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In this work mapping of quantum circuits to regular hexagonal grid with coupling degree of six has been investigated. Architectures involving superconducting qubits impose restrictions on 2-qubit gate operations to be carried out only between physically coupled qubits, also referred to as nearest-neighbor (NN) constraint. The noise introduced by the 2-qubit gates and the execution time greatly affect the computational reliability. Existing mapping techniques suffer either from the adopted approach to reduce gate overhead or from their inability to take advantage of such architectural regularity. We outlined three different qubit mapping approaches using Remote-CNOT templates, Swap gates and combination of both. We show the benefits of assigning the Cartesian coordinate system in hexagonal grid for runtime elevation and devised approaches for reduction in gate overheads. While the template-based approach gives a strict upper bound of additional gate overheads for a particular qubit mapping, the combined approach provides better result employing a larger lookahead window. Experiments on benchmark quantum circuits confirm that the proposed Swap-based method provides an average \(25\%\) improvement in gate overheads over a recent work and the combined approach contributes further \(15\%\) average improvement on the result at the expense of a little higher runtime. [ABSTRACT FROM AUTHOR]

Value at risk (VaR) is a quantitative measure used to evaluate the risk linked to the potential loss of investment or capital. Estimation of the VaR entails the quantification of prospective losses in a portfolio of investments, using a certain likelihood, under normal market conditions within a specific time period. The objective of this article is to construct a model and estimate the VaR for a diversified portfolio consisting of multiple cash commodity positions driven by standard Brownian motions and jump processes. Subsequently, a thorough analytical estimation of the VaR is conducted for the proposed model. The results are then applied to two distinct commodities—corn and soybean—enabling a comprehensive comparison of the VaR values in the presence and absence of jumps. [ABSTRACT FROM AUTHOR]

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton–Jacobi–Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio. [ABSTRACT FROM AUTHOR]

In this paper we implement a combination of data-science and fuzzy theory to improve the classical Barndorff-Nielsen and Shephard model, and implement this to analyze the S&P 500 index. We preprocess the index data based on fuzzy theory. After that, S&P 500 stock index data for the past 10 years are analyzed, and a deterministic parameter is extracted using various machine and deep learning methods. The results show that the new model, where fuzzy parameters are incorporated, can incorporate the long-term dependence in the classical Barndorff-Nielsen and Shephard model. The modification is based on only a few changes compared to the classical model. At the same time, the resulting analysis effectively captures the stochastic dynamics of the stock index time series. [ABSTRACT FROM AUTHOR]

Memristors can be used to build nonvolatile memory systems with in-memory computing (IMC) capabilities. A number of prior works demonstrate the design of an IMC-capable memory macro using a memristor crossbar. However, read disturbance limits the use of such memory systems built using a 0-transistor, 1-RRAM (0T1R) structure that suffers from the sneak path problem. In this paper, we introduce a scheme for both memory and logic operations using the 1-transistor, 1-RRAM (1T1R) memristor crossbar, which effectively mitigates the read disturbance problem. The memory array is designed using nMOS transistors and the VTEAM memristor model. The peripheral circuitry like decoders, voltage multiplexers, and sense amplifiers is designed using a 45 nm CMOS technology node. We introduce a mapping technique to realize arbitrary logic functions using Majority (MAJ) gate operations in the 1T1R crossbar. Through extensive experimentation on benchmark functions, it has been found that the proposed mapping method gives an improvement of 65% or more in terms of the number of time steps required, and 59% or more in terms of energy consumption as compared to some of the recent methods. [ABSTRACT FROM AUTHOR]