Motivation: The goal of the Russian Arctic Vegetation Archive (AVA-RU) is to unite and harmonize data of plot-based plant species and their abundance, vegetation structure and environmental variables from the Russian Arctic. This database can be used to assess the status of the Russian Arctic vegetation and as a baseline to document biodiversity changes in the future. The archive can be used for scientific studies as well as to inform nature protection and restoration efforts.Main types of variables contained: The archive contains 2873 open-access geobotanical plots. The data include the full species. Most plots include information on the horizontal (cover per species and morphological group) and vertical (average height per morphological group) structure of vegetation, site and soil descriptions and data quality estimations. In addition to the open-access data, the AVA-RU website contains 1912 restricted-access plots.Spatial location and grain: The plots of 1-100 m(2) size were sampled in Arctic Russia and Scandinavia. Plots in Russia covered areas from the West to the East, including the European Russian Arctic (Kola Peninsula, Nenets Autonomous district), Western Siberia (Northern Urals, Yamal, Taza and Gydan peninsulas), Central Siberia (Taymyr peninsula, Bolshevik island), Eastern Siberia (Indigirka basin) and the Far East (Wrangel island). About 72% of the samples are georeferenced.Time period and grain: The data were collected once at each location between 1927 and 2022.Major taxa and level of measurement: Plots include observations of >1770 vascular plant and cryptogam species and subspecies.Software format: CSV files (1 file with species list and abundance, 1 file with environmental variables and vegetation structure) are stored at the AVA-RU website (https://avarus.space/), and are continuously updated with new datasets. The open-access data are available on Dryad and all the datasets have a backup on the server of the University of Zurich. The data processing R script is available on Dryad.

Ongoing climate change can shift organism phenology in ways that vary depending on species, habitats and climate factors studied. To probe for large-scale patterns in associated phenological change, we use 70,709 observations from six decades of systematic monitoring across the former Union of Soviet Socialist Republics. Among 110 phenological events related to plants, birds, insects, amphibians and fungi, we find a mosaic of change, defying simple predictions of earlier springs, later autumns and stronger changes at higher latitudes and elevations. Site mean temperature emerged as a strong predictor of local phenology, but the magnitude and direction of change varied with trophic level and the relative timing of an event. Beyond temperature-associated variation, we uncover high variation among both sites and years, with some sites being characterized by disproportionately long seasons and others by short ones. Our findings emphasize concerns regarding ecosystem integrity and highlight the difficulty of predicting climate change outcomes. The authors use systematic monitoring across the former USSR to investigate phenological changes across taxa. The long-term mean temperature of a site emerged as a strong predictor of phenological change, with further imprints of trophic level, event timing, site, year and biotic interactions.

The article presents several scenarios for the development of the situation in the Russian banking system depending on different variants of changes in the Bank of Russia key rate. The scenarios are calculated using an optimization model of the Russian banking system, built on the principles of general equilibrium models, and an econometric add-on that allows the use of consistent scenarios of exogenous variables.

This paper presents the approach to solving optimal control problems that appear in economic models using the Lagrange’s multipliers method. This method is not as widely used as it might be, taking into accounts its benefits and convenience. The power of this method for intertemporal general equilibrium allows building complex structural models of the whole economy and work with the system of differential and finite equations instead of integral and functional ones as in dynamic programming. Not only deterministic, but also stochastic economic models might be solved using this method, although the theory of Lagrange’s method for stochastic optimal control models is less developed than the dynamic programming approach. In this paper, we develop their approach and specify the particular mathematical constructions underlying the mathematical formulation of the stochastic control problem. The presented paper demonstrates the Lagrange’s method on the example of the problem of a firm that makes decisions regarding investment, production and payment of dividends to the owners of the firm. The stochastic component in this model is represented by the random process of moments of time when making transactions is possible. The agent’s problem on a finite horizon differs from the infinite horizon problem by the presence of the boundary layer where the analysis might significantly change compared to the analysis of the solution within the planning horizon.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

We present a natural generalization of the Dixit-Stiglitz monopolistic competition model (DSM) — we assume that there is a continuum of industries, each of them described as in DSM, and each characterized with its own elasticity of substitution. Although firms in all industries share the same level of productivity and costs, exogenous technological progress leads to non-trivial reallocations of labor and production to industries with lower elasticities of substitution. Thus the model, despite is simplicity and the absence of additional assumptions about industry structure, generates the structural changes described in the economic growth literature.

This work is dedicated to modelling economic dynamics with random time scale. We propose a solution in the form a continuous time model where interactions of agents are random exchanges of finite portions of products and money at random points in time. In this framework, the economic agent determines the volume, but not the moments of the transactions and their order. The paper presents a correct formal description of optimal consumption and borrowing as a stochastic optimal control problem, which we study using the optimality conditions in the Lagrange's form. The solution appears to have a boundary layer near the end of planning horizon where the optimal control satisfies the specific functional equation. This equation was studied numerically using the functional Newton method adapted to a two-dimensional case.

This paper presents the approach to modelling the system of agents making transactions at random time. The two main ideas are, to obtain the agents’ optimal control in the form of synthesis (feedback) and, secondly, to make the aggregate dynamics stock-flow consistent on the average, not strictly at any moment of time. We present a model of a large number of consumers and producers that take loans from the bank to buy consumption goods or investment. The moments of deals form described the Poisson flow. Consumers and producers optimally solve their stochastic optimal control problems. The solution to the OC problems are in the closed-loop form, obtained using asymptotic methods for large frequency of transactions. The optimal policy functions appear to be linear in the state variables, if time is far from the planning horizon. This enables aggregation across a large population of consumers or producers. As a result, the description of the dynamics of their aggregate state might be substituted by deterministic dynamics. The system of equations for the aggregate dynamics is reduced to one differential equation. The equation is studied numerically and the results are presented.

For species to stay temporally tuned to their environment, they use cues such as the accumulation of degree-days. The relationships between the timing of a phenological event in a population and its environmental cue can be described by a population-level reaction norm. Variation in reaction norms along environmental gradients may either intensify the environmental effects on timing (cogradient variation) or attenuate the effects (countergradient variation). To resolve spatial and seasonal variation in species' response, we use a unique dataset of 91 taxa and 178 phenological events observed across a network of 472 monitoring sites, spread across the nations of the former Soviet Union. We show that compared to local rates of advancement of phenological events with the advancement of temperature-related cues (i.e., variation within site over years), spatial variation in reaction norms tend to accentuate responses in spring (cogradient variation) and attenuate them in autumn (countergradient variation). As a result, among-population variation in the timing of events is greater in spring and less in autumn than if all populations followed the same reaction norm regardless of location. Despite such signs of local adaptation, overall phenotypic plasticity was not sufficient for phenological events to keep exact pace with their cues-the earlier the year, the more did the timing of the phenological event lag behind the timing of the cue. Overall, these patterns suggest that differences in the spatial versus temporal reaction norms will affect species' response to climate change in opposite ways in spring and autumn.

This paper presents the advances in modelling the system of agents under the conditions of random transactions between them. We face certain challenges in this project which we would like to highlight in this presentation. The agents in the modelled system are a large number of consumers, a large number of producers and the bank as the intermediary. Consumers take loans from the bank to spend on consumption goods and producers borrow to make investment at random moments of time. The moments of time the agents deal form the Poisson flow. We present the approach to agents’ optimal control problems by the Lagrange method instead of dynamic programming. This enables us obtaining the expressions for the optimal feedback control which appear to be linear in state variables. The solution to the optimal control problems are obtained using asymptotic methods assuming large frequency of transactions. Using the linearity of the agents’ optimal control, we may aggregate description of agents, stock-flow consistent on the average. Instead of an ensemble of independent random transactions by agents, the description of the aggregate dynamics is deterministic. The system of equations for the aggregate dynamics is reduced to one equation. There are two cases of this equation, depending on the description of the bank. The equation has a specific form, its numerical analysis is challenging. We provide numerical results and discuss further directions of research.

A new approach to the transformation of solutions of optimal control problems based on the special form of relaxation of complementary slackness conditions is presented. The proposed approach is tested on the Russian banking system model, which is derived as a solution of a linear nonautonomous optimization problem with mixed constraints. It is shown that the use of this method regularizes the model in a sense it becomes applicable for the forecasting of the main Russian banking indicators.

В данной работе рассматривается классическая задача максимизации дисконтированной полезности при условии, что момент следующей покупки и получения кредита - случайный (пуассоновский). Цель исследования - моделирование случайного периода ожидания возможности изменения долга агента для того, чтобы учесть его влияние на потребление. Модель формулируется как задача оптимального стохастического управления. Потребитель в случайные моменты покупает продукт по неслучайной цене и в те же случайные моменты может брать и возвращать бессрочные кредиты. По кредитам агент непрерывно платит проценты. Он непрерывно получает дивиденды в виде внешнего поступления денег на счет и может накапливать беспроцентные безналичные деньги. Условия оптимальности получаются с помощью метода множителей Лагранжа. Достаточные условия оптимальности сводятся к уравнениям в частных производных с переменным и неизвестным запаздыванием. Их удается решить только сочетанием аналитических разложений по малому параметру (обратной величине большой частоты сделок-продаж) и численных расчетов. Особую трудность представляет регуляризация («смягчение») условий дополняющей нежесткости. В результате получены функции, определяющие оптимальное управление процессом покупок потребительского товара и размер кредита. На конечном интервале планирования можно проследить, как меняется потребление по мере приближения конца периода планирования. Во-первых, потребление определяется не запасом денег и долга в отдельности, а их разницей - собственными средствами потребителя. Во-вторых, вдали от горизонта планирования потребление мало и растет по мере приближения конечного момента времени. Такая модель может быть использована как часть описания агента-потребителя в динамических стохастических моделях общего равновесия.

It is shown by using a model that even a minor change in prices made by the seller is sufficient to coordinate the actions of independent purchasers so that they act as a single economic agent pursuing the aim of maximizing the effective utility function.

In this paper, we consider the classical problem of maximizing discounted utility, provided that the moment of the next purchase and receipt of a loan is random (Poisson). The purpose of the study is to take into account the uncertain waiting period for receipt of a credit in consumption decision-making. The model is formulated as the problem of optimal stochastic control. The consumer at random moments buys the product at a non-random price and at the same random moments can take and return indefinite loans. For loans, the agent continuously pays interest. He constantly receives dividends in the form of external receipt of money into the account and can accumulate non-interest non-cash money. The optimality conditions are obtained using the Lagrange multiplier method. Sufficient optimality conditions reduce to partial differential equations with variable and unknown delay. They can only be solved by using a combinations of analytic expansions with respect to a small parameter. A special difficulty is the regularization («softening») of the conditions of complementary slackness. As a result, functions were obtained that determine the optimal control of consumption purchases and the size of the loan. One can see how the consumption expenditures change as the end of the planning period approaches. First, consumption depends on money and debt not separately, but on their difference - own means of the consumer. Secondly, far from the planning horizon, consumption is small and grows as the final point in time approaches. This model can be used as part of the description of the consumer agent in dynamic stochastic general equilibrium models.

В работе предложена методика устранения сезонности, предназначенная для подготовки данных к использованию в прикладных моделях общего экономического равновесия. На примере существующих методик корректировки сезонности в данных демонстрируется, что они не удовлетворяют требованию инвариантности к дефлированию, что затрудняет их использование в моделях указанного типа. Показана невозможность одновременного выполнения свойств аддитивности и инвариантности к дефлированию (мультипликативности), что приводит к необходимости выбора одного из этих свойств в зависимости от специфики решаемой задачи.Предлагаемая процедура моделирует сезонность как набор мультипликативных фиктивных переменных, что обеспечивает возможность не только устранять сезонность в данных, но и возвращать ее на этапе прогнозирования для получения оценок наблюдаемых величин. Помимо этого, процедура оснащена детектором выбросов, благодаря чему она оказывается устойчива к различного рода шумам и выбросам в данных. Проводится проверка работоспособности предложенной процедуры на данных, сезонная компонента которых не эволюционирует, и сравнение ее с процедурой X12 по ряду критериев при помощи метода Монте-Карло. Показано, что в рамках выбранного класса задач, связанных с калибровкой моделей общего экономического равновесия, предлагаемая методика по качеству сопоставима с процедурой X12, прежде всего, с точки зрения устойчивости к шумам в данных и сохранения статистических свойств ряда. Приводится несколько примеров использования процедуры на реальных данных. Полученные результаты позволяют сделать вывод о применимости рассматриваемой процедуры к корректировке сезонности в данных специального типа в целях дальнейшего их использования при построении макроэкономических моделей.

We study the asymmetric one-dimensional telegraph process in the bounded domain. Lower boundary is absorbing and upper boundary is reflecting with delay. Point stays in the upper boundary until switch of regime occurs. We obtain the distribution of this process in terms of Laplace trasforms.