Signed networks form a particular class of complex networks that has many applications in sociology, recommender and voting systems. The contribution of this paper is twofold. First, we propose an approach aimed at determining the characteristic subgraphs of the network. Second, we apply the developed approach to the analysis of the network describing the Wikipedia adminship elections. It is shown that this network agrees with the status theory if one does not consider strongly tied vertices, i.e., the vertices that are connected in both directions. At the same time, the strongly connected vertices mostly agree with the structural balance theory. This result indicates that there is a substantial difference between single and double connections, the fact that deserves a detailed analysis within a broader context of directed signed networks.
Consider a difference operator H with periodic coefficients on the octant of the lattice. We show that for any integer N and any bounded interval I, there exists an operator H having N eigenvalues, counted with multiplicity on this interval, and does not exist other spectra on the interval. Also right and to the left of it are spectra and the corresponding subspaces have an infinite dimension. Moreover, we prove similar results for other domains and any dimension. The proof is based on the inverse spectral theory for periodic Jacobi operators.
We consider massless Dirac operators on the half-line with compactly supported potentials. We solve the inverse problems in terms of Jost function and scattering matrix (including characterization). We study resonances as zeros of Jost function and prove that a potential is uniquely determined by its resonances. Moreover, we prove the following: (1) resonances are free parameters and a potential continuously depends on a resonance, (2) the forbidden domain for resonances is estimated, (3) asymptotics of resonance counting function is determined, (4) these results are applied to canonical systems.
Online social networks have become an essential communi- cation channel for the broad and rapid sharing of information. Currently, the mechanics of such information-sharing is captured by the notion of cascades, which are tree-like networks comprised of (re)sharing actions. However, it is still unclear what factors drive cascade growth. Moreover, there is a lack of studies outside Western countries and platforms such as Facebook and Twitter. In this work, we aim to investigate what fac- tors contribute to the scope of information cascading and how to predict this variation accurately. We examine six machine learning algorithms for their predictive and interpretative capabilities concerning cascades’ structural metrics (width, mass, and depth). To do so, we use data from a leading Russian-language online social network VKontakte capturing cascades of 4,424 messages posted by 14 news outlets during a year. The results show that the best models in terms of predictive power are Gradient Boosting algorithm for width and depth, and Lasso Regression algorithm for the mass of a cascade, while depth is the least predictable. We find that the most potent factor associated with cascade size is the number of reposts on its origin level. We examine its role along with other factors such as content features and characteristics of sources and their audiences.
Dynamics of the New Keynesian model in continuous time with the Rotemberg pricing mechanism is considered within a framework of an optimal control problem. Various regimes of monetary and fiscal policy ('active' and 'passive') can lead to unstable dynamics in the economy. Parameters of the Taylor rules for both monetary and fiscal policies determine conditions for local equilibrium determinacy. Mapping out the ranges of the Taylor coefficient values where local determinacy cannot be obtained allows to control the economic system by controlling these parameters
We consider Dirac operators with dislocation potentials on the line. The dislocation potential is a periodic potential for x < 0 and the same potential but shifted by t ∈ R for x > 0. Its spectrum has an absolutely continuous part (the union of bands separated by gaps) plus at most two eigenvalues in each gap. Its resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface. We prove that it has only two simple poles on each open gap: eigenvalues or resonances. These poles are called states and there are no other poles. We prove: 1) states are continuous functions of t, and we obtain their local asymptotics; 2) for each t states in the gap are distinct; 3) states can be monotone or non-monotone functions of t; 4) we construct examples of operators with different types of states in gaps.
We consider Schrödinger operators with periodic potentials in the positive quadrant on
the plane with Dirichlet boundary conditions.We show that for any integer N and any
interval I there exists a periodic potential such that the Schrödinger operator has N
eigenvalues counted with multiplicity in this interval and there is no other spectrum in
the interval. Furthermore, to the right and to the left of it there is a essential spectrum.
Moreover, we prove similar results for Schrödinger operators for a product of an
orthant and Euclidean space. The proof is based on the inverse spectral theory for Hill
operators on the real line.
Fake news dissemination online can negatively affect public deliberation and opinion formation as well as contribute to conflicts in society. In recent years, the spread of misinformation has attracted ample attention of scholars who examine why people believe fake news. Nonetheless, existing research focusing on this phenomenon often lacks comparative perspective. This article is devoted to the methodological aspects of designing a cross-national online experiment on fake news perception. Based on our recent study, which tested the influence of news frames, sources and thinking styles on the ability to recognize fake news about foreign countries in Russia, Ukraine, and Kazakhstan, we provide a set of methodological steps that could be taken to design such an experiment. In particular, we demonstrate the necessity to create unique sets of stimulus material adjusted to specific national media systems. We also discuss the operationalization of complex variables (i.e. frames) and format of message presentation. Furthermore, we report the results of recruitment of participants through the ad campaigns on social network sites (Facebook and VKontakte) and suggest the approaches to creating samples representative of these platforms’ populations. This article is aimed to be a methodological toolkit, which points at the challenges that may occur while designing a cross-national experiment on media consumption—and provides practical recommendations to overcome them.
Drugs and diseases play a central role in many areas of biomedical research and healthcare. Aggregating knowledge about these entities across a broader range of domains and languages is critical for information extraction (IE) applications. To facilitate text mining methods for analysis and comparison of patient’s health conditions and adverse drug reactions reported on the Internet with traditional sources such as drug labels, we present a new corpus of Russian language health reviews.
The Russian Drug Reaction Corpus (RuDReC) is a new partially annotated corpus of consumer reviews in Russian about pharmaceutical products for the detection of health-related named entities and the effectiveness of pharmaceutical products. The corpus itself consists of two parts, the raw one and the labeled one. The raw part includes 1.4 million health-related user-generated texts collected from various Internet sources, including social media. The labeled part contains 500 consumer reviews about drug therapy with drug- and disease-related information. Labels for sentences include health-related issues or their absence. The sentences with one are additionally labeled at the expression level for identification of fine-grained subtypes such as drug classes and drug forms, drug indications and drug reactions. Further, we present a baseline model for named entity recognition (NER) and multilabel sentence classification tasks on this corpus. The macro F1 score of 74.85% in the NER task was achieved by our RuDR-BERT model. For the sentence classification task, our model achieves the macro F1 score of 68.82% gaining 7.47% over the score of BERT model trained on Russian data.
In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which occurs in the process of unifying agents. Explicit expressions of the dynamics of a single agent and dyad agents in the form of Brownian random processes were obtained. A qualitative analysis of the solutions of stochastic equations and systems was carried out.
The Maimonidean Controversy at the beginning of the 13th century was one of the most significant conflicts in the midst of the Jewish diasporas in the Middle Ages. The conflict followed a vivid discussion on the treatises of Maimonides and the interpretation of Judaism in the light of Aristotelian philosophy. Almost all of major Jewish communities in Europe were drawn in this conflict. Moreover, at some point the conflict expanded outside of the Jewish world, so that some works of Maimonides were burnt by the Christian Inquisition as heretical books. Despite the significance of these events and the trace left in the memory of the Jewish people, there is not much reliable evidence about them. The authors aim to discuss the history of this conflict, focusing on the problematic aspects of the Maimonides' teaching, and to make a reconstruction of the events occurred, to provide a specification of main characteristics of the conflict interaction (the players, their strategies and preferences, possible outcomes of the conflict, conflict dynamics, etc.), to design a game-theoretical model of the social conflict under consideration and to explore this model using the methods of mathematical game theory. It turns out that the majority of the players' actions correspond to optimal behavior concepts employed in game theory (bargaining solutions, Pareto efficiency, Nash equilibria). However, some actions obviously contradict the concept of rational behavior (one of the fundamental assumptions in mathematical game theory), and namely these actions induced the conflict escalation and such a tragic outcome.
Two laser heterostructures with active region based on seven InGaAs quantum wells
and on InGaAs/InGaAlAs superlattice were grown on InP substrates by molecular beam
epitaxy. Both active regions were designed for vertical-cavity surface-emitting lasers of 1535-
1565 nm spectral range and had total thickness about 80-90 nm. Characteristics of edgeemitting
laser diodes fabricated from grown laser heterostructures were studied and compared.
7th International School and Conference "Saint-Petersburg OPEN 2020" on Optoelectronics, Photonics, Engineering and Nanostructures was held on April 27 - 30, 2020. The Organizer of the conference is the Alferov Federal State Budgetary Institution of Higher Education and Science Saint Petersburg National Research Academic University of the Russian Academy of Sciences. Initially, the School and Conference was supposed to be held in full-time format at the Alferov Academic University (Saint-Petersburg, Russia), as it happened in the past. However, due to the restrictions imposed by the city authorities on holding mass events due to the threat of the spread of the COVID-19 infection, the conference committees decided to move the conference to the online format. The conference consisted of poster reports presented by the participants and online oral presentations by invited speakers. Posters and video reports of the participants were posted on the conference website. Invited speakers made their presentations online. During their speeches, participants could discuss and ask questions in the chat. The School and Conference included a series of invited talks given by leading professors with the aim to introduce young scientists with actual problems and major advances in physics and technology.
In this paper we introduce stochastic parameters into the network game
model with production and knowledge externalities. This model was proposed
by V. Matveenko and A. Korolev as a generalization of the two-period Romer
model. Agents differ in their productivities which have deterministic and stochastic
(Wiener) components. We study the dynamics of a single agent and the dynamics
of a dyad where two agents are aggregated. We derive explicit expressions for
the dynamics of a single agent and dyad dynamics in the form of Brownian
random processes, and qualitatively analyze the solutions of stochastic equations
and systems of stochastic equations.
Bitumen is a major component of asphalt. It, like other viscous petroleum products, is characterized by loss of fluidity during transport at low ambient temperatures. The paper proposes a new method for transporting road bitumen as a saturated cargo in the form of a pellet with a protective cover preventing moulding and forming a component of asphalt concrete. The process of transport of viscous petroleum products is discussed in detail. A system of mathematical models of the process of transport of viscous petroleum products was constructed, followed by simulation and functional-cost analysis.
We present an analysis of spectral and threshold characteristics of InGaAs/GaAs
quantum well-dot microdisk laser operated under cw current injection at room temperature
without external cooling. The experimental values of the threshold current for the disk and
ring microlasers are compared. We observe that the threshold current can be significantly
decreased in devices with large diameters (more than 30 m) by using the ring geometry
The problem of approximation by entire functions of exponential type defined on a countable set E of continua Gn, E = ⋃n∈ZGn⋃n∈ZGn is considered in this paper. It is assumed that all Gn are pairwise disjoint and are situated near the real axis. It is also assumed that all Gn are commensurable in a sense and have uniformly smooth boundaries. A function f is defined independently on each Gn and is bounded on E and f (r) has a module of continuity ω which satisfies the condition (1). An entire function Fσ of exponential type ≤σ is then constructed so that the following estimate of approximation of the function f by functions Fσ is valid
In this paper, we present a systematic overview of different endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, η-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effort and has a reasonable economic interpretation. In particular, the new characteristic function can be seen as a reduced version of the classical Neumann--Morgenstern characteristic function, where the players both from the coalition and from the complementary coalition use their previously computed strategies instead of solving respective optimization problems. Our finding are illustrated by a pollution control game with n non-identical players. For the considered game, we compute all characteristic functions and compare their properties. Quite surprisingly, it turns out that both the characteristic functions and the resulting cooperative solutions satisfy some symmetry relations.
New method of transportation of viscous petroleum products is proposed, ensuring their high average temperature and fluidity without the use of thermal insulation of the railway tank boiler and ground heating. A simulation model for the transportation of viscous petroleum products was constructed using a new method of modeling the physical process, allowing to estimate the amount of resources consumed
In this paper, a statistical game was defined and solved. Its solution is: the optimal randomized decision rule, the probability of a correct decision on this rule, and the worst a priori distribution of the test subjects knowledge levels. We have developed a method for assessment the accuracy and reliability of decision making by on test results. The proposed program allows you to assessment the reliability of the solution for a test containing 10 items with different levels of difficulty, and 11 different levels of knowledge level.