International political uncertainty and institutional instability as a response to COVID-19

The article examines the features of international political uncertainty and institutional instability that act as a reaction to COVID-19. It is concluding that the greater the "non-stationary" component of the business environment, the less important are the long-term dynamic opportunities and the less reliable are the models aimed at predicting policy changes. By focusing exclusively on the basic institutions or specific risks, a firm can easily lose sight of where, why and by whom the unknowns are generated, and what this threatens it in the future. This implies the need for greater progress towards a real option strategic logic with components of strategic and operational modularity, which allows for flexible response to changes in the institutional environment. Business analysts in the coming years should focus on the specific qualities of political leaders and how they influence countless firm decisions. Perhaps this is the only way to give firms and managers a chance to adapt to a rapidly changing global situation.

Simulation of non-stationary event flow with a nested stationary component

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

Simulation of non-stationary event flow with a nested stationary component

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

Simulation of non-stationary event flow with a nested stationary component

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

DEVELOPMENT OF A DATA FLOW CONTROL METHOD IN THE STATIONARY COMPONENT OF THE AIR FORCE COMMUNICATION SYSTEM OF THE ARMED FORCES OF UKRAINE

The article considers the solving an urgent scientific problem, which is to improve the flow control means in the coordinated implementation of multi-way routing strategies and preventive limitation of traffic intensity entering the transport network, based on improving the flow control method in the stationary component of the Air Force communication system in order to increase its productivity. The paper analyzes the problem and shows that an important place in modern and promising telecommunications networks, which are developing in the direction of creating next-generation NGN networks, is given to flow control means both within the transport network and at the stage of access to it. The solution to this problem is to improve the mathematical models of flow control, which are the basis of modern technological solutions. The article proposes a method of flow control which provides a coherent solution to the problems of multi-way routing and preventive limitation of traffic intensity on the basis of both relative and absolute priorities. To ensure more adequate service a model of traffic control based on relative priorities is proposed. The practical implementation of the work results envisages a set of organizational-technical measures related to the principles of organizational, technological and algorithmic nature, which will increase the productivity of the stationary component of the Air Force communication system of the Armed Forces of Ukraine.

Studies of stationary features in jets: BL Lacertae

Context. Monitoring of BL Lacertae at 15 GHz with the Very Long Baseline Array (VLBA) has revealed a quasi-stationary radio feature in the innermost part of the jet, at 0.26 mas from the radio core. Stationary features are found in many blazars, but they have rarely been explored in detail. Aims. We aim to study the kinematics, dynamics, and brightness of the quasi-stationary feature of the jet in BL Lacertae based on VLBA monitoring with submilliarcsecond resolution (subparsec-scales) over 17 years. Methods. We analysed position uncertainties and flux leakage effects of the innermost quasi-stationary feature and developed statistical tools to distinguish the motions of the stationary feature and the radio core. We constructed a toy model to simulate the observed emission of the quasi-stationary component. Results. We find that trajectories of the quasi-stationary component are aligned along the jet axis, which can be interpreted as evidence of the displacements of the radio core. The intrinsic motions of the core and quasi-stationary component have a commensurate contribution to the apparent motion of the stationary component. During the jet-stable state, the core shift significantly influences the apparent displacements of the stationary component, which shows orbiting motion with reversals. The quasi-stationary component has low superluminal speeds on time scales of months. On time-scales of few years, the apparent mean speeds are subrelativistic, of about 0.15 the speed of light. We find that the brightness profile of the quasi-stationary component is asymmetric along and transverse to the jet axis, and this effect remains unchanged regardless of epoch. Conclusions. Accurate positional determination, a high cadence of observations, and a proper accounting for the core shift are crucial for the measurement of the trajectories and speeds of the quasi-stationary component. Its motion is similar to the behaviour of the jet nozzle, which drags the outflow in a swinging motion and excites transverse waves of different amplitudes travelling downstream. A simple modelling of the brightness distribution shows that the configuration of twisted velocity field formed at the nozzle of the jet in combination with small jet viewing angle can account for the observed brightness asymmetry.

Review of stochastic differential equations in statistical arbitrage pairs trading

The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated.

Spacecraft and interplanetary contributions to the magnetic environment on-board LISA Pathfinder

ABSTRACT LISA Pathfinder (LPF) has been a space-based mission designed to test new technologies that will be required for a gravitational wave observatory in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime (mHz and below), the measurement band of interest for a space-based observatory. The magnetic field can couple to the magnetic susceptibility and remanent magnetic moment from the test masses and disturb them from their geodesic movement. LPF carried on-board a dedicated magnetic measurement subsystem with noise levels of 10 $\rm nT \ Hz^{-1/2}$ from 1 Hz down to 1 mHz. In this paper we report on the magnetic measurements throughout LPF operations. We characterize the magnetic environment within the spacecraft, study the time evolution of the magnetic field and its stability down to 20 μHz, where we measure values around 200 $\rm nT \ Hz^{-1/2}$, and identify two different frequency regimes, one related to the interplanetary magnetic field and the other to the magnetic field originating inside the spacecraft. Finally, we characterize the non-stationary component of the fluctuations of the magnetic field below the mHz and relate them to the dynamics of the solar wind.