Quantization Design for Distributed Optimization

We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a limited data-rate. A common technique to address the latter limitation is to apply quantization to the exchanged information. We propose two distributed optimization algorithms with an iteratively refining quantization design based on the inexact proximal gradient method and its accelerated variant. We show that if the parameters of the quantizers, i.e. the number of bits and the initial quantization intervals, satisfy certain conditions, then the quantization error is bounded by a linearly decreasing function and the convergence of the distributed algorithms is guaranteed. Furthermore, we prove that after imposing the quantization scheme, the distributed algorithms still exhibit a linear convergence rate, and show complexity upper-bounds on the number of iterations to achieve a given accuracy. Finally, we demonstrate the performance of the proposed algorithms and the theoretical findings for solving a distributed optimal control problem

Gauge-invariant Green function in 3+1 dimensional QED (QCD) and 2+1 dimensional Abelian (Non-Abelian) Chern-Simon theory

By applying the simple and effective method developed to study the the gauge-invariant fermion Green function in $2+1$ dimensional non-compact QED, we study the gauge-invariant Green function in $3+1$ dimensional QED and $2+1$ dimensional non-compact Chern-Simon theory. We also extend our results to the corresponding $SU(M)$ non-Abelian gauge theories. Implications for Fractional Quantum Hall effect are briefly discussed.Comment: 8 pages, 4 figures, published versio

On gauge-invariant Green function in 2+1 dimensional QED

Both the gauge-invariant fermion Green function and gauge-dependent conventional Green function in $2+1$ dimensional QED are studied in the large $N$ limit. In temporal gauge, the infra-red divergence of gauge-dependent Green function is found to be regulariable, the anomalous dimension is found to be $\eta= \frac{64}{3 \pi^{2} N}$. This anomalous dimension was argued to be the same as that of gauge-invariant Green function. However, in Coulomb gauge, the infra-red divergence of the gauge-dependent Green function is found to be un-regulariable, anomalous dimension is even not defined, but the infra-red divergence is shown to be cancelled in any gauge-invariant physical quantities. The gauge-invariant Green function is also studied directly in Lorentz covariant gauge and the anomalous dimension is found to be the same as that calculated in temporal gauge.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

Optimizing the management of financial flows based on assessment of regional multiplier effects

This article examines the issues of improving the effectiveness in the management of regional financial flows. As their main hypothesis, the authors provide a rationale for the argument that the management of regional financial flows must be optimized on the basis of multiplier economic effects that allow to better assess the performance of regional socio-economic policy. The article presents a multifactor model for managing the financial flows at the regional level, or the matrix of financial flows based on the principles of general economic equilibrium theory, Input—Output balancing method and methodology of national accounts system. The consolidated budgetary balance sheet of the region is presented as an important structural element of the model. A methodology has been developed for integrating the consolidated budgetary balance sheet of the region in the matrix of financial flows. By using the example of individual subjects of the Russian Federation, the authors calculated the matrix multipliers of consolidated budgetary balance sheet that allow to simulate the multiplier economic effects resulting from the impact of different types of exogenous economic factors on the development of regions, and to forecast the impact of changes in the fiscal reallocation on GRP and household income, assess the impact of external investment on the economic growth of the regions and study the effectiveness of federal tax policy at the regional level. The article demonstrates that the value of multiplier effect depends on several factors, including the external trade relations of the region, its dependence on imports, the share of value added in gross output, as well as the propensity of households to savings. The approach proposed by the authors can be used by the government authorities at different levels in the development of their strategies of socio-economic development, assessment of the extent and areas of impact made by various exogenous factors on the economy of the region, as well as in the analysis of the investment initiatives of the private sector seeking the financial support for its projects from the state. The authors propose the areas for improving the management of financial flows based on maximizing the multiplier economic effects in the short and medium term for the regions with a different level of fiscal capacity.The article has been prepared with the support of the Grant of the Russian Foundation for Humanities (project №15–02–00587)

Green Economy: Regional Priorities

The article is dedicated to transforming the economy of Russian regions to a green economy, which is an essential factor for the sustainable development. This is important not only for Russia but the whole world because our country has the great natural capital and provides important environmental services that support the planet biosphere. Based on the analysis of economic, social and ecological statistical data and Human Development Index (HDI) we have shown that the development of Russian Federal Districts is very unbalanced and each Russian region has its own way to new economic model. For instance, it is necessary to increase the well-being in the North Caucasus Federal District, it is important to reach higher life expectancy at birth in the Siberian and the Far Eastern Districts. It is necessary to move from the «brown» economy to a green one by using the human capital (building a knowledge economy), by applying Best Available Technologies (Techniques), by investing in efficiency of use of natural resources and by increasing energy efficiency. The transition to a green economy will help to achieve social equity and the development of human potential; it helps to move from the exploitation of non-renewable natural capital to renewable human capital. All these socio-economic measures should give decoupling effect, make risks lower, reduce the exploitation of natural capital, stop the environmental degradation and prevent the ecological crisis. Transition to the green economic model has to be accompanied by new economic development indicators, which take into account social and environmental factors.The research was supported by the grant of the Russian Foundation for Basic Research No. 14-06-00075