QUANTUM ERGODICITY FOR COMPACT QUOTIENTS OF IN THE BENJAMINI–SCHRAMM LIMIT

We study the limiting behavior of Maass forms on sequences of large-volume compact quotients of $\operatorname {SL}_d({\mathbb R})/\textrm {SO}(d)$ , $d\ge 3$ , whose spectral parameter stays in a fixed window. We prove a form of quantum ergodicity in this level aspect which extends results of Le Masson and Sahlsten to the higher rank case.

Failure propagation in interdependent multi-level networks

В этой работе разрабатываются новый подход и алгоритмические инструменты для моделирования и анализа живучести сетей с разнородными узлами, а также рассматривается их применение в космических сетях. Космические сети позволяют совместно использовать ресурсы космических аппаратов на орбите, такие как хранение, обработка и обмен данными. Каждый космический аппарат в сети может иметь различный состав и функциональность подсистем, что приводит к неоднородности узлов. Большинство традиционных анализов живучести сетей предполагают однородность узлов и в результате не подходят для анализа космических сетей. Эта работа предполагает, что гетерогенные сети могут быть смоделированы как взаимозависимые многоуровневые сети, что позволяет проводить анализ их живучести. Многоуровневый аспект фиксирует разбивку сети в соответствии с общими функциональными возможностями в различных узлах и позволяет создавать однородные подсети, в то время как аспект взаимозависимости ограничивает сеть для захвата физических характеристик каждого узла. In this paper, we develop a new approach and algorithmic tools for modeling and analyzing the survivability of networks with heterogeneous nodes, and also consider their application in space networks. Space networks allow the sharing of spacecraft resources in orbit, such as data storage, processing, and exchange. Each spacecraft in the network may have a different composition and functionality of subsystems, which leads to heterogeneity of nodes. Most traditional network survivability analyses assume node homogeneity and as a result are not suitable for space network analysis. This work suggests that heterogeneous networks can be modeled as interdependent multi-level networks, allowing analysis of their survivability. The multi-level aspect captures the network breakdown according to the common functionality in different nodes and allows for the creation of homogeneous subnets, while the interdependence aspect restricts the network to capture the physical characteristics of each node.

Types of synergetic effects in Russian economy

Introduction. In modern reality, great importance is given to synergetics and the synergetic effects that arise in Russian economy. Their appearance is influenced by such factors as various interactions of the economic system elements, the non-linear development of the economy, stable and dynamic processes in the economy of the country. Several aspects of the emergence and functioning of synergetic effects can be distinguished: the time trend, multiplicative changes, and the spatial-functional aspect. It is necessary to study these aspects and types of synergistic effects. This is the relevance of the research topic. Theoretical analysis. The analysis of the time aspect is of particular interest. The following types of synergy are distinguished: permanent, temporary, and trend (prolonged). From the position of the multiplicative changes monoenergetic effects and diversified (multiple) synergistic effects emerge. Optimal and non-optimal effects play a special role in the economy. The initial, pre-optimal and optimal synergy are considered from the point of view of the level aspect. Synergy, synergy and quasi-synergy are revealed using a historical-logical approach at the macro level. Internal and external, economic and non-economic factors of optimal and non-optimal synergistic effects are identified. Results. The consequences of synergetic effects for the development of the Russian economy are revealed.

Exploring BERT for Aspect Extraction in Portuguese Language

Sentiment Analysis is the computer science field that comprises techniques that aim to automatically extract opinions from texts. Usually, these techniques assign a Sentiment Orientation to the whole document (Document Level Sentiment Analysis). But a document can express sentiment about several aspects of an entity. Methods that extract those aspects, paired with the sentiment about them, operate in the Aspect Level. Aspect-Based Sentiment Analysis approaches can be split into two stages: Aspect Extraction and Aspect Sentiment Classification. The literature presents works mainly focused on reviews about hotels, smartphones, or restaurants. In this work, we present an approach for Aspect Extraction based on Multilingual (Google's) and Portuguese (BERTimbau) BERT pre-trained models. Our experiments show that Aspect Extraction based on BERT pre-trained for Portuguese achieved Balanced Accuracy of up to 93% on a corpus of reviews about the accommodation sector.

Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity

We improve upon the local bound in the depth aspect for sup-norms of newforms on $D^\times$, where $D$ is an indefinite quaternion division algebra over ${\mathbb {Q}}$. Our sup-norm bound implies a depth-aspect subconvexity bound for $L(1/2, f \times \theta _\chi )$, where $f$ is a (varying) newform on $D^\times$ of level $p^n$, and $\theta _\chi$ is an (essentially fixed) automorphic form on $\textrm {GL}_2$ obtained as the theta lift of a Hecke character $\chi$ on a quadratic field. For the proof, we augment the amplification method with a novel filtration argument and a recent counting result proved by the second-named author to reduce to showing strong quantitative decay of matrix coefficients of local newvectors along compact subsets, which we establish via $p$-adic stationary phase analysis. Furthermore, we prove a general upper bound in the level aspect for sup-norms of automorphic forms belonging to any family whose associated matrix coefficients have such a decay property.