On automorphism groups of affine surfaces

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic groups. At the same time, they can be studied from the viewpoint of the combinatorial group theory, so we put a special accent on group-theoretical aspects (ind-groups, amalgams, etc.). We provide different approaches to classification, prove certain new results, and attract attention to several open problems.Comment: Proposition 2.10 from the previous version (published in Algebraic Varieties and Automorphism Groups, ASPM 75) deleted. There is a mistake in the proof kindly indicated by J.-P. Furter; the validity of the result remains open. This does not affect the rest of the pape

Linear Self-Attention Approximation via Trainable Feedforward Kernel

In pursuit of faster computation, Efficient Transformers demonstrate an impressive variety of approaches -- models attaining sub-quadratic attention complexity can utilize a notion of sparsity or a low-rank approximation of inputs to reduce the number of attended keys; other ways to reduce complexity include locality-sensitive hashing, key pooling, additional memory to store information in compacted or hybridization with other architectures, such as CNN. Often based on a strong mathematical basis, kernelized approaches allow for the approximation of attention with linear complexity while retaining high accuracy. Therefore, in the present paper, we aim to expand the idea of trainable kernel methods to approximate the self-attention mechanism of the Transformer architecture

Role of Vertical Segregation in Semitransparent Organic Photovoltaics

In this work, the efficiency of semitransparent organic photovoltaic (OPV) devices for low intensity applications is investigated as a function of the processing conditions. It is observed that a thermal treatment of the organic layer induces fullerene migration toward the active layer/air interface. This physical process gives rise to different vertical segregation profiles of donor and acceptor molecules. Once the back contact is deposited, the amount of fullerene covering the surface will determine the contact selectivity and leakage current of the device. Control of this leakage current may not be essential for devices fabricated for high illumination condition applications. However, devices to be used under low illumination conditions may be highly influenced by the presence of this parasitic dark current which flows in the opposite direction to photogenerated current. At the proximity of the contacts, the vertical segregation profile is inferred from optical and electrical measurements. In particular, external quantum efficiency (EQE) measurements carried out from a relatively opaque back contact provide local information on the materials spatially close to the light source. Alternatively, capacitance–voltage measurements enable calculation of the percentage of fullerene molecules covering the cathode contact. Overall, a versatile method that can be used in regular and inverted configuration is presented that explains the different behavior observed for devices to be used under low illumination conditions.1) FP7 European collaborative project SUNFLOWER (FP7-ICT-2011-7-contract num. 287594). 2) Generalitat Valenciana (project ISIC/2012/008 Institute of Nanotechnologies for Clean Energies). 3) Brno University of Technology for financial support (CZ.1.07/2.3.00/30.0039

Information Model and Its Element for Displaying Information on Technical Condition of Objects of Integrated Information System

The suggested information elements for the system of information display of the technical condition of the integrated information system meet the essential requirements of the information presentation. They correlate with the real object simply and very accurately. The suggested model of information display of the technical condition of the objects of integrated information system improves the efficiency of the operator of technical diagnostics in evaluating the information about the technical condition of the integrated information system

Constructing Temporal Networks of OSS Programming Language Ecosystems

One of the primary factors that encourage developers to contribute to open source software (OSS) projects is the collaborative nature of OSS development. However, the collaborative structure of these communities largely remains unclear, partly due to the enormous scale of data to be gathered, processed, and analyzed. In this work, we utilize the World Of Code dataset, which contains commit activity data for millions of OSS projects, to build collaboration networks for ten popular programming language ecosystems, containing in total over 290M commits across over 18M projects. We build a collaboration graph representation for each language ecosystem, having authors and projects as nodes, which enables various forms of social network analysis on the scale of language ecosystems. Moreover, we capture the information on the ecosystems' evolution by slicing each network into 30 historical snapshots. Additionally, we calculate multiple collaboration metrics that characterize the ecosystems' states. We make the resulting dataset publicly available, including the constructed graphs and the pipeline enabling the analysis of more ecosystems.Comment: Accepted to SANER 202