primes

We will generalize the combinatorial algorithms for computing $π(x)$ to compute sums ${F(x) = \sum_{p \leq x} p^k}$ for $k \in \mathbb{Z}_{\geq 0}$. The detailed exposition of algorithms is included along with implementation details.

math.NT↗

arXiv2011

Spontaneous emission enhancement in metal-dielectric metamaterials

We study the spontaneous emission of a dipole emitter imbedded into a layered metal-dielectric metamaterial. We demonstrate ultra-high values of the Purcell factor in such structures due to a high density of states with hyperbolic isofrequency surfaces. We reveal that the traditional effective-medium approach greatly underestimates the value of the Purcell factor due to the presence of an effective nonlocality, and we present an analytical model which agrees well with numerical calculations.

physics.optics↗