arXiv subjects

Alexey Smirnov

Publications and source records attributed to Alexey Smirnov.

6 recordsLinked to original sources

arXiv2026

On the TVD property of second order methods for 2D scalar conservation laws

The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging to extend this approach to two-dimensional problems. Using the anisotropic definition for discrete total variation (TV), it was shown in \cite{Goodman} that TVD solutions of two-dimensional hyperbolic equations are at most first order accurate. We propose to use an alternative definition resulting from a full discretization of the semi-discrete Raviart-Thomas TV. We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definition.

math.NA↗

arXiv2025

Unpacking Maximum Extractable Value on Polygon: A Study on Atomic Arbitrage

The evolution of blockchain technology, from its origins as a decentralized ledger for cryptocurrencies to its broader applications in areas like decentralized finance (DeFi), has significantly transformed financial ecosystems while introducing new challenges such as Maximum Extractable Value (MEV). This paper explores MEV on the Polygon blockchain, with a particular focus on Atomic Arbitrage (AA) transactions. We establish criteria for identifying AA transactions and analyze key factors such as searcher behavior, bidding dynamics, and token usage. Utilizing a dataset spanning 22 months and covering 23 million blocks, we examine MEV dynamics with a focus on Spam-based and Auction-based backrunning strategies. Our findings reveal that while Spam-based transactions are more prevalent, Auction-based transactions demonstrate greater profitability. Through detailed examples and analysis, we investigate the interactions between network architecture, transaction sequencing, and MEV extraction, offering comprehensive insights into the evolution and challenges of MEV in decentralized ecosystems. These results emphasize the need for robust transaction ordering mechanisms and highlight the implications of emerging MEV strategies for blockchain networks.

cs.DC↗

arXiv2023

A note on the logical inconsistency of the Hotelling Rule: A Revisit from the System's Analysis Perspective

The "Hotelling rule" (HR) called to be "the fundamental principle of the economics of exhaustible resources" has a logical deficiency which was never paid a sufficient attention to. This deficiency should be taken into account before attempting to explain discrepancies between the price prediction provided by the HR and historically observed prices. Our analysis is focused on the HR in its original form, we do not touch upon other aspects such as varying extraction costs and other ways of upgrading the original model underlying the Hotelling rule. We conclude that HR can not be derived from the simple models as it was claimed, therefore it should be understood as an assumption on its own, and not as a rule derived from other more basic assumptions.

econ.TH↗

arXiv2022

Shadow prices and optimal cost in economic applications

Shadow prices are well understood and are widely used in economic applications. However, there are limits to where shadow prices can be applied assuming their natural interpretation and the fact that they reflect the first order optimality conditions (FOC). In this paper, we present a simple ad-hoc example demonstrating that marginal cost associated with exercising an optimal control may exceed the respective cost estimated from a ratio of shadow prices. Moreover, such cost estimation through shadow prices is arbitrary and depends on a particular (mathematically equivalent) formulation of the optimization problem. These facts render a ratio of shadow prices irrelevant to estimation of optimal marginal cost. The provided illustrative optimization problem links to a similar approach of calculating social cost of carbon (SCC) in the widely used dynamic integrated model of climate and the economy (DICE).

econ.GN↗

arXiv2021

Social Cost of Carbon: What Do the Numbers Really Mean?

Social cost of carbon (SCC) is estimated by integrated assessment models (IAM) and is widely used by government agencies to value climate policy impacts. While there is an ongoing debate about obtained numerical estimates and related uncertainties, little attention has been paid so far to the SCC calculation method itself. This work attempts to fill the gap by providing theoretical background and economic interpretation of the SCC calculation approach implemented in the open-source IAM DICE (Dynamic Integrated model of Climate and the Economy). Our analysis indicates that the present calculation method provides an approximation that might work pretty well in some cases, while in the other cases the estimated value substantially (by the factor of four) deviates from the "true" value. This deviation stems from the inability of the present calculation method to catch the linkages between two key IAM's components -- complex interconnected systems -- climate and economy, both influenced by emission abatement policies. Within the modeling framework of DICE, the presently estimated SCC valuates policy-uncontrolled emissions against economically unjustified consumption, which makes it irrelevant for application in climate-economic policies and, therefore, calls for a replacement by a more appropriate indicator. An apparent SCC alternative, which can be employed for policy formulation is the direct output of the DICE model -- the socially optimal marginal abatement cost (SMAC), which corresponds to technological possibilities at optimal level of carbon emissions abatement. In policy making, because of the previously employed implicit approximation, great attention needs to be paid to the use of SCC estimates obtained earlier.

econ.GN↗

arXiv2020

Convexification for an Inverse Problem for a 1D Wave Equation with Experimental Data

The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the recovery of that dielectric constant from backscattering boundary measurements. The data depend on one variable, which is time. To address this problem, a new version of the convexification method is analytically developed. The theory guarantees the global convergence of this method. Numerical testing is conducted for both computationally simulated and experimental data. Experimental data, which are collected in the field, mimic the problem of the recovery of the spatially distributed dielectric constants of antipersonnel land mines and improvised explosive devices.

math.NA↗