Geometric expansion of the log-partition function of the anisotropic Heisenberg model

We study the asymptotic expansion of the log-partition function of the anisotropic Heisenberg model in a bounded domain as this domain is dilated to infinity. Using the Ginibre's representation of the anisotropic Heisenberg model as a gas of interacting trajectories of a compound Poisson process we find all the non-decreasing terms of this expansion. They are given explicitly in terms of functional integrals. As the main technical tool we use the cluster expansion method.Comment: 38 page

Abstract cluster expansion with applications to statistical mechanical systems

We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions

Priority Directions for Facilitating Lifelong Learning in Armenia

This study aims to identify the priority areas for implementing lifelong learning in Armenia. A four-stage project-based learning method was applied in the context of the research; a total of 164 respondents participated in the survey and interviews, including educators, high school students, and students from pre-vocational educational institutions across four regions in Armenia. The analysis of responses to the questionnaire revealed the perceived importance of the teacher training, quality standards, programs, and educational materials. Additionally, external factors were considered, such as cooperation at both local and international levels, the need to update the material-technical base and incorporating new technologies, particularly digital ones. A key takeaway from this analysis is the unanimous agreement among participants on the essential need to embrace lifelong learning and to pursue the necessary reforms of the educational system in Armenia

Cloud-based mathematical models for self-organizing swarms of UAVs : design and analysis

Unmanned aerial vehicle (UAV) swarms have gained significant attention for their potential applications in various fields. The effective coordination and control of UAV swarms require the development of robust mathematical models that can capture their complex dynamics. The paper introduces mathematical models and relevant paradigms based on the design and analysis of self-organizing swarms of UAVs. The logical and technological construction of the model relies on the theorems developed by authors for obtaining full information exchange during the swarm quasi-random walk. The suggested rotor-router model interprets the discrete-time walk accompanied by the deterministic evolution of configurations of rotors randomly placed on the vertices of the swarm graph. The recommended optimal and fault-tolerant gossip/broadcast schemes support the resilience of swarm to internal failures and external attacks, and cryptographic protocols approve the security. The proposed cloud network topology serves as the implementation framework for the model, encompassing various connectivity options to ensure the expected behavior of the UAV swarms.Peer reviewe

Rumor Spreading and Invasion Percolation

We study the models of rumor spreading and invasion bond percolation aimed at the revelation of possible connections between them. Rumor spreading model describes the dissemination of a rumor due to the periodical repetition of sequential phone calls, whereas the invasion bond percolation refers to the spread of liquid in the porous environment. During a round of the rumor spreading, each node performs a call only once, meanwhile transmitting all the information that it knows at the moment of the call to its neighbors. The rumor reaches the receiver node during one round if there is a chain of successive calls between the source of the rumor and that node. The sequence of calls is taken uniformly at random from the set of all possible sequences (permutations of nodes). We compare the propagation of the rumor spreading with the invasion bond percolation in order to put forth necessary improvements of the percolation rules to map one model onto another, and vice versa</jats:p

Համավարակային և հետհամավարակային տնտեսաֆինանսական զարգացումներն ու մարտահրավերները / Pandemic and post-pandemic economic and financial developments and challenges

The 2020 pandemic had a shock effect on the economy and the stock market. Global GDP in 2021 surpassing the pre-covid level allows the 2020 recession to be described as a ``shock depression''. High short-term unemployment accompanied by widespread lockdowns has transformed into low natural unemployment and even labor shortages. Instead, sustained low inflation gave way to high, largely supply-driven inflation in the second half of 2021. Due to the large-scale injections of the economy, especially in the countries of the Anglo-American model, the progressive growth of the stock indices largely did not disrupt the long-lasting "bullish" trend. The pandemic did not stop the growth of global banking and non-banking financial assets, with some dominance of non-banking. From the second half of 2021, in connection with the increase in inflation and interest rates, accumulation of expectations of the "Minsk moment" was recorded in the stock markets. The main reason for the slowdown in global growth in 2022 is emerging challenges that have the potential to persist and deepen in 2023. In that regard, serious efforts are required from Armenia to maintain economic growth and capital market dynamics in the current year.</jats:p